A common assumption in matrix completion (MC) and tensor completion (TC) is that the missing locations are sampled randomly. However, in real-world scenarios, the unobserved elements are often not arbitrarily located, and may concentrate within entire rows or columns. We refer to this missing mechanism as structural missingness, and traditional MC and TC schemes suffer from drastic degradation under these circumstances. This work addresses the challenge of restoring structural missingness by introducing a novel framework for simultaneously reconstructing multiple matrices, called multi-matrix completion (MMC). In MMC, tri-factorization across matrices captures the correlation between matrices, and Tikhonov regularization on each matrix exploits its correlation. This design enables MMC to efficiently handle both random and structural missingness. In addition, MMC is not affected by the smoothness along matrices which makes it suitable for a wider variety of data compared to Fourier transform based TC methods. The alternating direction method of multipliers is utilized to solve the resultant optimization problem. The global convergence of the algorithm is supported by comprehensive theoretical analyses. We demonstrate the versatility of MMC through extensive experiments in image and video restoration, and showcase its superior performance in comparison to traditional MC and TC methods.

We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding p-value. The goal is to make decisions for all hypotheses simultaneously, using all available p-values. In practice, this problem resembles the detection problem over a sensor network during a period of time. To solve this problem, we extend the traditional two-groups model such that the prior probability of the null hypothesis and the alternative distribution of p-values can be inhomogeneous over the joint domain. We model the inhomogeneity via a generalized graph signal. This more flexible statistical model yields a more powerful detection strategy by leveraging the information from the joint domain.

Synthetic aperture radar (SAR) images are inherently affected by speckle noise. Deep learning-based methods have shown good potential in image denoising task. Most deep learning methods for denoising focus on additive Gaussian noise removal. However, SAR images are usually contaminated by non-Gaussian multiplicative speckle noise. In this paper, we propose a novel deep unrolling network named SAR-DURNet to deal with the SAR image despeckling problem. We establish optimization problem of speckle noise removal by using the priori of noise distribution, which can be sovled by half-quadratic splitting (HQS) method with iterative steps. We unroll the iterative process into a trainable deep unrolling network(SAR-DURNet). The parameters of the SAR-DURNet are trained end-to-end with simulated SAR image dataset. Experimental results on simulated test data and real SAR data show that the proposed approach has superior results in terms of quantitative performance metrics and the preservation of intricate visual details, compared to several well-known SAR image despeckling methods.

The instantaneous velocity of any moving object can be decomposed into two orthogonal components with reference to the observing radar, namely, radial velocity along the radar line of sight (LoS) and transversal velocity perpendicular to the LoS. It has been shown that the measurement of transversal velocity can significantly improve the performance of both radar target tracking and classification. Furthermore, the precision of transversal velocity estimation is proportional to the baseline length using static interferometry. However, the large baseline is impractical in applications, such as automotive radar with restrictions on the packaging size. This letter proposes synthetic interferometry exploiting radar motions. A large virtual baseline can be synthesized by moving the side-looking radar and synchronizing the received signals at two locations, thus improving the accuracy of transversal velocity measurement. We derive the conditions of time synchronization for successful interferometry in terms of the maximum moving distance and the maximum observation time. Both simulations and experiments have been conducted to validate the feasibility and effectiveness of the proposed synthetic interferometry.

We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on average as few samples as possible and keeping the detection and estimation errors below predefined levels. Based on mild assumptions on the underlying model, we propose an asymptotically optimal procedure, i.e., a procedure that becomes optimal when the tolerated detection and estimation error levels tend to zero. The implementation of the resulting asymptotically optimal stopping rule is computationally cheap and, hence, applicable for high-dimensional data. We further propose a projected quasi-Newton method to optimally choose the coefficients that parameterize the instantaneous cost function such that the constraints are fulfilled with equality. The proposed theory is validated by numerical examples.

Generative diffusion models have recently shown impressive results in image restoration. However, the predicted noise from existing diffusion-based methods may be inaccurate, especially when the noise amplitude is small, thereby leading to sub-optimal results. In this letter, an unsupervised diffusion model with latent low-rank regularization is proposed to alleviate this challenge. In particular, we first create a latent low-rank space using self-supervised learning for each degraded images, from which we derive corresponding latent low-rank regularization. This regularization, combining with observed prior information and smoothness regularization, guides the reserve sampling process, resulting in the generation of high-quality images with fine-grained textures and fewer artifacts. In addition, by utilizing the pre-trained unconditional diffusion model, the proposed model reconstructs the missing pixels in a zero-shot manner, which does not need any reference images for additional training. Extensive experimental results demonstrate that our proposed method is superior to the self-supervised tensor completion methods and representative diffusion model-based image restoration methods.

A wireless sensor network performs spatial inference on a physical phenomenon of interest. The areas in which this phenomenon exhibits interesting or anomalous behavior are identified whilst controlling false positives. We expand our previous work based on multiple hypothesis testing (MHT) and local false discovery rates to save energy and reduce spectrum use. The number of transmissions from sensors producing uninformative statistics are reduced by introducing censoring for MHT that imposes a communication rate constraint while maintaining the desired performance. Two novel methods are proposed. As our numerical experiments demonstrate, both approaches reduce the number of transmissions while maintaining false discovery rate control. In addition, one method allows to either define a fixed number of total transmissions or to trade the number of transmissions off against the achieved detection power.

Distributed networks are widely used in industrial and consumer applications. As the communication capabilities of such networks are usually limited, it is important to develop algorithms which are capable of handling the vast amount of data processing locally and only communicate some aggregated value. Additionally, these algorithms have to be robust against outliers in the data, as well as faulty or malicious nodes. Thus, we propose a robust distributed expectation maximization (EM) algorithm based on Real Elliptically Symmetric (RES) distributions, which is highly adaptive to outliers and moreover is combined with a robust data aggregation step which provides robustness against malicious nodes. In the simulations, the proposed algorithm shows its effectiveness over non-robust methods.

Matrix completion refers to recovering a matrix from a small subset of its entries. It is an important topic because numerous real-world data can be modeled as low-rank matrices. One popular approach for matrix completion is based on low-rank matrix factorization, but it requires knowing the matrix rank, which is difficult to accurately determine in many practical scenarios. We propose a novel algorithm based on rank-one approximation that a matrix can be decomposed as a sum of outer products. The key idea is to find the basis vectors of the underlying matrix according to the observed entries, and gradually increase the vector number until an appropriate rank estimate is reached. In contrast to the conventional rank-one schemes that employ unchanging rank-one basis matrices, our algorithm performs completion from the vector viewpoint and is able to generate continuously updated rank-one basis matrices. Besides, we theoretically show that the developed method has a linear convergence rate and a smaller recovery error than existing rank-one based algorithms. Experimental results using both synthetic data and real-world images demonstrate that our solution has the best recovery performance among the competing algorithms when the observations are contaminated by Gaussian noise.

A spatial signal is monitored by a large-scale sensor network. We propose a novel method to identify areas where the signal behaves interestingly, anomalously, or simply differently from what is expected. The sensors pre-process their measurements locally and transmit a local summary statistic to a fusion center or a cloud. This saves bandwidth and energy. The fusion center or cloud computes a spatially varying empirical Bayes prior on the signal’s spatial behavior. The spatial domain is modeled as a fine discrete grid. The contextual local false discovery rate is computed for each grid point. A decision on the local state of the signal is made for each grid point, hence, many decisions are made simultaneously. A multiple hypothesis testing approach with false discovery rate control is used. The proposed procedure estimates the areas of interesting signal behavior with higher precision than existing methods. No tuning parameters have to be defined by the user.

Many works have been done in direction-of-arrival (DOA) estimation in the presence of sensor gain and phase uncertainties in the past decades. Most of the existing approaches require either auxiliary sources with exactly known DOAs or perfectly partly calibrated arrays. In this work, we consider sparsely contaminated arrays in which only a few sensors are contaminated by sensor gain and phase errors, and moreover, the number of contaminated sensors as well as their positions are unknown. Such arrays exist in many real-world scenarios, and it can be regarded as a general case of the partly calibrated arrays, in which the number and positions of calibrated (or uncontaminated) sensors are known a priori. Based on the sparsity of sensor errors, we formulate the DOA estimation problem under the framework of low-rank and sparse decomposition. We develop an iteratively reweighted least squares method to solve the resulting problem. Our methods can estimate the DOAs of incoming signals and detect the contaminated sensors simultaneously. Numerical results exhibit the effectiveness and superiority of the proposed methods in both DOA estimation and contaminated sensors detection.

We present a robust copula model for landmine detection based on a likelihood ratio test. The test is applied to radar-based imagery from multiple viewpoints of the interrogation area. Different copula density functions are investigated in terms of their effectiveness in incorporating the statistical dependence between multi-view images. The test is designed to maximize the worst-case performance over all feasible mine and clutter distributions. Using numerical radar data of shallow buried targets under varying surface roughness, we demonstrate that the robust copula-based detector outperforms existing approaches and provides a high detection performance for a wide range of false-alarm rates.

We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on sequentially observed data whose distribution belongs to the exponential family. The aim is to design a scheme which minimizes the expected number of used samples while limiting the detection and estimation errors to pre-set lev-els. This constrained problem is first converted to an unconstrained problem which is then reduced to an optimal stopping problem. To solve the optimal stopping problem, we propose an asymptotically pointwise optimal (APO) stopping rule, i.e., a stopping rule that is optimal when the tolerated detection and estimation errors tend to zero. The policy parameterizing coefficients are then chosen such that the constraints on the detection and estimation errors are fulfilled. The proposed theory is illustrated with a numerical example.

The applicability of Doppler radar for gait analysis is investigated by quantitatively comparing the measured biomechanical parameters to those obtained using motion capturing and ground reaction forces. Nineteen individuals walked on a treadmill at two different speeds, where a radar system was positioned in front of or behind the subject. The right knee angle was confined by an adjustable orthosis in five different degrees. Eleven gait parameters are extracted from radar micro-Doppler signatures. Here, new methods for obtaining the velocities of individual lower limb joints are proposed. Further, a new method to extract individual leg flight times from radar data is introduced. Based on radar data, five spatiotemporal parameters related to rhythm and pace could reliably be extracted. Further, for most of the considered conditions, three kinematic parameters could accurately be measured. The radar-based stance and flight time measurements rely on the correct detection of the time instant of maximal knee velocity during the gait cycle. This time instant is reliably detected when the radar has a back view, but is underestimated when the radar is positioned in front of the subject. The results validate the applicability of Doppler radar to accurately measure a variety of medically relevant gait parameters. Radar has the potential to unobtrusively diagnose changes in gait, e.g., to design training in prevention and rehabilitation. As contact-less and privacy-preserving sensor, radar presents a viable technology to supplement existing gait analysis tools for long-term in-home examinations.

A novel ℓp-greedy pursuit (GP) algorithm for robust matrix completion, i.e., recovering a low-rank matrix from only a subset of its noisy and outlier-contaminated entries, is devised. The ℓp-GP uses the strategy of sequential rank-one update. In each iteration, a rank-one completion is solved by minimizing the ℓp-norm of the residual. Unlike the existing greedy methods that use the principal singular vectors of the residual matrix as the solution to the rank-one completion with the index information of the observed entries being ignored, the ℓp-GP employs alternating minimization to obtain an improved solution by fully exploiting the index information. More importantly, it achieves outlier-robustness by setting p = 1. For p = 1, only computing the weighted medians is involved, which yields that the complexity is near-linear with the number of observations. The low complexity enables the ℓ1-GP to be applicable to very large-scale problems. Simulation results demonstrate the superiority of the ℓp-GP over other approaches.

The problem of row-sparse signal reconstruction for complex-valued data with outliers is investigated in this paper. First, we formulate the problem by taking advantage of a sparse weight matrix, which is used to down-weight the outliers. The formulated problem belongs to LASSO-type problems, and such problems can be efficiently solved via cyclic coordinate descent (CCD). We propose an extended CCD algorithm to solve the problem for complex-valued measurements, which requires careful characterization and derivation. Numerical simulation results show that the proposed algorithm is robust against outliers and has a higher empirical probability of exact recovery compared with other tested methods.

We address the problem of robust network localization in realistic mixed LOS/NLOS environments. We make use of the fact that the bias of range measurement errors is not only non-negative but also sparse when LOS dominates, which has been long overlooked in the existing literature. To exploit these two properties, we introduce a sparsity-promoting regularization term and relax the resulting optimization problem to a semi-definite programming (SDP) problem. The proposed method admits a neat mathematical formulation and is computationally cheap. Moreover, its global convergence is guaranteed and it achieves good robustness against NLOS measurements. In numerical results, the proposed method outperforms representative state-of-the-art SDP approaches, in terms of both localization accuracy and computational efficiency.

Jointly testing multiple hypotheses and estimating a random parameter of the underlying model is investigated in a sequential setup. The optimal scheme is designed such that it minimizes the expected number of used samples while keeping the probabilities of falsely rejecting a hypothesis and the mean-squared estimation errors below a pre-set level. The underlying constrained problem is first converted to an unconstrained problem and then reduced to an optimal stopping problem, whose solution is characterized by a non-linear Bellman equation. The optimal cost coefficients are obtained by exploiting a connection between the derivatives of the cost function and the detection/estimation errors. The paper concludes with a numerical example, namely solving the problem of sequential joint amplitude-shift keying symbol decoding and noise power estimation.

We propose a robust likelihood-ratio test (LRT) to detect landmines and unexploded ordnance using forward-looking ground-penetrating radar. Instead of modeling the distributions of the target and clutter returns with parametric families, we construct a band of feasible probability densities under each hypothesis. The LRT is then devised based on the least favorable densities within the bands. This detector is designed to maximize the worst case performance over all feasible density pairs and, hence, does not require strong assumptions about the clutter and noise distributions. The proposed technique is evaluated using electromagnetic field simulation data of shallow-buried targets. We show that, compared to detectors based on parametric models, robust detectors can lead to significantly reduced false alarm rates, particularly in cases where there is a mismatch between the assumed model and the true distributions.

A phase-only robust minimum dispersion (PO-RMD) beamformer is devised for non-Gaussian signals. The proposed PO-RMD employs a constant-modulus constraint on the weights, which is equivalent to simply phase shifting at each antenna. It adopts the minimum dispersion criterion to utilize the non-Gaussianity of the signals while employing the worst-case constraint to achieve the robustness against model uncertainty. A gradient projection algorithmic framework is developed to solve the resulting nonconvex optimization problem. In order to find a feasible point in the intersection of the constant-modulus and robustness constraint sets, an alternating projection algorithm is devised. More importantly, the closed-form expressions of the projection onto the two sets are derived, respectively. Simulation results demonstrate the effectiveness, accuracy and robustness of the PO-RMD.

The problem of deciding whether a given set of data points forms one cluster or two clusters is investigated from a robust hypothesis testing perspective. It is assumed that a clustering algorithm exists that for both cases calculates cluster assignments and estimates of the corresponding probability density functions. Based on the latter, a statistical hypothesis test for the true number of clusters is formulated. In order to take falsely labeled data points into account, the clusters are then modeled as being contaminated with outliers. This leads to an uncertainty model for the cluster densities of the ε-contamination type, whose corresponding minimax optimal robust detector is well-known and can be implemented using least favorable densities. The performance of this detector under cluster overlap, cluster imbalance, and for different contamination ratios is evaluated numerically and is compared to that of a Bayesian cluster enumeration criterion. Significant performance improvements are shown in all cases.

Conventional approaches to matrix completion are sensitive to outliers and impulsive noise. This paper develops robust and computationally efficient M-estimation based matrix completion algorithms. By appropriately arranging the observed entries, and then applying alternating minimization, the robust matrix completion problem is converted into a set of regression M-estimation problems. Making use of differentiable loss functions, the proposed algorithm overcomes a weakness of the ℓp-loss (p ≤ 1), which easily gets stuck in an inferior point. We prove that our algorithm converges to a stationary point of the nonconvex problem. Huber's joint M-estimate of regression and scale can be used as a robust starting point for Tukey's redescending M-estimator of regression based on an auxiliary scale. Numerical experiments on synthetic and real-world data demonstrate the superiority to state-of-the-art approaches.

Data fusion (DF) from multiple heterogeneous sources is a typical task for many multisensor applications including remote sensing classification problems. Multiple classifier systems (MCS) provide a natural way to solve DF on the decision level by training individual classifiers separately on its own data source and then combine their outputs. In this paper, we consider a dynamic selection (DS) framework to select and fuse competent classifiers of MCS. For this, we propose a competence estimation and selection method to improve the performance of the DF system especially under class imbalance. We evaluate the method with synthetic and real datasets, demonstrating the applicability of the proposed framework.

The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a nonparametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the$f$-divergence-ball type, a pair of uncertainty sets of the density-band type can be constructed, which is equivalent in the sense that it admits the same pair of least favorable distributions. This result implies that robust tests under$f$-divergence-ball uncertainty, which are typically only minimax optimal for the single sample case, are also fixed sample size minimax optimal with respect to the equivalent density-band uncertainty sets.

The problem of sequential multiple hypothesis testing in a distributed sensor network is considered and two algorithms are proposed: the Consensus + Innovations Matrix Sequential Probability Ratio Test (CIMSPRT for multiple simple hypotheses and the robust Least-Favorable-Density- CIMSPRT for hypotheses with uncertainties in the corresponding distributions. Simulations are performed to verify and evaluate the performance of both algorithms under different network conditions and noise contaminations.

This paper is meant to share our experience on signal processing hands-on opportunities within the formal engineering education at Technische Universität Darmstadt. It is our strong belief that undergraduate students should be offered hands-on opportunities from the very beginning of their studies until their graduation. We describe our projects, lectures and seminars that we provide undergraduate students to gain hands-on experience inside signal processing along the time line of the curriculum. We further describe the variety of laboratories that we offer to expose students to state-of-the-art research and advanced equipment. Finally, we conclude by illustrating how we use competitions to motivate and challenge students with real-world problems.

The combination of multiple clustering solutions used to obtain accurate and novel output has attracted attention in data clustering research. Despite the success of clustering ensembles, there are still several fundamental limiting issues including the lack of a unified formalized problem formulation and an intuitive interpretation of the resulting solution. We formulate the clustering ensemble problem as a binary matrix factorization imposing assumptions of a binary structure on the resulting matrices. In such a framework, every data object is assigned to its representative ensemble centroid allowing for interpretation and validation of the consensus clustering results. We demonstrate that the formulated problem can be efficiently solved by means of iterative rank-one binary matrix approximation and apply the Proximus algorithm proposing an effective initialization scheme. The evaluation of the proposed clustering ensemble method demonstrates its efficacy on synthetic and real problems.

The Bayesian information criterion is generic in the sense that it does not include information about the specific model selection problem at hand. Nevertheless, it has been widely used to estimate the number of data clusters in cluster analysis. We have recently derived a Bayesian cluster enumeration criterion from first principles which maximizes the posterior probability of the candidate models given observations. But, in the finite sample regime, the asymptotic assumptions made by the criterion, to arrive at a computationally simple penalty term, are violated. Hence, we propose a Bayesian cluster enumeration criterion whose penalty term is derived by removing the asymptotic assumptions. The proposed algorithm is a two-step approach which uses a model-based clustering algorithm such as the EM algorithm before applying the derived criterion. Simulation results demonstrate the superiority of our criterion over existing Bayesian cluster enumeration criteria.

Advances in the field of inverse reinforcement learning (IRL) have led to sophisticated inference frameworks that relax the original modeling assumption of observing an agent behavior that reflects only a single intention. Instead of learning a global behavioral model, recent IRL methods divide the demonstration data into parts, to account for the fact that different trajectories may correspond to different intentions, e.g., because they were generated by different domain experts. In this work, we go one step further: using the intuitive concept of subgoals, we build upon the premise that even a single trajectory can be explained more efficiently locally within a certain context than globally, enabling a more compact representation of the observed behavior. Based on this assumption, we build an implicit intentional model of the agent's goals to forecast its behavior in unobserved situations. The result is an integrated Bayesian prediction framework that significantly outperforms existing IRL solutions and provides smooth policy estimates consistent with the expert's plan. Most notably, our framework naturally handles situations where the intentions of the agent change over time and classical IRL algorithms fail. In addition, due to its probabilistic nature, the model can be straightforwardly applied in active learning scenarios to guide the demonstration process of the expert.

Learning from demonstration (LfD) is the process of building behavioral models of a task from demonstrations provided by an expert. These models can be used, e.g., for system control by generalizing the expert demonstrations to previously unencountered situations. Most LfD methods, however, make strong assumptions about the expert behavior, e.g., they assume the existence of a deterministic optimal ground truth policy or require direct monitoring of the expert's controls, which limits their practical use as part of a general system identification framework. In this work, we consider the LfD problem in a more general setting where we allow for arbitrary stochastic expert policies, without reasoning about the optimality of the demonstrations. Following a Bayesian methodology, we model the full posterior distribution of possible expert controllers that explain the provided demonstration data. Moreover, we show that our methodology can be applied in a nonparametric context to infer the complexity of the state representation used by the expert, and to learn task-appropriate partitionings of the system state space.

The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.

We propose an improved version of the non-negative independent component analysis algorithm that uses a multiplicative update rule (M-NICA). We examine a challenging NICA application in a noise-embedded multi-speaker voice activity detection (VAD) setup. We present a novel approach that includes sparsity constraints to solve the energy separation problem with independent source signals. A sparse feature extraction step is performed to project the non-negative signals onto a dimension-reduced subspace and identify sparse principal components. Then, we maximize the signal decorrelation by employing a median measure of central tendency in the computation of the covariance matrix that contributes in robustness against outliers. Moreover, our approach supplies a straightforward multi-speaker VAD, for which no empirical thresholding or other ad-hoc decision rule is required. Instead, an active voice frame simply corresponds to a non-zero value of the separated energy signal. Numerical experiments using real data validate the superior performance of the proposed technique.

In this paper, we study distributed decision-making over mobile adaptive networks where nodes in the network collect data generated by two different models. The nodes need to decide which model to estimate and track. However, they do not know beforehand which model they observe. Therefore, an effective clustering technique is needed. We apply a clustering technique that reduces the clustering error. Furthermore, introduce an additional term to the motion model to ensure that the nodes move coherently without fragmentation in the network during the decision-making process. Once the network reaches agreement on the desired model, the cooperation among nodes enhances the performance of the estimation task by relaying data throughout the network.

Radar for indoor monitoring has recently attracted much attention that is driven by its safety, privacy-preserving, and non-wearable sensing mode. Micro-Doppler signatures offered by radars operating in the K-band can disclose intricate details and characteristics of human gait. This paper reveals key Doppler features associated with human legs in gait motions which have been overlooked or ignored by existing work in this area, including biomechanics simulators and electromagnetic modeling. These features are used to detect gait abnormalities and distinguish gait from other translational motions which exhibit similar signatures in the time-frequency domain, such as assistive walking devices.

Consensus clustering, also known as clustering ensembles is a technique that combines multiple clustering solutions to obtain stable, accurate and novel results. Over the last years several consensus clustering approaches were proposed addressing practical clustering problems with different degrees of success. In this paper, we consider data fragments as elements of a cluster ensemble framework. We propose a new dissimilarity measure on data fragments and build a consensus function that allows handling large scale clustering problems while not compromising on accuracy. We evaluate our proposed consensus function on a number of datasets showing its high performance with respect to other existing consensus functions.

A single-snapshot fast computational Fourier-based direction-of-arrival (DOA) estimation method is introduced. This method applies the fast Fourier transform (FFT) to sensor data and performs effective cancellation of spectral leakage caused by sidelobe interactions, leading to unbiased DOA estimates of multiple sources. Successful elimination of spectral leakage is achieved by a sequential removal of strong sinc functions in the spatial frequency domain through an iterative interpolation process. The simulation results demonstrate superior performance of the proposed method over beamforming and other iterative FFT-based DOA estimation techniques as well as the high-resolution Root-MUSIC algorithm.

Minimax robust hypothesis testing is studied for the cases where the collected data samples are corrupted by outliers and are mismodeled due to modeling errors. For the former case, Huber's clipped likelihood ratio test is introduced and analyzed. For the latter case, first, a robust hypothesis testing scheme based on the Kullback-Leibler divergence is designed. This approach generalizes a previous work by Levy. Second, Dabak and Johnson's asymptotically robust test is introduced, and other possible designs based on f-divergences are investigated. All proposed and analyzed robust tests are extended to fixed sample size and sequential probability ratio tests. Simulations are provided to exemplify and evaluate the theoretical derivations.

Decision making based on Markov decision processes (MDPs) is an emerging research area as MDPs provide a convenient formalism to learn an optimal behavior in terms of a given reward. In many applications there are critical states that might harm the agent or the environment and should therefore be avoided. In practice, those states are often simply penalized with a negative reward where the penalty is set in a trial-and-error approach. For this reason, we propose a modification of the well-known value iteration algorithm that guarantees that critical states are visited with a pre-set probability only. Since this leads to an infeasible problem, we investigate the effect of nonlinear and linear approximations and discuss the effects. Two examples demonstrate the effectiveness of the proposed approach.

We study severely quantized received signal strength (RSS)-based cooperative localization in wireless sensor networks. We adopt the well-known ‘sum-product algorithm over a wireless network’ (SPAWN) framework in our study. To address the challenge brought by severely quantized measurements, we adopt the principle of importance sampling and design appropriate proposal distributions. Moreover, we propose a parametric SPAWN in order to reduce both the communication overhead and the computational complexity. Experiments with real data corroborate that the proposed algorithms can achieve satisfactory localization accuracy for severely quantized RSS measurements. In particular, the proposed parametric SPAWN outperforms its competitors by far in terms of communication cost. We further demonstrate that knowledge about non-connected sensors can further improve the localization accuracy of the proposed algorithms.

Increased demand on spectrum sensing over a broad frequency band requires a high sampling rate and thus leads to a prohibitive volume of data samples. In some applications, e.g., spectrum estimation, only the second-order statistics are required. In this case, we may use a reduced data sampling rate by exploiting a low-dimensional representation of the original high-dimensional signals. In particular, the covariance matrix can be reconstructed from compressed data by utilizing its specific structure, e.g., the Toeplitz property. In this paper, we propose a general coprime sampling concept that implements effective compression of Toeplitz covariance matrices. Given a fixed number of data samples, we examine different schemes on covariance matrix acquisition, based on segmented data sequences. The effectiveness of the proposed technique is verified using simulation results.

Characterizing drops in a spray process is of high interest in many areas, such as car painting or spray drying. The Time Shift (TS) technique provides an efficient and accurate way to optically measure size and velocity of individual droplets in sprays. Its realization in practice is not wide spread, thus the necessary signal processing of the measured data has not yet been fully developed or optimized. However, the TS technique is the only technique deemed suitable for online spray monitoring. In this study, we derive a filtering concept by using only a single filter that can be used for detection of droplets measured by the TS technique. We show that our approach is optimal in terms of detection power. Additionally, we show that the average detection power does not exceed certain limits, close to the one of a conventional matched filter bank.

The usability of hand-held glucose meters to self-monitor blood sugar levels is crucially affected by the measurement time. We consider an image-based photometric measurement setup that optically tracks the chemical reaction that takes place on the blood covered test strip. The aim is to obtain a reliable estimate of the true underlying glucose concentration in the blood sample at an early stage of the observed chemical reaction in order to increase the testing speed. We propose using particle filtering to track the required image statistics that are subject to a non-linear process. Using real data, we show that the developed algorithm drastically reduces the measurement time at a comparable quality of results.

Learning from Demonstrations (LfD) has proven to be a powerful concept for solving optimal control problems in high-dimensional state spaces where demonstrations can be used to facilitate the search for efficient control policies. However, many existing LfD approaches suffer from either theoretical, practical, or computational drawbacks such as the need to learn a latent reward model, to monitor the expert's controls, or to repeatedly solve potentially demanding planning problems. In this work, we consider the LfD objective from a system identification perspective and propose a probabilistic policy recognition framework based on expectation maximization that operates directly on the observed expert trajectories, avoiding the aforementioned problems. Using a spatial prior over policies, we are able to make accurate predictions in regions of the state space that are scarcely explored.

Distributed radar networks for through-the-wall radar imaging (TWRI) have the advantage of flexibility, high accuracy, and fault tolerance. We propose a modified distributed orthogonal matching pursuit (MDOMP) algorithm with an efficient communication scheme for the sparse scene reconstruction in TWRI applications. The communication costs, computational complexity, and reconstruction performance are analyzed for the proposed algorithm and compared with existing distributed sparse reconstruction methods. Simulated and experimental data are used to demonstrate that the MDOMP provides desirable performance at moderate communication and computation costs.

A carrier sense multiple access network is considered and two distributions for random slot selection that minimize the expected delay of the first or the first successful transmission under a constraint on the collision probability are derived. The distribution that minimizes the delay of the first successful transmission is of finite support and can be calculated in a recursive manner. The distribution that minimizes the unconditional delay of the first transmission is a standard geometric distribution with an appropriately chosen parameter. The results are proved by means of dynamic programming.

In this paper, a framework for collaborative face recognition from video sequences in a multi-camera environment is proposed. Collaboration between cameras allows for higher recognition performance in both the common and non-common field-of-view (FOV) cases. For the latter, the appearance of an object in a nearby camera is predicted using the last tracked position of the object paired with a time-of-arrival model between camera pairs. An experiment using four cameras in an office environment confirms the applicability and performance gains of the proposed framework.

Today's wireless sensor networks provide the possibility to monitor physical environments via small low-cost wireless devices. Given the large amount of sensed data, efficient and robust classification becomes a critical task in many applications. Typically, the devices must operate under stringent power and communication constraints and the transmission of observations to a fusion center (FC) is, in many cases, infeasible or undesired. A challenging research question in such cases is the design of data clustering and classification rules when each sensor collects a set of unlabelled observations that are drawn from a known number of classes. We propose two robust distributed hybrid classification algorithms, i.e., the Diffusion K-Medians and the Communicationally Efficient Distributed K-Medians. An extensive performance analysis in comparison to a benchmark algorithm is provided that investigates the error rates in dependence of different parameters of a distributed sensor network, and also considers communication cost. Our proposed algorithms, which are insensitive to outliers and various parameters, are applicable to on-line classification problems and scale well w.r.t. the number of classes.

A novel algorithm for distributed labeling of speech sources is proposed. We consider a wireless sensor network comprising devices that are equipped with multiple microphones, which can “hear” a number of speech signals. The labeling task is performed in a decentralized fashion with a new two-step approach. The first step corresponds to the distributed extraction of proper source-specific features from the mixed signals. In the second step, these features are exploited via a distributed unsupervised learning technique. We present approaches that can be used in hierarchically organized or in non-hierarchically organized network configurations. Numerical examples using real data display the performance of the proposed technique.

Reinforcement Learning (RL) is an attractive tool for learning optimal controllers in the sense of a given reward function. In conventional RL, usually an expert is required to design the reward function as the efficiency of RL strongly depends on the latter. An alternative has been presented by the concept of Inverse Reinforcement Learning (IRL), where the reward function is estimated from observed data. In this work, we propose a novel approach for IRL based on a generative probabilistic model of RL. We derive an Expectation Maximization algorithm that is able to simultaneously estimate the reward and the optimal policy for finite state and action spaces, which can be easily extended for the infinite cases. By means of two toy examples, we show that the proposed algorithm works well even with a low number of observations and converges after only a few iterations.

The detection of abrupt changes in signals that are observed by wireless sensor networks (WSN), is an important research area with potential applications, e.g., in fault detection, prediction of natural catastrophic events, and speech segmentation. We consider the distributed robust detection of changes in the parameters of autoregressive (AR) models. Our method is robust on a single sensor level by suppressing the effect of outliers and impulsive noise via a robustified distance metric between a long-term and a short-term AR model. The new distributed change detector works without a fusion center and incorporates a weighting based on signal-to-noise-ratio (SNR) information, to ensure that every node will, at least, maintain its single node performance. A Monte-Carlo simulation study is provided which compares the proposed detector to a centralized version, in terms achievable detection rates and mean detection delay. Furthermore, an application example of distributed voice activity detection for a noisy speech signal is given.

In this paper, we consider multipath exploitation and sparse reconstruction in a network of distributed multistatic radar units for stationary target localization behind walls. Multipath exploitation leverages prior information of the indoor scattering environment to eliminate ghosts targets. However, uncertainties in interior wall positions severely impair the effectiveness of multipath exploitation. We develop a multipath signal model for the distributed radar network configuration, which parameterizes the wall locations, and perform joint optimization for simultaneously recovering the target and wall positions. Supporting simulation results are provided, which validate the effectiveness of the proposed method.

Solving a linear inverse problem may include difficulties such as the presence of outliers and a mixing matrix with a large condition number. In such cases a regularized robust estimator is needed. We propose a new-type regularized robust estimator that is simultaneously highly robust against outliers, highly efficient in the presence of purely Gaussian noise, and also stable when the mixing matrix has a large condition number. We also propose an algorithm to compute the estimates, based on a regularized iterative reweighted least squares algorithm. A basic and a fast version of the algorithm are given. Finally, we test the performance of the proposed approach using numerical experiments and compare it with other estimators. Our estimator provides superior robustness, even up to 40% of outliers, while at the same time performing quite close to the optimal maximum likelihood estimator in the outlier-free case.

This paper deals with several original contributions to an automatic target recognition (ATR) system, which is applied to underwater mine classification. The contributions concentrate on feature selection and object classification. First, a sophisticated filter method is designed for the feature selection. This filter method utilizes a novel feature relevance measure, the composite relevance measure (CRM). Feature relevance measures in the literature (e.g., mutual information and relief weight) evaluate the features only with respect to certain aspects. The CRM is a combination of several measures so that it is able to provide a more comprehensive assessment of the features. Both linear and nonlinear combinations of these measures are taken into account. A wide range of classifiers is able to provide satisfactory classification results by using the features selected according to the CRM. Second, in the step of object classification, an ensemble learning scheme in the framework of the Dempster–Shafer theory is introduced to fuse the results obtained by different classifiers. This fusion can improve the classification performance. We propose a reasonable construction of the basic belief assignment (BBA). The BBA considers both the reliability of the classifiers and the support of individual classifiers provided to the hypotheses about the types of test objects. Finally, this ATR system is applied to real synthetic aperture sonar imagery to evaluate its performance.

Diffusion adaptation techniques based on the least-mean-squares criterion have been proposed for distributed detection of a signal in Gaussian-distributed noise, forgoing the need for a fusion center. However, least-mean-squares solutions are generally non-robust against impulsive noise. In this work, we combine nonlinear filtering with diffusion adaptation and propose a strategy for distributed detection in the presence of impulsive noise. The superiority of the algorithm is validated experimentally.

Testing the stationarity of stochastic processes is required in a variety of signal processing applications. When dealing with real-world problems, the presence of outliers and impulsive (heavy-tailed) noise causes classical stationarity tests to break down. In this work, a set of robust stationarity tests that are based on a sphericity statistic test (SST) in the frequency domain is proposed. Different possible approaches are investigated and compared to existing robust and non-robust stationarity tests in terms of the receiver operating characteristic (ROC). In addition to extensive simulations, a real-world data example of a malfunctioning window regulator motor, for which the dominant frequencies show a modulating character that results in a non-stationary signal, is investigated. Both for simulated and real-world data, the proposed methods significantly outperform existing approaches.

We propose a robustification of the mean-shift algorithm. We understand robustness in the statistical sense as the deviation from the nominal, distributional assumption. The derivation of the robust mean-shift vector is based on a robust version of the kernel density estimator (KDE), where the KDE is interpreted as an inner product in a higher dimensional feature space. The mean in this formulation is replaced by an Ivies timate in order to robustify against outlying data points. We show the superiority of our algorithm compared to the standard mean-shift algorithm and to the median-shift algorithm using both simulated and real data in both contaminated and uncontaminated data. The real data stems from an image segmentation application for blood glucose measurement.

We show that the optimal design of non-randomized discrete sequential tests, i.e., tests whose test statistics take on only a countable number of states, can be modeled as a mixed integer linear problem. This is done by reformulating the difference equations describing the random walk on the integer lattice in terms of linear mixed integer constraints. We outline the general procedure and give a simple example to show how the proposed method can be used in practice.

Hyperspectral imaging (HSI) is a useful tool for the classification of vast areas. High accuracy is achieved by means of spectral information for each pixel, which inherently leads to a huge amount of data and, thus, requires costly processing. We present an Adaptive Compressed Classification (ACC) framework for HSI that allows a compressive acquisition of the scene of interest. Since classification is performed in the compressive domain, expensive reconstruction is avoided, significantly reducing computational requirements. For ACC, we propose an adaptive probabilistic approach to optimize the measurement and basis matrices. Based on real data sets, we show that Compressed Classification yields high classification accuracy close to results obtained for the complete data. Using the proposed adaptive approach, even higher accuracies are achieved in all tested cases.

Through-the-wall radar imaging aims at determining the locations and velocities of obscured targets. The slow velocities of indoor targets are in particular difficult to detect and estimate. It is shown by theoretical considerations and simulation that indirect propagation paths contain significant information on the target movements, which can be utilized for improved sensing. We propose a compressive sensing based method that exploits a multipath model to improve the velocity resolution of the reconstruction. Simulation results demonstrate the effectiveness of the proposed approach.

Literature on multiple testing is mostly concerned with fixed sample number testing. In this paper, we propose a sequential multiple testing procedure. This work is motivated by an application in multiband spectrum sensing for cognitive radio, in which a primary user or a cognitive radio user can use several bands at a time. The proposed procedure simultaneously controls the false alarm and miss detection rate not only for a single band, but also for the system (familywise). The common method to individually testing the hypotheses fails to achieve this. Furthermore, simulation results show that the proposed method has a smaller average sensing time (sample number) than Bonferroni's procedure, which makes it suitable for the scenario at hand.

Structures such as seawalls, levees and dikes prevent low lying land from flooding. The structural health of these constructions is critical and needs to be maintained. In this paper, we present a data-driven approach that uses the information of different in-situ measurements to detect structural anomalies at an early stage. Our approach is based on system identification, in which the dike is modeled as a single-input, multiple-output, linear system whose parameters can be learned based on training data. A statistical test is then deployed to perform a systematic detection of anomalies. We demonstrate the performance of the proposed approach on real data from an experimental dike setup.

The bootstrap is a powerful computational tool for statistical inference that allows for the estimation of the distribution of an estimate without distributional assumptions on the underlying data, reliance on asymptotic results or theoretical derivations. On the other hand, robustness properties of the bootstrap in the presence of outliers are very poor, irrespective of the robustness of the underlying estimator. This motivates the need to robustify the bootstrap procedure itself. Improvements to two existing robust bootstrap methods are suggested and a novel approach for robustifying the bootstrap is introduced. The methods are compared in a simulation study and the proposed method is applied to robust geolocation.

A system for automatic detection and classification (ADAC) of underwater objects for mine hunting applications is proposed. The system consists of three steps: segmentation, feature extraction, and classification. This paper focuses on two design issues: the selection of the optimal classifier and the selection of the optimal feature subset. Often, the comparison of classification systems is based on a pre-selected feature set. However, a different subset might yield a different ranking. We apply a resampling algorithm that assesses the classifier performance without constraints to any specific feature subset. Once a classifier is chosen, a feature selection algorithm estimates the optimal feature subset. We propose a novel extension of the sequential forward selection (SFS) and the sequential forward floating selection (SFFS) methods, which mitigates their main limitations, i.e., the nesting problem. Instead of keeping the best alternative at each iteration, a set of D options is stored. The performance of the so-called D-SFS and D-SFFS is tested on simulated and real data, significantly outperforming the standard algorithms. The proposed methods are also used for designing an ADAC system for mine hunting based on two extensive databases of synthetic aperture sonar images.

Super-Resolution Image Reconstruction is known to be sensitive to errors in assumptions such as accurate sub-pixel motion estimation. Even small errors can yield a significant degradation of image quality that complicates any follow-on task such as object detection or classification. We focus on the problem of automatic quality assessment of Super-Resolution image reconstruction. We propose a bootstrap-based method that provides an objective metric quantifying reconstruction quality and thus allowing to readjust the reconstruction.

Many of today's wireless sensor networks operate under the strict requirement that only a single sensor transmits data at a time. One way to guarantee this is to use protocols that detect and prevent package collisions on the MAC layer. These, however, come at the cost of increased transmission delays, reduced throughput and higher energy consumption. We propose a PHY layer approach to collision avoidance that is based on sequential detection and significantly reduces the risk of collisions while simultaneously minimizing the transmission delay. For this approach, a performance analysis is given whose results are shown to closely match numerical simulations.

We propose a minimax robust hypothesis testing strategy between two composite hypotheses determined by the neighborhoods of two nominal distributions with respect to the squared Hellinger distance. The robust tests obtained are the nonlinearly transformed versions of the nominal likelihood ratios, whereas the least favorable densities are derived in three different regions. In two of them, they are scaled versions of the corresponding nominal densities and in the third region they form a composite version of the two nominal densities. The outcomes and implications of the proposed robust test are discussed through comparisons with the recent literature.

Intracranial pressure (ICP) is an important physiological signal for patients with traumatic brain injuries. Accurate ICP forecasting enables active and early interventions for more effective control of ICP levels. To achieve high accuracy, most existing methods require a high sampling rate (100 Hz), which is infeasible for online medical applications. Therefore, we propose an online ICP forecasting method requiring only low rate signal sampling (0.1 Hz). Our ARIMA based forecasting method applies empirical mode decomposition (EMD) to remove non-stationarities from the ICP signal, and robust estimation to mitigate the influence of motion induced artifacts. Experimental performance assessment with simulated and clinically collected data demonstrate that the proposed method is more accurate compared to previously proposed and standard methods.

A synthetic aperture sonar (SAS) system borne by an autonomous underwater vehicle is state-of-the-art for highresolution sea floor mapping. In the application of automatic target recognition, e.g., for naval mine hunting, the high-resolution SAS images serve as input to a detection and classification post-processing stage, which highly relies on excellent image quality. Future autonomous mine hunting systems must include an assessment scheme to ensure sufficient quality for performing target recognition. We propose to assess the focusing capability during the reconstruction of an SAS image to evaluate its quality by probing the instantaneous cross-range resolution of a synthetic sub-aperture and comparing it with its theoretical resolution.

Multipath propagation can create ghost targets that severely affect the reconstruction quality of through-the-wall radar images. We propose a compressive sensing (CS) based reconstruction method, which inverts a specular multipath model through exploitation of the structured sparsity in the scene. This allows suppression of the ghost targets and increased signal-to-clutter ratio at the target locations, leading to `clean' images of stationary scenes. Simulation results demonstrate the effectiveness of the proposed approach.

We present a generalized sequential probability ratio test for composite hypotheses wherein the thresholds are updated in an adaptive manner based on the data recorded up to the current sample using the parametric bootstrap. The resulting test avoids the asymptotic assumption usually made in earlier works. The increase of the average sample number of the proposed method is not significant compared to the sequential probability ratio test which is based on known parameters, especially in a low SNR region. In addition, the probability of false alarm and the probability of missed detection are maintained below the preset values. A comparison shows that the thresholds based on the parametric bootstrap are in close agreement with the thresholds based on Monte-Carlo simulations.

We consider received-signal-strength-based robust geolocation in mixed line-of-sight/non-line-of-sight propagation environments. Herein, we assume a mode-dependent propagation model with unknown parameters. We propose to jointly estimate the geographical coordinates and propagation model parameters. In order to approximate the maximum-likelihood estimator (MLE), we develop an iterative algorithm based on the well-known expectation and maximization criterion. As compared to the standard ML implementation, the proposed algorithm is simpler to implement and capable of reproducing the MLE. Simulation results show that the proposed algorithm attains the best geolocation accuracy as the number of measurements increases.

In this paper, a Sparse Representation based Classification (SRC) approach is employed for mine hunting using Synthetic Aperture Sonar (SAS) images. Given a training database with enough samples, SRC exploits the properties of sparse signals and expresses a sample of unknown class as a sparse linear combination of the training samples. The class of the training samples with greater weight is likely to be the candidate sample class. The method was introduced for face recognition, where the face images are directly taken as feature sets. Due to the greater variability of sonar images, for mine hunting applications it is more convenient to transform the image samples into a different feature domain. Several feature sets are considered, and the results are compared with those provided by a linear discriminant analysis classifier. We have tested the method on an extensive SAS database with more than 400 mines.

Direction-of-arrival (DOA) estimation of two targets with a single snapshot plays an important role in many pulsed radar array applications. We consider the case when the targets are spaced by more than the beamwidth of the array. In this case, the conventional beamformer (BF) is able to resolve them, but results in biased DOA estimation due to the leakage effect. We propose computationally simple strategies to reduce this bias. A novel method is presented, based on the analysis of the noise-free BF spectrum and a local approximation. We comment on computational cost and present simulation results.

The problem of source enumeration in array processing is investigated. In an information theoretic criterion framework, we use in addition to the probability density function of observations, the probability density function of the sample eigenvalues obtained from the sample covariance matrix of the observations. Although the latter adds information to the criterion it is widely ignored by most traditional approaches. Simulations show that the significant performance gain offered by the proposed criterion in terms of correctly detecting the number of sources in some difficult situations, such as small sample sizes, low signal-to-noise power ratio, close spacing and high correlation between sources.

There has been much activity on model selection for multi-dimensional data in recent years under the assumption of a Gaussian noise distribution. However, methods which are optimal for Gaussian noise are very sensitive against brief sensor failures. We suggest two robust model order selection schemes for multi-dimensional data based on the MM-estimator of the covariance of the r-mode unfoldings of the complex valued data tensor. Simulation results are given for 2-D and 3-D uniform rectangular arrays based source enumeration, both for Gaussian noise and a brief sensor failure.

The problem of locating a mobile station in a wireless network has been extensively investigated due to the growing need for reliable location-based services. In non-line-of-sight environments, the positioning accuracy of classical least-squares based solutions is inaccurate. In order to mitigate the effect induced by non-line-of-sight errors, we address a novel robust nonparametric approach. Herein, we first estimate the range error distribution using nonparametric adaptive kernel density estimation and then optimize the approximate log-likelihood function via a quasi-Newton method. In simulations, the proposed approach shows improved positioning accuracy when the non-line-of-sight contamination is high as compared to several other competitors. Furthermore, it requires only a small amount of computational time.

This paper presents a new filter method for feature selection, which maximizes a hybrid relevance measure using a sequential forward searching scheme (mHRM-SFS). An individual relevance measure provides the classification information only in a certain aspect. Thus, we choose a modified Relief weight, mutual information, and the information entropy to formalize a hybrid relevance measure (HRM) to identify the most characterizing features. Because of its efficiency, a sequential forward searching scheme is used for maximizing the HRM. The resulting feature selection obtained by mHRM-SFS is appropriate to serve as an input for various classifiers. The mHRM-SFS can also determine the cardinality of the feature selection automatically while choosing the optimal features. Finally, the mHRM-SFS is applied to select features of underwater objects for the classification purpose. The selected features are tested by different classifiers. The classification results are compared to those of 4 existing feature selection methods.

We consider the problem of active high-resolution imaging using synthetic aperture techniques, such as synthetic aperture radar (SAR) or synthetic aperture sonar (SAS). In order to reduce storage, processing power and energy requirements a compressive sensing framework is adopted that allows to reduce the number of measurements while maintaining range resolution and image quality. We consider the approach from Alonso et al. where compressive sensing is considered as an alternative to matched filtering for range focusing while keeping along-track focusing for imaging unmodified. This approach is extended by a sparse basis transform for range profiles that allows for deviations from the implicit point target model assumption. A synthetic aperture ultrasound imaging system is build that implements the presented techniques in a laboratory setup. Range profiles and images of this setup are considered to evaluate the system performance in terms of resolution and image quality.

The reconstruction of high-resolution Synthetic Aperture Sonar (SAS) images requires precise knowledge about sensor positions for consecutive transmission times in order to build a synthetic aperture. In order to support the navigation system, typically motion compensation techniques based on estimating the time delays of the raw echo signals are performed. However, given operational hardware constraints, an undersampling of the carrier phase introduces biased time delay estimates due to phase wrap errors, leading to wrong position estimates. In this paper, we propose a new approach based on binary image processing techniques to compensate the bias.

We consider the problem of through-the-wall radar imaging (TWRI), in which polarimetric imaging is used for automatic target detection. Two generalized statistical detectors are proposed which perform joint detection and fusion of a set of multipolarization radar images. The first detector is an extension of a previously proposed iterative target detector for multiview TWRI. This extension allows the detector to automatically adapt to statistics that may vary, depending on target locations and electromagnetic-wave polarizations. The second detector is based on Bayes' test and is of interest when target pixel occupancies are known from, e.g., secondary data. Properties of the proposed detectors are delineated and demonstrated by real data measurements using wideband sum-and-delay beamforming, acquired in a semicontrolled lab environment. We examine the performance of the proposed detectors when imaging both metal objects and humans.

A scheme for target detection using segmentation by classification is proposed. The scheme is applied to through-the-wall microwave images obtained using frequency-domain back-projection in a wideband radar. We consider stationary targets where Doppler and change-detection-based techniques are inapplicable. The proposed scheme uses features from polarimetric images to segment and classify the image observations into target, clutter, and noise segments. We map target polarization signatures from copolarized and cross-polarized target returns to a pixel-by-pixel feature space, then oversegment the image to homogeneous regions called superpixels depending on this feature space. The features of each superpixel are used subsequently to group homogeneous superpixels into clusters. The clusters are then classified using decision trees. Real data collected using an indoor radar imaging scanner are used for performance validation.

We consider the problem of detecting targets behind walls using radar imaging technology. An image-domain based detection technique is proposed that allows to adapt to specific targets of interest. By doing so, clutter as well as targets of no-interest are strongly reduced in the radar image. The proposed detector is automatic in the sense that no or only little prior knowledge on the image statistics is required. The detection procedure is detailed, including the choice of suitable optimality criteria. The evaluation of the proposed technique is performed using data collected from Through-the-Wall radar imaging experiments whereby we specifically consider on the detection of humans.

To maintain the performance of direction-of-arrival (DOA) estimation, an accurate model of the array response is required. In a time-varying sensor environment, this is only possible with autocalibration. For a uniform linear array, there exist algorithms for autocalibration which exploit the Toeplitz structure of the unperturbed spatial covariance matrix. In this paper, we develop an autocalibration method for 2-D DOA estimation with a uniform rectangular array, in which we exploit a Toeplitz-block Toeplitz structure. We present a simple algorithm for gain and phase estimation, discuss ambiguity problems and evaluate the performance using simulations.

High resolution through-the-wall radar imaging (TTWRI) demands wideband signals and large array apertures. Thus a vast amount of measurements is needed for a detailed reconstruction of the scene of interest. For practical TTWRI systems it is imperative to reduce the number of samples to cut down on hardware cost and/or acquisition time. This can be achieved by employing compressive sensing (CS). Existing approaches imply a point target assumption, which may not hold in practical applications. We apply a novel CS approach for TTWRI using the 2D discrete wavelet transform to sparsify images. In this fashion, we overcome the above stated limitation and are able to deal with extended targets. Experimental results show that high image qualities are obtained, similar to images generated using the full measurement set.

We consider the problem of source number estimation in array processing when impulsive noise is present. To combat impulsive noise more effectively, two robust estimators with high breakdown points, i.e., the minimum covariance determinant (MCD) estimator and the MM-estimator are applied in combination with the bootstrap. The MCD estimator is applied to discard the outliers in observations caused by impulsive noise, while the MM-estimator is suggested to estimate robustly the covariance matrix of observations. Simulations show the significant performance gain offered by the two proposed methods in terms of correctly estimating the number of sources at low SNR in the presence of impulsive noise.

Corneal height data, typically measured with a videokeratoscope, is modeled as a set of Zernike polynomials. Accurate corneal modeling is important, e.g. prior to surgery. The measurements require a good quality of the pre-corneal tear film and sufficiently wide eyelid aperture, which is not always fulfilled in practice. This results in missing values or outliers in the corneal topography map. We suggest to treat this problem by a new two step model selection procedure and introduce a criterion based on r-estimation, which is simultaneously statistically robust and efficient. For this, we exploit the asymptotic equivalence of τ-estimation to M-estimation. The performance is evaluated using simulations, as well as real data.

The traditional searching method for model-order selection in linear regression is a nested full-parameters-set searching procedure over the desired orders, which we call full-model order selection. On the other hand, a method for model-selection searches for the best sub-model within each order. In this paper, we propose using the model-selection searching method for model-order selection, which we call partial-model order selection. We show by simulations that the proposed searching method gives better accuracies than the traditional one, especially for low signal-to-noise ratios over a wide range of model-order selection criteria (both information theoretic-based and bootstrap-based). Also, we show that for some models the performance of the bootstrap-based criterion improves significantly by using the proposed partial-model selection searching method.

This paper deals with the problem of automatic target classification or Through-the-Wall radar imaging. The proposed scheme considers stationary objects in enclosed structures and works on the SAR image rather than the raw data. It comprises segmentation, feature extraction based on superquadrics, and classification. We present a recursive splitting tree to obtain optimum parameters for feature extraction. Support vector machines and nearest neighbor classifiers are then applied to successfully classify among different indoor targets. The classification methods are tested and evaluated using real data generated from synthetic aperture Through-the-Wall radar imaging experiments.

The problem of distributed detection and decision fusion in Through-the-Wall Radar Imaging (TWRI) is considered. We deal with the multi-viewing case in which images corresponding to different radar locations can be collected. We present a method to adapt conventional distributed detection schemes to the scenario when no a priori knowledge about image statistics from any view is available. Further, a new scheme for estimating quality information of local detectors in a distributed detection scenario is proposed. We apply bootstrap techniques to draw inference from the radar measurements of the behind the wall scene. Simulation results as well as experimental data are used to demonstrate the performance of the proposed approach.

In this paper bootstrap resampling techniques are applied to assess speech quality and thereby evaluate performance of distinct speech enhancement algorithms, under the assumption that the speech segments can be approximated by an autoregressive model. A bootstrap-based multiple hypotheses testing procedure is constructed to test a distance measure based on linear predictive coding, which is the log-likelihood ratio distance. It is shown that the multiple hypotheses test results correlate well with conventional numerical distance measures, which suggests the applicability of the proposed procedure in assessment of speech quality as well as speech enhancement algorithms.

We address the problem of human detection with mobile platforms such as robots. Instead of using an optical system, we propose to employ an acoustic 2D array to reliably obtain an image of a human in a 3D spatial power spectrum which is independent of lighting conditions and uses cheap acoustic sensors. We show that humans have a distinct acoustic signature and propose to model the echoes from reflecting parts of objects in the scene by a Gaussian-Mixture-Model. When it is fitted to the acoustic image, we can extract geometric relations between the present echoes and represent the acoustic signatures in a low-dimensional parameter space. We present results based on real data measurements that demonstrate that different objects can be reconstructed from the data and discriminated. The obtained parameter space forms the basis for subsequent detection and classification of humans.

Time-frequency methods can utilize the non-stationarity of signals to enhance the resolution capability and accuracy in direction-of-arrival estimation. In this paper, we consider the problem of non-stationary sources impinging on an array of sensors in an impulsive noise environment. We apply a robust time-frequency method in combination with morphological image processing to estimate the instantaneous frequency of the sources. Then, for the extracted time-frequency points, we employ robust methods to calculate the averaged spatial time-frequency matrix, which is then used for direction-of-arrival estimation.

Biased estimation has the advantage of reducing the mean squared error (MSE) of an estimator. The question of interest is how biased estimation affects model selection. In this paper, we introduce biased estimation to a range of model selection criteria. Specifically, we analyze the performance of the minimum description length (MDL) criterion based on biased and unbiased estimation and compare it against modern model selection criteria such as Kay's conditional model order estimator (CME), the bootstrap and the more recently proposed hook-and-loop resampling based model selection. The advantages and limitations of the considered techniques are discussed. The results indicate that, in some cases, biased estimators can slightly improve the selection of the correct model. We also give an example for which the CME with an unbiased estimator fails, but could regain its power when a biased estimator is used.

We consider the problem of target detection in Through-the-wall Radar Imaging when no a priori knowledge about the image statistics is available. An iterative approach which adapts itself to the unknown image statistics and thus allows for automatic target detection is presented. Two variants, based on 2D median filtering and morphological operations, are described in details. The proposed detection schemes are tested using experimental data, considering the problem of 3D reconstruction of a scene hidden behind a concrete wall.

An extended Kalman filter-based interacting multiple model algorithm (IMM-EKF) is proposed for mobile terminal tracking in cellular networks based on time of arrival estimates. The proposed IMM-EKF is able to cope with line-of-sight (LOS) and non-line-of-sight (NLOS) conditions modeled by a Markov chain, where the LOS and NLOS errors are described by different noise models. Road-constraints are included into the IMM-EKF to improve performance. Simulation results show that the IMM-EKF outperforms conventional methods. A comparison to the posterior Cramer-Rao lower bound is given to demonstrate the effectiveness of the IMM-EKF.

The presence of impulsive noise can severely degrade the accuracy performance of conventional direction of arrival (DOA) estimation algorithms, such as MUSIC and ESPIRIT. We propose a two-stage robust adaptive trimming approach. We first apply Shapiro-Wilk's goodness-of-fitWtest for Gaussianity, as a preprocessing stage. We then robustly estimate the covariance matrix in order to minimize the impact of impulsive noise on conventional DOA estimation algorithms. Numerical simulations are presented to illustrate the efficacy of the proposed approach for high resolution direction finding in highly-impulsive environments.

A detector of targets behind walls and in enclosed structures is presented. The detector is applied to through-the-wall radar images obtained by wideband delay and sum beamforming. We consider the detection problem using single- and multiple-view imaging. The statistics of noise, clutter, and target images are examined and formulated using sample scenes. The effects of wall parameter errors on the image statistics are shown. An iterative detection scheme, which adapts itself to the image statistics, is presented. The proposed detection schemes are evaluated using real data.

In this paper we address the problem of parametric spectral estimation for non-stationary signals. An extension of the recursive maximum likelihood (RML) algorithm which iteratively tracks the time-varying signature of the process parameters is proposed. In particular we deal with the problem of estimating the parameters of time-varying autoregressive (TVAR) processes. Computer simulations are conducted that demonstrate the performance of the new method for parameter estimation as well as for time-varying spectral estimation.

Robust parameter estimation in impulsive noise has risen a lot of attention in wireless communications. Previously, we proposed a non-parametric estimator for multiuser detection based on non-parametric density estimation. Here, we present a semi-parametric estimator that outperforms its non-parametric counterpart by combating multiple access interference and impulsive noise altogether. The approach is termed semi-parametric since a nonlinear parametric function is used to transform the noise data while non-parametric estimation of the score function is performed using the transformed sample. This estimate is then used to determine the parameters of interest, i.e., the transmitted symbols. We also propose a parametric function and an estimator for its parameter.

Bootstrap-based model selection has been shown in many practical instances to be superior to classical methods such the AIC and MDL. This is particularly noticeable when the distribution of modelling noise is unknown and/or when the available data samples are small. One of the main problems of using bootstrap model selection with real data is the necessity of tuning the residual scaling parameter or estimating the length of a sub-sample. Recently, we have developed a new hook and loop (HL) resampling plane, in which the scaling of the residuals is avoided. Here, we compare the performance of the range of resampling planes that can be used in the context of model selection and show that the HL-based model selection is superior to its predecessors. Moreover, in the context of fitting parametric models to corneal data measured by videokeratoscopes, the HL provides results that are consistent with clinical expectations.

In-cylinder pressure and combustion torque provide feedback information that can be utilized in advanced control and diagnosis strategies for combustion engines. One challenge in torque estimation is the compensation of the torsional effects of the crankshaft. This paper presents a novel torque estimation method using a gray-box model (motivated from a physical model) of the crankshaft in combination with one in-cylinder pressure and one engine speed measurement. The MISO system inversion is described and the approach is benchmarked against an existing method. The results using a four-cylinder spark ignition engine encourage the further investigation of the approach.

We present a constant-false alarm rate detection scheme for use in Through-the-Wall Radar Imaging. We consider multiple-viewing scenarios with an arbitrary number of vantage points. Classical detection theory is used to fuse the obtained radar images to one reference image. By doing so, clutter and noise artifacts which are strongly represented in the individual images are reduced and targets of interest are more clearly visible.

We address the problem of parameter estimation of signals in noise of unknown distribution and propose a semiparametric estimator. Classical parametric estimators, such as the least-squares or Huber's minimax methods, are limited in terms of robustness and generally suboptimal in practice. Alternative methods which are based on nonparametric probability density function (pdf) estimation have been proposed recently. They automatically adapt to the measurements and thus outperform classical techniques. The semiparametric technique we suggest, which also automatically adapts to the data and relies on transformation pdf estimation, provides a further improvement and overcomes the computational weaknesses of the previous methods. The power of the technique is highlighted in an example of amplitude estimation of sinusoidal signals in impulsive noise.

This work deals with the estimation of near-field parameters using passive sensor arrays. A transformation of the array data is proposed which allows the extraction of near-field time-frequency signatures from data containing a mixture of far- and near-field sources. Spatial time-frequency distribution matrices are then used as a means for solving the near-field parameter estimation problem. The estimation accuracy of the proposed approach is compared to existing methods via simulation analysis. An experimental validation of theoretical ideas is also presented.

We consider the problem of direction finding for nonstationary signals impinging on an array of sensors. Making use of a time-frequency representation of the data, we are able to exploit the non-stationary nature of the source signals. We employ morphological image processing to estimate time-frequency signature segments of each source. Optional overlapping segments are splitted and recombined after direction finding. The proposed method also allows direction finding for the underdetermined case, i.e. when there are more sources than the number of array sensors.

Acoustic imaging has been used in a variety of applications, but its use in air has been limited due to the slow propagation of sound and high attenuation. We address the problem of ultrasound imaging of a scene in air with a 2D array under the constraint of a fixed platform. The presented system uses a single transmit pulse combined with a Capon beamformer at the receiving array under a near-field model to obtain three-dimensional images of a scene. Results from experiments conducted in a laboratory demonstrate that it is possible to detect position and edge information from which an object can be reconstructed.

We propose confidence intervals for the conditional coherence using the bootstrap. The asymptotic distribution of the empirical conditional coherence is inaccurate when signal and noise are non-Gaussian and/or the data size is small. The confidence intervals obtained with the bootstrap are shown to be accurate, maintaining the preset level of confidence.

In many situations, interdependency between motion estimation and other estimation tasks is observable. This is for instance true in the area of super-resolution (SR). In order to successfully reconstruct a SR image, accurate motion vector fields are needed. On the other hand, one can only get accurate (subpixel) motion vectors, if there exist highly accurate higher-resolution reference images. Neglecting this interdependency may lead to poor estimation results for motion estimation as well as for the SR image. To address this problem, a new motion estimation scheme is presented that jointly optimises the motion vector field and a SR reference image. For this purpose and in order to attenuate aliasing and noise, which deteriorate the motion estimation, an observation model for the image acquisition process is applied and a maximum a posteriori (MAP) optimisation is performed, using Markov random field image models for regularisation. Results show that the new motion estimator provides more accurate motion vector fields than classical block motion estimation techniques. The joint optimisation scheme yields an estimate of the motion vector field as well as a SR image.

We consider source enumeration and identification in the context of monitoring the cooling circuit of a pressurized-water-reactor (PWR) nuclear plant. We employ a linear instantaneous-mixture to describe the system. We use the Gerschgorin radii of the transformed covariance matrix of the data to detect the number of sources. In particular, we illustrate the advantage of employing the boot-strap in a scenario where no or little a priori knowledge is available on the statistical properties of the measured data. A specific denoising procedure is also applied to the data to alleviate the effect of small variations of the noise power over the sensors, and allow a more accurate source separation. The results show the potential of both Gerschgorin-based detection and the bootstrap in practice.

An estimator for the phase parameters of mono- and multi-component FM signals, with both good numerical properties and statistical performance is proposed. The proposed approach is based on the Hough transform of the pseudo Wigner-Ville time-frequency distribution (PWVD). It is shown that the numerical properties of the estimator may be improved by varying the PWVD window length. The effect of the window time extent on the statistical performance of the estimator is delineated. Experimental data is used for validation of statistical properties

We address estimation for the multivariate Poisson distribution with second order correlation structure. Existing estimators such as maximum likelihood estimators are too computationally expensive whereas the moment estimator has low efficiency. The proposed estimator uses on the concept of composite likelihood and is, in terms of computational complexity and efficiency, in between a simple moment estimator and the complex maximum likelihood approach

An adaptive matched subspace CFAR detector of Gaussian distributed signals is analyzed. The detector is an extension of the one developed in F. Gini and A. Farina (1999) to the case of unknown disturbance covariance matrix. This matrix is estimated from secondary data which can be non homogenous. In this latter case we use a robust estimate of the covariance matrix based on the sample spatial sign covariance matrix (SSCM). The performance of the adaptive scheme, specifically, the impact on the false alarm rate is studied by means of Monte Carlo simulations. The results show that the adaptive detector using the SSCM maintains the false alarm approximately constant in non homogenous situations

We consider the problem of source number estimation in the presence of unknown spatially nonuniform noise. A sequential hypothesis test is formulated based on Gerschgorin's theorem. As no assumption is made on the distribution of the noise or the signals, the bootstrap is used to estimate the distribution of the proposed test statistics. Performance of the new detector is assessed through simulations and its advantage is illustrated in different scenarios against a Gerschgorin-based information criterion.

We consider the problem of direction finding for nonstationary signals impinging on an array of sensors. Making use of a time-frequency representation of the data, we are able to exploit the non-stationary nature of the source signals. We employ a generalized Hough transform to estimate the time-frequency signature of each source. The proposed method also allows direction finding when there are more sources than the number of array sensors.

The paper presents adaptive blind channel estimation and tracking algorithms for CDMA systems. Using only the spreading code of the user of interest, three blind estimation algorithms are proposed to estimate the channel response from the received data sequence. The idea is based on minimum variance (MV) receivers. Simulation results show that the proposed algorithms perform better than previously proposed algorithms, also they are less complex and have a fast convergence rate.

We address the problem of confidence interval estimation for the coherence function. We revisit a recently proposed approach to calculate confidence intervals from the asymptotic distribution function of the sample coherence function. We then propose a bootstrap based approach and compare the level of confidence obtained by the two methods as well as a well-established method proposed by Enochson and Goodman (1965). Extensive simulations have shown that the bootstrap approach is more accurate, in particular for a large coherence and non-Gaussian data.

A sequential M-estimation algorithm is proposed as an alternative to sequential least squares (LS). Being an approximation to exact M-estimation, the proposed technique is robust to non-Gaussian noise and outperforms sequential LS. A low-cost technique is introduced for initialization. We also show that sequential LS is a special case of the proposed algorithm.

We consider the problem of source number estimation in the presence of unknown spatially nonuniform noise. Successive array element suppression is applied to isolate the contribution of the noise powers and a likelihood function is derived. When it is combined with the appropriately defined penalty function, a MDL-like criterion is defined. Performance of the new criterion is assessed through simulations and it is shown that the method is powerful in a nonuniform noise environment.

We consider the problem of scale estimation when a nominal distribution is contaminated. Knowledge of the scale is necessary in many signal detection and estimation problems and poor estimates of the scale can have deleterious effects on subsequent processing. The approach considered here is based on the M-estimation concept of Huber (1981), but employs a score function which is a linear combination of basis functions whose weights are adaptively estimated from the observations. Results suggest that this adaptivity increases robustness over static M-estimators.

A method for detection of source signal auto-term regions in the time-frequency plane, based on spatial time-frequency distribution matrices is presented. As opposed to previous methods, a multiple hypothesis test is used in order to control the family wise error rate strongly when testing multiple locations on the time-frequency plane simultaneously. A bootstrap based method for estimating the distribution of the test statistic is also proposed, and the performance in terms of operating characteristics is compared to that of using an asymptotic distribution.

We propose a sequential M-estimation algorithm as an alternative to sequential least squares. Being an approximation of the exact M-estimator, the proposed technique is robust to nonGaussian processes and outperforms sequential least squares. Simulation results demonstrate the power of the proposed sequential M-estimator.

We consider the problem of direction of arrival estimation in the presence of unknown spatially nonuniform noise. A subspace separation approach is applied, based on successive array element elimination, to isolate the contribution of the noise powers. A high resolution estimator based on MUSIC is described for nonuniform noise. Performance of the estimator is assessed through simulations and is compared to the Cramer-Rao bound.

We propose a blind separation technique for nonstationary sources that exploits both auto-terms and cross-terms of the time-frequency distributions. The technique is based on the simultaneous joint diagonalization and off-diagonalization of spatial time-frequency distributions. Computer simulations demonstrate the superiority of the approach in comparison with other time-frequency based methods.

In this paper, we address the problem of multiuser detection in multiple receive antenna based multicarrier code division multiple access (MC-CDMA) systems. Specifically, we consider frequency selective fading channels with frequency offset and use our previously proposed multiple receive antenna based blind adaptive subspace multiuser detectors to recover transmitted data of the user of interest The adaptive detectors rely on a blind subspace technique to estimate the channel parameters. For performance comparison, we extend maximum ratio combining (MRC) detector, which is often used in conventional single transmit and single receive antenna based MC-CDMA systems to single transmit and multiple receive antenna based MC-CDMA systems and evaluate its theoretical performance. Simulation results show that our blind adaptive subspace-based detection techniques perform better than the new MRC detector (with perfect channel parameters) at high frequency offset.

The effect of missing observations, caused by random sensor errors or periodic blocking of the signal, on the estimation of signal parameters is to reduce estimator performance. For the class of polynomial phase signals, existing estimators may suffer a severe degradation in performance depending on the location of the missing observations. Reasons for the drop in performance are determined and several estimators are proposed which behave well even with a large proportion of missing observations.

We consider the problem of joint detection and decoding for CDMA systems that employ forward error control (FEC). The main problems encountered in designing this type of receiver include high complexity and a lack of robustness in impulsive noise and contamination in the prior model. We propose that the extrinsic information may not need to be absolutely reliable as we consider impulsive interference. By allowing the judgement of confidence in using this extrinsic information, the proposed M-estimation based soft-in soft-out (SISO) detector exhibits robust performance for a low complexity.

We address the problem of confidence interval estimation of spectral densities using the bootstrap. Of special interest is the choice of the kernel global bandwidth. First, we investigate resampling based techniques for the choice of the bandwidth. We then address the question of whether the accuracy of the distributional bootstrap estimation is influenced by using the resample version, rather than the sample version of an empirical bandwidth. Aligned with recent results on non-parametric probability density estimation, we found that varying an empirical bandwidth across resamples is largely unnecessary and thus, the computational burden is greatly reduced while maintaining estimation accuracy.

We consider a bootstrap-based approach to enhance the performance of RAKE receivers in multi-user CDMA systems over a multipath frequency selective slowly fading channel. A training based strategy is proposed to identify a low order channel. In this approach we use an FIR filter model with unknown length, estimating the model directly with low complexity in the time domain. Based on the estimates, bootstrap-based multiple hypothesis tests are applied to identify the non-zero coefficients of the FIR filter; in other words low order estimates of the channel. Simulation results demonstrate the power of using this technique in RAKE receivers in unknown noise environments.

We propose a robust multiuser detector which combats multiple access interference and noise of unknown distribution in CDMA systems. The detector follows the M-estimation concept of robust statistics, except that the influence function is modelled as a weighted sum of a set of basis functions and is estimated from the observations. Simulations show that performance is improved in impulsive noise compared to conventional and previously presented non-linear schemes.

Robust estimation of signal parameters in the additive noise model has become an important problem. Its relevance can be attributed to the realisation that impulsive noise is present in communications channels. The approach to robust estimation taken here follows the M-estimation concept of robust statistics, except the score function is modeled as a linear combination of bases and is estimated from the observations. The asymptotic covariance of the M-estimates is derived and both the small and large sample performance is investigated. By imposing suitable constraints when estimating the score function small sample performance is improved with minimal large sample loss.

Historically, metal detectors have been essential tools for demining. However they have been unable to keep pace with developments that made landmines more difficult to find. Here, techniques for the detection of buried objects using a metal detector are presented, evaluated and compared. The findings highlight a number of deficiencies, as well as a number of strengths, in the proposed detectors. Of particular interest are the parameters found using Prony's method, as well as the difference operator, reverse arrangements test and the median filter. Suggestions are made for the improvement of a number of detectors.

The problem of selecting auto- and cross-terms of time-frequency distributions (TFDs) of nonstationary signals impinging on a multi-antenna receiver is considered. A detection approach is introduced which allows performance measurement and comparison of various schemes via receiver operating characteristics. Array averaging and array differencing techniques are both employed to form a basis for time-frequency (t-f) point selection. The proposed classification method is evaluated against the bootsrap-based method. It is shown that the former offers improved performance and simplified implementations.

We consider the problem of designing detectors using tolerance intervals. Signal detection based on tolerance intervals allows us to force the actual level of significance not to exceed the preset level with a given probability. The results presented in this letter demonstrate the accuracy with which these detectors can control the false-alarm rate when little is known about the noise distribution and only a small sample is available.

We address the problem of blind source separation of non-stationary signals of which only instantaneous linear mixtures are observed. A blind source separation approach exploiting both auto-terms and cross-terms of the time-frequency (TF) distributions of the sources is considered. The approach is based on the simultaneous diagonalization and anti-diagonalization of spatial TF distribution matrices made up of, respectively, auto-terms and cross-terms. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach and compare its performances with existing TF-based methods.

This paper deals with noisy phase monocomponent signals in additive noise. This model is more appropriate for real world applications in particular for radar and communications. The problem is introduced and a maximum likelihood solution is proposed. Specifically, the Cramer-Rao bound is explicitly derived and compared to the case of noise free phase.

We consider detection of constant amplitude phase modulated signals in noise. A simple detector based on second- and fourth-order moments is proposed. The detector has several good properties including independence of the signal phase, consistency, and computational efficiency. Numerical simulations are used to compare the detector to a bootstrap-based one. The moment-based detector is shown to have better performance for higher-order polynomial phase signals.

In this paper we consider the identification of a time-varying quadratic Volterra model. In the model, a set of known basis sequences are used to approximate the time-variation of the true system to enable identification. To reduce the number of parameters in the model we wish to determine which sequences can be considered significant in this approximation. The Bonferroni multiple hypothesis testing procedure is used for the selection of individual basis sequences to include in the model. This is compared with treating the multiple hypotheses separately. Not only does the Bonferroni procedure allow strong control over the false alarm but has more power when selecting the true model in low noise.

The problem of detecting known signals in the presence of correlated interference with symmetric alpha-stable excitation is considered. An estimation procedure for the signal strength is devised, based on the minimum dispersion criterion, then blind channel identification is performed. Several detection schemes are presented based on locally optimum (LO) and locally optimum rank (LOR) procedures, as well as some more computationally efficient suboptimal tests. The approximate distributions of the corresponding test statistics are derived. Simulation results indicate the levels of significance are maintained and all detectors achieve similar detection rates. The conclusion is drawn that the LOR and the suboptimal tests are able to achieve near locally optimal performance but with a far lighter computational burden.

It has been suggested that the accuracy of the cyclic moments-based estimator of the frequency of a random amplitude sinusoid in additive noise may be increased by using the squared observations rather than the raw observations. This paper extends this idea to random amplitude polynomial phase signals of arbitrary order. The covariance matrix of the cyclic moments-based estimators is derived for the cases where either the observations or the squared observations are used. It is found that, for first and second order phases, the use of the squared observations results in more accurate phase parameter estimates in a wide range of conditions. For higher order phases the use of the squared observations is more accurate only under restrictive conditions.

A general bootstrap procedure for signal detection is presented. Two methods under this general procedure are given. One method requires a regression model to be available to generate the bootstrap data while the other method assumes a pivot. Examples of detecting known signals, signals with unknown parameters and random signals are given. Performance in terms of false alarm and detection rates of the bootstrap methods are found using simulations and compared with the performance of the constant false alarm rate (CFAR) matched filter, the CFAR subspace matched filter bank and a test for zero skewness. Results in an application using ground penetrating radar data to detect buried landmines are also presented.

An approach for identifying time-varying nonlinear systems is presented. The time-variation of the system is approximated by a weighted combination of sequences from a given basis. In this case, to identify the system it is sufficient to estimate the time-invariant coefficients of the sequences. The focus of our investigation is on selecting these sequences to use in the approximation. We propose using a search method to determine which sequences contribute significantly to the approximation and thus lead to a parsimonious model that is able to characterise the system dynamics and time-variation together.

We use Edgeworth expansions to show the higher-order accuracy of the bootstrapped matched filter (MF). Specifically, the bootstrapped MF has a probability of false alarm of order n/sup -1/ distant from the preset level, where n is the sample size. We also show that the order is n/sup -3/2/ for sinusoidal signals. Simulation results compare the bootstrapped MF with the classical MF. We briefly discuss the bootstrapping approach when the noise variance is unknown and when signal parameters are unknown.

This paper presents a CFAR detector based on the bootstrap for detecting signals with unknown amplitude, phase and frequency such as found in conventional pulsed radar and sonar systems. The detector is robust against non-Gaussian noise, and can still maintain the false alarm rate without much modification if consistent estimates are substituted for unknown parameters. Preliminary asymptotic results are given on the performance of the detector, and simulations are used to study the performance for small samples sizes.

The problem of model selection is addressed (in a signal processing framework). Bootstrap methods based on residuals are used to select the best model according to a prediction criterion. Both the linear and the nonlinear models are treated. It is shown that bootstrap methods are consistent and in simulations that in most cases they outperform classical techniques such as Akaike's (1974) information criterion and Rissanen's (1983) minimum description length. We also show how the methods apply to dependent data models such as autoregressive models.

The Adichie (1984) rank test and signed rank test are adapted for signal detection. We establish a relationship with the correlation between a function of the signal to be detected and the ranks of the observed data. A comparison between the power of these tests and the constant false alarm rate matched filter (CFAR MF) shows that the rank tests perform better when longer observations are available and for the symmetric alpha stable distributions encountered in applications with impulsive interference.

We consider the problem of estimating the order of the phase of a complex valued signal, having a constant amplitude and a polynomial phase, measured in additive noise. A new method based on the bootstrap is introduced. The proposed approach does not require knowledge of the distribution of the noise, is easy to implement, and unlike existing techniques, it achieves high performance when only a small amount of data is available. The proposed technique can be easily extended to non-stationary signals which have a polynomial amplitude and phase, provided a consistent estimator for the parameters can be obtained.

In this paper, the design of optimal schemes for detecting deterministic narrowband signals with unknown parameters in correlated interference modelled by the GBK (generalised Bessel function K) distribution is considered. Theoretical derivations of an optimal detector, in the Neyman-Pearson sense, are given for the case where the signal amplitude and phase are unknown. The performance of the detector is then evaluated using extensive computer simulations. Radar target detection is used as an example.

We present a non-stationary signal classification algorithm based on a time-frequency representation and a multiple hypothesis test. The time-frequency representation is used to construct a time-dependent quadratic discriminant function. At selected points in time we evaluate the discriminant function and form a set of statistics which are used to test the multiple hypotheses. The multiple hypotheses are treated simultaneously using the sequentially rejective Bonferroni test to control the probability of incorrect classification of one class. We show results for classifying three classes of humpback whale calls. The results demonstrate that this time-frequency method performs favourably when compared with a frequency domain method which assumes stationarity.

Nonlinear system identification involves selecting the order of the given model based on the input-output data. A bootstrap model selection procedure which selects the model by minimising bootstrap estimates of the prediction error is developed. Bootstrap based model selection procedures are attractive because the bootstrap observations generated for the model selection can also be used in subsequent inference procedures. The proposed method is simple and computationally efficient.

We approximate a class of time-varying nonlinear models, called the time-varying Hammerstein series, using basis sequences in order to reduce the number of coefficients required in system modelling. The problem is motivated by the practical need to parsimoniously characterise time-varying nonlinear systems. A significant advantage of the approach is that only a single input-output record is required to obtain least-squares estimates of the model parameters. The judicious selection of basis sequence is also discussed. The method represents a simple and practical time-varying nonlinear system identification procedure. Examples are presented to demonstrate the usefulness of the technique.

This paper proposes and demonstrates a practical parameter estimation scheme for estimating the height, speed, range and acoustic frequency of an overflying aircraft. This scheme is based on the phase of the acoustic signal emitted by the aircraft as heard by a stationary observer. Bootstrap techniques are employed to determine confidence bounds for the aircraft parameters given only a single acoustic realisation. This estimation scheme, and the novel use of the bootstrap, are demonstrated by computer simulation and with aircraft acoustic data which was collected by the authors under accurately monitored experimental conditions.

Testing the Gaussianity of a random process has been identified as an important problem in many engineering applications. Tests based on the bispectrum such as Subba Rao and Gabr's (1980) test or Hinich's (1982) test for Gaussianity have been proposed more than a decade ago. They have received considerable interest and application among the signal processing community. However, their application is limited to cases where a large amount of data is available. To overcome this problem, we incorporate the bootstrap into the bispectrum based Gaussianity test, and demonstrate how we can achieve high power. The proposed bootstrap procedure can also be used for setting confidence bands for bispectra.

We wish to formulate a test for the hypothesis X/sub i//spl sim/N(/spl mu/,/spl sigma//sup 2/) for i=0,1,...,N-1 against unspecified alternatives. We assume independence of the components of X=[X/sub 0/,X/sub 1/,...,X/sub N-1/]. This is a problem of universal importance as the assumption of Gaussianity is prevalent and fundamental to many statistical theories and engineering applications. Many such tests exist, the most well-known being the /spl chi//sup 2/ goodness-of-fit test with its variants and the Kolmogorov-Smirnov one-sample cumulative probability function test. More powerful modern tests for the hypothesis of Gaussianity include the D'Agostino (1977) K/sup 2/ and Shapiro-Wilk (1968) W tests. Tests for Gaussianity have been proposed which use the characteristic function. It is the purpose of this paper to highlight and resolve problems with these tests and to improve performance so that the test is competitive with, and in some cases better than, the most powerful known tests for Gaussianity.

We consider the identification of systems which are both time-varying and nonlinear. This class of systems is more likely to be encountered in practice, but is often avoided due to the difficulties that arise in modelling and estimation. We attempt to address this problem by considering a new time-varying nonlinear model, the time-varying Hammerstein model, which effectively characterises time-variation and nonlinearity in a simple manner. Using this model we formulate a procedure to find least-squares estimates of the coefficients. The model is general and can be used when little is known about the time-variation of the system. In addition, we do not require that the input is stationary or Gaussian. Finally, an application to automobile knock modelling is presented, where a time-varying nonlinear model is seen to more accurately characterise the system than a time-varying linear one.

A comparative study of techniques for finding optimal sensor positions in a group of vibration sensors for knock detection in spark ignition engines is presented. The methods assume the transmission of the acoustical oscillations in the combustion chamber to the engine housing to be time invariant and linear. Based on this model, suitable multiple tests have been performed to reject sequentially irrelevant sensors from the sensor group under consideration. It was found in various simulations that two of the proposed methods that do not assume any probability distribution of the data lead to the expected results. In a real experiment performed on a test bed using a four cylinder spark ignition engine, the two methods reveal the same optimal sensor location for monitoring knock in two cylinders at three different speeds.

In this study, we propose a method for finding optimum sensor positions in a group of vibration sensors for knock detection in spark ignition engines. It differs from other techniques in that only signal processing and statistical tests are used. Our method is based on linearly predicting a reference signal from the output signals of an array of sensors, distributed arbitrarily on the engine block. We derive a linear regression model in the frequency domain and discuss parametric tests for various hypotheses that are tested with respect to the model parameters. This leads us to a technique for testing irrelevancy of sensors in the considered group. Simulation and experimental results emphasize the applicability of the method.>

We review bootstrap methods for testing statistical hypotheses. We begin with single hypothesis testing and give an example of its use. We then consider multiple testing based on Holm's step-down procedure and discuss how the bootstrap can incorporate relevant correlation and distributional characteristics. These techniques are applied to tests for zeros of transfer functions of linear systems at different frequencies, conventionally solved using "large sample" approximations. Our results highlight the applicability of the bootstrap in a situation where asymptotic results are not valid.>

A review of recent developments in statistical signal processing for application to over-the-horizon radar (OTHR) is presented. Three different signal processing issues are considered. The first two issues relate to the radar interference characterisation, namely a Gaussianity test and a K-distribution test. The third issue relates to target detection in clutter based on rank tests. All techniques are applied to simulated as well as real OTHR data.>

A method to find optimum sensor positions in an array of sensors for engine knock detection is presented. It is less complex than holographic techniques because only signal processing and statistical tests are used. The method is based on linearly predicting an arbitrary sensory output from the remaining outputs in the sensor group. The relevancy of the sensor is characterized by the closeness to zero of the multiple coherence of the sensor output with the remaining sensor outputs at some frequencies of interest. A suitable statistic is chosen, its distribution is approximated, and a simultaneous test is constructed. It was found in an experiment that a proposed sensor position was not optimum.>