Extended Bayesian information criterion (EBIC) and extended Fisher information criterion (EFIC) are two popular criteria for model selection in sparse high-dimensional linear regression models. However, EBIC is inconsistent in scenarios when the signal-to-noise-ratio (SNR) is high but the sample size is small, and EFIC is not invariant to data scaling, which affects its performance under different signal and noise statistics. In this paper, we present a refined criterion called EBICRwhere the ‘R’ stands for robust. EBICRis an improved version of EBIC and EFIC. It is scale-invariant and a consistent estimator of the true model as the sample size grows large and/or when the SNR tends to infinity. The performance of EBICRis compared to existing methods such as EBIC, EFIC and multi-beta-test (MBT). Simulation results indicate that the performance of EBICRin identifying the true model is either at par or superior to that of the other considered methods.

The Bayesian information criterion (BIC) is one of the most well-known criterion used for model order estimation in linear regression models. However, in its popular form, BIC is inconsistent as the noise variance tends to zero given that the sample size is small and fixed. Several modifications of the original BIC have been proposed that takes into account the high-SNR consistency, but it has been recently observed that the performance of the high-SNR forms of BIC highly depends on the scaling of the data. This scaling problem is a byproduct of the data dependent penalty design, which generates irregular penalties when the data is scaled and often leads to greater underfitting or overfitting losses in some scenarios when the noise variance is too small or large. In this paper, we present a new form of the BIC for order selection in linear regression models where the parameter vector dimension is small compared to the sample size. The proposed criterion eliminates the scaling problem and at the same time is consistent for both large sample sizes and high-SNR scenarios.

We consider a finite-state Discrete-Time Markov Chain (DTMC) source that can be sampled for detecting the events when the DTMC transits to a new state. Our goal is to study the trade-off between sampling frequency and staleness in detecting the events. We argue that, for the problem at hand, using Age of Information (AoI) for quantifying the staleness of a sample is conservative and therefore, study another freshness metricage penalty, which is defined as the time elapsed since the first transition out of the most recently observed state. We study two optimization problems: minimize average age penalty subject to an average sampling frequency constraint, and minimize average sampling frequency subject to an average age penalty constraint; both are Constrained Markov Decision Problems. We solve them using the Lagrangian MDP approach, where we also provide structural results that reduce the search space. Our numerical results demonstrate that the computed Markov policies not only outperform optimal periodic sampling policies, but also achieve sampling frequencies close to or lower than that of an optimal clairvoyant (non-causal) sampling policy, if a small age penalty is allowed.

In this paper, we propose a novel model selection method named multi-beta-test (MBT) for the sparse high-dimensional linear regression model. The estimation of the correct subset in the linear regression problem is formulated as a series of hypothesis tests where the test statistic is based on the relative least-squares cost of successive parameter models. The performance of MBT is compared to existing model selection methods for high-dimensional parameter space such as extended Bayesian information criterion (EBIC), extended Fisher Information criterion (EFIC), residual ratio thresholding (RRT) and orthogonal matching pursuit (OMP) with a priori knowledge of the sparsity. Simulation results indicate that the performance of MBT in identifying the true support set surpasses that of EBIC, EFIC and RRT in certain regions of the considered parameter settings.

We consider the problem of offline change point detection from noisy piecewise constant signals. We propose normalized fused LASSO (FL), an extension of the FL, obtained by normalizing the columns of the sensing matrix of the LASSO equivalent. We analyze the performance of the proposed method, and in particular, we show that it is consistent in detecting change points as the noise variance tends to zero. Numerical experiments support our theoretical findings.

In this paper, the optimal jamming of wireless localization systems is investigated. Two optimal power allocation schemes are proposed for jammer nodes in the presence of total and peak power constraints. In the first scheme, power is allocated to jammer nodes in order to maximize the average Cramér-Rao lower bound (CRLB) of target nodes, whereas in the second scheme, the power allocation is performed for the aim of maximizing the minimum CRLB of target nodes. Both the schemes are formulated as linear programs, and a closed-form solution is obtained for the first scheme. For the second scheme, under certain conditions, the property of full total power utilization is specified, and a closed-form solution is obtained when the total power is lower than a specific threshold. In addition, it is shown that non-zero power is allocated to at most NTjammer nodes according to the second scheme in the absence of peak power constraints, where NTis the number of target nodes. In the presence of parameter uncertainty, robust versions of the power allocation schemes are proposed. Simulation results are presented to investigate the performance of the proposed schemes and to illustrate the theoretical results.

We investigate the range estimate between two wireless nodes without time stamps exchanging. Considering practical aspects of oscillator clocks, we propose a new model for ranging in which the measurement errors include the sum of two distributions, namely, uniform and Gaussian. We then derive an approximate maximum likelihood estimator (AMLE), which poses a difficult global optimization problem. To avoid the difficulty in solving the complex AMLE, we propose a simple estimator based on the method of moments. Numerical results show a promising performance for the proposed technique.

We propose a method for high dimensional sparse estimation in the multiple measurement vector case. The method is based on the covariance matching technique and with a sparse penalty along the ideas of the square-root LASSO (sr-LASSO). The method not only benefits from the strong characteristics of sr-LASSO (independence of the hyper-parameter selection from the noise variance), but also offers a performance near maximum likelihood. It performs close to the Cramer-Rao bound even at low signal to noise ratios and it is generalized to manage correlated noise. The only assumption in this matter is that the noise covariance matrix structure is known. The numerical simulation provided in an array processing application illustrates the potential of the method.

We develop a greedy algorithm for the basis-pursuit problem. The algorithm is empirically found to provide the same solution as convex optimization based solvers. The method uses only a subset of the optimization variables in each iteration and iterates until an optimality condition is satisfied. In simulations, the algorithm converges faster than standard methods when the number of measurements is small and the number of variables large.

In sparse recovery from measurement data a common approach is to use greedy pursuit reconstruction algorithms. Most of these algorithms have a correlation filter for detecting active components in the sparse data. In this paper, we show how modifications can be made for the greedy pursuit algorithms so that they use beamformers instead of the standard correlation filter. Using these beamformers, improved performance in the algorithms is obtained. In particular, we discuss beamformers for the average and worst case scenario and give methods for constructing them.

In certain direction-of-arrival (DOA) estimation scenarios some of the source directions are known to the operator even before measurements are acquired. It is then undesirable to use regular DOA-algorithms which waste data-samples estimating the known directions. Additionally, in some applications it is known that the signals emanating from the known directions are uncorrelated with those coming from the unknown directions. In this article we present a novel algorithm which exploits the combination of such prior knowledge in a manner more efficient (in terms of accuracy) than any algorithm known to the authors. Through numerical Monte-Carlo simulations we show the estimator to attain the theoretical accuracy bound for significantly lower signal-to-noise ratios than current state-of-the-art methods. Additionally we show the proposed algorithm to treat the stricter problem of entirely uncorrelated emitters better than current state of the art.

This paper considers the problem of reconstructing low-rank matrices from undersampled measurements, when the matrix has a known linear structure. Based on the iterative reweighted least-squares approach, we develop an algorithm that exploits the linear structure in an efficient way that allows for reconstruction in highly undersampled scenarios. The method also enables inferring an appropriate regularization parameter value from the observations. The performance of the method is tested in a missing data recovery problem.

In this paper, we address the problem of egomotion estimation using an inertial measurement unit and visual observations of planar features on the ground. The main practical difficulty of such a system is correctly determining the ground planar features from the visual observations. Herein, we propose a novel vision-aided inertial navigation system through simultaneous motion estimation and ground plane feature detection. We present a state-space formulation for the pose estimation problem and solve it via an augmented unscented Kalman filter. First, the predictions obtained by the Kalman filter are used to detect the ground plane features. Second, the detected features are fed back to the motion estimation algorithm to be used in the measurement update phase of the filter. The developed detection algorithm consists of two steps, namely homography-based and normal-based outlier rejection. The presented integration algorithm allows 6-DoF motion estimation in a practical scenario where the camera is not restricted to observe only the ground plane. Real-world experiments in an indoor scenario indicate the accuracy and reliability of our proposed method in the presence of outliers and non-ground obstacles.

In this paper, we present an observability analysis of a vision-aided inertial navigation system (VINS) in which the camera is downward looking and observes a single point feature on the ground. In our analysis, the full INS parameter vector (including position, velocity, rotation, and inertial sensor biases) as well as the 3D position of the observed point feature are considered as state variables. In particular, we prove that the system has only three unobservable directions corresponding to global translations along the x and y axes, and rotations around the gravity vector. Hence, compared to general VINS, an advantage of using only ground features is that the vertical translation becomes observable. The findings of the theoretical analysis are validated through real-world experiments.

For array processing, we consider the problem of estimating signals of interest, and their directions of arrival (DOA), in unknown colored noise fields. We develop an estimator that efficiently utilizes a set of noise-only samples and, further, can incorporate prior knowledge of the DOAs with varying degrees of certainty. The estimator is compared with state of the art estimators that utilize noise-only samples, and the Cramér-Rao bound, exhibiting improved performance for smaller sample sets and in poor signal conditions.

For compressive sensing of dynamic sparse signals, we develop an iterative greedy search algorithm based on subspace pursuit (SP) that can incorporate sequential predictions, thereby taking advantage of its low complexity while improving recovery performance by exploiting correlations described by a state space model. The algorithm, which we call dynamic subspace pursuit (DSP), is presented and experimentally validated. It exhibits a graceful degradation at deteriorating signal conditions while capable of yielding substantial performance gains as conditions improve.

In this paper, a method for determining ground plane features in a sequence of images captured by a mobile camera is presented. The hardware of the mobile system consists of a monocular camera that is mounted on an inertial measurement unit (IMU). An image processing procedure is proposed, first to extract image features and match them across consecutive image frames, and second to detect the ground plane features using a two-step algorithm. In the first step, the planar homography of the ground plane is constructed using an IMU-camera motion estimation approach. The obtained homography constraints are used to detect the most likely ground features in the sequence of images. To reject the remaining outliers, as the second step, a new plane normal vector computation approach is proposed. To obtain the normal vector of the ground plane, only three pairs of corresponding features are used for a general camera transformation. The normal-based computation approach generalizes the existing methods that are developed for specific camera transformations. Experimental results on real data validate the reliability of the proposed method.

In certain applications involving direction of arrival (DOA) estimation the operator may have a-priori information on some of the DOAs. This information could refer to a target known to be present at a certain position or to a reflection. In this study, the authors investigate a methodology for array processing that exploits the information on the known DOAs for estimating the unknown DOAs as accurately as possible. Algorithms are presented that can efficiently handle the case of both correlated and uncorrelated sources when the receiver is a uniform linear array. The authors find a major improvement in estimator accuracy in feasible scenarios, and they compare the estimator performance to the corresponding theoretical stochastic Cramér–Rao bounds as well as to the performance of other methods capable of exploiting such prior knowledge. In addition, real data from an ultra-sound array is applied to the investigated estimators.

For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori knowledge of matrix structure. In particular, we consider linearly structured matrices, such as Hankel and Toeplitz, as well as positive semidefinite matrices. The performance of the algorithm, referred to as alternating least-squares (ALS), is evaluated by simulations and compared to the Cramér-Rao bounds.

We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE) estimate of the state is given by the conditional mean. Since finding the conditional mean requires multidimensional integration, an approximate MMSE estimator is proposed. The performance of the proposed estimator is evaluated in a positioning problem. Finally, the application of the estimator in inequality constrained recursive filtering is illustrated by applying the estimator to a dead-reckoning problem. The MSE of the estimator is compared with two related posterior Cramér-Rao bounds.

In a number of direction of arrival (DOA) estimation applications there exists prior knowledge about the sources whose bearings are to be determined. We study the case when this prior information concerns some of the source positions and their correlation state, which is a relevant case in, for example, RADAR scenarios where stationary objects exists in the regions of interest. Traditional DOA methods are not designed to exploit such information, and thus cannot obtain the highest theoretical accuracy. We present a method that can utilize in an asymptotically efficient manner both knowledge on some source positions and that the source signals are uncorrelated.

For small-scale Unmanned Aerial Vehicles (UAV) to operate indoor, in urban canyons or other scenarios where signals from global navigation satellite systems are denied or impaired, alternative estimation and control strategies must be applied. In this paper a system is proposed that estimates the self-motion and wind velocity by fusing information from airspeed sensors, an inertial measurement unit (IMU) and a monocular camera. Such estimates can be used in control systems for managing wind disturbances or chemical plume based tracking strategies. Simulation results indicate that while the inertial dead-reckoning process is subject to drift, the system is capable of separating the self-motion and wind velocity from the airspeed information.

In this paper, we first look at the problem of estimating the transformation between an inertial measurement unit (IMU) and a calibrated camera, based on images of planar mirror reflections (IPMR) of arbitrary feature points with unknown positions. Assuming that only the reflection of the feature points are observable by the camera, the IMU-camera calibration parameters and the position of the feature points in the camera frame are estimated using the Sigma-Point Kalman filter framework. In the next step, we consider the case of estimating varying camera intrinsic parameters using the estimated static parameters from the previous stage. Therefore, the estimated parameters are used as initial values in the state space model of the system to estimate the camera intrinsic parameters together with the rest of the parameters. The proposed method does not rely on using a fixed calibration pattern whose feature points' positions are known relative to the navigation frame. Additionally, the motion of the camera, which is mounted on the IMU, is not limited to be planar with respect to the mirror. Instead, the reflection of the feature points with unknown positions in the camera body frame are tracked over time. Simulation results show subcentimeter and subdegree accuracy for both IMU-camera translation and rotation parameters as well as submillimeter and subpixel accuracy for the position of the feature points and camera intrinsic parameters, respectively.

In this paper, a simple method to calibrate the accelerometer cluster of an inertial measurement unit (IMU) is proposed. The method does not rely on using a mechanical calibration platform that rotates the IMU into different precisely controlled orientations. Although the IMU is rotated into different orientations, these orientations do not need to be known. Assuming that the IMU is stationary at each orientation, the norm of the input is considered equal to the gravity acceleration. As the orientations of the IMU are unknown, the calibration of the accelerometer cluster is stated as a blind system identification problem where only the norm of the input to the system is known. Under the assumption that the sensor noises have a white Gaussian distribution the system identification problem is solved using the maximum likelihood estimation method. The accuracy of the proposed calibration method is compared with the Cramér-Rao bound for the considered calibration problem.

An estimation procedure for calibration of a low-cost inertial measurement unit (IMU), using a rigidly mounted monocular camera, is presented. The parameters of a sensor model that captures misalignments, scale and offset errors are estimated jointly with the IMU-camera coordinate transformation parameters using a recursive Sigma-Point Kalman Filter. The method requires only a simple visual calibration pattern. A simulation study indicates the filter's ability to reach subcentimeter and subdegree accuracy.

The estimation of signal covariance matrices is a crucial part of many signal processing algorithms. In some applications, the structure of the problem suggests that the underlying, true, covariance matrix is the Kronecker product of two matrices. Examples of such problems are channel modelling for MIMO communications and signal modelling of EEG data. In applications it may also be that the Kronecker factors in turn can be assumed to possess additional, linear, structure. The maximum likelihood (ML) estimator for the problem has been proposed previously. It is asymptotically efficient but has the drawback of requiring an iterative search. Two methods that are both non-iterative and asymptotically efficient are proposed in this paper. The first method is derived from a well-known iterative maximization technique for the likelihood function. It performs on par with ML in simulations, but has the drawback of not allowing for extra structure in addition to the Kronecker structure. The second method is based on covariance matching principles, and does not suffer from this drawback. However, while the large sample performance is shown to be identical to ML, it performs somewhat worse in small samples than the first estimator. In addition, the Cramer-Rao lower bound (CRB) for the problem is derived in a compact form.

The weighted low-rank approximation (WLRA) problem is considered. The problem is that of approximating one matrix with another matrix of lower rank, such that the weighted norm of the difference is minimized. The problem is fundamental in a new method for reduced rank linear regression that is outlined, as well as in areas such as two-dimensional filter design and data mining. The WLRA problem has no known closed form solution in the general case, but iterative methods have previously been suggested. Non-iterative methods that are asymptotically optimal for the linear regression and related problems are developed. Computer simulations, where the new methods are compared to one step of the well-known alternating projections algorithm, show significantly improved performance.

Mapping of the data output vector from an existing antenna array onto the data vector of an imaginary array of more suitable configuration is well known in array signal processing. By mapping onto an array manifold of lower dimension or uniform structure for example., processing speed can be improved. Conditions for the retaining of DOA error variance under such mapping have been formulated by several authors but the equally important systematic mapping errors, the bias, has been less treated to date. This paper uses a geometrical interpretation of a Taylor expansion of the DOA estimator cost function to derive an alternative design of the mapping matrix that almost completely removes the bias. The key feature of the proposed design is that it takes the orthogonality between the manifold mapping errors and certain gradients of the estimator cost function into account.

The problem of estimating a positive semi-definite Toeplitz covariance matrix consisting of a low rank matrix plus a scaled identity from noisy data arises in many applications. We propose a computationally attractive (noniterative) covariance matrix estimator with certain optimality properties. For example, under suitable assumptions the proposed estimator achieves the Cramer-Rao lower bound on the covariance matrix parameters. The resulting covariance matrix estimate is also guaranteed to possess all of the structural properties of the true covariance matrix. Previous approaches to this problem have either resulted in computationally unattractive iterative solutions or have provided estimates that only satisfy some of the structural relations.

This paper describes generalizations of the MUSIC and root-MUSIC algorithms for direction of arrival (DOA) estimation to arrays composed of multiple translated subarrays. The advantage of these new approaches is that the DOAs can be estimated using either a one-dimensional search or by rooting a polynomial, as opposed to a multidimensional search as required by the multiple invariance (MI)-ESPRIT algorithm. While MI-MUSIC and root-MI-MUSIC are not statistically efficient like MI-ESPRIT, they do perform better than a single invariance implementation of ESPRIT, and are thus better suited for finding the initial conditions required by the MI-ESPRIT search.

In some applications the covariance matrix of the observations is not only symmetric with respect to its main diagonal but also with respect to the anti-diagonal. The standard forward-only sample covariance estimate does not impose this extra symmetry. In such cases one often uses the so-called forward-backward sample covariance estimate. In this paper, a direct comparative study of the relative accuracy of the two sample estimates is performed. An explicit expression for the difference between the estimation error covariance matrices of the two sample estimates is given. The presented results are also useful in the analysis of estimators based on either of the two sample covariances. As an example, spatial power estimation by means of the Capon method is considered. It is shown that Capon based on the forward-only sample covariance (F-Capon) underestimates the power spectrum, and also that the bias for Capon based on the forward-backward sample covariance is half that of F-Capon.

Subspace based methods for frequency estimation rely on a low-rank system model that is obtained by collecting the observed scalar valued data samples into vectors. Estimators such as MUSIC and ESPRIT have for some time been applied to this vector model. Also, a statistically attractive Markov-like procedure for this class of methods has been proposed in the literature. Herein, the Markov estimator is re-investigated. Several results regarding rank, performance, and structure are given in a compact manner. The results are used to establish the large sample equivalence of the Markov estimator and the approximate maximum likelihood (AML) algorithm proposed by Stoica et al. (see Automatica, vol.30, no.1, p.131-45, 1994).

Model error sensitivity is an issue common to all high resolution direction of arrival estimators. Much attention has been directed to the design of algorithms for minimum variance estimation taking only finite sample errors into account. Approaches to reduce the sensitivity due to array calibration errors have also appeared in the literature. Herein, a weighted subspace fitting method for a wide class of array perturbation models is derived. This method provides minimum variance estimates under the assumption that the prior distribution of the perturbation model is known. Interestingly enough, the method reduces to the WSF (MODE) estimator if no model errors are present. On the other hand, when model errors dominate, the proposed method turns out to be equivalent to the "model-errors-only subspace fitting method". Unlike previous techniques for model errors, the estimator can be implemented using a two-step procedure if the nominal array is uniform and linear, and it is also consistent even if the signals are fully correlated.

This paper deals with direction estimation of signals impinging on a uniform linear sensor array. A well known algorithm for this problem is iterative quadratic maximum likelihood (IQML). Unfortunately, the IQML estimates are in general biased, especially in noisy scenarios. We propose a modification of IQML (MIQML) that gives consistent estimates at approximately the same computational cost. In addition, an algorithm with an estimation error covariance which is asymptotically identical to the asymptotic Cramer-Rao lower bound is presented. The optimal algorithm resembles weighted subspace fitting or MODE, but achieves optimal performance without having to compute an eigendecomposition of the sample covariance matrix.

In a previous paper we presented a novel method for spatial and temporal frequency estimation assuming that the sources are uncorrelated. The current paper analyzes this method in the case of spatial frequency estimation. In particular an optimal weighting matrix is derived and it is shown that the asymptotic variance of the frequency estimates coincides with the relevant Cramer-Rao lower bound. This means that the estimator is in large samples an efficient subspace-based spatial frequency estimator. The proposed method thus utilizes the a priori knowledge about the signal correlation as opposed to previously known subspace estimators. Moreover, when a uniform linear array is employed, it is possible to implement the estimator in a non-iterative fashion.