One-bit quantization has gained significant attention in communications and signal processing due to its potential for reducing energy consumption and system costs. However, parameter estimation methods that account for the quantization model tend to be complex and computationally intensive. Consequently, many applications opt to ignore the quantization effects during estimation, leading to model misspecification. This results in estimation errors that are influenced not only by the inherent information loss from quantization but also by the inaccuracies due to model misspecification. In this paper, we derive the misspecified Cramér-Rao bound (MCRB) for the problem of direction-of-arrival (DOA) estimation using one-bit quantized data from a sensor array. The MCRB serves as a valuable analytical tool for assessing the expected performance degradation caused by both model misspecification and quantization. Simulations demonstrate that the MCRB accurately predicts the expected performance of the maximum-likelihood estimator, and the unique effects arising from quantization are thoroughly investigated.

This paper proposes a cognitive beamforming method for target tracking using multiple-input multiple-output (MIMO) radar. This method minimizes a Bayesian performance criterion on direction-of-arrival (DOA) estimation error with respect to the transmit signal auto-correlation matrix. Traditionally, the Bayesian Cramér-Rao bound (BCRB) serves as an optimization criterion for cognitive radars. However, when the corresponding deterministic Fisher information is parameter-dependent, the BCRB is unachievable, even asymptotically. In order to obtain a reliable criterion in the asymptotic region, the semi-expected Cramér-Rao bound (SECRB) is adopted. Our approach utilizes the SECRB for target tracking as a criterion in order to sequentially determine the transmit signal auto-correlation matrix based on past measurements. Simulations indicate that the proposed method outperforms DOA estimation using the BCRB-based cognitive approach and MIMO radar with orthogonal signals. This paper demonstrates that the proposed method automatically focuses the transmit beampattern towards the target direction within fewer steps compared to the BCRB-based cognitive approach.

In many applications of estimation theory, the true data model is not perfectly known, leading to mismatch between the assumed model used for parameter estimation and the actual model. The non-Bayesian misspecified Cramér-Rao bound (MCRB) allows considering the effect of model misspecification on the estimator performance, and it has been extended to the Bayesian framework. Unlike the non-Bayesian MCRB, the corresponding Bayesian bound is asymptotically unattainable. In this paper, we derive an asymptotically tight misspecified Bayesian Cramér-Rao bound. We demonstrate that under some mild and common regularity conditions, this bound is asymptotically achieved by the maximum a-posteriori probability (MAP) estimator. The proposed bound is applied to the problems of variance estimation and direction-of-arrival estimation under model misspecification, illustrating its asymptotic attainability by the MAP estimator.

Automotive radar is the main sensor enabling autonomous driving and active safety features. It is required to provide high-resolution information on the vehicle’s surroundings, accurately localize surrounding objects, and estimate their velocity in two dimensions. Conventional automotive radars operating in the far-field regime estimate only the target’s radial velocity and cannot obtain its tangential velocity. However, the near-field propagation conditions allow the tangential radar target velocity estimation. This work proposes to extend the radar aperture using the synthetic aperture radar (SAR) approach for automotive applications to extend the near-field operation conditions to cover the automotive radar ranges of interest. This work derives the near-field synthetic aperture model and defines the near-field synthetic aperture to conduct an identifiability study using the Cramér-Rao bound for the near-field model. It is demonstrated that it is possible to estimate the tangential radar target velocity in practical automotive scenarios.

In many applications of estimation theory, the true data model is unknown, and a set of parameterized models are used to approximate it. This problem is encountered in learning systems, where the assumed model parameters are estimated using training data. One of the challenges in these problems is choosing the architecture used for the approximated model. Complex and high-order models with limited training data size may lead to overfitting, while simple and low-order models may lead to model misspecification. In this paper, we propose to use the misspecified Cramér-Rao bound (MCRB) as a criterion for model selection. The MCRB takes into account modeling errors due to both overfitting and model misspecification. The performance of the proposed approach is evaluated via simulations for model order selection in a linear regression problem. The proposed method outperforms the minimum description length and the Akaike information criterion.

The Cramér-Rao bound (CRB) has been extensively used as a benchmark for estimation performance in both Bayesian and non-Bayesian frameworks. In many practical periodic parameter estimation problems, such as phase, frequency, and direction-of-arrival estimation, the observation model is periodic with respect to the unknown parameters and thus, the appropriate criterion is periodic in the parameter space. Consequently, the widely-used Bayesian lower bounds on the mean-squared-error (MSE) are not valid bounds for periodic estimation problems. In addition, many Bayesian MSE lower bounds cannot be derived in the periodic case due to their restrictive regularity conditions. For example, the regularity conditions of the Bayesian CRB (BCRB) are not satisfied for parameters with uniform prior distribution. In this letter, we derive a Bayesian Cramér-Rao-type lower bound on the mean-squared-periodic-error (MSPE). The proposed periodic BCRB (PBCRB) is a lower bound on the MSPE of any estimator and has less restrictive regularity conditions compared to the BCRB. The PBCRB is compared with the MSPE of the minimum MSPE estimator for phase estimation in Gaussian noise and it is shown that the PBCRB is a valid and tight lower bound for this problem.

The constrained Cramér-Rao bound (CCRB) is a benchmark for constrained parameter estimation. However, the CCRB unbiasedness conditions are too strict and thus, the CCRB may not be a lower bound for estimators under constraints. The recently developed Lehmann-unbiased-CCRB (LU-CCRB) was shown to be a lower bound for the commonly used constrained maximum likelihood (CML) estimator performance in cases where the CCRB is not. In constrained parameter estimation, the estimator is usually required to satisfy the constraints. However, the LU-CCRB is a lower bound for Lehmann-unbiased estimators that do not necessarily satisfy the constraints. In this letter, we consider the norm constraint and derive a novel bound, called norm-constrained CCRB (NC-CCRB), which is a lower bound on the mean-squared-error matrix trace of Lehmann-unbiased estimators that satisfy the norm constraint. The NC-CCRB is shown to be tighter than the LU-CCRB. In the simulations, we consider a linear estimation problem under norm constraint in which the proposed NC-CCRB better predicts the performance of the CML estimator than the CCRB trace and the LU-CCRB.

In many stochastic filtering problems, some of the states have periodic nature, i.e. the observation model is periodic with respect to these states. For estimation of these periodic states, we are interested in the modulo- T error and not in the plain error value. Thus, in this case, the commonly-used Bayesian mean-squared-error (MSE) lower bounds are inappropriate for performance analysis, since the MSE risk is based on the plain error and is inappropriate for periodic state estimation. In contrast, the mean-cyclic-error (MCE) is an appropriate risk for estimation of periodic states. In a mixed periodic and nonperiodic setting, a mixed MCE and MSE lower bound can be useful for performance analysis and design of filters. In this paper, we present the mixed Bayesian Cramér-Rao bound (BCRB) for stochastic filtering. The mixed BCRB is composed of a cyclic part and a noncyclic part for estimation of the periodic and the nonperiodic states, respectively. Direct computation of the mixed BCRB is not practical, since it requires matrix inversion, whose dimensions increase with time. Therefore, we propose a recursive method with low computational complexity for computation of the mixed BCRB at each time step. The mixed BCRB is examined for direction-of-arrival tracking scenarios and compared to the performance of a particle filter. It is shown that in the considered scenarios the mixed BCRB is informative and can be approached by the particle filter. In addition, the inappropriateness of MSE bounds for estimation of periodic states is demonstrated.

Mean-squared-error (MSE) lower bounds are commonly used for performance analysis and system design. Recursive algorithms have been derived for computation of Bayesian bounds in stochastic filtering problems. In this letter, we consider stochastic filtering with a mixture of periodic and nonperiodic states. For periodic states, the modulo- T estimation error is of interest and the MSE lower bounds are inappropriate. Therefore, in this case, the mean-cyclic error and the MSE risks are used for estimation of the periodic and nonperiodic states, respectively. We derive a Bobrovsky-Zakai-type bound for mixed periodic and nonperiodic stochastic filtering. Then, we derive a recursive computation method for this bound in order to allow its computation in dynamic settings. The proposed recursively-computed mixed Bobrovsky-Zakai bound is useful for the design and performance analysis of filters in stochastic filtering problems with both periodic and nonperiodic states. This bound is evaluated for a target tracking example and is shown to be a valid and informative bound for particle filtering performance.

This paper deals with non-Bayesian parameter estimation under the mean-squared-error (MSE), which is a topic of great interest in various engineering fields. Although the unbiasedness condition is commonly used in non-Bayesian MSE estimation, in many cases biased estimation may result in better performance. However, no method for determining the optimal bias function in general cases is available. We propose a new approach for uniform minimum MSE biased estimation, where the optimal bias is chosen in accordance with Lehmann-unbiasedness definition. The proposed approach is based on modifying the MSE risk by its multiplication with a weighting function of the unknown parameter, g2. Under this modified risk, Lehmann's definition of unbiasedness provides a condition referred to as g-unbiasedness. By using the g-unbiasedness, we derive a novel Cramér-Rao-type lower bound on the MSE of locally g-unbiased estimators. In addition, we show that if there exists an estimator that achieves the new bound, then it is produced by the penalized maximum likelihood estimator with a penalty function log g. Simulations show that the proposed approach can lead to non-trivial estimators with lower MSE than existing mean-unbiased estimators.

The classes of large-error bounds that are based on the covariance inequality, in both Bayesian and non-Bayesian approaches, are characterized as projection-based bounds. Tightening of bounds in these classes involves high computational complexity due to multidimensional optimization procedure. Consequently, projection-based large-error bounds have little popularity, while small-error bounds are frequently preferred, although they are not necessarily tight. In this letter, we first introduce a unified formulation for Bayesian and non-Bayesian projection-based lower bounds and set a general framework, which allows for their approximation via a greedy-based method. This framework is then used to propose the use of optimized orthogonal matching pursuit approach for computing projection-based large-error bounds. We analyze the complexity of the proposed algorithm and show that it is significantly lower than the complexity of the conventional approach. Finally, we apply the algorithm for the problem of multitone estimation and show that for fixed computational resources, the Weiss-Weinstein bound implemented with the proposed algorithm, provides a tighter bound compared to conventional approaches.

How accurately can one estimate a deterministic parameter subject to other unknown deterministic model parameters? The most popular answer to this question is given by the Cramer-Rao bound (CRB). The main assumption behind the derivation of the CRB is local unbiased estimation of all model parameters. The foundations of this work rely on doubting this assumption. Each parameter in its turn is treated as a single parameter of interest, while the other model parameters are treated as nuisance, as their mis-knowledge interferes with the estimation of the parameter of interest. Correspondingly, a new Cramer-Rao-type bound on the mean squared error (MSE) of non-Bayesian estimators is established with no unbiasedness condition on the nuisance parameters. Alternatively, Lehmann's concept of unbiasedness is imposed for a risk that measures the distance between the estimator and the locally best unbiased (LBU) estimator which assumes perfect knowledge of the nuisance parameters. The proposed bound is compared to the CRB and MSE of the maximum likelihood estimator (MLE). Simulations show that the proposed bound provides a tight lower bound for this estimator, compared with the CRB.

Parameter estimation using quantized observations is of importance in many practical applications. Under a symmetric 1-bit setup, consisting of a zero-threshold hard-limiter, it is well known that the large sample performance loss for low signal-to-noise ratios (SNRs) is moderate (2/Π or -1.96dB). This makes low-complexity analog-to-digital converters (ADCs) with 1-bit resolution a promising solution for future wireless communications and signal processing devices. However, hardware imperfections and external effects introduce the quantizer with an unknown hard-limiting level different from zero. In this paper, the performance loss associated with pilot-based channel estimation, subject to an asymmetric hard limiter with unknown offset, is studied under two setups. The analysis is carried out via the Cramér-Rao lower bound (CRLB) and an expected CRLB for a setup with random parameter. Our findings show that the unknown threshold leads to an additional information loss, which vanishes for low SNR values or when the offset is close to zero.

Tracking problems are usually investigated using the Bayesian approach. Many practical tracking problems involve some unknown deterministic nuisance parameters such as the system parameters or noise statistical parameters. This paper addresses the problem of state estimation in linear discrete-time dynamic systems in the presence of unknown deterministic system parameters. A Cramér-Rao-type bound on the mean-sqaure-error (MSE) of the state estimation is introduced. The bound is based on the concept of risk-unbiasedness and can be computed recursively. It allows evaluating the optimality of the estimation procedure. Some sequential estimators for this problem are proposed such that the estimation procedure can be considered an on-line technique. Simulation results show that the proposed bound is asymptotically achieved by the considered estimators.

In this paper, we derive a Bayesian Cramér-Rao type bound in the presence of unknown nuisance deterministic parameters. The most popular bound for parameter estimation problems which involves both deterministic and random parameters is the hybrid Cramér-Rao bound (HCRB). This bound is very useful especially, when one is interested in both the deterministic and random parameters and in the coupling between their estimation errors. The HCRB imposes locally unbiasedness for the deterministic parameters. However, in many signal processing applications, the unknown deterministic parameters are treated as nuisance, and it is unnecessary to impose unbiasedness on these parameters. In this work, we establish a new Cramér-Rao type bound on the mean square error (MSE) of Bayesian estimators with no unbiasedness condition on the nuisance parameters. Alternatively, we impose unbiasedness in the Lehmann sense for a risk that measures the distance between the estimator and the minimum MSE estimator which assumes perfect knowledge of the nuisance parameters. The proposed bound is compared to the HCRB and MSE of Bayesian estimators with maximum likelihood estimates for the nuisance parameters. Simulations show that the proposed bound provides tighter lower bound for these estimators.

This paper addresses the problem of adaptive sequential waveform design for system parameter estimation. This problem arises in several applications such as radar, sonar, or tomography. In the proposed technique, the transmit/input signal waveform is optimally determined at each step, based on the measurements in the previous steps. The waveform is determined to minimize the Bayesian Cramér-Rao bound (BCRB) for estimation of the unknown system parameter at each step. The algorithm is tested for spatial transmit waveform design in multiple-input multiple-output radar target angle estimation at very low signal-to-noise ratio. The simulations show that the proposed adaptive waveform design achieves significantly higher rate of performance improvement as a function of the pulse index, compared to identical signal transmission.

One of the uses of sensor arrays is for spatial filtering or beamforming. Current digital signal processing methods facilitate complex-weighted beamforming, providing flexibility in array design. Previous studies proposed the use of real-valued beamforming weights, which although reduce flexibility in design, may provide a range of benefits, e.g., simplified beamformer implementation or efficient beamforming algorithms. This paper presents a new method for the design of arrays with real-valued weights, that achieve maximum directivity, providing closed-form solution to array weights. The method is studied for linear and spherical arrays, where it is shown that rigid spherical arrays are particularly suitable for real-weight designs as they do not suffer from grating lobes, a dominant feature in linear arrays with real weights. A simulation study is presented for linear and spherical arrays, along with an experimental investigation, validating the theoretical developments.

In many practical parameter estimation problems, the appropriate criterion is periodic in the parameter space. This paper considers the mean square periodic error (MSPE) criterion combined with periodic unbiasedness for which the conventional Cramer-Rao bound (CRB) does not provide a valid bound. The periodic unbiasedness is defined using the Lehmann-unbiasedness concept, and a Cramer-Rao type bound on the MSPE of any periodic unbiased estimator is derived. The proposed bound and performance of some periodic unbiased estimators for phase estimation problem are compared in terms of MSPE in a phase estimation problem with Gaussian noise.

In this paper, a new method for multiple fundamental frequency estimation for speech and music signals is proposed. Applications of audio and speech processing include many well-reviewed algorithms for estimating the fundamental frequency of monophonic speech and music signals. In the case of polyphonic signals, it is more difficult to successfully estimate each of the fundamental frequencies, as reflected by the dearth of existing methods addressing this problem. In this paper, a new method based on the combination of the maximum likelihood and maximum a posteriori probability criteria is derived for fundamental frequencies tracking where each one of the fundamental frequencies is modeled by a first-order Markov process. The dominant signal is modeled as a harmonic source with unknown deterministic amplitudes, while the remaining signals, including other harmonic signals, are modeled as Gaussian interference sources with an unknown covariance matrix. After estimation of the dominant source, it is removed from the signal by projection of the signal into the null subspace spanned by the estimated signal. This procedure is iterated for all the harmonic sources in the data. The algorithm is tested with speech, music, and synthetic signals where in each case, two harmonic sources of the same kind were mixed. The performance of the proposed algorithm is evaluated and compared to an existing reference method in terms of gross-error-rate as a function of signal-to-interference ratio.

In this paper, a new structured approach for obtaining uniformly best non-Bayesian biased estimators, which attain minimum-mean-square-error performance at any point in the parameter space, is established. We show that if a uniformly best biased (UBB) estimator exists, then it is unique, and it can be directly obtained from any locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived. It is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and its closed-form expression is obtained. The proposed approach is exemplified in two nonlinear estimation problems, where uniformly minimum-variance-unbiased estimators do not exist. In the considered examples, we show that the UBB estimators outperform the corresponding maximum-likelihood estimators in the MSE sense.

In this paper, a new transmit waveform design algorithm for MIMO-OFDM systems is proposed. The algorithm is based on a geometric channel model consisting of different paths, where the geometric channel parameters are assumed to be known. Using the spatial channel information at the transmitter, the frequency selective MIMO channel is transformed into a number of uncoupled flat-fading SISO channels. This suboptimal algorithm significantly simplifies the computational complexity of the optimal joint space-frequency water-filling (JSF-WF) algorithm. The performance of the proposed algorithm is evaluated and compared to the JSF-WF algorithm via simulations in terms of bit-error-rate and bit-rate, and it is shown to be low complex with suboptimal performance.

Recently, some general classes of non-Bayesian, Bayesian and Hybrid lower bounds on the mean square error (MSE) of estimators have been developed via projection of each entry of the vector of estimation error on some Hilbert subspaces of L2. In this paper, we utilize this framework for derivation of order relations between lower bounds on the MSE of unbiased estimators. We show that some existing and new order relations can be simply obtained by comparing the corresponding Hilbert subspaces on which each entry of the vector of estimation error is projected.

In this paper, a new class of lower bounds on the mean square error (MSE) of unbiased estimators of deterministic parameters is proposed. Derivation of the proposed class is performed by projecting each entry of the vector of estimation error on a Hilbert subspace of L2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform of the likelihood-ratio function. The integral transform generalizes the traditional derivative and sampling operators, which are applied on the likelihood-ratio function for computation of performance lower bounds, such as Cramér-Rao, Bhattacharyya, and McAulay-Seidman bounds. It is shown that some well-known lower bounds on the MSE of unbiased estimators can be derived from this class by modifying the kernel of the integral transform. A new lower bound is derived from the proposed class using the kernel of the Fourier transform. In comparison with other existing bounds, the proposed bound is computationally manageable and provides better prediction of the threshold region of the maximum-likelihood estimator, in the problem of single tone estimation.

In this paper, a new class of Bayesian lower bounds is proposed. Derivation of the proposed class is performed via projection of each entry of the vector-function to be estimated on a Hilbert subspace ofL2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform, applied on functions used for computation of bounds in the Weiss-Weinstein class. The integral transform generalizes the traditional derivative and sampling operators, used for computation of existing performance lower bounds, such as the Bayesian Cramér-Rao, Bayesian Bhattacharyya, and Weiss-Weinstein bounds. It is shown that some well-known Bayesian lower bounds can be derived from the proposed class by specific choice of the integral transform kernel. A new lower bound is derived from the proposed class using the Fourier transform kernel. The proposed bound is compared with other existing bounds in terms of signal-to-noise ratio (SNR) threshold region prediction in the problem of frequency estimation. The bound is shown to be computationally manageable and provides better prediction of the SNR threshold region, exhibited by the maximum a posteriori probability (MAP) and minimum-mean-square-error (MMSE) estimators.

In this paper, a new class of lower bounds on the mean-square-error (MSE) of unbiased estimators of deterministic parameters is proposed. Derivation of the proposed class is performed by approximating each entry of the vector of estimation error in a closed Hilbert subspace of L2- This Hilbert subspace is spanned by a set of linear combinations of elements in the domain of an integral transform of the likelihood-ratio function. It is shown that some well known lower bounds on the MSE of unbiased estimators, can be derived from this class by inferring the integral transform. A new lower bound is derived from this class by choosing the Fourier transform. The bound is computationally manageable and provides better prediction of the signal-to-noise ratio (SNR) threshold region, exhibited by the maximum-likelihood estimator. The proposed bound is compared with other existing bounds in term of threshold SNR prediction in the problem of single tone estimation.

The problem of blind source separation (BSS) for multiple-input multiple-output (MIMO) autoregressive (AR) mixtures is addressed in this paper. A new time-domain method for system identification and BSS is proposed based on the Gaussian mixture model (GMM) for sources distribution. The algorithm is based on the generalized expectation-maximization (GEM) method for joint estimation of the AR model parameters and the GMM parameters of the sources. The method is tested via simulations of synthetic and real audio signals. The results show that the proposed algorithm outperforms the well-known multidimensional linear predictive coding (LPC), and it achieves higher signal-to-interference ratio (SIR) in the BSS problem.

In this paper, a new efficient iterative algorithm for approximate joint diagonalization of positive-definite Hermitian matrices is presented. The proposed algorithm, named as SVDJD, estimates the diagonalization matrix by iterative optimization of a maximum likelihood based objective function. The columns of the diagonalization matrix is not assumed to be orthogonal, and they are estimated separately by using iterative singular value decompositions of a weighted sum of the matrices to be diagonalized. The performance of the proposed SVDJD algorithm is evaluated and compared to other existing state-of-the-art algorithms for approximate joint diagonalization. The results imply that the SVDJD algorithm is computationally efficient with performance similar to state-of-the-art algorithms for approximate joint diagonalization.

The problem of maneuvering target tracking is addressed in this paper. The main challenge in maneuvering target tracking stems from the nonlinearity and non-Gaussianity of the problem. The Singer model was used to model the maneuvering target dynamics and abrupt changes in the acceleration. According to this model, the heavy-tailed Cauchy distribution driving noise is used to model the abrupt changes in the target acceleration. The nonlinear, non-Gaussian Kalman filter was applied to this problem. The algorithm is based on the Gaussian mixture model for the posterior state vector. The nonlinear, non-Gaussian Kalman filter for this problem was tested using simulations, and it is shown that it outperforms both the particle filter and the extended Kalman filter

In this paper, a novel method for voiced-unvoiced decision within a pitch tracking algorithm is presented. Voiced-unvoiced decision is required for many applications, including modeling for analysis/synthesis, detection of model changes for segmentation purposes and signal characterization for indexing and recognition applications. The proposed method is based on the generalized likelihood ratio test (GLRT) and assumes colored Gaussian noise with unknown covariance. Under voiced hypothesis, a harmonic plus noise model is assumed. The derived method is combined with a maximum a-posteriori probability (MAP) scheme to obtain a pitch and voicing tracking algorithm. The performance of the proposed method is tested using several speech databases for different levels of additive noise and phone speech conditions. Results show that the GLRT is robust to speaker and environmental conditions and performs better than existing algorithms.

We study the performances of several electrical dispersion compensation (EDC) equalizers in the presence of chromatic dispersion and polarization mode dispersion for optical coherent- and direct-detection on–off keying systems. The EDCs that are analyzed include decision-feedback equalizer, linear equalizer, and maximum-likelihood sequence estimator (MLSE). We present an inclusive quantitative analysis of the performance difference between the various techniques. The MLSE gives a good indication of the best possible performance.

We study the performances of several electrical dispersion compensation (EDC) equalizers in the presence of chromatic dispersion (CD) and polarization mode dispersion (PMD) for optical coherent and direct detection on-off keying systems. The EDCs that are analyzed include the decision-feedback equalizer, linear equalizer, and maximum-likelihood sequence estimator (MLSE). We present an inclusive quantitative analysis of the performance difference between the various techniques. The MLSE gives a good indication of the best possible performance

A novel approach for the spectral analysis of nonstationary signals is presented. For this purpose, Capon's time frequency representation (CTFR) is employed. It is shown that CTFR is an upper bound on the range of nonunique solutions for power estimation of a complex sinusoid contaminated with unknown noise. A new local autocorrelation function using a nonstationary auto-regressive (NAR) model is defined and used in CTFR. This method efficiently models the autocorrelations of NAR processes. Synthetic signals are generated in order to illustrate the superiority of CTFR with the NAR model in comparison to other methods.

The problem of higher-order cumulants estimation is addressed in this paper. Higher-order cumulants are necessary in many applications, such as blind source separation (BSS) and blind deconvolution. In these applications, the cumulants are usually estimated using sample estimation. In this paper, a parametric method for cumulants estimation using the Gaussian mixture model (GMM) is derived. The cumulants are expressed in terms of the GMM parameters, and estimated using the maximum-likelihood estimator. The performance of the proposed model-based method was evaluated and compared to sample estimation using computer simulations. The results show that the model-based estimation outperforms the sample estimation in terms of root-mean-square error.

A new method for target localization by radar or sonar systems based on spatially coded signal transmission is proposed. Recently, it has been shown that spatially-coded signal transmission allows us to obtain virtual sensors. We show that for any array geometry, these virtual sensors are grouped into subarrays with identical structures. The transmission diversity, embedded in the spatially-coded signal model, is used to spatially smooth the signal covariance matrix in order to enable the use of eigenstructure-based methods for multiple coherent target localization. Unlike conventional spatial smoothing and forward-backward averaging, the proposed transmission diversity smoothing (TDS) algorithm is not limited to uniform or symmetric arrays, and does not decrease the array aperture. The performance of the algorithm implemented with MUSIC is tested using simulations and compared to the spatial smoothing method. The results show that the TDS algorithm is consistent and outperforms the spatial smoothing method.

This paper addresses the problem of target detection and localization by radar or active sonar systems. A novel configuration, in which the transmitted signals are spatially coded, is proposed. The main advantages of this new configuration are: avoiding beam-shape loss, having a larger virtual array aperture and therefore narrower beams, increasing the angular resolution, and having the ability to detect and localize a greater number of targets. This configuration enables array processing in the transmit mode in addition to the receive mode. The generalized likelihood ratio test (GLRT) and the maximum-likelihood (ML) estimator are derived for target detection and localization according to the new model configuration. The performance of the array processing algorithms for this problem is studied theoretically and via simulations.

We propose a new method for source separation that is based on directionally- disjoint estimation of the transfer functions between microphones and sources at different frequencies and at multiple times. The directions are estimated from eigenvectors of the microphones' correlation matrix. Smoothing and association of transfer function parameters across different frequencies is achieved by simultaneous Kalman filtering of the noisy amplitude and phase estimates. This approach allows estimating transfer functions even in the case where the difference between the sources is in delay only and it can operate both for wideband and narrowband sources. Simulation results show superior performance in comparison to other, existing methods.

An electromagnetic vector-sensor enables estimation of the direction of arrival (DOA) and polarization of an incident electromagnetic wave with arbitrary polarization. In this letter, an efficient vector-sensor configuration is proposed. This configuration includes the minimal number of sensors, which enables DOA estimation of an arbitrary polarized signal from any direction except two opposite directions on the z-axis. The configuration is obtained by analyzing the Cramer-Rao lower bound (CRLB) for source localization using a single vector-sensor. The resulting vector-sensor configuration consists of two electric and two magnetic sensors. It is shown that this quadrature configuration satisfies the necessary and sufficient conditions for the DOA estimation problem. The CRLB for DOA estimation of signals in the azimuth plane is identical for the quadrature and the complete vector-sensor configurations.

Modern speech processing applications require operation on signal of interest that is contaminated by high level of noise. This situation calls for a greater robustness in estimation of the speech parameters, a task which is hard to achieve using standard speech models. In this paper, we present an optimal estimation procedure for sound signals (such as speech) that are modeled by harmonic sources. The harmonic model achieves more robust and accurate estimation of voiced speech parameters. Using maximum a posteriori probability framework, successful tracking of pitch parameters is possible in ultra low signal to noise conditions (as low as -15 dB). The performance of the method is evaluated using the Keele pitch detection database with realistic background noise. The results show best performance in comparison to other state-of-the-art pitch detectors. Application of the proposed algorithm in a simple speaker identification system shows significant improvement in the performance.

In this paper, a novel method for voiced/invoiced decision in speech and music signals is presented. Voiced/unvoiced decision is required for many applications, including better modeling for analysis/synthesis, detection of model changes for segmentation purposes and better signal characterization for indexing and recognition applications. The proposed method is based on the generalized likelihood ratio test (GLRT) and assumes colored Gaussian noise with unknown covariance. Under voiced hypothesis, a harmonic plus noise model is assumed. The derived method is combined with a maximum a-posteriori probability (MAP) scheme to obtain a voiced unvoiced tracking algorithm. The performance of the proposed method is tested under the Keele University database for different signal-to-noise ratios (SNRs), and the results show that the algorithm performs well even under severe noise conditions.

This paper addresses the problem of coherent/fully correlated source localization using vector sensor arrays. A novel method for "decorrelating" the incident signals is presented. The method is based on vector sensor smoothing (VSS) and enables the use of eigenstructure-based techniques, which require uncorrelated or partially correlated signals. The method is implemented as a preprocessing stage before applying eigenstructure-based techniques, such as MUSIC. The performance of the proposed VSS preprocessing combined with MUSIC is evaluated and it is shown that it asymptotically achieves the Cramer-Rao bound.

In this paper we present a procedure for estimating the parameters of speech signals that are contaminated by high level of noise. The proposed estimation method is developed by assuming a harmonic model for the voiced frame hypothesis. A Maximum A-posteriori Probability tracking method is developed for estimating time-varying pitch. Signal recoIl8truction is achieved by projecting the signal onto the subspace of harmonic signals with the optimal estimates of the fundamental frequency. The performance of the proposed method is evaluated and compared to other existing methods using a large pitch detection database. It is shown that the proposed method for pitch estimation is more robust and much more accurate in terms of mean-square-error and gross error rate, in comparison to other existing methods, specially at ultra low signal-to-noise ratios (as low as −15 dB). Examples of speech reconstruction/enhancement are also presented in the paper.

This paper addresses the problem of underwater acoustic channel estimation for communications in time-varying environments. In the case of a rapidly time-varying environment, the channel needs to be estimated and tracked continuously. In this case, prior information on the channel can be used to improve channel estimation performance. In this paper, a-priori statistics on the channel time-variations are used in order to obtain a maximum a-posteriori estimator for channel tap-coefficients. It is also shown that in a shallow water waveguide, typical channel time-variations span a small subspace of channel tap-coefficients variations. This fact is used to reduce the number of parameters to be estimated and improve the channel estimation performance. The results demonstrate a performance gain of 5-10 dB in terms of the signal-to-noise ratio in decision-feedback equalizer mean-squared error, compared to the least-squares method which ignores the a-priori statistics on the channel time-variations.

This paper presents a novel method for calculating the hybrid Cramer-Rao lower bound (HCRLB) when the statistical model for the data has a Markovian nature. The method applies to both the non-linear/non-Gaussian as well as linear/Gaussian model. The approach solves the required expectation over unknown random parameters by several one-dimensional integrals computed recursively, thus simplifying a computationally-intensive multi-dimensional integration. The method is applied to the problem of refractivity estimation using radar clutter from the sea surface, where the backscatter cross section is assumed to be a Markov process in range. The HCRLB is evaluated and compared to the performance of the corresponding maximum a-posteriori estimator. Simulation results indicate that the HCRLB provides a tight lower bound in this application.

It is not possible, in practice, to precisely model a complex propagation channel, such as shallow water. This lack of accuracy causes a deterioration in the performance of the optimal detector and motivates the search for sub-optimal detectors which are insensitive to uncertainties in the propagation model. We present a novel, robust detector, which measures the degree of spatial-stationarity of the received field, exploiting the fact that a signal propagating in a bounded channel induces non-spatial-stationarity. The performance of the proposed detector is evaluated using both simulated data and experimental data collected in the Mediterranean Sea. This performance is compared to those of three other detectors, employing different extents of prior information. It is shown that when the propagation channel is not completely known, as is the case of the experimental data, the novel detector outperforms the others. That is, this detector couples good performance with robustness to propagation uncertainties.

Matched-field methods are known to have a severe ambiguity problem. In low signal-to-noise-ratios (SNRs), where the estimator cannot distinguish between the ambiguity function peak near the true source location and ambiguous ones, its mean square error deviates radically from the Cramer-Rao lower bound (CRLB). The Barankin bound for the source localization problem in an uncertain shallow water environment is derived. In particular, a method of selection of the test-points for evaluation of the bound is presented. The bound is evaluated using a "general mismatch" benchmark scenario. The results presented predict the threshold SNR below which the performance degrades dramatically. Channel uncertainties in the benchmark scenario are shown to increase this threshold SNR by as much as 3 dB.

This paper presents a new, non-parametric test for detecting modeling mismatches in a propagation medium, as shallow water. The test is based on the fact that if there are no model uncertainties, the corresponding modal spectrum of the received signal is strictly band-limited to an a-priori known band. Any mismatches in the assumed model cause the modal spectrum out of this band to be non-zero. To make the test independent of the emitters characteristic we use the generalized likelihood ratio test which uses maximum likelihood estimate of the unknown modal spectrum. We demonstrate the operation of the proposed test by applying it (via computer simulations) to a complex, practical scenario.

This paper presents a robust maximum-likelihood estimator for matched-field source localization in the presence of uncertainties in the ocean environment. The method is based on a decomposition of the field into predictable and unpredictable subspaces of the acoustic normal mode representation. The performance of the method is evaluated and compared to other matched-field methods using simulations and acoustic array data from the Mediterranean Sea. The algorithm has superior probability of correct localization than the maximum-likelihood, matched-mode-processing, and Bartlett methods.

Source localization in a waveguide involves a multidimensional search procedure. The authors propose a new algorithm, in which the search in the depth direction is replaced by polynomial rooting. The proposed algorithm decreases the search dimension to one for a 2D localization problem (range and depth) and to two for a 3D one (range, depth) and direction-of arrival (DOA), independently of the number of sources. Consequently, the presented algorithm requires significantly less computation.