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Upper and lower bounds on the minimum mean square error for additive noise channels are derived when the input distribution is constrained to be close to a Gaussian reference distribution in terms of the Kullback–Leibler divergence. The upper bound is tight and is attained by a Gaussian distribution whose mean is identical to that of the reference distribution and whose covariance matrix is defined implicitly via a system of non-linear equations. The estimator that attains the upper bound is identified as a minimax optimal estimator that is robust against deviations from the assumed prior. The lower bound provides an alternative to well-known inequalities in estimation and information theory—such as the Cramér–Rao lower bound, Stam's inequality, or the entropy power inequality—that is potentially tighter and defined for a larger class of input distributions. Several examples of applications in signal processing and information theory illustrate the usefulness of the proposed bounds in practice. [ABSTRACT FROM AUTHOR]

We investigate the problem of enumerating source signals impinging on an array of sensors given noisy, limited observations. The assumption of a large sample size is indispensable for most of the existing approaches so that they suffer significant performance degradation when only a small number of samples is available. Random matrix theory can capture the asymptotic distributions of the eigenvalues accurately and provide good approximations even for a finite sample size. In this paper, we take into account the relationship and distributions of the noise and signal eigenvalues based on random matrix theory and derive a simple two-step test. Numerical simulations demonstrate that it is capable of correctly determining the number of sources in the case of small sample sizes. [ABSTRACT FROM PUBLISHER]

Two new procedures are proposed using random matrix theory to evaluate theoretically the performance of the Bayesian information criterion (BIC) for source enumeration in array processing. The proposed procedures can predict precisely the estimation results of the BIC. Also, they shed light on the behavior of the BIC. In order to remedy the limitation of the BIC, that is, the BIC tends to underestimate the number of sources by one in most cases, an extra parameter is introduced into the BIC formulation, which results in a new criterion for source enumeration, referred to as the flexible detection criterion (FDC). By carefully choosing this parameter, the FDC is capable of substantially reducing the probability of underestimation, which is validated by theoretical analysis and simulations. Note that the FDC is consistent and has low computational complexity, as the BIC. [ABSTRACT FROM PUBLISHER]

We propose a parametric waveform design approach for improved detection of extended targets embedded in uncorrelated signal-dependent clutter and noise, whose spectral densities are assumed to be known. Unlike canonical waveform design approaches, the transmit waveform is represented as a weighted linear combination of discrete prolate spheroidal sequences. In the optimization problem, the probability of detection is maximized with respect to the weighting factors of the associated discrete prolate spheroidal sequences under the transmit energy constraint. The weighting factors, which are resolved using a numerical method, lead directly to the desired transmit waveform in the time domain. In comparison to the canonical waveform design approaches, the extra step for time sequence synthesis is avoided and the loss in probability of detection produced therein is remedied. Simulation results demonstrate the improvement in the probability of detection for the proposed approach. However, the improvement comes at the cost of higher computational complexity. [ABSTRACT FROM PUBLISHER]

An algorithm for mobile terminal (MT) tracking based on time-of-arrival measurements in non-line-of-sight (NLOS) environments where NLOS measurements are modeled as positive outliers is proposed. Standard filters such as the extended Kalman filter (EKF) fail because they are sensitive to outliers. In contrast, a robust EKF (REKF) always trades off efficiency in line-of-sight (LOS) versus robustness in NLOS environments and it is not possible to achieve both with the same filter. Instead, we propose to use two filters in parallel in a multiple model framework. An EKF yields high precision in LOS environments whereas an REKF provides robust state estimates when NLOS propagation comes into play. The state estimates of either filters are combined automatically based on the confidence we have for the underlying situation. It is shown via numerical studies that the proposed algorithm yields positioning accuracy similar to the EKF in LOS environments and even significantly outperforms the REKF in NLOS environments. [ABSTRACT FROM PUBLISHER]

An algorithm for mobile terminal (MT) tracking based on time-of-arrival measurements in non-line-of-sight (NLOS) environments is proposed. It is based on NLOS detection together with a modified probabilistic data association approach where different subgroups of range measurements are constructed. Each of the subgroups provide a position estimate of the MT with it's corresponding covariance matrix that are both used in a hypothesis test for NLOS detection. The accepted position estimates are weighted with different probabilities in a Kalman filter framework. Simulation results show a significant increase in positioning accuracy in NLOS environments with respect to both, the extended Kalman filter (EKF) and a NLOS mitigation algorithm from the literature. In LOS environments similar performance to the EKF is achieved. The proposed method does not assume any statistical knowledge of the NLOS errors and only assumes the sensor noise variance to be known. [ABSTRACT FROM PUBLISHER]

An adaptive detection scheme is proposed for radar imaging. The proposed detector is a postprocessing scheme derived for one-, two-, and three-dimensional data, and applied to through-the-wall imaging using synthetic aperture radar. The target image statistics depend on the target three-dimensional orientation and position. The statistics can also vary with the standoff distance of the imaging system because of the change in the corresponding scene image resolution. We propose an iterative target detection scheme for the cases in which no or partial a priori knowledge of the target image statistics is available. Properties of the proposed scheme, such as conditions of convergence and optimal configurations are introduced. The detector performance is examined under synthetic and real data. The latter is obtained using a synthetic aperture through-the-wall radar indoor imaging scanner implementing wideband delay and sum beamforming. [ABSTRACT FROM PUBLISHER]

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-fit W test 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. [ABSTRACT FROM AUTHOR]