Array signal processing for maximum likelihood direction-of-arrival estimation

Emitter Direction-of-Arrival (DOA) estimation is a fundamental problem in a variety of applications including radar, sonar, and wireless communications. The research has received considerable attention in literature and numerous methods have been proposed. Maximum Likelihood (ML) is a nearly optimal technique producing superior estimates compared to other methods especially in unfavourable conditions, and thus is of significant practical interest. This paper discusses in details the techniques for ML DOA estimation in either white Gaussian noise or unknown noise environment. Their performances are analysed and compared, and evaluated against the theoretical lower bounds

Amplitude estimation of a signal with known waveform in the presence of steering vector uncertainties

In this correspondence, we address the problem of estimating the amplitude of a signal with known waveform received on an array of sensors and we consider the case where there exist uncertainties about the spatial signature of the signal of interest. Closed-form expressions for the Cramer–Rao bound are derived and the respective influence of the uncertainties and the number of snapshots is studied. The maximum likelihood estimator (MLE) of the signal of interest amplitude along with the covariance matrix of the interferences and noise is also derived and an iterative algorithm is presented to obtain the ML estimates

Maximum likelihood DOA estimation in unknown colored noise fields

Direction-of-arrival (DOA) estimation in unknown noise environments is an important but challenging problem. Several methods based on maximum likelihood (ML) criteria and parameterization of signals or noise covariances have been established. Generally, to obtain the exact ML (EML) solutions, the DOAs must be jointly estimated along with other noise or signal parameters by optimizing a complicated nonlinear function over a high-dimensional problem space. Although the computation complexity can be reduced via derivation of suboptimal approximate ML (AML) functions using large sample assumption or least square criteria, nevertheless the AML estimators still require multi-dimensional search and the accuracy is lost to some extent. A particle swarm optimization (PSO) based solution is proposed here to compute the EML functions and explore the potential superior performances. A key characteristic of PSO is that the algorithm itself is highly robust yet remarkably simple to implement, while processing similar capabilities as other evolutionary algorithms such as the genetic algorithm (GA). Simulation results confirm the advantage of paring PSO with EML, and the PSO-EML estimator is shown to significantly outperform AML-based techniques in various scenarios at less computational costs

Estimation of the Number of Sources in Unbalanced Arrays via Information Theoretic Criteria

Estimating the number of sources impinging on an array of sensors is a well known and well investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is known to be a consistent estimator, robust against deviations from the Gaussian assumption, and non-robust against deviations from the point source and/or temporally or spatially white additive noise assumptions. Over the years several alternative estimation algorithms have been proposed and tested. Usually, these algorithms are shown, using computer simulations, to have improved performance over the MDL estimator, and to be robust against deviations from the assumed spatial model. Nevertheless, these robust algorithms have high computational complexity, requiring several multi-dimensional searches. In this paper, motivated by real life problems, a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken. An MDL type estimator that is robust against deviation from assumption of equal noise level across the array is studied. The consistency of this estimator, even when deviations from the equal noise level assumption occur, is proven. A novel low-complexity implementation method avoiding the need for multi-dimensional searches is presented as well, making this estimator a favorable choice for practical applications.Comment: To appear in the IEEE Transactions on Signal Processin

A review of closed-form Cramér-Rao Bounds for DOA estimation in the presence of Gaussian noise under a unified framework

The Cramér-Rao Bound (CRB) for direction of arrival (DOA) estimation has been extensively studied over the past four decades, with a plethora of CRB expressions reported for various parametric models. In the literature, there are different methods to derive a closed-form CRB expression, but many derivations tend to involve intricate matrix manipulations which appear difficult to understand. Starting from the Slepian-Bangs formula and following the simplest derivation approach, this paper reviews a number of closed-form Gaussian CRB expressions for the DOA parameter under a unified framework, based on which all the specific CRB presentations can be derived concisely. The results cover three scenarios: narrowband complex circular signals, narrowband complex noncircular signals, and wideband signals. Three signal models are considered: the deterministic model, the stochastic Gaussian model, and the stochastic Gaussian model with the a priori knowledge that the sources are spatially uncorrelated. Moreover, three Gaussian noise models distinguished by the structure of the noise covariance matrix are concerned: spatially uncorrelated noise with unknown either identical or distinct variances at different sensors, and arbitrary unknown noise. In each scenario, a unified framework for the DOA-related block of the deterministic/stochastic CRB is developed, which encompasses one class of closed-form deterministic CRB expressions and two classes of stochastic ones under the three noise models. Comparisons among different CRBs across classes and scenarios are presented, yielding a series of equalities and inequalities which reflect the benchmark for the estimation efficiency under various situations. Furthermore, validity of all CRB expressions are examined, with some specific results for linear arrays provided, leading to several upper bounds on the number of resolvable Gaussian sources in the underdetermined case

Localization and tracking of electronic devices with their unintended emissions

The precise localization and tracking of electronic devices via their unintended emissions has a broad range of commercial and security applications. Active stimulation of the receivers of such devices with a known signal generates very low power unintended emissions. This dissertation presents localization and tracking of multiple devices using both simulation and experimental data in the form of five papers. First the localization of multiple emitting devices through active stimulation under multipath fading with a Smooth MUSIC based scheme in the near field region is presented. Spatial smoothing helps to separate the correlated sources and the multipath fading and results confirm improved accuracy. A cost effective near-field localization method is proposed next to locate multiple correlated unintended emitting devices under colored noise conditions using two well separated antenna arrays since colored noise in the environment degrades the subspace-based localization techniques. Subsequently, in order to track moving sources, a near-field scheme by using array output is introduced to monitor direction of arrival (DOA) and the distance between the antenna array and the moving source. The array output, which is a nonlinear function of DOA and distance information, is employed in the Extended Kalman Filter (EKF). In order to show the near- and far-field effect on estimation accuracy, computer simulation results are included for localization and tracking techniques. Finally, an L-shaped array is constructed and a suite of schemes are introduced for localization and tracking of such devices in the three-dimensional environment. Experimental results for localization and tracking of unintended emissions from single and multiple devices in the near-field environment of an antenna array are demonstrated --Abstract, page iv