MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

Relaxed concentrated MLE for robust calibration of radio interferometers

In this paper, we investigate the calibration of radio interferometers in which Jones matrices are considered to model the interaction between the incident electromagnetic field and the antennas of each station. Specifically, perturbation effects are introduced along the signal path, leading to the conversion of the plane wave into an electric voltage by the receptor. In order to design a robust estimator, the noise is assumed to follow a spherically invariant random process (SIRP). The derived algorithm is based on an iterative relaxed concentrated maximum likelihood estimator (MLE), for which closed-form expressions are obtained for most of the unknown parameters

Joint ML calibration and DOA estimation with separated arrays

This paper investigates parametric direction-of-arrival (DOA) estimation in a particular context: i) each sensor is characterized by an unknown complex gain and ii) the array consists of a collection of subarrays which are substantially separated from each other leading to a structured noise covariance matrix. We propose two iterative algorithms based on the maximum likelihood (ML) estimation method adapted to the context of joint array calibration and DOA estimation. Numerical simulations reveal that the two proposed schemes, the iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint array calibration and DOA estimation, outperform the state of the art methods and the MIML algorithm reaches the Cram\'er-Rao bound for a low number of iterations

Bayesian learning scheme for sparse DOA estimation based on maximum-a-posteriori of hyperparameters

In this paper, the problem of direction of arrival estimation is addressed by employing Bayesian learning technique in sparse domain. This paper deals with the inference of sparse Bayesian learning (SBL) for both single measurement vector (SMV) and multiple measurement vector (MMV) and its applicability to estimate the arriving signal’s direction at the receiving antenna array; particularly considered to be a uniform linear array. We also derive the hyperparameter updating equations by maximizing the posterior of hyperparameters and exhibit the results for nonzero hyperprior scalars. The results presented in this paper, shows that the resolution and speed of the proposed algorithm is comparatively improved with almost zero failure rate and minimum mean square error of signal’s direction estimate

Neural Network-Based DOA Estimation in the Presence of Non-Gaussian Interference

This work addresses the problem of direction-of-arrival (DOA) estimation in the presence of non-Gaussian, heavy-tailed, and spatially-colored interference. Conventionally, the interference is considered to be Gaussian-distributed and spatially white. However, in practice, this assumption is not guaranteed, which results in degraded DOA estimation performance. Maximum likelihood DOA estimation in the presence of non-Gaussian and spatially colored interference is computationally complex and not practical. Therefore, this work proposes a neural network (NN) based DOA estimation approach for spatial spectrum estimation in multi-source scenarios with a-priori unknown number of sources in the presence of non-Gaussian spatially-colored interference. The proposed approach utilizes a single NN instance for simultaneous source enumeration and DOA estimation. It is shown via simulations that the proposed approach significantly outperforms conventional and NN-based approaches in terms of probability of resolution, estimation accuracy, and source enumeration accuracy in conditions of low SIR, small sample support, and when the angular separation between the source DOAs and the spatially-colored interference is small.Comment: Submitted to IEEE Transactions on Aerospace and Electronic System

Robust and Sparse M-Estimation of DOA

A robust and sparse Direction of Arrival (DOA) estimator is derived for array data that follows a Complex Elliptically Symmetric (CES) distribution with zero-mean and finite second-order moments. The derivation allows to choose the loss function and four loss functions are discussed in detail: the Gauss loss which is the Maximum-Likelihood (ML) loss for the circularly symmetric complex Gaussian distribution, the ML-loss for the complex multivariate $t$-distribution (MVT) with $\nu$ degrees of freedom, as well as Huber and Tyler loss functions. For Gauss loss, the method reduces to Sparse Bayesian Learning (SBL). The root mean square DOA error of the derived estimators is discussed for Gaussian, MVT, and $\epsilon$-contaminated data. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian noise

K-distribution fading models for Bayesian estimation of an underwater acoustic channel

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2011Current underwater acoustic channel estimation techniques generally apply linear MMSE estimation. This approach is optimal in a mean square error sense under the assumption that the impulse response fluctuations are well characterized by Gaussian statistics, leading to a Rayleigh distributed envelope. However, the envelope statistics of the underwater acoustic communication channel are often better modeled by the K-distribution. In this thesis, by presenting and analyzing field data to support this claim, I demonstrate the need to investigate channel estimation algorithms that exploit K-distributed fading statistics. The impact that environmental conditions and system parameters have on the resulting distribution are analyzed. In doing so, the shape parameter of the K-distribution is found to be correlated with the source-to-receiver distance, bandwidth, and wave height. Next, simulations of the scattering behavior are carried out in order to gain insight into the physical mechanism that cause these statistics to arise. Finally, MAP and MMSE based algorithms are derived assuming K-distributed fading models. The implementation of these estimation algorithms on simulated data demonstrates an improvement in performance over linear MMSE estimation.This work was supported by the Office of Naval Research grant #N00014-05-10085 and the National Science Foundation grant #OCE-0519903

3D Localization and Tracking Methods for Multi-Platform Radar Networks

Multi-platform radar networks (MPRNs) are an emerging sensing technology due to their ability to provide improved surveillance capabilities over plain monostatic and bistatic systems. The design of advanced detection, localization, and tracking algorithms for efficient fusion of information obtained through multiple receivers has attracted much attention. However, considerable challenges remain. This article provides an overview on recent unconstrained and constrained localization techniques as well as multitarget tracking (MTT) algorithms tailored to MPRNs. In particular, two data-processing methods are illustrated and explored in detail, one aimed at accomplishing localization tasks the other tracking functions. As to the former, assuming a MPRN with one transmitter and multiple receivers, the angular and range constrained estimator (ARCE) algorithm capitalizes on the knowledge of the transmitter antenna beamwidth. As to the latter, the scalable sum-product algorithm (SPA) based MTT technique is presented. Additionally, a solution to combine ARCE and SPA-based MTT is investigated in order to boost the accuracy of the overall surveillance system. Simulated experiments show the benefit of the combined algorithm in comparison with the conventional baseline SPA-based MTT and the stand-alone ARCE localization, in a 3D sensing scenario

Subband beamforming with higher order statistics for distant speech recognition

This dissertation presents novel beamforming methods for distant speech recognition (DSR). Such techniques can relieve users from the necessity of putting on close talking microphones. DSR systems are useful in many applications such as humanoid robots, voice control systems for automobiles, automatic meeting transcription systems and so on. A main problem in DSR is that recognition performance is seriously degraded when a speaker is far from the microphones. In order to avoid the degradation, noise and reverberation should be removed from signals received with the microphones. Acoustic beamforming techniques have a potential to enhance speech from the far field with little distortion since they can maintain a distortionless constraint for a look direction. In beamforming, multiple signals propagating from a position are captured with multiple microphones. Typical conventional beamformers then adjust their weights so as to minimize the variance of their own outputs subject to a distortionless constraint in a look direction. The variance is the average of the second power (square) of the beamformer\u27s outputs. Accordingly, it is considered that the conventional beamformer uses second orderstatistics (SOS) of the beamformer\u27s outputs. The conventional beamforming techniques can effectively place a null on any source of interference. However, the desired signal is also canceled in reverberant environments, which is known as the signal cancellation problem. To avoid that problem, many algorithms have been developed. However, none of the algorithms can essentially solve the signal cancellation problem in reverberant environments. While many efforts have been made in order to overcome the signal cancellation problem in the field of acoustic beamforming, researchers have addressed another research issue with the microphone array, that is, blind source separation (BSS) [1]. The BSS techniques aim at separating sources from the mixture of signals without information about the geometry of the microphone array and positions of sources. It is achieved by multiplying an un-mixing matrix with input signals. The un-mixing matrix is constructed so that the outputs are stochastically independent. Measuring the stochastic independence of the signals is based on the theory of the independent component analysis (ICA) [1]. The field of ICA is based on the fact that distributions of information-bearing signals are not Gaussian and distributions of sums of various signals are close to Gaussian. There are two popular criteria for measuring the degree of the non-Gaussianity, namely, kurtosis and negentropy. As described in detail in this thesis, both criteria use more than the second moment. Accordingly, it is referred to as higher order statistics (HOS) in contrast to SOS. HOS is not considered in the field of acoustic beamforming well although Arai et al. showed the similarity between acoustic beamforming and BSS [2]. This thesis investigates new beamforming algorithms which take into consideration higher-order statistics (HOS). The new beamforming methods adjust the beamformer\u27s weights based on one of the following criteria: • minimum mutual information of the two beamformer\u27s outputs, • maximum negentropy of the beamformer\u27s outputs and • maximum kurtosis of the beamformer\u27s outputs. Those algorithms do not suffer from the signal cancellation, which is shown in this thesis. Notice that the new beamforming techniques can keep the distortionless constraint for the direction of interest in contrast to the BSS algorithms. The effectiveness of the new techniques is finally demonstrated through a series of distant automatic speech recognition experiments on real data recorded with real sensors unlike other work where signals artificially convolved with measured impulse responses are considered. Significant improvements are achieved by the beamforming algorithms proposed here.Diese Dissertation präsentiert neue Methoden zur Spracherkennung auf Entfernung. Mit diesen Methoden ist es möglich auf Nahbesprechungsmikrofone zu verzichten. Spracherkennungssysteme, die auf Nahbesprechungsmikrofone verzichten, sind in vielen Anwendungen nützlich, wie zum Beispiel bei Humanoiden-Robotern, in Voice Control Systemen für Autos oder bei automatischen Transcriptionssystemen von Meetings. Ein Hauptproblem in der Spracherkennung auf Entfernung ist, dass mit zunehmendem Abstand zwischen Sprecher und Mikrofon, die Genauigkeit der Spracherkennung stark abnimmt. Aus diesem Grund ist es elementar die Störungen, nämlich Hintergrundgeräusche, Hall und Echo, aus den Mikrofonsignalen herauszurechnen. Durch den Einsatz von mehreren Mikrofonen ist eine räumliche Trennung des Nutzsignals von den Störungen möglich. Diese Methode wird als akustisches Beamformen bezeichnet. Konventionelle akustische Beamformer passen ihre Gewichte so an, dass die Varianz des Ausgangssignals minimiert wird, wobei das Signal in "Blickrichtung" die Bedingung der Verzerrungsfreiheit erfüllen muss. Die Varianz ist definiert als das quadratische Mittel des Ausgangssignals.Somit werden bei konventionellen Beamformingmethoden Second-Order Statistics (SOS) des Ausgangssignals verwendet. Konventionelle Beamformer können Störquellen effizient unterdrücken, aber leider auch das Nutzsignal. Diese unerwünschte Unterdrückung des Nutzsignals wird im Englischen signal cancellation genannt und es wurden bereits viele Algorithmen entwickelt um dies zu vermeiden. Keiner dieser Algorithmen, jedoch, funktioniert effektiv in verhallter Umgebung. Eine weitere Methode das Nutzsignal von den Störungen zu trennen, diesesmal jedoch ohne die geometrische Information zu nutzen, wird Blind Source Separation (BSS) [1] genannt. Hierbei wird eine Matrixmultiplikation mit dem Eingangssignal durchgeführt. Die Matrix muss so konstruiert werden, dass die Ausgangssignale statistisch unabhängig voneinander sind. Die statistische Unabhängigkeit wird mit der Theorie der Independent Component Analysis (ICA) gemessen [1]. Die ICA nimmt an, dass informationstragende Signale, wie z.B. Sprache, nicht gaußverteilt sind, wohingegen die Summe der Signale, z.B. das Hintergrundrauschen, gaußverteilt sind. Es gibt zwei gängige Arten um den Grad der Nichtgaußverteilung zu bestimmen, Kurtosis und Negentropy. Wie in dieser Arbeit beschrieben, werden hierbei höhere Momente als das zweite verwendet und somit werden diese Methoden als Higher-Order Statistics (HOS) bezeichnet. Obwohl Arai et al. zeigten, dass sich Beamforming und BSS ähnlich sind, werden HOS beim akustischen Beamforming bisher nicht verwendet [2] und beruhen weiterhin auf SOS. In der hier vorliegenden Dissertation werden neue Beamformingalgorithmen entwickelt und evaluiert, die auf HOS basieren. Die neuen Beamformingmethoden passen ihre Gewichte anhand eines der folgenden Kriterien an: • Minimum Mutual Information zweier Beamformer Ausgangssignale • Maximum Negentropy der Beamformer Ausgangssignale und • Maximum Kurtosis der Beamformer Ausgangssignale. Es wird anhand von Spracherkennerexperimenten (gemessen in Wortfehlerrate) gezeigt, dass die hier entwickelten Beamformingtechniken auch erfolgreich Störquellen in verhallten Umgebungen unterdrücken, was ein klarer Vorteil gegenüber den herkömmlichen Methoden ist