Underwater Direction-of-Arrival Finding: Maximum Likelihood Estimation and Performance Analysis

In this dissertation, we consider the problems of direction-of-arrival: DOA) finding using acoustic sensor arrays in underwater scenarios, and develop novel signal models, maximum likelihood: ML) estimation methods, and performance analysis results. We first examine the underwater scenarios where the noise on sensor arrays are spatially correlated, for which we consider using sparse sensor arrays consisting of widely separated sub-arrays and develop ML DOA estimators based on the Expectation-Maximization scheme. We examine both zero-mean and non-zero-mean Gaussian incident signals and provide detailed estimation performance analysis. Our results show that non-zero means in signals improve the accuracy of DOA estimation. Then we consider the problem of DOA estimation of marine vessel sources such as ships, submarines, or torpedoes, which emit acoustic signals containing both sinusoidal and random components. We propose a mixed signal model and develop an ML estimator for narrow-band DOA finding of such signals and then generalize the results to the wide-band case. We provide thorough performance analysis for the proposed signal model and estimators. We show that our mixed signal model and ML estimators improve the DOA estimation performance in comparison with the typical stochastic ones assuming zero-mean Gaussian signals. At last, we derive a Barankin-type bound: BTB) on the mean-square error of DOA estimation using acoustic sensor arrays. The typical DOA estimation performance evaluation are usually based on the Cram\u27{e}r-Rao Bound: CRB), which cannot predict the threshold region of signal-to-noise ratio: SNR), below which the accuracy of the ML estimation degrades rapidly. Identification of the threshold region has important applications for DOA estimation in practice. Our derived BTB provides an approximation to the SNR threshold region

Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework

In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations of multi-source estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the interference parameters. The conventional multidimensional optimization problem reduces, thanks to this relaxation, to a simple spectral search. Following this principle, we propose estimators based on the Deterministic Maximum Likelihood, Weighted Subspace Fitting and covariance fitting methods. To calculate the pseudo-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that the performance of the proposed estimators is superior to the conventional methods especially in the case of low Signal-to-Noise-Ratio and low number of snapshots, irrespectively of any specific structure of the sensor array while maintaining a comparable computational cost as MUSIC.Comment: This work has been submitted to IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

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

Advanced interferometric techniques for high resolution bathymetry

International audienceCurrent high-resolution side scan and multibeam sonars produce very large data sets. However, conventional interferometry-based bathymetry algorithms underestimate the potential information of such soundings, generally because they use small baselines to avoid phase ambiguity. Moreover, these algorithms limit the triangulation capabilities of multibeam echosounders to the detection of one sample per beam, i.e., the zero-phase instant. In this paper we argue that the correlation between signals plays a very important role in the exploration of a remotely observed scene. In the case of multibeam sonars, capabilities can be improved by using the interferometric signal as a continuous quantity. This allows consideration of many more useful soundings per beam and enriches understanding of the environment. To this end, continuous interferometry detection is compared here, from a statistical perspective, first with conventional interferometry-based algorithms and then with high-resolution methods, such as the Multiple Signal Classification (MUSIC) algorithm. We demonstrate that a well-designed interferometry algorithm based on a coherence error model and an optimal array configuration permits a reduction in the number of beam formings (and therefore the computational cost) and an improvement in target detection (such as ship mooring cables or masts). A possible interferometry processing algorithm based on the complex correlation between received signals is tested on both sidescan sonars and multibeam echosounders and shows promising results for detection of small in-water targets

A pre-filtering maximum likelihood approach to multiple source direction estimation.

Imperial Users onl

Advanced array processing techniques and systems

Research and development on smart antennas, which are recognized as a promising technique to improve the performance of mobile communications, have been extensive in the recent years. Smart antennas combine multiple antenna elements with a signal processing capability in both space and time to optimize its radiation and reception pattern automatically in response to the signal environment. This paper concentrates on the signal processing aspects of smart antenna systems. Smart antennas are often classified as either switched-beam or adaptive-array systems, for which a variety of algorithms have been developed to enhance the signal of interest and reject the interference. The antenna systems need to differentiate the desired signal from the interference, and normally requires either a priori knowledge or the signal direction to achieve its goal. There exists a variety of methods for direction of arrival (DOA) estimation with conflicting demands of accuracy and computation. Similarly, there are many algorithms to compute array weights to direct the maximum radiation of the array pattern toward the signal and place nulls toward the interference, each with its convergence property and computational complexity. This paper discusses some of the typical algorithms for DOA estimation and beamforming. The concept and details of each algorithm are provided. Smart antennas can significantly help in improving the performance of communication systems by increasing channel capacity and spectrum efficiency, extending range coverage, multiplexing channels with spatial division multiple access (SDMA), and compensating electronically for aperture distortion. They also reduce delay spread, multipath fading, co-channel interference, system complexity, bit error rates, and outage probability. In addition, smart antennas can locate mobile units or assist the location determination through DOA and range estimation. This capability can support and benefit many location-based services including emergency assistance, tracking services, safety services, billing services, and information services such as navigation, weather, traffic, and directory assistance

Space-Time Parameter Estimation in Radar Array Processing

This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance