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

Multi-source parameter estimation and tracking using antenna arrays

This thesis is concerned with multi-source parameter estimation and tracking using antenna arrays in wireless communications. Various multi-source parameter estimation and tracking algorithms are presented and evaluated. Firstly, a novel multiple-input multiple-output (MIMO) communication system is proposed for multi-parameter channel estimation. A manifold extender is presented for increasing the degrees of freedom (DoF). The proposed approach utilises the extended manifold vectors together with superresolution subspace type algorithms, to achieve the estimation of delay, direction of departure (DOD) and direction of arrival (DOA) of all the paths of the desired user in the presence of multiple access interference (MAI). Secondly, the MIMO system is extended to a virtual-spatiotemporal system by incorporating the temporal domain of the system towards the objective of further increasing the degrees of freedom. In this system, a multi-parameter es- timation of delay, Doppler frequency, DOD and DOA of the desired user, and a beamformer that suppresses the MAI are presented, by utilising the proposed virtual-spatiotemporal manifold extender and the superresolution subspace type algorithms. Finally, for multi-source tracking, two tracking approaches are proposed based on an arrayed Extended Kalman Filter (arrayed-EKF) and an arrayed Unscented Kalman Filter (arrayed-UKF) using two type of antenna arrays: rigid array and flexible array. If the array is rigid, the proposed approaches employ a spatiotemporal state-space model and a manifold extender to track the source parameters, while if it is flexible the array locations are also tracked simultaneously. Throughout the thesis, computer simulation studies are presented to investigate and evaluate the performance of all the proposed algorithms.Open Acces

Simultaneous Source Localization and Polarization Estimation via Non-Orthogonal Joint Diagonalization with Vector-Sensors

Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods

Direction of Arrival Estimation and Tracking with Sparse Arrays

Direction of Arrival (DOA) estimation and tracking of a plane wave or multiple plane waves impinging on an array of sensors from noisy data are two of the most important tasks in array signal processing, which have attracted tremendous research interest over the past several decades. It is well-known that the estimation accuracy, angular resolution, tracking capacity, computational complexity, and hardware implementation cost of a DOA estimation and/or tracking technique depend largely on the array geometry. Large arrays with many sensors provide accurate DOA estimation and perfect target tracking, but they usually suffer from a high cost for hardware implementation. Sparse arrays can yield similar DOA estimates and tracking performance with fewer elements for the same-size array aperture as compared to the traditional uniform arrays. In addition, the signals of interest may have rich temporal information that can be exploited to effectively eliminate background noise and significantly improve the performance and capacity of DOA estimation and tracking, and/or even dramatically reduce the computational burden of estimation and tracking algorithms. Therefore, this thesis aims to provide some solutions to improving the DOA estimation and tracking performance by designing sparse arrays and exploiting prior knowledge of the incident signals such as AR modeled sources and known waveforms. First, we design two sparse linear arrays to efficiently extend the array aperture and improve the DOA estimation performance. One scheme is called minimum redundancy sparse subarrays (MRSSA), where the subarrays are used to obtain an extended correlation matrix according to the principle of minimum redundancy linear array (MRLA). The other linear array is constructed using two sparse ULAs, where the inter-sensor spacing within the same ULA is much larger than half wavelength. Moreover, we propose a 2-D DOA estimation method based on sparse L-shaped arrays, where the signal subspace is selected from the noise-free correlation matrix without requiring the eigen-decomposition to estimate the elevation angle, while the azimuth angles are estimated based on the modified total least squares (TLS) technique. Second, we develop two DOA estimation and tracking methods for autoregressive (AR) modeled signal source using sparse linear arrays together with Kalman filter and LS-based techniques. The proposed methods consist of two common stages: in the first stage, the sources modeled by AR processes are estimated by the celebrated Kalman filter and in the second stage, the efficient LS or TLS techniques are employed to estimate the DOAs and AR coefficients simultaneously. The AR-modeled sources can provide useful temporal information to handle cases such as the ones, where the number of sources is larger than the number of antennas. In the first method, we exploit the symmetric array to transfer a complex-valued nonlinear problem to a real-valued linear one, which can reduce the computational complexity, while in the second method, we use the ordinary sparse arrays to provide a more accurate DOA estimation. Finally, we study the problem of estimating and tracking the direction of arrivals (DOAs) of multiple moving targets with known signal source waveforms and unknown gains in the presence of Gaussian noise using a sparse sensor array. The core idea is to consider the output of each sensor as a linear regression model, each of whose coefficients contains a pair of DOAs and gain information corresponding to one target. These coefficients are determined by solving a linear least squares problem and then updating recursively, based on a block QR decomposition recursive least squares (QRD-RLS) technique or a block regularized LS technique. It is shown that the coefficients from different sensors have the same amplitude, but variable phase information for the same signal. Then, simple algebraic manipulations and the well-known generalized least squares (GLS) are used to obtain an asymptotically-optimal DOA estimate without requiring a search over a large region of the parameter space

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

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