A Joint Doppler Frequency Shift and DOA Estimation Algorithm Based on Sparse Representations for Colocated TDM-MIMO Radar

We address the problem of a new joint Doppler frequency shift (DFS) and direction of arrival (DOA) estimation for colocated TDM-MIMO radar that is a novel technology applied to autocruise and safety driving system in recent years. The signal model of colocated TDM-MIMO radar with few transmitter or receiver channels is depicted and “time varying steering vector” model is proved. Inspired by sparse representations theory, we present a new processing scheme for joint DFS and DOA estimation based on the new input signal model of colocated TDM-MIMO radar. An ultracomplete redundancy dictionary for angle-frequency space is founded in order to complete sparse representations of the input signal. The SVD-SR algorithm which stands for joint estimation based on sparse representations using SVD decomposition with OMP algorithm and the improved M-FOCUSS algorithm which combines the classical M-FOCUSS with joint sparse recovery spectrum are applied to the new signal model’s calculation to solve the multiple measurement vectors (MMV) problem. The improved M-FOCUSS algorithm can work more robust than SVD-SR and JS-SR algorithms in the aspects of coherent signals resolution and estimation accuracy. Finally, simulation experiments have shown that the proposed algorithms and schemes are feasible and can be further applied to practical application

AN ALTERNATING DESCENT ALGORITHM FOR THE OFF-GRID DOA ESTIMATION PROBLEM WITH SPARSITY CONSTRAINTS

Publication in the conference proceedings of EUSIPCO, Bucharest, Romania, 201

Sparsity Promoting Off-grid Methods with Applications in Direction Finding

University of Minnesota Ph.D. dissertation. May 2017. Major: Electrical/Computer Engineering. Advisor: Mostafa Kaveh. 1 computer file (PDF); x, 99 pages.In this dissertation, the problem of directions-of-arrival (DoA) estimation is studied by the compressed sensing application of sparsity-promoting regularization techniques. Compressed sensing can recover high-dimensional signals with a sparse representation from very few linear measurements by nonlinear optimization. By exploiting the sparse representation for the multiple measurement vectors or the spatial covariance matrix of correlated or uncorrelated sources, the DoA estimation problem can be formulated in the framework of sparse signal recovery with high resolution. There are three main topics covered in this dissertation. These topics are recovery methods for the sparse model with structured perturbations, continuous sparse recovery methods in the super-resolution framework, and the off-grid DoA estimation with array self-calibration. These topics are summarized below. For the first topic, structured perturbation in the sparse model is considered. A major limitation of most methods exploiting sparse spectral models for the purpose of estimating directions-of-arrival stems from the fixed model dictionary that is formed by array response vectors over a discrete search grid of possible directions. In general, the array responses to actual DoAs will most likely not be members of such a dictionary. Thus, the sparse spectral signal model with uncertainty of linearized dictionary parameter mismatch is considered, and the dictionary matrix is reformulated into a multiplication of a fixed base dictionary and a sparse matrix. Based on this sparse model, we propose several convex optimization algorithms. However, we are also concerned with the development of a computationally efficient optimization algorithm for off-grid direction finding using a sparse observation model. With an emphasis on designing efficient algorithms, various sparse problem formulations are considered, such as unconstrained formulation, primal-dual formulation, or conic formulation. But, because of the nature of nondifferentiable objective functions, those problems are still challenging to solve in an efficient way. Thus, the Nesterov smoothing methodology is utilized to reformulate nonsmooth functions into smooth ones, and the accelerated proximal gradient algorithm is adopted to solve the smoothed optimization problem. Convergence analysis is conducted as well. The accuracy and efficiency of smoothed sparse recovery methods are demonstrated for the DoA estimation example. In the second topic, estimation of directions-of-arrival in the spatial covariance model is studied. Unlike the compressed sensing methods which discretize the search domain into possible directions on a grid, the theory of super resolution is applied to estimate DoAs in the continuous domain. We reformulate the spatial spectral covariance model into a multiple measurement vectors (MMV)-like model, and propose a block total variation norm minimization approach, which is the analog of Group Lasso in the super-resolution framework and that promotes the group-sparsity. The DoAs can be estimated by solving its dual problem via semidefinite programming. This gridless recovery approach is verified by simulation results for both uncorrelated and correlated source signals. In the last topic, we consider the array calibration issue for DoA estimation, and extend the previously considered single measurement vector model to multiple measurement vectors. By exploiting multiple measurement snapshots, a modified nuclear norm minimization problem is proposed to recover a low-rank matrix with high probability. The definition of linear operator for the MMV model is given, and its corresponding matrix representation is derived so that a reformulated convex optimization problem can be solved numerically. In order to alleviate computational complexity of the method, we use singular value decomposition (SVD) to reduce the problem size. Furthermore, the structured perturbation in the sparse array self-calibration estimation problem is considered as well. The performance and efficiency of the proposed methods are demonstrated by numerical results

Wideband Direction of Arrival estimation and sparse modeling for underwater surveillance

In underwater surveillance sources, such as ships or submarines, are localized using the acoustic noise emitted by the source engines, propellers and other machinery. The acoustic signals propagate in the sea and are recorded with an array of acoustic sensors. Processing the recorded signals to obtain the locations of the sources is known as Direction of Arrival (DOA) estimation in the field of signal processing. A simple mathematical model relating the sensor array geometry to the DOA of the source exists when the frequency of the source signal is known. The model is directly applicable to a narrowband DOA estimation problem where the energy of the source signals is concentrated around a single carrier frequency. For underwater surveillance, however, the source signals are wideband which complicates the problem. This thesis reviews existing methods for wideband DOA estimation: Simple extensions of well known narrowband methods MVDR and MUSIC, the so called coherent methods and the most recent methods belonging into the sparse framework. An original idea for extending MVDR using a likelihood based combining of subbands, MVDR-LBC is developed. The thesis models the sensor signals as a sparse autoregressive process by linear prediction and the original algorithm GRLS. The sparse model is shown to be effective compared to the conventional non-sparse one. The model can be used to compress the data recorded in underwater surveillance. The wideband DOA estimation methods are tested with a number of simulations and with real data recorded in the sea. MVDR is shown to be robust and effective, the accuracy and resolution of which can be improved using MVDR-LBC. MUSIC provides good resolution, is computationally efficient and can be implemented quite simply. The coherent methods are the most complicated and need good pre-estimations for the source directions but can resolve close sources best

Sparse Representations & Compressed Sensing with application to the problem of Direction-of-Arrival estimation.

PhDThe significance of sparse representations has been highlighted in numerous signal processing applications ranging from denoising to source separation and the emerging field of compressed sensing has provided new theoretical insights into the problem of inverse systems with sparsity constraints. In this thesis, these advances are exploited in order to tackle the problem of direction-of-arrival (DOA) estimation in sensor arrays. Assuming spatial sparsity e.g. few sources impinging on the array, the problem of DOA estimation is formulated as a sparse representation problem in an overcomplete basis. The resulting inverse problem can be solved using typical sparse recovery methods based on convex optimization i.e. `1 minimization. However, in this work a suite of novel sparse recovery algorithms is initially developed, which reduce the computational cost and yield approximate solutions. Moreover, the proposed algorithms of Polytope Faces Pursuits (PFP) allow for the induction of structured sparsity models on the signal of interest, which can be quite beneficial when dealing with multi-channel data acquired by sensor arrays, as it further reduces the complexity and provides performance gain under certain conditions. Regarding the DOA estimation problem, experimental results demonstrate that the proposed methods outperform popular subspace based methods such as the multiple signal classification (MUSIC) algorithm in the case of rank-deficient data (e.g. presence of highly correlated sources or limited amount of data) for both narrowband and wideband sources. In the wideband scenario, they can also suppress the undesirable effects of spatial aliasing. However, DOA estimation with sparsity constraints has its limitations. The compressed sensing requirement of incoherent dictionaries for robust recovery sets limits to the resolution capabilities of the proposed method. On the other hand, the unknown parameters are continuous and therefore if the true DOAs do not belong to the predefined discrete set of potential locations the algorithms' performance will degrade due to errors caused by mismatches. To overcome this limitation, an iterative alternating descent algorithm for the problem of off-grid DOA estimation is proposed that alternates between sparse recovery and dictionary update estimates. Simulations clearly illustrate the performance gain of the algorithm over the conventional sparsity approach and other existing off-grid DOA estimation algorithms.EPSRC Leadership Fellowship EP/G007144/1; EU FET-Open Project FP7-ICT-225913