Fast sequential source localization using the projected companion matrix approach

International audienceThe sequential forms of the spectral MUSIC algorithm, such as the Sequential MUSIC (S-MUSIC) and the Recursively Applied and Projected MUSIC (RAP-MUSIC) algorithms, use the previously estimated DOA (Direction Of Arrival) to form an intermediate array gain matrix and project both the array manifold and the signal subspace estimate into its orthogonal complement. By doing this, these methods avoid the delicate search of multiple maxima and yield a more accurate DOA estimation in difficult scenarios. However, these high-resolution algorithms adapted to a general array geometry suffer from a high computational cost. On the other hand, for linear equispaced sensor array, the root- MUSIC algorithm is a fast and accurate high-resolution scheme which also avoids the delicate search of multiple maxima but a sequential scheme based on the root-MUSIC algorithm does not exist. This paper fills this need. Thus, we present a new sequential high-resolution estimation method, called the Projected Companion Matrix MUSIC (PCM-MUSIC) method, in the context of source localisation in the case of linear equispaced sensor array. Remark that the proposed algorithm can be used without modification in the context of spectral analysis

SAGE-Based Algorithm for Direction-of-Arrival Estimation and Array Calibration

Most existing array processing algorithms are very sensitive to model uncertainties caused by the mutual coupling and sensor location error. To mitigate this problem, a novel method for direction-of-arrival (DOA) estimation and array calibration in the case of deterministic signals with unknown waveforms is presented in this paper. The analysis begins with a comprehensive perturbed array output model, and it is effective for various kinds of perturbations, such as mutual coupling and sensor location error. Based on this model, the Space Alternating Generalized Expectation-Maximization (SAGE) algorithm is applied to jointly estimate the DOA and array perturbation parameters, which simplifies the multidimensional search procedure required for finding maximum likelihood (ML) estimates. The proposed method inherits the characteristics of good convergence and high estimation precision of the SAGE algorithm. At the same time, it forms a unified framework for DOA and array perturbation parameters estimation in the presence of mutual coupling and sensor location error. The simulation results demonstrate the effectiveness of the algorithm

Sequential estimation of the range and the bearing using the zero-forcing MUSIC approach

International audienceIn this paper, we consider the range and bearing estimation of near-field narrow-band sources from noisy data observed across a passive sensor array. For some difficult scenarios as for correlated and largely spaced sources at low SNRs, or correlated and closely spaced sources, the Near FieLd (NFL) version of the MUltiple SIgnal Classification (MUSIC) algorithm is no longer reliable. In this paper, we adapt and extend the sequential Zero-Forcing MUSIC (ZF-MUSIC) algorithm, which avoids the delicate search of multiple maxima, to the NFL context. In order to compare the NFL ZF-MUSIC with the Second-Order Statistics Weighted Prediction (SOS-WP) algorithm, we assumed an uniform sampling in the spatial domain. However, the proposed algorithm can be exploited for general array geometries. Finally numerical simulations show that the variance of the proposed algorithm achieves the Cram'er-Rao Bound (CRB) in difficult scenarios and for sufficient Signal to Noise Ratio (SNR)

Air Force Institute of Technology Contributions to Air Force Research and Development, Calendar Year 1979

This report provides the listing of the Master of Science Theses, Doctoral dissertations, faculty consultations, and selected faculty publications completed during the 1979 calendar year at the Air Force Institute of Technology, at Wright-Patterson Air Force Base, Ohio

HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms

A Sequential MUSIC algorithm for Scatterers Detection 2 in SAR Tomography Enhanced by a Robust Covariance 3 Estimator

Synthetic aperture radar (SAR) tomography (TomoSAR) is an appealing tool for the extraction of height information of urban infrastructures. Due to the widespread applications of the MUSIC algorithm in source localization, it is a suitable solution in TomoSAR when multiple snapshots (looks) are available. While the classical MUSIC algorithm aims to estimate the whole reflectivity profile of scatterers, sequential MUSIC algorithms are suited for the detection of sparse point-like scatterers. In this class of methods, successive cancellation is performed through orthogonal complement projections on the MUSIC power spectrum. In this work, a new sequential MUSIC algorithm named recursive covariance canceled MUSIC (RCC-MUSIC), is proposed. This method brings higher accuracy in comparison with the previous sequential methods at the cost of a negligible increase in computational cost. Furthermore, to improve the performance of RCC-MUSIC, it is combined with the recent method of covariance matrix estimation called correlation subspace. Utilizing the correlation subspace method results in a denoised covariance matrix which in turn, increases the accuracy of subspace-based methods. Several numerical examples are presented to compare the performance of the proposed method with the relevant state-of-the-art methods. As a subspace method, simulation results demonstrate the efficiency of the proposed method in terms of estimation accuracy and computational load