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Abstract: The linear least squares (LLS) technique is widely used in time-difference-of-arrival based positioning because of its computational efficiency. Two-step weighted least squares (2WLS) and constrained weighted least squares (CWLS) algorithms are two common LLS schemes where an additional variable is introduced to obtain linear equations. However, they both have the same measurement matrix that becomes ill-conditioned when the sensor geometry is a uniform circular array and the source is close to the array center. In this paper, a new CWLS estimator is proposed to circumvent this problem. The main strategy is to separate the source coordinates and the additional variable to different sides of the linear equations where the latter is first solved via a quadratic equation. In doing so, the matrix to be inverted has a smaller condition number than that of the conventional LLS approach. The performance of the proposed method is analyzed in the presence of zero-mean white Gaussian disturbances. Numerical examples are also included to evaluate its localization accuracy by comparing with the existing 2WLS and CWLS algorithms as well as the Cramér–Rao lower bound. [Copyright &y& Elsevier]

Abstract: In this fast communication, we derive the statistical resolution limit (SRL), characterizing the minimal parameter separation, to resolve two closely spaced known near-field sources impinging on a linear array. Toward this goal, we conduct on the first-order Taylor expansion of the observation model a Generalized Likelihood Ratio Test (GLRT) based on a Constrained Maximum Likelihood Estimator (CMLE) of the SRL. More precisely, the minimum separation between two near-field sources, that is detectable for a given probability of false alarm and a given probability of detection, is derived herein. Finally, numerical simulations are done to quantify the impact of the array geometry of the signal sources power distribution and of the array aperture on the statistical resolution limit. [Copyright &y& Elsevier]

Abstract: This paper presents reduced-rank linearly constrained minimum variance (LCMV) beamforming algorithms based on joint iterative optimization of filters. The proposed reduced-rank scheme is based on a constrained joint iterative optimization of filters according to the minimum variance criterion. The proposed optimization procedure adjusts the parameters of a projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe LCMV expressions for the design of the projection matrix and the reduced-rank filter. We then describe stochastic gradient and develop recursive least-squares adaptive algorithms for their efficient implementation along with automatic rank selection techniques. An analysis of the stability and the convergence properties of the proposed algorithms is presented and semi-analytical expressions are derived for predicting their mean squared error (MSE) performance. Simulations for a beamforming application show that the proposed scheme and algorithms outperform in convergence and tracking the existing full-rank and reduced-rank algorithms while requiring comparable complexity. [Copyright &y& Elsevier]