This paper investigates the localization of multiple near-field narrowband sources with a symmetric uniform linear array, and a new linear prediction approach based on the truncated singular value decomposition (LPATS) is proposed by taking an advantage of the anti-diagonal elements of the noiseless array covariance matrix. However, when the number of array snapshots is not sufficiently large enough, the saturation behavior is usually encountered in most of the existing localization methods for the near-field sources, where the estimation errors of the estimated directions-of-arrival (DOAs) and ranges cannot decrease with the signal-to-noise ratio. In this paper, an oblique projection based alternating iterative scheme is presented to improve the accuracy of the estimated location parameters. Furthermore, the statistical analysis of the proposed LPATS is studied, and the asymptotic mean-square-error expressions of the estimation errors are derived for the DOAs and ranges. The effectiveness and the theoretical analysis of the proposed LPATS are verified through numerical examples, and the simulation results show that the LPATS provides good estimation performance for both the DOAs and ranges compared to some existing methods.
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