Subspace-Based Algorithms for Localization and Tracking of Multiple Near-Field Sources

In this paper, we investigate the problems of estimating and tracking the location parameters [i.e., directions-of-arrival (DOAs) and ranges] of multiple near-field (NF) narrowband sources impinging on a symmetric uniform linear array, and a simple subspace-based algorithm for localization of NF sources (SALONS) is presented, where the computationally burdensome eigendecomposition and spectrum peak searching are avoided. In the SALONS, the DOAs and ranges are estimated separately with a one-dimensional subspace-based estimation technique, where the null spaces are obtained through the linear operation of the correlation matrices formed from the antidiagonal elements of the noiseless array covariance matrix, and the estimated DOAs and ranges are automatically paired without any additional procedure. Then the statistical analysis of the presented batch SALONS is studied, and the asymptotic mean-squared-error expressions of the estimated DOAs and ranges are derived. Furthermore, an online algorithm is developed for tracking the multiple moving NF sources with crossover points on their trajectories. The effectiveness and the theoretical analysis of the presented algorithms are verified through numerical examples, and the simulation results show that the proposed algorithms provide good estimation and tracking performance for DOAs and show satisfactory estimation and tracking performance for ranges.