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Grid Optimization for Matrix-Based Source Localization Under Inhomogeneous Sensor Topology

Herein, the problem of non-parametric source localization based on signal strength measured at different sensor locations is examined. A recently developed matrix-based method is considered. This method first arranges the measurements into an observation matrix based on a uniform grid defined in the target area and the sensor locations, and then exploits sparse matrix processing techniques to localize the source. This paper finds that the localization performance degrades when the spatial pattern of the sensors is highly non-uniform, and the uniform grid formation is only a suboptimal solution. Rather, the grid should be optimized according to the specific sensor topology. With the insight from the Cramér-Rao bound (CRB) analysis of matrix completion, a clustering problem is formulated to optimize the grid. It is demonstrated that with grid optimization, both the matrix completion and the source localization performance can be significantly improved. The proposed strategy is robust under inhomogeneous sensor topology and substantially outperforms weighted centroid localization (WCL) algorithms.