Active Target Localization using Low-Rank Matrix Completion and Unimodal Regression

Abstract: The detection and localization of a target from samples of its generated field is a problem of interest in a broad range of applications. Often, the target field admits structural properties that enable the design of lower sample detection strategies with good performance. This paper designs a sampling and localization strategy which exploits separability and unimodality in target fields and theoretically analyzes the trade-off achieved between sampling density, noise level and convergence rate of localization. In particular, the strategy adopts an exploration-exploitation approach to target detection and utilizes the theory of low-rank matrix completion, coupled with unimodal regression, on decaying and approximately separable target fields. The assumptions on the field are fairly generic and are applicable to many decay profiles since no specific knowledge of the field is necessary, besides its admittance of an approximately rank-one representation. Extensive numerical experiments and comparisons are performed to test the efficacy and robustness of the presented approach. Numerical results suggest that the proposed strategy outperforms algorithms based on mean-shift clustering, surface interpolation and naive low-rank matrix completion with peak detection, under low sampling density.