Multi-target Localization Based on an Improved FOCUSS Algorithm with Missing Information

Abstract

The situation where the observation stations or the sensors cannot fully detect the targets is called missing information, which makes it difficult to locate targets. Due to its sparsity, Compressed Sensing (CS) can be applied to multi-target localization with missing information. An improved Focal Undetermined System Solver (IFOCUSS) algorithm is proposed, by dynamically updating the regularized factor that has a significant impact on the convergence of iteration processes. What’s more, a re-weighting method is adopted for the weighting matrix to improve convergence property and accelerate convergence, and a new method of choosing correct items from a sparse estimation vector is proposed to improve the positioning accuracy. Several simulations corroborate its notable reconstruction performance, which is illustrated by correctly estimating five targets with only 11 sensors on a moving station, achieving better convergence at lower signal-to-noise ratios (such as 12 dB) with about half the run time of Regularized FOCUSS (RFOCUSS) and being able to estimate two targets even with missing information up to 60%. Under the same conditions of missing information, IFOCUSS can estimate more targets with smaller positioning errors than RFOCUSS, achieving better convergence performance by eliminating almost all interference terms.