Direct position determination based on sparse signal representation via overcomplete dictionary design

In this paper, a sparse signal representation direct position determination algorithm (SSR-DPD) based on overcomplete dictionary matrix design is investigated. In spite of the fact that the existing SSR-DPD algorithm is able to overcome the deterioration in positioning performance of the super resolution direct position determination (SR-DPD) algorithm under conditions of low signal-to-noise ratio (SNR) and small snapshot number, its precision depends heavily on the accuracy of the overcomplete dictionary and the fineness of the grid division. Consequently, we propose an improved SSR-DPD algorithm, which uses the total least squares (TLS) method to design the overcomplete dictionary matrix and enhances positioning accuracy via multilevel grid (MG) division. Specifically, the method involves obtaining the source prior position using subspace data fusion (SDF), followed by denser grid division in the surrounding area, and finally, using the orthogonal matching pursuit method (OMP) to recover the sparse position vector. Simulation results demonstrate superior performance of the proposed algorithm.