EquiDistribution Grid Evolution Method for Line Spectrum Estimation

Abstract

The grid for traditional estimation methods is usually uniform. This is a conservative strategy to form a grid without using any prior information. Estimation results may become better if the true values of parameters are near the artificial grid points. Therefore, a dense grid is usually used to reach expected accuracy, resulting in heavy computation workload. Notice that the performance of estimation is related to the distribution of its grid. Aiming to achieve higher accuracy while use less grid points, a strategy called equidistribution is proposed in this paper. Estimation problem is reformulated by adding the constraint of equidistribution and is solved by a modified grid evolution method, named as EquiDistribution Grid Evolution (EDGE) method. In EDGE, a nonuniform distribution of grid points is evolved according to the distribution of information, and the distribution of information is progressively updated based on the nonuniform grid. The two procedures iterate alternatively. Finally a spectrum based on the adaptively evolved grid is obtained. Compared with previous methods, the proposed method shows advantages on both accuracy and time consumption. The controlling parameter is significantly simplified compared with previous grid evolution method. Furthermore, the resolution and accuracy in parameters’ domain are adaptive and nonuniform. The effectiveness of the EDGE method is demonstrated by numerical simulations.