Gridless co-evolutionary algorithm for single snapshot DOA estimation with unknown number of sources

Single snapshot direction of arrival (DOA) estimation gains traction in automotive MIMO radar. Gridless methods based on atomic norm show superiority in single snapshot DOA estimation. However, the atomic norm is a convex relaxation of the atomic l0 norm, which leads to resolution limitations. To avoid the disadvantage of resolution limitation, we propose a multi-objective DOA estimation model with atomic l0 norm and measurement errors as optimization objectives. It can estimate the angle and the number of sources simultaneously and has the advantage of directly exploiting sparsity through the atomic l0 norm. Then, we design a cooperative co-evolution crayfish optimization algorithm (CO3) to solve this model. The algorithm contains two innovations, one of which is the proposal of a new multi-population cooperative co-evolutionary decomposition strategy that efficiently decomposes a multi-objective DOA estimation model into multiple single-objective problems without having to consider the fitness allocation problem. Each single-objective problem is then solved using a crayfish optimization algorithm. The other is to propose a variable-length neighbor-hood orthogonal crossover operator to carry out the work of information exchange between populations, which can effectively speed up the convergence of the algorithm. Simulation results and actual data verify the superiority of the method in this paper in terms of source number selection and DOA estimation.