Multiobjective bilevel evolutionary approach for off-grid direction-of-arrival estimation

The source number identification is an essential step in direction-of-arrival (DOA) estimation. Existing methods may provide a wrong source number due to modeling errors caused by relaxing sparse penalties, especially in impulsive noise. This paper proposes a novel idea of simultaneous source number identification and DOA estimation to address this issue. We formulate a multiobjective off-grid DOA estimation model to realize this idea, by which the source number can be automatically identified together with DOA estimation. In particular, the source number is correctly exploited by the l norm of impinging signals without relaxations, guaranteeing accuracy. We further design a multiobjective bilevel evolutionary algorithm to solve this model. The source number identification and sparse recovery are simultaneously optimized at the on-grid (lower) level. A forward search strategy is developed to further refine the grid at the off-grid (upper) level. This strategy does not need linear approximations and can eliminate the off-grid gap with low computational complexity. Simulation results demonstrate the outperformance of our method in terms of source number and root mean square error.