Adaptive robust MIMO radar target localization via capped Frobenius norm

Most of the existing algorithms for multiple-input multiple-output radar target localization assume that the bistatic range measurements are contaminated by one certain kind of noise only, such as Gaussian noise and impulsive noise. However, when the practical noise violates the original assumed distribution, their localization performance degrades severely. Therefore, adaptive and robust localization algorithms that can achieve good localization performance under both Gaussian and impulsive noise are highly desirable. In this paper, we exploit the truncated least squares loss function called capped Frobenius norm (CFN) to resist outliers. An adaptive update scheme is developed to automatically determine the upper bound of CFN using the normalized median absolute deviation. Then, the nonconvex and nonsmooth CFN-based formulation is transformed into a regularized ℓ₂-norm optimization problem based on the half-quadratic theory. The alternating optimization (AO) algorithm is adopted as the solver, and closed-form solutions for both subproblems are derived. We also show that the sequence of objective function value generated by the devised algorithm converges. Experimental results verify the superiority of the proposed algorithm over several existing algorithms in terms of localization accuracy under impulsive noise. Furthermore, the devised algorithm can attain comparable performance to ℓ₂-norm based methods without tweaking hyperparameters under Gaussian noise.