An Optimization Algorithm for State Estimation Under Heavy-Tailed and Skewed Noise

State-space models, while fundamental to dynamic system analysis, face significant challenges in handling non-Gaussian outliers characterized by skewness and heavy tails. This paper addresses robust state estimation problems utilizing various asymmetric noise distributions and loss functions. We propose an optimization algorithm based on the Successive Convex Approximation (SCA) scheme. Our paper presents different interpretations of the proposed state estimation algorithm, offering different perspectives on robust filters. Comprehensive experiments demonstrate that our methods provide robust and efficient performance under non-Gaussian noise conditions, validating the algorithm’s effectiveness.