Robust recursive sigma point Kalman filtering for Huber-based generalized M-estimation

For nonlinear state estimation driven by non-Gaussian noise, the estimator is required to be updated iteratively. Since the iterative update approximates a linear process, it fails to capture the nonlinearity of observation models, and this further degrades filtering accuracy and consistency. Given the flaws of nonlinear iteration, this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy. The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method. The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction. Considering the correlated state and observation noise induced by recursions, a separately reweighting strategy is adopted to build a robust nonlinear system. Analogous to the nonlinear recursion, a robust nonlinear recursive update strategy is proposed, where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics, thereby completing the nonlinear solution of the robust system. Compared with the iterative update strategies under non-Gaussian observation noise, the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy, stronger robustness, and better consistency. Therefore, the proposed strategy is more suitable for the robust nonlinear filtering framework.