We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and tools from convex analysis. Our approach does not rely on restrictive noise assumptions and employs a Bellman-like update instead of a Bayesian update. Our proposed estimator is computationally efficient, with only modest overhead compared to a standard Kalman filter. Simulations demonstrate that our estimator achieves lower root mean squared error (RMSE) than the Kalman filter and has comparable performance to state-of-the-art estimators, while requiring significantly less computational power.
Nooshabadi et al. (Fri,) studied this question.