Robust State Estimation with Sparse Outliers

One of the major challenges for state estimation algorithms, such as the Kalman filter, is the impact of outliers that do not match the assumed process and measurement noise. When these errors occur, they can induce large state estimate errors and even filter divergence. Although there are robust filtering algorithms that can address measurement outliers, in general, they cannot provide robust state estimates when state propagation outliers occur. This paper presents a robust recursive filtering algorithm, the l1-norm filter, which can provide reliable state estimates in the presence of both measurement and state propagation outliers. In addition, Monte Carlo simulations and vision-aided navigation experiments demonstrate that the proposed algorithm can provide improved state estimation performance over existing robust filtering approaches.