Laplace l1 Square-Root Cubature Kalman Filter for Non-Gaussian Measurement Noises

The cubature Kalman filter (CKF) and its square-root version, namely the square-root cubature Kalman filter (SCKF), are commonly used nonlinear estimators under Gaussian noises. Particularly, the latter has the added advantage of low computational complexity and guaranteed positive semi-definiteness. However, the estimation accuracy often degrades substantially when the measurements are contaminated by outliers. This paper proposes a robust Laplace l(1) square-root cubature Kalman filter (LSCKF). The proposed filter employs the heavy-tailed Laplace distribution to model the measurement noises and solves the maximum posterior estimation using the majorization minimization (MM) approach and Gauss-Newton method. Besides, the filter is derived in square root and uses the orthogonal transformations to realize reliable computation of state estimates. Therefore, the new filter not only has good robustness against measurement outliers, but also retains the advantages of high numerical stability. Two numerical simulations are performed to test the performance of the proposed algorithm.