Laplace ℓ1 robust Kalman filter based on majorization minimization

In this paper, we attack the estimation problem in Kalman filtering when the measurements are contaminated by outliers. We employ the Laplace distribution to model the underlying non-Gaussian measurement process. The maximum posterior estimation is solved by the majorization minimization (MM) approach. This yields an MM based robust filter, where the intractable ℓ1 norm problem is converted into an ℓ2 norm format. Furthermore, we implement the MM based robust filter in the Kalman filtering framework and develop a Laplace ℓ1 robust Kalman filter. The proposed algorithm is tested by numerical simulations. The robustness of our algorithm has been borne out when compared with other robust filters, especially in scenarios of heavy outliers.