Robust Kalman filtering with generalized Laplace observational noises

Abstract

          It is well known that the Kalman filter fails to provide optimal state estimates in the sense of minimum mean of squared state error, when measurement outliers occur in a linear stochastic system. This is primarily due to the usual Gaussian assumptions made on the measurement noise term in the state space model. In this manuscript, robust filters are derived by using generalized Laplace measurement noise with single and multi scale factors to replace Gaussian assumptions. The performance of the proposed robust filters is compared to the Kalman filter and other robust filters through Monte-Carlo simulations.