Robust Filtering for Linear State-space Models with Non-propagating Outliers Following a Mixture of Gaussian Distributions

The problem of recursive filtering in linear state-space models is considered. The solution to this problem is the classical Kalman filter which is optimal in the sense that it minimizes the variance of the estimated states, if the error processes of the state and observation equations are both Gaussian. However, the Kalman filter is well known to be sensitive to outliers, so robustness is an issue. Two approximate conditional-mean (ACM) type filters for vector-valued observations are proposed that generalize existing univariate filters of similar type to the multivariate case.These new ACM-type filters are compared by simulations in a multivariate setting with additive outliers to the classical Kalman filter and the robust least squares (rLS) filter, another approach robustifying the Kalman filter. Additionally, different settings of tuning parameters and their impact are investigated. The results of the simulation experiments show that in the presence of additive outliers the multivariate ACM-type filters not only outperform the classical Kalman filter, as expected, but they also outperform the rLS filter.