Robust Kalman filter and smoother for errors-in-variables state space models with observation outliers based on the minimum-covariance determinant estimator

In this paper, we propose a robust Kalman filter and smoother for the errors-in-variables (EIV) state space models subject to observation noise with outliers. We introduce the EIV problem with outliers and then present the minimum covariance determinant (MCD) estimator which is a highly robust estimator in terms of protecting the estimate from the outliers. Then, we propose the randomized algorithm to find the MCD estimate. However, the uniform sampling method has a high computational cost and may lead to biased estimates, therefore we apply the sub-sampling method. A Monte Carlo simulation result shows the efficiency of the proposed algorithm.