Robust Kalman filter and smoother for errors-in-variables model with observation outliers

In this paper, we propose a robust Kalman filter and smoother for the errors-in-variables (EIV) state space model subject to observation noise with outliers. We introduce the EIV problem with outliers and then we present the minimum covariance determinant (MCD) estimator which is highly robust estimator to detect outliers. As a result, a new statistical test to check the existence of outliers which is based on the Kalman filter and smoother has been formulated. Since the MCD is a combinatorial optimization problem the randomized algorithm has been proposed in order to achieve the optimal estimate. However, the uniform sampling method has a high computational cost and may lead to biased estimate, therefore we apply the sub-sampling method. A Monte Carlo simulation result shows the efficiency of the proposed algorithm.