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We propose a diagnostics technique for the state space model fitting formed by deleting observations from the data and measuring the change in the estimates of the parameters. A method is proposed for distinguishing an observational outlier from an innovational one. The presented subspace system identification algorithm is robust and less sensitive to outliers. We give a numerical result to show effectiveness of the proposed method.

In this paper, we propose a robust Kalman filter and smoother for the errors-invariables (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.

This paper advocates a new subspace system identification algorithm for the errors-in-variables (EIV) state space model via the EM algorithm. To initialize the EM algorithm an initial estimate is obtained by the errors-in-variables subspace system identification method: EIV-MOESP (Chou et al. [1997]) and EIV-N4SID (Gustafsson [2001]). The EM algorithm is an algorithm to compute the maximum value for the likelihood function that is consists of two steps; namely the E- and M-steps. The E- and M-steps in the EM algorithm are calculated by computing the conditional expectation under the assumption that the input-output data is completely observed. Numerical example shows that the EM algorithm can monotonically improve the initial estimates obtained by subspace identification methods.