Adaptive Kalman filter is proposed to estimate the states of a system where the system noise is assumed to be a multivariate generalized Laplace random vector. In the presence of outliers in the system noise, it is shown that improved state estimates can be obtained by using an adaptive factor to estimate the dispersion matrix of the system noise term. A Monte-Carlo investigation is carried out to access the performance of the proposed filters and other robust filters. The results show that the proposed filter is superior to other filters when the magnitude of system change is moderate or large.

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