Abstract
The Kalman filter yields the optimum estimate in the sense of the minimum error variance when the noises are Gaussian distributed. However its performance will deteriorate so that the estimates may not be good for anything, if it is contaminated by any noise with non-Gaussian distribution.
As an approach to the practical solution of this problem, a new algorithm is here constructed, in which the test of statistical hypothesis is used to predict the appearance of outliers. The information is then used to switch the two kinds of Kalman filters. Using the ε-contaminated Gaussian distribution model, two cases are investigated in this paper where a) system noise is Gaussian and observation noise is non-Gaussian, and b) system noise is non-Gaussian and observation noise is Gaussian.
The resultant filter, being readily constructed as a combination of two linear filters, provides significantly better performance over the conventional Kalman filter. Furthermore it is shown by the simulation for the proposed filter to have the robust property, for the case where prior knowledge about outlier is not sufficient.
