Bayesian Kalman filtering with elliptically contoured errors
Francisco Javier Girón, J. C. Rojano · Biometrika · 1994
SUMMARY The basic recursive equations of the Kalman filter, for independent normally distributed error sources in both the observation and the system equations, are shown to hold for a larger class of distributions. It is shown that, for error sources following jointly a general elliptical distribution, the conditional posterior distribution of the parameters and the one-step ahead predictive distribution at every stage t are also elliptical. This generalizes some recent results of Meinhold & Singpurwalla for error sources distributed as multivariate Student t and some older results of Zellner for the linear regression model.