Bayesian comparison of Kalman filters with known covariance matrices

A growing-window recursive procedure for model comparison is proposed based on the Bayesian inference principle. This procedure, compared to the batch one, is capable of processing unlimited increases in the uncertainty of the initial parameter settings, which is a characteristic of Kalman type algorithms. The present paper applies the suggested procedure to assess the degree of support for the state point estimates generated by multiple Kalman filters. We investigate a case where the covariance of the measurement noise and the normalized covariance matrix of the process noise are both available.