Comparison of Kalman filters formulated as the statistics of the Normal-inverse-Wishart distribution

A novel growing-window recursive procedure for Kalman filter comparison is proposed based on the Bayesian inference principle. This procedure is capable of processing unlimited growth of 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 Kalman filters differing in their system model descriptions. The algebraic form of the comparison algorithm covers the situation when the covariance of the measurement noise is known as well as is unknown and the normalized covariance matrix of the process noise is always available. In this respect, the Kalman filter is formulated here as recursive learning of the sufficient statistics of the Normal and Normal-inverse-Wishart distributions.