Robust Blind Pairwise Kalman Algorithms Using QR Decompositions

The Pairwise Kalman Filter (PKF) [W. Pieczynski and F. Desbouvries, “Kalman Filtering Using Pairwise Gaussian Models,” in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Hong Kong, Apr. 2003] is an extension of the classical Kalman filter that keeps propagation equations explicit, i.e. it does not require time consuming simulations. The contribution of this note is twofold. First, new robust equations for filtering, smoothing and unsupervised off-lined parameters estimation based on QR decompositions are presented. Second, since the model is over-parametrized, we give a simple condition to uniquely characterize a filter of interest when the dimension of observations is equal to the dimension of states. Unsupervised experiments based on simulated data confirm the nice behavior of the robust PKF, even for a limited number of observations.