The Kantorovich inequality for error analysis of the Kalman filter with unknown noise distributions

The state-space model with random noises is widely used to model dynamic systems. In many practical problems, the noise terms will have unknown probability distributions, which is contrary to the usual assumption of Gaussian noises made in state-vector estimation; this assumption is usually made for reasons of mathematical tractability. A problem arises, however, in that inference based on the incorrect Gaussian assumption can lead to misleading or erroneous conclusions. This note shows how the Kantorovich inequality from probability theory has potential for characterizing the estimation error of a Kalman filter in such a non-Gaussian (distribution-free) setting