Divergence of the Kalman filter

The Kalman estimation technique is examined from the point of view of the asymptotic behavior of the errors in the estimates. It is shown that, under certain conditions, the mean-square errors may become unbounded with time, and that this divergence may or may not be correctable by increasing the intensity of process noise assumed in the filtering model General results are derived for multidimensional systems, and both "true" and "apparent" divergence are demonstrated by a simple scalar system. Divergence due to numerical inaccuracies is considered, and an example problem in orbital navigation is used to demonstrate divergence and its elimination.