Julier, SJ; LaViola, JJ; (2007) On Kalman Filtering with Nonlinear Equality Constraints. IEEE Transactions on Signal Processing , 55 (6) pp. 2774-2784. 10.1109/TSP.2007.893949.

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Abstract

The state space description of some physical systems possess nonlinear equality constraints between some state variables. In this paper, we consider the problem of applying a Kalman filter-type estimator in the presence of such constraints. We categorize previous approaches into pseudo-observation and projection methods and identify two types of constraints-those that act on the entire distribution and those that act on the mean of the distribution. We argue that the pseudo-observation approach enforces neither type of constraint and that the projection method enforces the first type of constraint only. We propose a new method that utilizes the projection method twice-once to constrain the entire distribution and once to constrain the statistics of the distribution. We illustrate these algorithms in a tracking system that uses unit quaternions to encode orientation.

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