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On Kalman Filtering With Nonlinear Equality Constraints

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2 Author(s)
Julier, S.J. ; Naval Res. Lab., Washington, DC ; LaViola, J.J.

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

Published in:

Signal Processing, IEEE Transactions on  (Volume:55 ,  Issue: 6 )

Date of Publication:

June 2007

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