Julier, SJ and LaViola, JJ (2007) On Kalman Filtering with Nonlinear Equality Constraints. IEEE Transactions on Signal Processing , 55 (6) 2774 - 2784. 10.1109/TSP.2007.893949.
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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.
|Title:||On Kalman Filtering with Nonlinear Equality Constraints|
|Open access status:||An open access version is available from UCL Discovery|
|Additional information:||Imported via OAI, 7:29:01 11th Sep 2007|
|Keywords:||kalman filtering, quaternions, measurement matrix, nonlinear constraints|
|UCL classification:||UCL > School of BEAMS > Faculty of Engineering Science > Computer Science|
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