Title
On Kalman Filtering With Nonlinear Equality Constraints
Keywords
Kalman filtering; Measurement matrix; Nonlinear constraints; Quaternions
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. © 2007 IEEE.
Publication Date
6-1-2007
Publication Title
IEEE Transactions on Signal Processing
Volume
55
Issue
6 II
Number of Pages
2774-2784
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1109/TSP.2007.893949
Copyright Status
Unknown
Socpus ID
34249794868 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/34249794868
STARS Citation
Julier, Simon J. and LaViolar, Joseph J., "On Kalman Filtering With Nonlinear Equality Constraints" (2007). Scopus Export 2000s. 6560.
https://stars.library.ucf.edu/scopus2000/6560