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

Socpus ID

34249794868 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/34249794868

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