Mathematically equivalent approaches for equality constrained Kalman Filtering

Details Mathematically equivalent approaches for equality constrained Kalman Filtering Mathematically equivalent approaches for equality constrained Kalman Filtering

2009-02-10

arxiv.org/abs/0902.1565v1

Mathematics

Optimization and Control

12 pages, no figures

Scientific paper

Kalman Filtering problems often have inherent and known constraints in the physical dynamics that are not exploited despite potentially significant gains (e.g., fixed speed of a motor). In this paper, we review existing methods and propose some new ideas for filtering in the presence of equality constraints. We then show that three methods for incorporating state space equality constraints are mathematically equivalent to the more general "Projection" method, which allows different weighting matrices when projecting the estimate. Still, the different approaches have advantages in implementations that may make one better suited than another for a given application.

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