On Kalman filtering with nonlinear equality constraints
Abbreviated Journal Title
IEEE Trans. Signal Process.
Kalman filtering; quaternions; measurement matrix; nonlinear constraints; TARGET TRACKING; IDENTIFICATION; Engineering, Electrical & Electronic
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.
Ieee Transactions on Signal Processing
"On Kalman filtering with nonlinear equality constraints" (2007). Faculty Bibliography 2000s. 7273.