Bounded Kalman Filter

Question

Can Upper and lower limit constraints be applied to the estimates updated by kalman filter?

I have one of the states which can have only non negative values in practical life. When I apply Kalman Filter, this state is updated to have negative values instead. How can I apply this limit constraint in kalman filter?

Please reply

Thanks

Answer 1

This can actually be implemented very trivially in every linear or nonlinear Kalman filter formulation: just do min(xmax, max(xmin, x_plus)) in every time step, where x_plus is your state estimate after the update step. While this may sound like a very bad hack losing all of a Kalman filters nice properties etc., it is actually nicely justified by theory. For details, refer to D. Simon (2010), "Kalman filtering with state constraints: a survey of linear and nonlinear algorithms", IET. Simon discusses the case of general linear inequality constraints which is more complex, but in the case of a simple bounding box the "state projection method" reduces to the above operation.