Moving Horizon Estimation for Staged QP Problems
Proceedings IEEE Conference on Decision and Control, December 2012.
This paper considers moving horizon estimation
(MHE) approach to solution of staged quadratic programming
(QP) problems. Using an insight into the constrained solution
structure for the growing horizon, we develop a very accurate
iterative update of the arrival cost in the MHE solution. The
update uses a quadratic approximation of the arrival cost and
information about the previously active or inactive constraints.
In the absence of constraints, the update is the familiar Kalman
filter in information form. In the presence of the constraints,
the update requires solving a sequence of linear systems with
varying size. The proposed MHE update provides very good
performance in numerical examples. This includes problems
with 
regularization where optimal estimation allows us to
perform online segmentation of streaming data.