A Note on State Estimation as a Convex Optimization Problem
2003 (English)Report (Other academic)
The Kalman filter computes the maximum a posteriori (MAP) estimate of the states for linear state space models with Gaussian noise. We interpret the Kalman filter as the solution to a convex optimization problem, and show that we can generalize the MAP state estimator to any noise with a log-concave density function and any combination of linear equality and convex inequality constraints on the states. We illustrate the principle on a hidden Markov model, where the state vector contains probabilities that are positive and sum to one.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2003. , 6 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2497
Kalman filter, Convex optimization, State estimation
IdentifiersURN: urn:nbn:se:liu:diva-55914ISRN: LiTH-ISY-R-2497OAI: oai:DiVA.org:liu-55914DiVA: diva2:316616