A Note on State Estimation as a Convex Optimization Problem
2003 (English)In: Proceedings of the 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003, Vol. 6, no 6-10, 61-64 vol.6 p.Conference paper (Refereed)
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
2003. Vol. 6, no 6-10, 61-64 vol.6 p.
State estimation, Kalman filter, Convex optimization, Hidden Markov Models
Engineering and Technology Control Engineering
IdentifiersURN: urn:nbn:se:liu:diva-13918DOI: 10.1109/ICASSP.2003.1201618ISBN: 0-7803-7663-3OAI: oai:DiVA.org:liu-13918DiVA: diva2:22191
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, Hong Kong, China, April, 2003