DocumentCode :
3479617
Title :
A note on state estimation as a convex optimization problem
Author :
Schön, Thomas ; Gustafsson, Fredrik ; Hansson, Anders
Author_Institution :
Dept. of Electr. Eng., Linkoping Univ., Sweden
Volume :
6
fYear :
2003
fDate :
6-10 April 2003
Abstract :
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.
Keywords :
Gaussian noise; Kalman filters; hidden Markov models; maximum likelihood estimation; optimisation; probability; state estimation; state-space methods; Gaussian noise; Kalman filter; MAP estimation; convex inequality constraints; convex optimization problem; hidden Markov model; linear equality constraints; linear state space models; log-concave density function; maximum a posteriori estimation; state estimation; state vector; Automatic control; Constraint optimization; Density functional theory; Hidden Markov models; Probability density function; Signal processing; State estimation; State-space methods; Stochastic resonance; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on
ISSN :
1520-6149
Print_ISBN :
0-7803-7663-3
Type :
conf
DOI :
10.1109/ICASSP.2003.1201618
Filename :
1201618
Link To Document :
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