A note on state estimation as a convex optimization problem
Thomas B. Schön, Fredrik Gustafsson, Anders Hansson · 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). · 2004
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.