A Note on State Estimation as a Convex Optimization Problem

• 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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Nyckelord

State estimation

Kalman filter

Convex optimization

Hidden Markov Models

TECHNOLOGY

TEKNIKVETENSKAP

Automatic control

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