State Estimation in Linear Systems with Statistically Unknown Observation Noise

概要

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A solution is presented of a state estimation problem in linear systems driven by white noise. No statistical information is assumed on the observation noise except finiteness of mean power, while the driving noise is characterized by (known) constant power spectral density. The problem is considered as a game between the estimator and the noise by means of introducing a cost function that evaluates the mean-square estimation error subtracted by the mean power of the observation noise. Based on the positive definite solution of a certain Lyapunov equation, a state estimator of Kalman-Luenberger form is obtained as minimax solution of the game.
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