Moderate Deviations of the Random Riccati Equation

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We characterize the invariant filtering measures resulting from Kalman filtering with intermittent observations (Bruno), where the observation arrival is modeled as a Bernoulli process. In Riccati-weakconv, it was shown that there exists a γ{sb>0 such that for every observation packet arrival probability γ, γ>γ{sb>0, the sequence of random conditional error covariance matrices converges in distribution to a unique invariant distribution μγ (independent of the filter initialization.) In this paper, we prove that, for controllable and observable systems, γ{sb=0 and that, as γ 1, the family {μγ}γ>0 of invariant distributions satisfies a moderate deviations principle (MDP) with a good rate function I. The rate function I is explicitly identified. In particular, our results show: