On the Stability of Kalman Filter with Random Coefficients

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Inspired by the random packet dropout problem widely existing in the networked control systems, we investigate the stability of Kalman filter with random coefficients. We present an excitation condition about the regression vectors to establish the Lp-stability and Lp-exponential stability of random Riccati equation. Furthermore, we prove the stability of the error equations of Kalman filter under the excitation condition and some conditions on the system matrix and noises, without relying on any stationarity or independence assumptions about the regressors.