Abstract
The problem considered is that of selecting an initial covariance matrix for the Kalman filter to ensure that the closed-loop filter at every subsequent time instant is exponentially asymptotically stable as a time-invariant filter. Sufficient conditions are derived based on monotonicity properties of the solution of the Riccati difference equation. The results have application in observer design, and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included.
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