A comparison theorem for matrix Riccati difference equations
Systems & Control Letters
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Asymptotic Optimality of the Minimum-Variance Fixed-Interval Smoother
IEEE Transactions on Signal Processing
An EM-Based Forward-Backward Kalman Filter for the Estimation of Time-Variant Channels in OFDM
IEEE Transactions on Signal Processing - Part II
Optimal and robust noncausal filter formulations
IEEE Transactions on Signal Processing
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This correspondence investigates the convergence of a Kalman filter-based expectation-maximization (EM) algorithm for estimating variances. It is shown that if the variance estimates and the error covariances are initialized appropriately, the underlying Riccati equation solution and the sequence of iterations will be monotonically nonincreasing. Further, the process noise variance estimates converge to the actual values when the measurement noise becomes negligibly small. Conversely, when the process noise variance becomes negligible, the measurement noise variance estimates asymptotically approach the true values. An inertial navigation application is discussed in which performance depends on accurately estimating the process variances.