Riccati Equation and EM Algorithm Convergence for Inertial Navigation Alignment

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...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2009-01, Vol.57 (1), p.370-375
Main Authors: Einicke, G.A., Malos, J.T., Reid, D.C., Hainsworth, D.W.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Asymptotic properties
Convergence
Detection, estimation, filtering, equalization, prediction
Estimates
Exact sciences and technology
Filtering
Inertial navigation
Information, signal and communications theory
Iterative algorithms
Kalman filtering
Kalman filters
Miscellaneous
Noise
Noise measurement
Parameter estimation
Riccati equation
Riccati equations
Signal and communications theory
Signal processing
Signal, noise
State estimation
stationary alignment
Telecommunications and information theory
Trajectory
Variance
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2008.2007090