Stable, Unstable and Center Manifolds for Fast Filtering Algorithms
Christopher I. Byrnes, Anders Lindquist, Yishao Zhou · Birkhäuser Boston eBooks · 1991
In the paper [4] we initiated an analysis of the discrete-time Kalman filter as a nonlinear dynamical system, motivated by a desire to understand the asymptotic dependence of the Kalman filter on the parameters determining it. Since in the Kalman filtering of systems in statistical steady state the filtering equations often rely on estimates of either covariance data or noise intensities, and since such estimates may or may not correspond to statistics generated by an underlying stochastic system, it becomes important to understand the convergence properties and the sensitivity to variation in parameters of the Kalman filter, for arbitrary parameters. As is well-known, parameters corresponding to a stochastic system satisfy various positivity constrains reflecting either positive definiteness of the infinite covariance matrix or positive realness of the corresponding modelling filter. On the other hand, it has been known for some time that such positivity conditions are not necessary for convergence of the Kalman filter. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.