Discrete-Time Filtering for Linear Systems in Correlated Noise with Non-Gaussian Initial Conditions: Formulas and Asymptotics
Richard B. Sowers, Armand M. Makowski · Birkhäuser Boston eBooks · 1990
We consider the one-step prediction problem for discrete-time linear systems in correlated plant and observation noises, and non-Gaussian initial conditions. Explicit representations are obtained for the MMSE and LMMSE (or Kalman) estimates of the state given past observations, as well as for the expected square of their difference. These formulae are obtained with the help of the Girsanov transformation for Gaussian white noise sequences, and display explicitly the dependence of the quantities of interest on the initial distribution. With the help of these formulae, we completely characterize the asymptotic behavior of the error sequence in the scalar time-invariant case. 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.