@inproceedings{0e4e2ac552714aa8b862090471dc2a3f,

title = "Discrete-Time Filtering for Linear Systems in Correlated Noise with Non-Gaussian Initial Conditions: Formulas and Asymptotics",

abstract = "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.",

keywords = "Probability Measure, Noise Sequence, Observation Noise, Correlate Noise, Prediction Problem",

author = "Sowers, {Richard B.} and Makowski, {Armand M.}",

year = "1990",

doi = "10.1007/978-1-4612-4484-4_39",

language = "English (US)",

isbn = "978-1-4612-8839-8",

series = "Progress in Systems and Control Theory",

publisher = "Birkhauser Boston",

pages = "407--419",

editor = "Kaashoek, {M A} and {van Schuppen}, {J H} and Ran, {A C M}",

booktitle = "Robust Control of Linear Systems and Nonlinear Control",

address = "United States",

}