Some reduced-order non-Riccati equations for linear least-squares estimation : the stationary, single-output case†
作者:
ANDERS LINDQUIST,
期刊:
International Journal of Control
(Taylor Available online 1976)
卷期:
Volume 24,
issue 6
页码: 821-842
ISSN:0020-7179
年代: 1976
DOI:10.1080/00207177608932864
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The problem of determining the Kalman—Bucy filter for ann-dimensional single-output model is the topic of this paper. Both the discrete-time case and continuous-time case are considered. The model processes are assumed to be stationary. It is shown that, under certain regularity conditions, onlynfirst-order difference or differential equations are required for determining the error covariance function, and hence also the filter gain, rather than 1/2n(n+ 1) equations as with the Riccati approach or 2nas in the previous non-Riccati algorithm. This reduction is achieved by constructing a system of simple integrals for the 2nnon-Riccati equations. The reduced-order algorithms have non-trivial steady-state versions, which are equivalent to the algebraic equations obtained by spectral factorization. The stationary and single-output assumptions are for convenience. In fact, the basic method works also in a more general setting.
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