Optimal simultaneous maximuma posterioriestimation of states, noise statistics and parameters I. Algorithm
作者:
D. SASTRY,
M. GAUVRIT,
期刊:
International Journal of Systems Science
(Taylor Available online 1980)
卷期:
Volume 11,
issue 11
页码: 1351-1381
ISSN:0020-7721
年代: 1980
DOI:10.1080/00207728008967092
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The simultaneous state and parameter estimation problem for a linear discrete-time system with unknown noise statistics is treated as a large-scale optimization problem. Thea posterioriprobability density function is maximized directly with respect to the states and parameters subject to the constraint of the system dynamics. The resulting optimization problem is too large for any of the standard non-linear programming techniques and hence an hierarchical optimization approach is proposed. It turns out that the states can be computed at thefirst levelfor given noise and system parameters. These, in turn, are to be modified at thesecond level.The states are to be computed from a large system of linear equations and two solution methods are considered for solving these equations, limiting the horizon to a suitable length. The resulting algorithm is a filter-smoother, suitable for off-line as well as on-line state estimation for given noise and system parameters. The second level problem is split up into two, one for modifying the noise statistics and the other for modifying the system parameters. An adaptive relaxation technique is proposed for modifying the noise statistics and a modified Gauss-Newton technique is used to adjust the system parameters.
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