Extended Levinson and Chandrasekhar equations for general discrete-time linear estimation problems

Recursive algorithrms for the solution of linear least-squares estimation problems have been based mainly on state-space models. It has been known, however, that recursive Levinson-Whittle-Wiggins-Robinson (LWR) algorithms exist for stationary time-series, using only input-output information (i.e, c...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 23; no. 4; pp. 653 - 659
Main Authors: Friedlander, B., Kailath, T., Morf, M., Ljung, L.
Format: Journal Article
Language:English
Published: IEEE 01.08.1978
Subjects:
Chandrasekhar equations
Control systems
Covariance matrices
Covariance matrix
Equations
Frequency modulation
Geophysics computing
Least-squares estimation
Linear systems
Pulse modulation
Recursive estimation
Regulators
State estimation
Steady-state
Time varying systems
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:Recursive algorithrms for the solution of linear least-squares estimation problems have been based mainly on state-space models. It has been known, however, that recursive Levinson-Whittle-Wiggins-Robinson (LWR) algorithms exist for stationary time-series, using only input-output information (i.e, covariance matrices). By introducing a way of classifying stochastic processes in terms of an "index of nonstationarity" we derive extended LWR algorithms for nonstationary processes We show also how adding state-space structure to the covariance matrix allows us to specialize these general results to state-space type estimation algorithms. In particular, the Chandrasekhar equations are shown to be natural descendants of the extended LWR algorithm.
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content type line 23
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.1978.1101797