Levinson- and chandrasekhar-type equations for a general discrete-time linear estimation problem

Recursive algorithms for the solution of linear least-squares estimation problems have been based mainly on state-space models. It has been know, however, that such algorithms exist for stationary time-series, using input-output descriptions (e.g., covariance matrices). We introduce a way of classif...

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Bibliographic Details
Published in1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes pp. 910 - 915
Main Authors Friedlander, B., Morf, M., Kailath, T., Ljung, L.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.1976
Subjects
Computational efficiency
Covariance matrix
Equations
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Summary:Recursive algorithms for the solution of linear least-squares estimation problems have been based mainly on state-space models. It has been know, however, that such algorithms exist for stationary time-series, using input-output descriptions (e.g., covariance matrices). We introduce a way of classifying stochastic processes in terms of their "distance" from stationarity that leads to a derivation of an efficient Levinson-type algorithm for arbitrary (nonstationary) processes. By adding structure to the covariance matrix, these general results specialize to state-space type estimation algorithms. In particular, the Chandrasekhar equations are shown to be the natural descendants of the Levinson algorithm.
DOI:10.1109/CDC.1976.267856