A Modified Displacement Rank and Some Applications.
STANFORD UNIV CALIF DEPT OF ELECTRICAL ENGINEERING
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Recursive Algorithms for linear least squares estimation problems have been based mainly on state-space models. Recently, some new recursive solutions were obtained for processes classified in terms of their index of nonstationarity or equivalently--the displacement rank of their covariance functions. While this definition provides a natural explanation of the properties of constant-coefficient state-space models, it is not satisfactory for time-variant models. However a modified definition of the displacement rank makes it possible to imbed time-varying state-space models in the more general input-output framework. In so doing, one is able to show the mutual relationships of the Kalman filter Riccati equation, the time-varying Chandrasekhar equations and the Krein-Levinson equations.
- Statistics and Probability