A stochastic realization approach to the smoothing problem
- 1 December 1979
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 24 (6) , 878-888
- https://doi.org/10.1109/tac.1979.1102174
Abstract
The purpose of this paper is to develop a theory of smoothing for finite dimensional linear stochastic systems in the context of stochastic realization theory. The basic idea is to embed the given stochastic system in a class of similar systems all having the same output process and the same Kalman-Bucy filter. This class has a lattice structure with a smallest and a largest element; these two elements completely determine the smoothing estimates. This approach enables us to obtain stochastic interpretations of many important smoothing formulas and to explain the relationship between them.Keywords
This publication has 28 references indexed in Scilit:
- New smoothing algorithms based on reversed-time lumped modelsIEEE Transactions on Automatic Control, 1976
- Backwards Markovian models for second-order stochastic processes (Corresp.)IEEE Transactions on Information Theory, 1976
- A unified approach to smoothing formulasAutomatica, 1976
- Partitioned estimation algorithms, I: Nonlinear estimationInformation Sciences, 1974
- A theorem on duality between estimation and control for linear stochastic systems with time delayJournal of Mathematical Analysis and Applications, 1972
- Dissipative dynamical systems Part II: Linear systems with quadratic supply ratesArchive for Rational Mechanics and Analysis, 1972
- Optimal non-linear estimation†International Journal of Control, 1971
- On optimal smoothing of continuous time Kalman processesInformation Sciences, 1969
- The inverse problem of stationary covariance generationJournal of Statistical Physics, 1969
- Controllability and Observability in Time-Variable Linear SystemsSIAM Journal on Control, 1967