Discrete-time complementary models and smoothing algorithms: The correlated noise case
- 1 April 1983
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 28 (4) , 536-539
- https://doi.org/10.1109/tac.1983.1103251
Abstract
The concept of complementary models for discrete-time linear finite-dimensional systems with correlated observation and process noise is developed. Using this concept, a new algorithm for the fixed interval smoothing problem is obtained. The new algorithm offers great flexibility with respect to changes in the initial state variance Pi_{0} . Next, the relationship among the new smoothing algorithm, the two-filter smoother, and the reversed-time Kalman filter is explored. It is shown that a similarity transformation on the Hamiltonian system simultaneously produces the new smoothing algorithm, as well as the reversed-time Kalman filter.Keywords
This publication has 14 references indexed in Scilit:
- Discrete-time complementary models and smoothing algorithms: The correlated noise casePublished by Institute of Electrical and Electronics Engineers (IEEE) ,1981
- On the fixed-interval smoothing problemStochastics, 1981
- A stochastic realization approach to the smoothing problemIEEE Transactions on Automatic Control, 1979
- Efficient change of initial conditions, dual chandrasekhar equations, and some applicationsIEEE Transactions on Automatic Control, 1977
- 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
- An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noiseIEEE Transactions on Automatic Control, 1968
- A solution of the smoothing problem for linear dynamic systemsAutomatica, 1966