An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise
- 1 December 1968
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 13 (6), 655-660
- https://doi.org/10.1109/tac.1968.1099019
Abstract
The innovations method of Part I is used to obtain, in a simple way, a general formula for the smoothed (or noncausal) estimation of a second-order process in white noise. The smoothing solution is shown to be completely determined by the results for the (causal) filtering problem. When the signal is a lumped process, differential equations for the smoothed estimate can easily be derived from the general formula. In several cases, both the derivations and the forms of the solution are significantly simpler than those given in the literature.Keywords
This publication has 8 references indexed in Scilit:
- Application of a Resolvent Identity to a Linear Smoothing ProblemSIAM Journal on Control, 1969
- On Optimal Fixed Point Linear SmoothingInternational Journal of Control, 1967
- On optimal linear smoothing theoryInformation and Control, 1967
- Orthogonal Projection and Discrete Optimal Linear SmoothingSIAM Journal on Control, 1967
- A solution of the smoothing problem for linear dynamic systemsAutomatica, 1966
- Maximum likelihood estimates of linear dynamic systemsAIAA Journal, 1965
- On the estimation of state variables and parameters for noisy dynamic systemsIEEE Transactions on Automatic Control, 1964
- Solutions to the linear smoothing problemIEEE Transactions on Automatic Control, 1963