Optimal filters for bilinear systems with nilpotent Lie algebras
- 1 December 1979
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 24 (6) , 948-953
- https://doi.org/10.1109/tac.1979.1102190
Abstract
We consider a bilinear signal process driven by a Gauss-Markov process which is observed in additive, white, Gaussian noise. An exact stochastic differential equation for the least squares filter is derived when the Lie algebra associated with the signal process is nilpotent. It is shown that the filter is also bilinear and moreover that it satisfies an analogous nilpotency condition. Finally, some special cases and an example are discussed, indicating ways of reducing the filter dimensionality.Keywords
This publication has 8 references indexed in Scilit:
- Algebraic Structure and Finite Dimensional Nonlinear EstimationSIAM Journal on Mathematical Analysis, 1978
- Structural features of factorable Volterra systemsIEEE Transactions on Automatic Control, 1976
- Signal detection for bilinear systemsInformation Sciences, 1975
- Estimation for rotational processes with one degree of freedom--Part I: Introduction and continuous-time processesIEEE Transactions on Automatic Control, 1975
- An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noiseIEEE Transactions on Automatic Control, 1968
- Dynamical equations for optimal nonlinear filteringJournal of Differential Equations, 1967
- A general theory of nonlinear estimation problems in control systemsJournal of Mathematical Analysis and Applications, 1964
- New Results in Linear Filtering and Prediction TheoryJournal of Basic Engineering, 1961