Journal ArticleDOI
A note on Kalman-Bucy filters with zero measurement noise
Reads0
Chats0
TLDR
The limiting form of the Kalman-Bucy filter as measurement noise tends to zero does not, in general, correspond to the optimal filter derived assuming zero measurement noise as discussed by the authors.Abstract:
The limiting form of the Kalman-Bucy filter as measurement noise tends to zero does not, in general, correspond to the optimal filter derived assuming zero measurement noise. This may be considered to be due to a difference in initial conditions.read more
Citations
More filters
Journal ArticleDOI
Singular perturbations and order reduction in control theory - An overview
TL;DR: The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.
Journal ArticleDOI
Singular Perturbations and Order Reduction in Control Theory - An Overview
TL;DR: The content of main theorems on singular perturbations is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.
Journal ArticleDOI
Explicit solution to the singular discrete-time stationary linear filtering problem
TL;DR: In this paper, a closed form solution to the stationary discrete-time linear filtering problem is obtained explicitly in terms of the system state-space matrices in the limiting singular case where the measurement noise tends to zero.
Book ChapterDOI
Singular perturbations and optimal control
TL;DR: In this paper, the authors provide an elementary account of recent mathematical effort in applying singular perturbations theory to optimal control problems, and demonstrate the practical importance of this asymptotic technique to current engineering studies, and suggest several open problems needing further research.
Journal ArticleDOI
Limiting performance of optimal linear filters
TL;DR: This work studies the lowest achievable mean-square estimation error in two limiting optimal linear filtering problems and links these results with Bode integral characterisations of performance limitations in linear filtering.
References
More filters
Journal ArticleDOI
New Results in Linear Filtering and Prediction Theory
R. E. Kalman,R. S. Bucy +1 more
TL;DR: The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.
Journal ArticleDOI
Linear filtering for time-varying systems using measurements containing colored noise
Arthur E. Bryson,D. Johansen +1 more
TL;DR: In this paper, it is shown that if correlation times are not short, or if some measurements are free of noise, the optimal filter is a modification of the Kalman-Bucy filter which, in general, contains differentiators as well as integrators.
Journal ArticleDOI
The maximally achievable accuracy of linear optimal regulators and linear optimal filters
H. Kwakernaak,R. Sivan +1 more
TL;DR: In this article, the authors considered a linear system with a quadratic cost function, which is a weighted sum of the integral square regulation error and the input cost, and showed that the necessary and sufficient condition for reducing the regulation error to zero is that the number of inputs be at least as large as the control variables, and the system possess no right-half plane zeros.