Journal ArticleDOI
The Kalman-Bucy Filter as a True Time-Varying Wiener Filter
Brian D. O. Anderson,John B. Moore +1 more
- Vol. 1, Iss: 2, pp 119-128
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TLDR
It is shown that the Kalman-Bucy filter is constructible knowing precisely those covariances required to construct a Wiener filter, and no more, and that the filter is independent of the particular models of the processes generating these Covariances.Abstract:
The notion is exploded that to build a Kalman-Bucy filter, one needs to know the whole structure of the signal generating process. It is shown that the filter is constructible knowing precisely those covariances required to construct a Wiener filter, and no more, and that the filter is independent of the particular models of the processes generating these covariances. Performance of the Kalman-Bucy filter does depend on the models, however. Results are also obtained for the smoothing problem.read more
Citations
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Journal ArticleDOI
A view of three decades of linear filtering theory
TL;DR: Developments in the theory of linear least-squares estimation in the last thirty years or so are outlined and particular attention is paid to early mathematica[ work in the field and to more modern developments showing some of the many connections between least-Squares filtering and other fields.
Book
Lectures on Wiener and Kalman Filtering
TL;DR: In this paper, the authors consider two random variables X, Y with a known joint density function fx,y(.,.). Assume that in a particular experiment, the random variable Y can be measured and takes the value y. What can be said about the corresponding value of the unobservable variable X?
Journal ArticleDOI
An innovations approach to least squares estimation--Part IV: Recursive estimation given lumped covariance functions
Thomas Kailath,R. Geesey +1 more
TL;DR: In this paper, the covariance function of the signal process is known and not a specific state-variable model is used, and the solutions are based on the innovations representation for the observation process.
Journal ArticleDOI
An innovations approach to least-squares estimation--Part VI: Discrete-time innovations representations and recursive estimation
Michel Gevers,Thomas Kailath +1 more
TL;DR: In this paper, a causal and causally invertible innovations representation (IR) whose existence depends only on the positive definite nature of the separable covariance is presented, and it is shown that least squares filtered and smoothed estimates of one process given observations of a related colored process can be expressed as linear combinations of the state vector of the IR of the observed process.
Proceedings ArticleDOI
Modelling of two-dimensional covariance functions with application to image restoration
TL;DR: In this paper, exact models for the horizontal line scan of monochromatic pictorial images whose light intensity at each point can be represented by a class of two-dimensional homogeneous random fields are derived.
References
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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
An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise
Thomas Kailath,P. Frost +1 more
TL;DR: In this article, a simple derivation of the classical Wiener filtering problem for stationary processes over a semi-infinite interval is given for nonstationary continuous-time processes over finite intervals.
Journal ArticleDOI
Fredholm resolvents, Wiener-Hopf equations, and Riccati differential equations
TL;DR: The solution of Fredholm equations with symmetric kernels of a certain type can be reduced to the solution of a related Wiener-Hopf integral equation, which may be a more convenient form for digital computer evaluation.
Journal ArticleDOI
Spectral factorization of time-varying covariance functions
TL;DR: It is shown that a symmetric state covariance matrix provides the key link between the state-space equations of a system and the system output covariance matrices.
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