Journal ArticleDOI
Correlated noise filtering and invariant directions for the Riccati equation
TLDR
In this article, the Riccati equation associated with a class of discrete-time correlated noise problems is examined, and the concept of invariant directions for this equation is introduced.Citations
More filters
Journal ArticleDOI
Square-root algorithms for least-squares estimation
Martin Morf,Thomas Kailath +1 more
TL;DR: Several new algorithms are presented, and more generally a new approach, to recursive estimation algorithms for linear dynamical systems, based on certain simple geometric interpretations of the overall estimation problem.
Journal ArticleDOI
Some new algorithms for recursive estimation in constant, linear, discrete-time systems
TL;DR: In this paper, the Chandrasekhar-type Riccati-type difference equation is replaced by another set of difference equations, which are then used for recursive estimation in constant continuous-time linear systems.
Book ChapterDOI
Discrete Riccati Equations: Alternative Algorithms, Asymptotic Properties, and System Theory Interpretations
TL;DR: In this paper, the authors present a self-contained exposition of the properties of the class of discrete-time Riccati equations that arise in the filtering problem, and show the relationship between various alternative algorithms and the Richecati equation while connecting up the asymptotic theory of such equations with the developments in linear systems theory.
Journal ArticleDOI
Linear and nonlinear filtering
TL;DR: In this paper, a review of the theory of filtering for stochastic processes is provided, in particular the sequential theory of linear filtering and the nonlinear filtering theory of non-linear filtering.
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.
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
On the general theory of control systems
TL;DR: In this paper, a general theory of control systems is outlined which answers many basic questions (what is controllable? why? how?) and gives a highly efficient method of computation.
Effective construction of linear state-variable models from input/output functions.
B. L. Ho,R. E. Kalman +1 more
TL;DR: Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data is presented in this article, where a Markov-parametric algorithm is used to construct the minimal realization.
Journal ArticleDOI
Inversion of multivariable linear systems
TL;DR: In this article, a new algorithm for constructing an inverse of a multivariable linear dynamical system is presented, which is considerably more efficient than previous methods, and incorporates a relatively simple criterion for determining if an inverse system exists.