Journal ArticleDOI
Constant, predictable and degenerate directions of the discrete-time riccati equation
Michel Gevers,Thomas Kailath +1 more
TLDR
In this article, the authors introduced the concept of predictable directions along which the solution goes to zero rather than a nonzero constant, and showed how to convert constant directions to predictable directions and how the concept may be extended to time-variant systems.About:
This article is published in Automatica.The article was published on 1973-11-01. It has received 20 citations till now. The article focuses on the topics: Constant (mathematics) & Riccati equation.read more
Citations
More filters
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.
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
A strong controllability and observability in linear multivariable control
TL;DR: In this paper, a particular family of strong controllability and observability properties is shown to be relevant to problems in linear multivariable control, and explicit interrelations are established between these system properties and several approaches to multivariability control: in particular, the abstract vector-space approach of Wonham and Morse, and the explicit algorithm approach of Silverman.
Journal ArticleDOI
Efficient solution of linear systems of equations with recursive structure
TL;DR: In this article, a unified algorithm of order N2 for N×N matrices with recursive structure is presented. And several known algorithms as well as some new ones for Toeplitz type, Hilbert type, and Vandermonde type matrices are given.
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
More filters
Journal ArticleDOI
Estimation using sampled data containing sequentially correlated noise.
A.E. Bryson,L.J. Henrikson +1 more
TL;DR: Improved filtering, prediction, and smoothing procedures for multi-stage linear dynamic systems when the measured quantities are linear combinations of the state variables with additive sequentially correlated noise.
Journal ArticleDOI
Structure and stability of discrete-time optimal systems
D. Rappaport,L. Silverman +1 more
TL;DR: In this paper, a complete stability theory for discrete-time linear systems with respect to general quadratic costs, including singular cases, is presented, and several tests for perfect observability are also given.
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.