Cart (Loading....) | Create Account
Close category search window
 

Modelling and Estimation for Finite State Reciprocal Processes

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Carravetta, F. ; Ist. di Analisi dei Sist. ed Inf. “Antonio Ruberti”, Rome, Italy ; White, L.B.

A reciprocal equation is a kind of descriptor linear discrete-index stochastic system which is well known be satisfied (pathwise) by all Gaussian reciprocal processes. From a system-theoretic point of view, it is a kind of `noncausal' linear system, in the sense that the solution of it cannot be determined by only an `initial' condition, indeed requiring the `terminal' state as well, besides all the `input' function between initial and terminal states. Also, nice properties are known of a reciprocal equation, such as the equivalence of it with a couple of ordinary (causal) dynamic systems running in opposite directions. For these reasons, here we assume a reciprocal equation as the target of stochastic realization for the class of finite state reciprocal processes, also named reciprocal chains. The central result of the present paper is showing that any canonical reciprocal chain, i.e. valued in the canonical base of REALRN , N being the cardinality of the set of chain's states, satisfies (pathwise) a reciprocal equation in a N2 dimensional canonical variable, or in other word a quadratic reciprocal equation, named `Augmented state reciprocal model' (ASRM). Also, for a partially observed reciprocal chain, a linear-optimal smoother is derived. All the results here presented are based upon the idea that a reciprocal chain is a `combination' of Markov bridges, to this purpose other forms, besides the ASRM, are presented in order to make clear the meaning of this `combination', as well as to prove that the linear smoother can be actually implemented as N smoothers all operating independently on each Markov bridge component.

Published in:

Automatic Control, IEEE Transactions on  (Volume:57 ,  Issue: 9 )

Date of Publication:

Sept. 2012

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.