Abstract
In this technical brief, the problem of the estimation of a remote signal generated by a discrete-time dynamical system with periodic coefficients subject to multiplicative and additive white noise perturbations is investigated. To measure the quality of the estimation achieved by an admissible filter, we introduced a performance criterion described by the Cesaro limit of the mean square of the deviation between the estimated signal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zF</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> ) and the remote signal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> ). The dimension of the state space of the admissible filters is not prefixed. The state-space representation of the optimal filter is constructed based on the unique periodic solution of a discrete-time linear equation together with the stabilizing solution of a suitable discrete-time Riccati equation with periodic coefficients.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
