Advertisement

Classical Approach

  • R. S. Bucy
Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)

Abstract

The following will illustrate the classical Wiener approach to a discrete filtering problem followed by the Riccati equation approach in a later chapter. The development here follows [29]; note that in all that follows, t takes on integer values, and t0 = - ∞:
$$ \begin{gathered} {{x}_{{n + 1}}} = \lambda {{x}_{n}} + {{u}_{n}},\quad \left| \lambda \right| < 1 \hfill \\ {{z}_{n}} = {{x}_{n}} + {{v}_{n}},\quad E{{v}_{i}}{{v}_{j}} = {{\delta }_{{ij}}}r. \hfill \\ \end{gathered} $$
$$ \begin{gathered} E\left\{ {z(t + \tau )z'(t)} \right\} = o(\tau ) = m{{\lambda }^{{|\tau |}}} + r \hfill \\ E\left\{ {x(t + \tau )z'(t)} \right\} = c(\tau ) = m{{\lambda }^{{|\tau |}}} \hfill \\ E\{ x(t + \tau )x'(t)\} = s(\tau ) = m{{\lambda }^{{|\tau |}}} \hfill \\ \end{gathered} $$

Keywords

Classical Approach Riccati Equation Normed Linear Space Output Sequence Negative Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • R. S. Bucy
    • 1
  1. 1.Department of Aerospace EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations