1 / 12

# Tracking of Time-Varying Systems - PowerPoint PPT Presentation

Tracking of Time-Varying Systems. Adviser: Dr. Yung-An Kao Student: Chin-Chuan Chang. Outline. Introduction Markov Model for System Identification Degree of Nonstationary Criteria for tracking assessment Mean-Square Deviation Misadjustment. Introduction.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Tracking of Time-Varying Systems' - jacoba

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Tracking of Time-Varying Systems

Student: Chin-Chuan Chang

• Introduction

• Markov Model for System Identification

• Degree of Nonstationary

• Criteria for tracking assessment

• Mean-Square Deviation

• In previous study, we considered the average behavior of standard LMS and RLS algorithm operating in a stationary environment.

• we try to examine the operation of these two filter algorithms in a nonstationary environment, for which the optimum Wiener solution takes on a time varying form.

• we will discuss to evaluate the tracking performances of the stand LMS and RLS algorithm operating in a nonstationary environment.

• An environment may become nonstationary in practice in one of two ways:

• The frame of reference provided by the desired response may be time varying. EX: system identification

• The stochastic process supplying the tap inputs of the adaptive filter is nonstationary. EX: equalize a time varying channel.

• First-order Markov process.

• is noise vector, assumed to be zero mean and correlation matrix

• The value of parameter a is very close to unity

• Multiple regression

• Where ν(n) is white noise, zero mean and variance σ2

• In order to provide a clear definition of the concept of “slow” and “fast” statistical variations of the model, it define (Macchi, 1995)

• It may be rewritten as

• Hence, we may reformulate the degree of nonstationary to

• The degree of nonstationary, , bears a useful relation to the misadjustment of adaptive filter.

• With the state of unknown dynamical system denoted by , and with the tap-weight vector of the adaptive transversal filter denoted by .

• We formally define the tap-error vector as

• On the basis of , we may go on to define two figure of merit for assessing the tracking capability of an adaptive filter

• Mean-Square Deviation

• MSD can defined by

• The tap-weight error may be expressed as

• Weight vector noise:

• Weight vector lag:

• By ,we may express MSD as

• Estimation variance defined by

• Lag variancedefined by

• Another commonly used figure of merit for assessing the tracking capability of adaptive filter is misadjustment

• is called the noise misadjustment

• is called the lag misadjustment