Chapter 7. Change Detection Based on Filter Banks
Published Online: 16 OCT 2001
Copyright © 2000 John Wiley & Sons, Ltd
Adaptive Filtering and Change Detection
How to Cite
Gustafsson, F. (2001) Change Detection Based on Filter Banks, in Adaptive Filtering and Change Detection, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/0470841613.ch7
- Published Online: 16 OCT 2001
Print ISBN: 9780471492870
Online ISBN: 9780470841617
- data segmentation;
- change detection;
- jump Markov model;
- piecewise linear regression model;
- Matlab toolbox;
- signal processing;
- adaptive signal processing;
- adaptive systems;
- fault diagnosis;
- signal detection;
- decision making;
- stochastic processes;
- parameter estimation;
- state estimation;
- stochastic systems;
- time-varying systems;
- discrete time systems;
- sampled data systems;
- communication systems;
- adaptive control
Segmentation is the problem of estimating all change times in a non-stationary time series from a given batch of data. Two types of optimality criteria have been proposed:
Statistical criterion: the maximum likelihood or maximum a posteriori estimate of the change times is studied.
Information based criterion: the information of data in each segment is the sum of squared residuals, and the total information is the sum of these. Here, a penalty term is needed to avoid a degenerated solution. Similar problems have been studied in the context of model structure selection, and from this literature Akaike's AIC and BIC criteria have been proposed for segmentation.
The real challenge in segmentation is to cope with the curse of dimensionality. The number of segmentations increases exponentially in time. Here, several strategies have been proposed:
Numerical searches based on dynamic programming or MCMC techniques.
Recursive local search schemes.
The main part of this chapter is devoted to the second approach, which provides a solution to adaptive filtering, which is an on-line problem.