This chapter addresses the most general problem formulation of detection in linear systems. Basically, all problem formulations that have been discussed so far are included in the framework considered. The main purpose is to survey multiple model algorithms, and a secondary purpose is to overview and compare the state of the art in different application areas for reducing complexity, where similar algorithms have been developed independently. | Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic 10 Change detection based on multiple models . . Examples of . On-line . General . Pruning . Merging . A literature . Off-line . The EM . MCMC . Local pruning in blind equalization .395 . . Posterior distribution of the continuous . Unknown noise . Basics This chapter addresses the most general problem formulation of detection in linear systems. Basically all problem formulations that have been discussed so far are included in the framework considered. The main purpose is to survey multiple model algorithms and a secondary purpose is to overview and compare the state of the art in different application areas for reducing complexity where similar algorithms have been developed independently. The goal is to detect abrupt changes in the state space model t i yt Ct 6t t DUit 8t ut et vt GN m i Ji Qi et GN me i M 378 Change detection based on multiple models Here is a discrete parameter representing the mode of the system linearized mode faulty mode etc. and it takes on one of S different values mostly we have the case S 2 . This model incorporates all previously discussed problems in this book and is therefore the most general formulation of the estimation and detection problem. Section gives a number of applications including change detection and segmentation but also model structure selection blind and standard equalization missing data and outliers. The common theme in these examples is that there is an unknown discrete parameter mode in a linear system. One natural strategy for choosing a 5 is the following For each possible J filter
