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Adaptive lọc và phát hiện thay đổi P7

Let us start with considering change detection in linear regressions as an offline problem. which will be referred to as segmentation . The goal is to find a Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright © 2000 John Wiley & Sons, Ltd ISBNs: 0-471-49287-6 (Hardback); 0-470-84161-3 (Electronic) 232 Chanae detection b baanskes df il toenr sequence of time indices kn = (kl, k2, , kn), where both the number n and the locations ki are unknown, such that a linear regression model with piecewise constant parameters,. | Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic 7 Change detection based on filter banks 7.1. Basics.231 7.2. Problem setup.233 7.2.1. The changing regression model.233 7.2.2. Notation.234 7.3. Statistical criteria.234 7.3.1. The MML estimator.234 7.3.2. The a posteriori probabilities.236 7.3.3. On the choice of priors.237 7.4. Information based criteria.240 7.4.1. The MGL estimator.240 7.4.2. MGL with penalty term.241 7.4.3. Relation to MML.242 7.5. On-line local search for optimum.242 7.5.1. Local tree search.243 7.5.2. Design parameters.245 7.6. Off-line global search for optimum.245 7.7. Applications .246 7.7.1. Storing EKG signals.247 7.7.2. Speech segmentation.248 7.7.3. Segmentation of a car s driven path .249 7.A. Two inequalities for likelihoods.252 7.A.I. The first inequality.252 7.A.2. The second inequality.254 7.A.3. The exact pruning algorithm.255 7.B. The posterior probabilities of a jump sequence . 256 7.B.I. Main theorems.256 7.1. Basics Let us start with considering change detection in linear regressions as an offline problem which will be referred to as segmentation. The goal is to find a 232 Change detection based on filter banks sequence of time indices kn Aq k 2 . kn where both the number n and the locations ki are unknown such that a linear regression model with piecewise constant parameters yt cpf 0 i et E et X i Rt when Aq_x t ki 7.1 is a good description of the observed signal yt. In this chapter the measurements may be vector valued and the nominal covariance matrix of the noise is Rt and A z is a possibly unknown scaling which is piecewise constant. One way to guarantee that the best possible solution is found is to consider all possible segmentations kn estimate one linear regression model in each segment and then choose the particular kn that minimizes an optimality criteria kn arg min V kn . n l O ki kn N The .