TAILIEUCHUNG - Adaptive lọc và phát hiện thay đổi P4

This chapter surveys off-line formulations of single and multiple change point estimation . Although the problem formulation yields algorithms that process data , many important algorithms have natural on-line implementations and recursive approximations . This chapter is basically a projection of the more general results in Chapter 7 to the case of signal estimation . There are, however. some dedicated algorithms for estimating one change point offline that apply to the current case of a scalar signal model . In the literature of mathematical statistics. this area is known as change point estimation | Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic 4 Off-line approaches . Basics. 89 . Segmentation criteria. 91 . ML change time sequence estimation. 91 . Information based segmentation . 92 . On-line local search for optimum. 94 . Local tree search. 94 . A simulation example. 95 . Off-line global search for optimum. 98 . Local minima. 98 . An MCMC approach. 101 . Change point . The Bayesian approach. 103 . The maximum likelihood approach. 104 . A non-parametric approach. 104 . Applications .106 . Photon emissions. 106 . Altitude sensor quality. 107 . Rat EEG. 108 . Basics This chapter surveys off-line formulations of single and multiple change point estimation. Although the problem formulation yields algorithms that process data batch-wise many important algorithms have natural on-line implementations and recursive approximations. This chapter is basically a projection of the more general results in Chapter 7 to the case of signal estimation. There are however some dedicated algorithms for estimating one change point offline that apply to the current case of a scalar signal model. In the literature of mathematical statistics this area is known as change point estimation. In segmentation the goal is to find a sequence kn ki k2 kn of time indices where both the number n and the locations ki are unknown such that 90 Off-line approaches the signal can be accurately described as piecewise constant . yt 0 z et when ki-i t ki is a good description of the observed signal yt. The noise variance will be denoted E e R. The standard assumption is that et E N 0 R but there are other possibilities. Equation will be the signal model used throughout this chapter but it should be noted that an important extension to the case where the parameter is slowly varying within each .

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