The basic assumption in this part. signal estimationis. that them easurements gt consist of a deterministic component Ot ~ the signal ~ and additive white noise et. yt = Ot + et . Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright © 2000 John Wiley & Sons, Ltd ISBNs: 0-471-49287-6 (Hardback); 0-470-84161-3 (Electronic) 58 On-line amroaches For change detection, this will be labeled as a change in the mean model. The task of determining Bt from yt will be referred to as estimation, and change detection or alarming is the task of finding abrupt, or rapid, changes in dt, which is assumed to start at time L, referred to as the change. | Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic Part II Signal 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 3 On-line approaches . Introduction. 57 . Filtering approaches . 59 . Summary of least squares approaches. 59 . Recursive least squares. 60 . The least squares over sliding window. 61 . Least mean square. 61 . The Kalman filter. 62 . Stopping rules and the CUSUM test. 63 . Distance measures. 64 . One-sided tests. 65 . Two-sided tests. 67 . The CUSUM adaptive filter. 67 . Likelihood based change detection. 70 . Likelihood theory. 70 . ML estimation of nuisance parameters. 71 . ML estimation of a single change time. 73 . Likelihood ratio ideas. 75 . Model validation based on sliding windows . 77 . Applications . 81 . Fuel monitoring. 81 . Paper refinery. 82 . Derivations. 84 . Marginalization of likelihoods. 84 . Likelihood ratio approaches. 86 . Introduction The basic assumption in this part signal estimation is that the measurements yt consist of a deterministic component Ot - the signal - and additive white noise Ct yt et- 3-1 58 On-line approaches For change detection this will be labeled as a change in the mean model. The task of determining from yt will be referred to as estimation and change detection or alarming is the task of finding abrupt or rapid changes in 0t which is assumed to start at time k referred to as the change time. Surveillance comprises all these aspects and a typical application is to monitor levels flows and so on in industrial processes and alarm for abnormal values. The basic assumptions about model in change detection are The deterministic component Of undergoes an abrupt change at time t k. Once this change is
