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## ELIMINATING THE INITIAL STATE FOR THE GENERALIZED LIKELIHOOD RATIO TEST

Citations: | 1 - 1 self |

### Citations

760 |
Matrix Analysis and Applied Linear Algebra
- Meyer
- 2001
(Show Context)
Citation Context ...The basis for x in the measurement space is O, so estimating the term Ox can be done as Ox̂ = O(S−1/2O)†S−1/2︸ ︷︷ ︸ ,P Z, (13) where P is an oblique projection onto R(O) along R (S1/2(S−1/2O)⊥), see (=-=Meyer 2000-=-, p.387). 3.3 Smoothed Estimate The initial state of the window can be known from prior information or be estimated with a Kalman filter from old data. The information about the initial state is assum... |

389 |
Fundamentals of statistical signal processing : detection theory, vol
- Kay
- 1998
(Show Context)
Citation Context ... is necessary to compute their distributions. While having Gaussian noise, the test statistics will be Chi-Square distributed variables. For a thorough review of statistics in signal processing, see (=-=Kay 1998-=-). The normalized residual is distributed as r̄ ∼ N(W̄T⋆ H̄θθ, I), where ⋆ is 1 or 2 (method) and θ = 0 under the null hypothesis (17a). The test statistic is then distributed as the non-central Chi-S... |

369 |
Fault Detection and Diagnosis in Engineering Systems.
- Gertler
- 1998
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Citation Context ...ing a projection that removes the influence of initial conditions as done in the classical parity space approach (Basseville and Nikiforov 1993, Chow and Willsky 1984, Ding et al. 1999, Gertler 1997, =-=Gertler 1998-=-). • Using prior knowledge of the initial state obtained with a causal Kalman filter on past data preceding the data batch under consideration (Willsky and Jones 1976). This gives a correct state esti... |

258 | Adaptive Filtering and Change Detection.
- Gustafsson
- 2000
(Show Context)
Citation Context ...ed change detection is to first compute a residual from a batch of data based on the model, and then check if this residual is significantly different from zero, see (Basseville and Nikiforov 1993), (=-=Gustafsson 2001-=-, Chapters 6, 11). For state space models as considered here, the initial state affects the residual significantly, and its influence has to be removed. The unknown initial state can be approached in ... |

176 |
Chebyshev polynomials
- Rivlin
- 1974
(Show Context)
Citation Context ...is used, so the fault can be parameterized as F = ΦT θ, (6) where the columns of ΦT = (ΦT1 , ΦT2 , . . . ) are orthogonal vectors generated by a Chebyshev polynomial, see (Abramowitz and Stegun 1965, =-=Rivlin 1974-=-), and θ contains the parameters. The regressors obtained has the form of a constant, linear, quadratic term and so on. This means that a step fault can be described using a one dimensional basis and ... |

174 |
Analytical Redundancy and the De- sign of Robust Failure Detection Systems
- Chow, Willsky
- 1984
(Show Context)
Citation Context ...ial state can be approached in the following ways: • Using a projection that removes the influence of initial conditions as done in the classical parity space approach (Basseville and Nikiforov 1993, =-=Chow and Willsky 1984-=-, Ding et al. 1999, Gertler 1997, Gertler 1998). • Using prior knowledge of the initial state obtained with a causal Kalman filter on past data preceding the data batch under consideration (Willsky an... |

50 |
Fault Detection and Isolation using Parity Relations,”
- Gertler
- 1997
(Show Context)
Citation Context ...ing ways: • Using a projection that removes the influence of initial conditions as done in the classical parity space approach (Basseville and Nikiforov 1993, Chow and Willsky 1984, Ding et al. 1999, =-=Gertler 1997-=-, Gertler 1998). • Using prior knowledge of the initial state obtained with a causal Kalman filter on past data preceding the data batch under consideration (Willsky and Jones 1976). This gives a corr... |

37 |
Detection of Abrupt Changes: Theory and Application. Information and System Science Series. Englewood Cliffs.
- Basseville, Nikiforov
- 1993
(Show Context)
Citation Context ... A standard approach to model-based change detection is to first compute a residual from a batch of data based on the model, and then check if this residual is significantly different from zero, see (=-=Basseville and Nikiforov 1993-=-), (Gustafsson 2001, Chapters 6, 11). For state space models as considered here, the initial state affects the residual significantly, and its influence has to be removed. The unknown initial state ca... |

21 |
A characterization of parity space and its application to robust fault detection,”
- Ding, Guo, et al.
- 1999
(Show Context)
Citation Context ...ched in the following ways: • Using a projection that removes the influence of initial conditions as done in the classical parity space approach (Basseville and Nikiforov 1993, Chow and Willsky 1984, =-=Ding et al. 1999-=-, Gertler 1997, Gertler 1998). • Using prior knowledge of the initial state obtained with a causal Kalman filter on past data preceding the data batch under consideration (Willsky and Jones 1976). Thi... |