Optimal statistical fault detection with nuisance parameters

Fault detection is addressed within a statistical framework. The goal of this paper is to propose an optimal statistical tool to detect a fault in a linear stochastic (dynamical) system with uncertainties (nuisance parameters or nuisance faults). It is supposed that the nuisance parameters are unknown but non-random; practically, this means that the nuisance can be intentionally chosen to maximize its negative impact on the monitored system (for instance, to mask a fault). Examples of ground station based and receiver autonomous Global Positioning System (GPS) integrity monitoring illustrate the proposed method.

[1]  E. Lehmann Testing Statistical Hypotheses , 1960 .

[2]  Jason L. Speyer,et al.  Optimal stochastic fault detection filter , 2003, Autom..

[3]  Janos Gertler,et al.  Fault detection and diagnosis in engineering systems , 1998 .

[4]  A. Wald Tests of statistical hypotheses concerning several parameters when the number of observations is large , 1943 .

[5]  George V. Moustakides,et al.  Optimum robust detection of changes in the AR part of a multivariable ARMA process , 1987 .

[6]  Paul M. Frank,et al.  Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results , 1990, Autom..

[7]  Richard A. Brown,et al.  Introduction to random signals and applied kalman filtering (3rd ed , 2012 .

[8]  Michèle Basseville,et al.  FAULT ISOLATION FOR DIAGNOSIS: NUISANCE REJECTION AND MULTIPLE HYPOTHESES TESTING , 2002 .

[9]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[10]  Louis L. Scharf,et al.  Matched subspace detectors , 1994, IEEE Trans. Signal Process..

[11]  R. Patton,et al.  A Review of Parity Space Approaches to Fault Diagnosis , 1991 .

[12]  Michèle Basseville,et al.  Information criteria for residual generation and fault detection and isolation , 1997, Autom..

[13]  Karl-Rudolf Koch,et al.  Parameter estimation and hypothesis testing in linear models , 1988 .

[14]  M. Pratt,et al.  A General RAIM Algorithm Based on Receiver Clock , 1995 .