Sequential Detection/Isolation of Abrupt Changes With Some Applications
The problem of change diagnosis (detection and isolation) in random signals and dynamical systems is addressed in the presentation. Statistical decision tools for detecting and isolating abrupt changes in the properties of random signals and dynamical systems have numerous applications, from on-line fault diagnosis in complex technical systems to detection of signals with unknown arrival time in geophysics, radar and sonar signal processing.
We start with the sequential change detection problem (binary hypothesis case). The main goal of this first part is to describe the CUSUM test and its statistical properties for simple and composite hypotheses. The second part is devoted to the multiple hypothesis change detection and isolation problem. Here, new criteria of optimality are introduced and the lower bounds in a certain class of sequential tests are established. The main goal of this second part is to generalize the CUSUM test to the multiple hypothesis case and to describe its statistical properties.
Several statistical parametric models will be considered. Special attention will be paid to the rejection of nuisance parameters. Distinguishing two subsets of components of the parameter vector, the parameters of interest and the nuisance parameters, may be necessary because some parameters are of no interest for monitoring but they are necessary to build the statistical model.
Several applications of the theoretical results are discussed in the third part of the presentation. Navigation systems integrity monitoring outlines the importance of online change detection and isolation problem with nuisance parameters and presents some new unexpected issues in the case of safety-critical applications. Another example is the sequential detection and isolation of unusual and significant changes in network origin-destination traffic volumes from simple network management protocol measurements.