On a class of quadratic tests for detection of abrupt changes in signals and systems

Abstract

We address the problem of detecting changes (faults) in systems and signals. We establish new results on a class of quadratic change detection algorithms which are based on the /spl chi//sup 2/ statistic (/spl chi//sup 2/-CUSUM, /spl chi//sup 2/-GLR and /spl chi//sup 2/-FSS algorithms). We compare optimal sequential and nonsequential (fixed-size sample) strategies in the problem of abrupt change detection in multivariate Gaussian signals. However, the optimal sequential algorithms lead to a burdensome number of arithmetical operations. In order to reduce the computational burden we examine the recursive versions of the /spl chi//sup 2/-CUSUM and /spl chi//sup 2/-GLR algorithms. It is shown that these recursive algorithms have statistical performances which are similar to the original algorithms. We also propose a very simple heuristic solution to the case of unknown magnitude of change. This solution is a competitor for the window-limited GLR algorithm.