Clustering algorithms for Bayesian fault detection in linear systems

The authors study sensor failure in noise-perturbed discrete-time linear systems represented by the usual state space model Kalman filtering. The Bayesian approach to failure detection is used. The best estimates are obtained from the outputs of a linearly growing bank of Kalman filters (KFs), giving conditional distributions which are Gaussian mixtures. A method originally introduced by D.J. Salmond (1989, 1990) for dealing with clutter in target tracking problems is used here for combining components of this mixture in a way which causes minimum distortion. By using this, an approximate algorithm can be derived, which uses no more than a fixed number of KFs. The algorithm is straightforward to implement and demonstrated excellent performance