Defect Detection and Localization of Nonlinear System Based on Particle Filter with an Adaptive Parametric Model

Algorithm 1

The update of GMM in the likelihood by -means approximation.

Input: ,

Output:

Step  1. Update weights of the Gaussian items by ,

where is the learning rate, is 1 for the model matched by and 0 for the

remaining models. If none of the distributions matches , the least probable distribution

is replaced with a distribution with as its mean, a high variance, and low weight.

Step  2. Update parameters of the Gaussian item: satisfies , compute

   ,

with .