The behavior of model probability in multiple model algorithms

The behavior of the model probability is closely related to the performance of multiple model algorithm. A clear view about the behavior of model probability will benefit the performance analysis and the model set design for multiple model algorithm. We investigate the behavior of the model probability of multiple model algorithm for parameter estimation and filtering. It turns out that the Kullback-Leibler information between the true model and the model in the model set plays an important role to determine the evolution of model probability. Most importantly, we draw a connection between multiple model algorithm and the comparison of multiple estimation algorithms through the view of multiple hypotheses. The behavior of the model probability suggests a feasible way to combine multiple algorithms to obtain a new method of better performance. An illustrative example is also presented.