KNN particle filters for dynamic hybrid Bayesian networks

In state estimation of dynamic systems, sequential Monte Carlo methods, also known as particle filters, have been introduced to deal with practical problems of nonlinear, non-Gaussian situations. They allow us to treat any type of probability distribution, nonlinearity and non-stationarity although they usually suffer major drawbacks of sample degeneracy and inefficiency in high-dimensional cases. In this paper, we show how we can exploit the structure of partially dynamic hybrid Bayesian networks (PD-HBN) to reduce "sample depletion" and increase the efficiency of particle filtering, by combining the well-known KNN majority voting strategy and the concept of evolution algorithm. Essentially, the novel method re-samples part of the variables and randomly combines them with the existing samples of other variables to produce new particles. As new observations become available, the algorithm allows the particles to incorporate the latest information so that the top K fittest particles associated with a proposed objective rule will be kept for re-sampling. With simulations, we show that this new approach has a superior estimation/classification performance compared to other related algorithms.