Auxiliary particle filtering for structural system identification

The most common choice of importance density is the transition prior density function for particle filter (it is also known as SIR filter, Monte Carlo filter, Bayesian bootstrap filter, condensation, etc.), since it is intuitive and simple to implement, but using the prior as the importance density suffers from drawback of without any knowledge of the observations, and hence the state space is explored without direct knowledge of the observations, maybe lead to poor performance for the particle filtering. To accomplish this, it is necessary to incorporate the current observation in the importance density. In this paper, we propose an auxiliary particle filter (APF) method to identify a non-stationary dynamic system with abrupt change of system parameters. In the APF, the importance density is proposed as a mixture density that depends upon the past state and the most recent observations, and hence which has a good time tracking ability is more suitable for tracking the non-stationary system than the conventional particle filters. The numerical simulations confirm effectiveness of the proposed method for the structural system identification.