A sampling-based approach to nonparametric dynamic system identification and estimation

We propose a probabilistic framework for nonparametric identification and estimation of dynamic systems. Under the parametric paradigm, a model of the system and a set of observations are given and the parameter space of the model is searched to optimize an objective function. However, if we are uncertain about the model, the parametric approach can easily overfit data and lead to risky decisions. In nonparametric estimation, the model uncertainty is introduced in a systematic manner to find both the model and associated parameters of the system. In this paper, we consider a dynamic system consisting of a varying number of subsystems with noisy observations. The objective is to identify the subsystems at each time step and estimate the associated parameters such that the observations are explained the best. We develop an efficient algorithm based on Markov chain Monte Carlo methods and apply our approach to multiple target tracking problems. We address the issues with the subsystem initiation and termination and initial state estimation. In simulation our algorithm shows excellent performance for tracking a varying number of maneuvering targets with nonlinear dynamics. In some cases our algorithm outperforms any linear filtering algorithm with perfect associations.