Joint estimation of states and transition functions of dynamic systems using cost-reference particle filtering

The recently introduced cost-reference particle filter (CRPF) methodology allows for recursive estimation of unobserved states of dynamic systems without a priori knowledge of probability distributions of the noise in the system. We use CRPFs in problems where we eliminate one more strong assumption about the state space model, the one of knowing the function governing the state evolution. We replace this function by a linearly combined set of basis functions where the linear combination coefficients are unknown. We show how CRPFs can be modified to cope with this scenario and demonstrate their performance for positioning a moving vehicle in a two-dimensional space.