A New Numerical Approximation CDD Method Based for Particle Filtering Algorithm Research and Its Applications to TA System

In order to improve the estimation precise of particle filtering algorithm in the state estimation problems of transfer alignment (TA) nonlinear systems for large initial misalignment angles, based on the UKPF theory, this paper developed the CDDPF algorithm which made use of the CDDF algorithm as the proposal distribution. The CDDF Algorithm based on Stirling polynomial interpolation formula is used to generate local linearization approximations to nonlinear system equations and/or measurement equations which can be easy to implement, and whose Cholesky factorization of prediction error variance matrix is employed to guarantee the positive definiteness of the estimation error variance matrix, and the higher-order truncation errors of local linearization are decreased to some degree. The CDDPF algorithm generates a set of particles which can integrate the latest observation information into system state transition density so that expands the overlap region between proposal distribution and posterior density distribution of system states, and can effectively improve the approximation precision of proposal distribution to the system state posterior probabilistic distribution. Finally the simulation experiments on TA nonlinear system for large misalignment angles are implemented with the new CDDPF and UKPF algorithms. The simulation results indicate that, comparing to UKPF algorithm, the CDDPF algorithm has better numerical stability, and its estimation precision is improved obviously.