Identification of nonlinear state-space models using joint state particle smoothing

On the basis of a previous expectation maximization (EM) algorithm, this paper applies the particle Markov chain Monte Carlo (MCMC) technique to estimate nonlinear state-space models (SSMs). The smoothed simultaneous particles for joint states are generated by importance resampling (IR) and are directly used to compute a log-likelihood function and its Jacobian vector and Hessian matrix. As a result, a relatively less computational load can thus be obtained, which is crucial to practical applications of the particle MCMC. In addition, the SSM parameters can be recursively iterated by the more efficient Newton method, in which an optimal step length for parameter update in each iteration is optimized by a 1-D search method. This presented identification method has a good global parameter convergence in case iteration parameters are initialized from quite large intervals of their respective true values. Finally, a numerical simulation for identification of a classical SSM is used to show the effectiveness of the studied identification method.