Particle filter-based algorithm of simultaneous output and parameter estimation for output nonlinear systems under low measurement rate constraints

In applications of system identification where the inputs and outputs are scheduled at different sampling rates, the traditional gradient-based iterative (GI) identification scheme can be applied to approximate the unknown outputs from which the unknown model parameters can be estimated. A limitation of the GI method lies in the fact that the measured outputs are not employed effectively to adjust/improve the missing output estimates. To address this, an improved GI method using the particle filters is designed to jointly estimate the outputs and parameters of output nonlinear systems from the dual-rate data. The key idea is to use a bank of weighted particles to represent the posterior probability density function of the unknown outputs. The kernel density estimation method is then developed to update the weights of these particles at each iteration. The negative gradient search principle and the parameter separation technique are subsequently combined to obtain the required parameter estimation of the plant model. A numerical example including comparisons with the existing algorithms is reported to demonstrate the effectiveness and limitations of the proposed methodology.