Particle Filter-Weight Estimation and Dual Particle Filter

When the clean state is not available, a dual estimation approach is required. A dual algorithm, dual particle filter, for nonlinear state and parameters estimation is presented. Dual filter is combined with particle filter for nonlinear situation. Two separate particle filters run con-currently: one for signal estimation which is called particle state filter, and another for model estimation which is called particle weight filter. The signal filter uses the current estimate of the system parameters for signal particle filtering, and the new estimate of signal with observations are used for parameters estimation. Sequential approaches instead of iterative approaches are chosen with respecting on line processing. And particle filter is more appropriate for rough nonlinear problems compared with extended Kalman filter. Methods are compared on several simulations of nonlinear noisy time series.