Bayesian Estimation and Tracking: A Practical Guide

17.2 The Combination Particle Filter

In Figure 17.1, the importance density is not specified. Thus, the GPF is not complete and still requires the specification of an importance density. In Ref. [1], it is suggested that a Gaussian distribution be used as the importance density, that is, let , where and are obtained from the prior density using any of the nonlinear Kalman filters developed in Part II of this book. This approach combines the GPF with one of the nonlinear Kalman filters and is therefore called a generalized Monte Carlo combination particle filter (CPF).

The CPF can be subdivided into two classes, those that use an EKF to generate the importance density and those that use a sigma point Kalman filter. The sigma point Kalman filter class can be further subdivided into the four possible numerical integration Kalman filters, the MCKF, UKF, SSKF, or GHKF. The recursive process flow diagram for the CPF-EKF estimation filter is shown in Figure 17.2 while that of the CPF that uses a sigma point Kalman filter is presented in Figure 17.3. Along the bottom of the figures the Gaussian particle filter structure can be identified and along the right side the nonlinear Kalman filter ...