Bayesian Estimation and Tracking: A Practical Guide

13.2 Sigma Point Kalman Filters

In Chapter 8, we presented a method for replacing the Jacobian and Hessian matrices with their central finite difference approximations resulting in several versions of the FDKF. The covariance prediction equations for the standard FDKF, given by (8.41), (8.43), and (8.47), differed in form from those of the remaining sigma point methods. In addition, the modified version of the FDKF covariance prediction equations, (8.49), (8.50), and (8.51), were shown to be identically to those of the UKF. For these reasons, the FDKF will not be included in our summary of the sigma point Kalman filters.

The sigma point Kalman filters, UKF, SSKF, and GHKF, as well as the MCKF, share a similar structure so that all follow the common process flow shown in Figure 13.3, but differ in and . The values for and for each of the filters are presented in Tables 13.1 and 13.2, respectively. It is relatively easy to write a general subroutine for the sigma point Kalman filter, based on the process flow shown in Figure 13.3, that calls a second subroutine which selects the appropriate ...