16.6 Approximations to the SIS Auxiliary Particle Filter
An alternate approach to the SIS particle filter has been proposed that is similar to the APF presented above. Suppose the posterior density p(xn|z1:n) and the optimal importance density q() are approximated by Gaussian densities. That is, the posterior density is approximated as
and the proposal distribution is approximated by a Gaussian proposal distribution for each particle
That is, at time tn−1, one uses one of the Gaussian Kalman filter variations from Part II of this book, along with the new observation, to compute the mean and covariance of the importance distribution for each particle. Then one can sample the i th particle from this distribution.
16.6.1 The Extended Kalman Particle Filter
In the extended Kalman particle filter (EKPF), first proposed by Merwe et al. , both the nonlinear dynamic and observation equations are expanded in Taylor series and used in an EKF to generate the first two moments for the i th particle used in (16.67) to defined the Gaussian proposal distribution. Then, the i th ...