  In practical nonlinear filtering, the assessment of achievable filtering
performance is important. In this paper, we focus on the problem of efficiently
approximate the posterior Cramer-Rao lower bound (CRLB) in a recursive manner.
By using Gaussian assumptions, two types of approximations for calculating the
CRLB are proposed: An exact model using the state estimate as well as a
Taylor-series-expanded model using both of the state estimate and its error
covariance, are derived. Moreover, the difference between the two approximated
CRLBs is also formulated analytically. By employing the particle filter (PF)
and the unscented Kalman filter (UKF) to compute, simulation results reveal
that the approximated CRLB using mean-covariance-based model outperforms that
using the mean-based exact model. It is also shown that the theoretical
difference between the estimated CRLBs can be improved through an improved
filtering method.
