Online Estimation of the Approximate Posterior Cramer-Rao Lower Bound for Discrete-Time Nonlinear Filtering

Abstract

Although it is difficult to assess the achievable performance of nonlinear tracking applications, it nevertheless remains extremely important to do so. This paper illustrates how the mean and covariance of the estimated online state can be used to recursively calculate an approximate posterior Cramer-Rao lower bound (CRLB). Most CRLB implementations require the true state, but this is impractical except for appropriately designed experiments or simulations where the exact value of the state is given as prior knowledge. The performance of the approximate posterior CRLB (PCRLB) used in conjunction with the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) for online state estimation are investigated. To test the validity of the proposed method, it was applied to the problem of tracking a ballistic object on reentry. Simulation results confirm the theory and reveal that the proposed approximate PCRLB is sufficiently accurate and that the PCRLB approximations obtained using different state filters are in general very close to each other.