Posterior Cramér-Rao Lower Bound for Angle-Only Filtering in 3D

In our previous work, we compared the performance of a number of nonlinear filters for the angle-only filtering (AOF) problem in 3D using bearing and elevation measurements from a single maneuvering sensor. These filters used Cartesian coordinates and modified spherical coordinates for the state vector and were based on discrete-time dynamic and measurement models. The target followed a nearly constant velocity motion. In this paper, we compute the posterior Cramer-Rae lower bound (PCRLB) for the problem so that the performance of the nonlinear filters can be judged relative to the best possible performance. Results from Monte Carlo simulations show that as the measurement accuracy decreases, the difference between root mean square position and velocity errors and corresponding PCRLBs increases.