Cramer-Rao Lower Bound For Single Target Tracking Accuracy With Coordinated Turn Maneuvers Using Range and Bearing Measurements

This paper provides a Cramer-Rao lower bound (CRLB) on range, cross range, speed and heading tracking accuracy for a class of maneuvering target trajectories using nonlinear noisy range and bearing measurements when both the target and the sensor platform are moving. It is assumed that there are no missing or false measurements. This analysis is valid only for single target two-dimensional tracking scenarios. The target trajectory is assumed to have a constant velocity with a single coordinated turn maneuver. Hence, the target trajectory has three legs where the first and last ones are straight and level trajectories. Therefore, these two legs are characterised by their initial target position and velocity. The second trajectory leg is assumed to be a constant velocity-coordinated turn (CV-CT) maneuver where maneuver start time, maneuver duration and turn rate are the unknown parameters. Hence, the overall target trajectory is characterised by the sufficient statistics which are the initial target position and velocity in the horizontal (x, y) plane, maneuver start time, maneuver duration and maneuver turn rate. First, the CRLB on the accuracy of the sufficient statistics is obtained by deriving Fisher information matrices (FIMs) from partial derivatives of range and bearing measurements with respect to sufficient statistics for different target trajectory legs. Then, the CRLB is derived for the tracking accuracy on parameters of interest, namely, target range, cross range, speed and heading by taking partial derivatives of these parameters with respect to the sufficient statistics. A single target tracking example is provided where the CRLB on tracking accuracy is illustrated with different radar measurement sampling periods. This example also provides the Cramer-Rao lower bound on estimation error on other parameters of interest, namely the maneuver start time and duration.