Design and analyze a radar tracking algorithm. Consider a surveillance radar that measures range and bearing and scans with a period of 4 s. The radar measures range with standard deviation of 25 m and bearing with standard deviation of 0.02 degree. Targets that perform maneuvers with acceleration as much as 30 m/s2 are expected. Use the design techniques of Section 19.2.2.1 to find process noise covariances for tracking in range and cross-range. Make a small angle assumption to approximate the cross-range errors in Cartesian space. The process noise covariance for tracking in cross-range will be a function of the range of the target. The radar is to track targets at ranges from 5 km to 400 km. (a) Recommend a single process noise covariance tracking targets at all ranges in the field of regard. (b) Recommend a range dependent function for selecting the process noise covariance for both coordinates for tracking. (c) Develop a formulation of the process noise covariance that accounts for a different process noise variances in the range and cross range coordinates. It will be a function of the bearing of the target. (d) Assume target maneuvers are restricted to 30 m/s2 perpendicular to the velocity vector of the target and 10 m/s2 along the velocity vector. Extend the results of (c) to include these limitations on the target acceleration in the selection of the process noise covariance. (e) Consider a target starting at (250, 250) km and moving with a velocity of (150, 150) m/s. After 100 s, the target maneuvers with acceleration of (7, 7) for 15 s. At 200 s, the target starts maneuvering with acceleration of (20,20) m/s2 and the acceleration is orthogonal to the velocity for 16 s. At 300 s, the target starts maneuvering with acceleration of 24 m/s2 orthogonal to the velocity for a right turn for 16 s. At 400 s, the target slows down at 10 m/s2 for 15 s. The scenario ends at 500 s. Simulate the target and radar and compare the performances of the four track filter designs with 200 Monte Carlo runs. (f) Implement an IMM estimator with two NCV filters and compare its performance with that of the NCV filters. Use the NCV filter formulation of (d) and use the process noise covariance the minimizes the MMSE as the maneuver model.