2-17] VELOCITY AND HEADING ESTIMATES 87 



velocity will be the difference of the extreme measurements divided by the 

 total time, ni^c, where n is the number of scans and 4c is the scan time. The 

 estimated direction is simply that determined by the two extreme measure- 

 ments. The velocity and heading errors are expressed in terms of the 

 parallel and normal components of the relative position errors. Thus 



(2-13) 



'^^ = ^7^ = — (2-14) 



where F = true velocity of object being tracked. 



For example, assume that position measurements are made on an 800-fps 

 target 75 n.mi. from the AEW aircraft. This range represents a likely value 

 of the maximum range at which accurate tracking will be required for the 

 generation of vectoring information as explained in Paragraph 2-13. 



With the assumed parameters of the provisional AEW system, the total 

 position error of a single measurement was derived to be Equation 2-8: 



ar = 2.09 n.mi. = 2 n.mi. (2-15) 



Thus, the standard deviations of the two components of the relative 

 error between two measurements are from Equations 2-11 and 2-12: 



ap.Po - 2 n.mi. (rms) = 12,000 ft (rms) (2-16) 



(^NiNi = 2 n.mi. (rms) = 12,000 ft (rms). (2-17) 



Thus the rms errors in the estimated velocity and heading are calculated 

 by Equations 2-13 and 2-14 to be 



av = 12,000/(6) (10) = 200 fps (rms) (2-18) 



cT^ = 12,000/(800) (6) (10) = 0.25 rad = 14.5° (rms). (2-19) 



Accordingly, we see that the accuracy of the velocity and heading 

 estimates depends upon the following factors: 



1. Accuracy of each position measurement 



2. Number of position measurements used for estimates of velocity 

 and heading 



3. Elapsed time between position measurements 



4. Velocity of object being tracked 



In addition, accelerations of the object being tracked during the time 

 interval, ntsc, also give rise to additional errors in the position and velocity 

 estimates. 



