2-21] EVALUATION OF TENTATIVE DESIGN PARAMETERS 99 



the range of required detection. The remaining five would appear as one 

 or two large targets until they reached a range close enough to the AEW 

 radar to be resolved. Tracking can begin on each of the targets indicated 

 by the AEW radar. The average standard deviations of the raid considered 

 as a whole would tend to approach the standard deviations of one track 

 divided by the square root of the number of separate target tracks. 



By the time the targets have closed to 75 n.mi., it is possible to make 

 further refinements in the measurements of target velocities. Two addi- 

 tional 3-minute intervals are available for this purpose. Neglecting the 

 decrease in position error for each interval and considering that the meas- 

 urement made in each interval is independent of the previous measurement, 

 the error can be reduced by the square root of 3 by averaging the three 

 readings taken over a 9-minute period. This process yields an error of 



142 fps error 142 ^ in i . ^o on\ 



<rvT = I . = = —j= = 82 fps = 49 knots. (2-29) 



VNo. of velocity measurements V3 



Smoothing times consistent with this magnitude are allowable for 

 velocity measurements because it is not reasonable to expect large changes 

 in target velocity. 



A somewhat different situation attends the measurement of heading. 

 The target can make heading changes at a maximum rate of 3° per second. 

 Thus, it is not desirable to use long smoothing times for heading informa- 

 tion. In fact, a major problem in the design of the data-processing system 

 is to choose an observation time and smoothing technique for heading 

 information that provide a satisfactory compromise between maneuvering 

 and nonmaneuvering targets. This is a complicated problem which cannot 

 be considered here in detail. However, the basic nature of the problem 

 will be indicated. 



The development so far has considered the very simplest type of heading 

 measurement; the target position is measured at two different times, / and 

 f + ntsc, and the heading is determined by the direction of the straight-line 

 passing through these points (Fig. 2-22). 



At a range of 75 n.mi., with an observation time nisc equal to 60 seconds, 

 this technique gives rise to an error (Equation 2-19) in measured heading 

 equal to 



(2) (6080) (57.3) ., ^o .. .r,. 



""'^ = (800)(60) = ^^-^ ^^-^^^ 



where the constants 6080 and 57.3 have been previously defined. 



Now, let us assume a scan time isc of 6 seconds. The heading of the 

 previous expression was calculated on the basis of information obtained 

 from two scans, which we may relate to each other by calling the first scan 

 number 1, and the second scan, occurring 60 seconds later, number 11. A 



