A X E L B Y • C. 



CHAPTER 9 



AUTOMATIC TRACKING CIRCUITS* 



9-1 GENERAL PROBLEMS OF AUTOMATIC TRACKING 



The general tracking problem has already been mentioned as one of 

 prediction. It is desired to know not only where a target is but also where 

 it will be in the near future. If this can be determined, the target can be 

 intercepted and destroyed. Mathematically, this is not a particularly 

 difficult problem. If the past and present motion of the target is known, 

 its course can be projected into future time. Theoretically, the equations 

 of target motion may be formulated rather easily, and they can be solved 

 rapidly with an analogue or digital computer to determine the target 

 position at any time. Paragraphs 1-4 and 2-7 illustrated some of the basic 

 principles. 



Practically, however, the information needed to formulate the equations 

 must be obtained from measurements made with physical equipment at 

 a considerable distance from the target. Unfortunately, there are no 

 perfect measuring devices and the true signal information cannot be found 

 exactly. Actually, it is obtained as an electrical signal veiled with noise 

 and shrouded with the inaccuracies of physical equipment. The true signal 

 — the desired information about the target — can be completely extracted 

 from the noise with appropriate filtering only if infinite time is used to 

 obtain it. Of course, this would be of no use in predicting a future target 

 position because, in actual time, the target would have passed over the 

 course and the real time errors would be infinite. 



Therefore there must be a compromise between the length of time that 

 the signal can be filtered and the accuracy of the real time prediction that 

 can be obtained. As shown by Wiener,^ there is an optimum filter for any 

 specified signal, noise, and prediction time which yields the required signal 

 with an error that is the minimum theoretically obtainable with perfect 

 physical equipment. 



This noise problem is much more severe if the target is an enemy target 

 because, through countermeasure methods, the target will generate noise 



*Secs. 9-1 through 9-9 are by G. S. Axelby. Sees. 9-10 through 9-14 are by C. F. White. 

 IN. Wiener, Extrapolation, Interpolation and Smoothing oj Stationary Time Devices, John 

 Wiley & Sons, Inc., New York, 1949. (Published in a classified report in 1942.) 



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