40 



ELEMENTS OF AIRBORNE RADAR SYSTEMS DESIGN PROBLEM 



L tcAL 



MEASURED LENGTH 



Fig. 1-28 Measurement Errors Obtained in Determining Length. 



instrument measuring the same distance might give rise to a distribution 

 of values about some mean value as shown in Fig. 1-28. If these measure- 

 ments are compared with a standard, we see that two sources of error 

 exist: (1) a calibration or bias error, and (2) a random error. The calibra- 

 tion error — so long as it remains fixed or if its variations can be predicted 

 — is obviously a correctable source of inaccuracy. However, the random 

 error is just that — random. Any given measurement may be in error by 

 an amount determined by the character — usually Gaussian — of the 

 randomness. 



Measurement uncertainties are a vitally important problem in any 

 weapons system analysis. Unlike many engineering problems, where 

 measurements may be made with whatever degree of preciseness is neces- 

 sary to render inconsequential the measurement error, weapons systems 

 habitually are required to work with measurement uncertainties that 

 exercise a profound and usually decisive influence upon their performance. 



Example 2 — Dice Throwing. The cast of a die is an example of a process 

 that is, theoretically, completely predictable; however, because of the 

 extreme complexity of the mechanisms that govern its behavior, the 

 whole process is more easily handled by probability concepts. For example, 

 if we knew the exact orientation of the die, its velocity, direction of motion, 

 physical size, shape and weight distribution, condition, characteristics 

 and orientation of the die table, etc., we could predict with certainty which 

 of the die faces would appear on top. However, the amount of information 

 that must be obtained and processed to arrive at this result is usually 

 prohibitive. It is much easier — and, also, as in the case of representations 

 of this type, less profitable — to characterize such a process by saying 

 that for any input (legal throw) the system (balanced die cube) may 

 produce any output from 1 to 6 with equal probability. 



Weapons systems contain many processes of similar brand. Ballistic 

 trajectories are a prime example. The behavior of a human being in a 



