may again be used to represent the spread of individual position determinations . 

 The error in using a circle instead of the appropriate ellipse is only a few per- 

 cent, as indicated in Table III-l . 



TABLE III-l 



ERROR PROBABILITY CONTAINED IN CIRCLES 

 OF VARYING RADIUS 



Probability for Probability for 



Radius of Cii 



■cle 



°x = "y 



Oy = 



1 d 



r 





0.632 



0.683 



2 d 

 r 





0.982 



0.954 



3d^ 





0.999 



0.997 



The use of d to describe the navigational fix radial error distribution 

 is not standardized but is finding wider favor, especially among the newer sys - 

 tems being evaluated. However, other methods are sometimes used which are 

 interrelated to the root -mean -square distribution d^., as indicated in Table III-2. 

 By using the conversion factors of Table III -2, one can intercompare systems 

 using methods other than d error. 



TABLE III -2 



COMPARISON OF STATISTICS OF ERROR FOR o -^ a 



X V 



Statistical Value in Terms Normalized 



Measure of a to d^ 



Root -Mean -Square Error 

 Standard Deviation of d 



Variance of d 



a 



Circular Probable Error CEP 1.18 a 0.833 



27 



d 



r 



1.41 



1.00 



"d 



0.65 o 



0.463 



0.2 



0.430^ 



0.304 



artbur ai.lLtttlcIlnr. 



