734 AIRBORNE NAVIGATION AND GROUND SURVEILLANCE 



Accuracy is the basic measuring-stick of navigation system performance. 

 The position accuracy of a doppler navigation system depends on the 

 following four sources of error: 



1. Doppler ground speed (or along-heading velocity) error, ay 



2. Doppler drift angle (or cross-heading velocity) error, an 



3. Heading reference error, an 



4. Computer error, ac 



The total position error may then be expressed approximately on a root- 

 sum-squared basis by 



(jp = yjav' + o-D" + cnr + ac'^ (14-7) 



where ap is the standard deviation (or rms) positional error in percent 



ay, (TD, and ac are the standard deviation (or rms) per cent errors of 

 the quantities defined above. When (td is expressed as drift angle 

 error rather than as cross-heading velocity error, it must first be 

 converted to an equivalent velocity or distance error through 

 division by 57.3° (1 radian) 

 an is the standard deviation (or rms) heading reference error 

 converted to an equivalent distance error through division by 

 57.3° (1 radian). 



As an example, if we assume a standard deviation doppler ground speed 

 error of 0.2 per cent, a doppler drift angle error of 0.15°, a heading reference 

 error of 0.5° and a computer error of 0.25 per cent, then an overall position 

 error of 0.97 per cent of distance traveled results. If three of the component 

 errors are left unchanged, and only the heading reference error is changed 

 from 0.5° to 0.25°, the overall system error now becomes 0.6 per cent of 

 distance traveled. These two cases are typical and illustrate the importance 

 of the heading reference error with regard to system accuracy performance. 



One important aspect of error analysis is the statistical behavior of the 

 data; that is, the question arises, What is the frequency of occurrence or 

 what is the probability of occurrence of certain errors? If and only if one 

 has a sufficiently large number of samples, can one realistically talk about 

 a measured probability distribution, i.e. about probable errors (50 per cent 

 probability) and maximum errors (95 per cent probability). 



A somewhat more accurate method of calculating the system error than 

 that indicated by Equation 14-7 is based on statistical probability consid- 

 erations as a two-dimensional error problem.' The two dimensions chosen 

 are the along-track and the cross-track directions, frequently called range 

 and transverse directions, respectively. The along-track or range error (tr 



'For a detailed treatment of statistical analysis applied to the two-dimensional error problem 

 see Merrill, Goldberg, Helmholz, Operations Research, Armament, Launching, p. 102, D. Van 

 Nostrand, Co., Inc., Princeton, N. J., 1956. 



