736 AIRBORNE NAVIGATION AND GROUND SURVEILLANCE 



for a case of or/o-^ = 2, the 95 per cent probability {maximum) error circle 

 has a radius of 2.04o-r, while the radius of the 50 per cent probability 

 {probable) error circle has a radius of O.Syor, or a ratio of maximum to 

 probable error of nearly 2.34. For the case of ar I(tr = 1, the 95 per cent 

 probability circle has a radius of nearly 2.45a-r, while the 50 per cent 

 probability circle has a radius of nearly 1.1 Sot. 



Measured results, described later, have shown that the per cent range 

 error (tr, the per cent transverse error or, and hence the per cent position 

 error, of a doppler navigation system are inversely proportional to the 

 square root of the distance traveled. This is expressed mathematically by 



Kr 



(14-1 la) 



(14-llb) 



This behavior can be explained by the fact that the additional smoothing 

 afforded by longer flights decreases the eflP"ect of certain slowly varying 

 random errors and of any end-point errors. Thus if the standard deviations 

 of the component errors listed earlier are known for a given distance (as is 

 frequently the case for doppler radars and heading references), the con- 

 stants Kr and Kt above can be determined from Equation 14-8 through 

 14-11. The range, transverse, and radial position errors for any desired 

 distance can then be found by means of Equations 14-1 la and 14-llb. 



14-4 MAJOR CHARACTERISTICS AND COMPONENTS OF A 

 DOPPLER RADAR NAVIGATION SYSTEM 



Type of Transmission. The types of transmission for doppler radars 

 can be divided into four general categories: 



Low-duty cycle pulse (5 per cent or less) 



Continuous wave (CW) 



High-duty cycle pulse (25 to 50 per cent) 



Frequency modulation — continuous wave (FM-CW) 



The pulse systems can be further subdivided into incoherent and coherent 

 pulse systems; low-duty cycle pulse systems are normally found in the 

 incoherent class, while high-duty cycle pulse systems are found in both the 

 incoherent and coherent classes. The order in which these types are listed 

 above coincides approximately with the historic development of doppler 

 radars. The low-duty cycle pulse system employs techniques and compo- 

 nents most similar to those used in conventional pulse radar systems. 

 Although this type of transmission is the least efficient of the four, it is the 



