Title :
Number/theoretic solutions to intercept time problems
Author :
Clarkson, I. Vaughan L ; Perkins, Jane E. ; Mareels, Iven M Y
Author_Institution :
Div. of Electron. Warfare, Defence Sci. & Technol. Organ., Salisbury, SA, Australia
fDate :
5/1/1996 12:00:00 AM
Abstract :
A good radar warning receiver should observe a radar very soon after it begins transmitting, so in designing our radar warning receiver we would like to ensure that the intercept time is low or the probability of intercept after a specified time is high. We consider a number of problems concerning the overlaps or coincidences of two periodic pulse trains. We show that the first intercept time of two pulse trains started in phase is a homogeneous Diophantine approximation problem which can be solved using the convergents of the simple continued fraction (s.c.f.) expansion of the ratio of their pulse repetition intervals (PRIs). We find that the intercept time for arbitrary starting phases is an inhomogeneous Diophantine approximation problem which can be solved in a similar manner. We give a recurrence equation to determine the times at which subsequent coincidences occur. We then demonstrate how the convergents of the s.c.f. expansion can be used to determine the probability of intercept of the two pulse trains after a specified time when one or both of the initial phases are random. Finally, we discuss how the probability of intercept varies as a function of the PRIs and its dependence on the Farey points
Keywords :
approximation theory; convergence of numerical methods; number theory; probability; radar detection; radar receivers; recursive estimation; Farey points; arbitrary starting phases; coincidences; convergence; homogeneous Diophantine approximation problem; intercept probability; intercept time problems; number-theoretic solutions; overlaps; periodic pulse trains; pulse repetition interval ratio; radar warning receiver; random phases; recurrence equation; simple continued fraction expansion; Antenna measurements; Australia; Difference equations; Directional antennas; Helium; Particle measurements; Radar antennas; Radar equipment; Radar measurements; Time measurement;
Journal_Title :
Information Theory, IEEE Transactions on