Abstract :
It is the topic of this paper to present the findings of a computer simulation study that examined the properties of a particular type of vehicular locating system, and to discuss its inclusion in a system to direct and control a vehicle (in this case, a farm vehicle) in a particular geographic area. The vehicle locating system requires that the vehicle has an r-f transmitter that is transmitting a sharp rise time r-f pulse omnidirectionaly. There are three receiving stations located at A, B and C (see Figure 1) tuned to the same frequency as the trasmitter. The locations A, B and C are known geographically. Each receiving station has a clock, the clocks are synchronized. The receiving stations record the time of arrival of the pulse. We shall refer to these times as TA, TBand TCfor A, B and C respectively. The quantity TA-TB=ΔTABis the difference in time of arrival of the pulse at stations A and B, and λATAB, where λ is the propagation speed of the r-f pulse, is the difference in distance of the vehicle from points A and B. Such a locus of points is defined in mathematics as a hyperbola [4] and has the form x2/a2- y2/b2= 1, where a2+b2= c2. The foci of the hyperbola are at (-C,0) and (C,0). In the case of Figure 1 c = 1 and a= 1/2λ |ΔTAB| for the station pair A, B. By the same token, the difference TB-TChas its own corresponding hyperbolas. The point of intersection of these hyperbolas is the location of the vehicle. Since the third time difference TA-TCis the sum of ΔTABand ΔTBCit does not generate a separate pair of hyperbolas. This paper presents a recursive algorithm that determines the location of the vehicle based on measuring the differences in time of arrival of the r-f pulses at the receiving stations. A simulation program was written in PASCAL for the receiving antenna configuration shown in Figure 1 with the vehicle assumed to be in the interior of the angle formed by the stations A, B and C.
