GPS World, January 2013

innovation algorithms and Methods P Y signal energy This degrades the auto correlation peak of the P Y signal Even though the gain of the high pass lter is the same for both the C A and the P Y signals this effect on their auto correlation is different That is because the percentage of the low frequency energy of the C A signal is much higher than that of the P Y signal This however is not a signi cant drawback as it may appear initially To see why this is so note that the objective of the high pass lter is to obtain the greatest false peak rejection ratio de ned to be the ratio between the peak value of P Y auto correlation and that of the C A auto correlation The false peak rejection ratio of the non ltered signals is 05 Therefore all one has to do is adjust the cut off frequency of the high pass lter to achieve a desired false peak rejection ratio The simulation results in FIGURE 5 show that one simple highpass lter rather than multiple match lters can be designed to achieve an acceptable false peak rejection ratio The autocorrelation peak value of the ltered C A signal and that of the ltered P Y signal is plotted in the gure While the P Y signal is attenuated by about 25 percent the C A code signal is attenuated by 915 percent the non ltered C A autocorrelation peak is 2 The false peak rejection ratio is boosted from 05 to 436 by using the appropriate high pass lter Position Calculation Consider the situation depicted in FIGURE 6 where the authenticator and the supplicant have multiple common satellites in view In this case not only can we perform the signal authentication but also obtain an estimate of the pseudorange information from the authentication Thus the authenticated pseudorange information can be further used to calculate the supplicants position if we have at least three estimates of pseudoranges between the supplicant and GPS satellites Since this position solution of the supplicant is based on the P Y watermark signal rather than the supplicants C A signal it is an independent and authentic solution of the supplicants position By comparing this authentic position with the reported position of the supplicant we can authenticate the veracity of the supplicants reported GPS position The situation shown in Figure 6 is very similar to doubledifference differential GPS The major difference between what is shown in the gure and the traditional double difference is how the differential ranges are calculated Figure 6 shows how the range information can be obtained during the signal authentication process Let us assume that the authenticator and the supplicant have four common GPS satellites in view SAT1 SAT2 SAT3 and SAT4 The signals transmitted from the satellites at time t are S 1 t S 2 t S 3 t and S 4 t respectively Suppose a signal broadcast by SAT1 at time t s where ν 0 arrives at the supplicant at t 0 ν 1 s is the travel 1 time of the signal At the same time signals from SAT2 09 07 05 03 01 01 03 07424 01701 Filtered P Y signal Filtered C A signal 3 2 1 0 1 2 3 Shift time milliseconds Auto correlation FIGURE 5 Auto correlation of the filtered C A and P Y signals SAT1 SAT2 SAT3 SAT4 a S 2 Authenticator x a y a z a s S 3 Supplicant x s y s z s x y z ECEF a S 1 a S 3 a S 4 s S 2 s S 4 s S 1 FIGURE 6 Positioning using a watermark signal SAT3 and SAT4 are received by the supplicant Let us denote the travel time of these signals as ν s ν 2 s and ν 3 s respectively 4 These same signals will be also received at the authenticator We will denote the travel times for the signals from satellite to authenticator as ν a ν 1 a ν 2 a and ν 3 a 4 The signal at a receivers antenna is the superposition of the signals from all the satellites This is shown in FIGURE 7 where a snapshot of the signal received at the supplicants antenna at time t s includes GPS signals from SAT1 SAT2 SAT3 0 ν 1 and SAT4 Note that even though the arrival times of these signals are the same their transmit times that is the times they were broadcast from the satellites are different because the ranges are different The signals received at the supplicant will be S s ν 1 t 0 S 2 t 0 ν 1 s S 2 s ν 3 t 0 ν 1 s and S 3 s 4 t 0 ν 1 s This same snapshot of the signals at the supplicant is used to detect the matched watermark signals from SAT1 SAT2 SAT3 and SAT4 at the authenticator Thus the correlation peaks between the supplicants and the authenticators signal should occur at t ν 4 a t 0 ν 1 s ν 0 ν 1 s ν 2 a t 2 s ν 0 ν 1 s ν 3 a 3 and t s ν 0 ν 1 s ν 4 a 4 Referring to Figure 6 again suppose the authenticators GPS World January 2013 www gpsworld com 70