GPS World, April 2015

INNOVATION Algorithms Methods 00 05 10 15 20 25 30 35 40 45 50 10 09 08 07 06 05 04 03 02 01 00 Time minutes Horizontal position error meters FIGURE 10 Widelane only triple frequency PPP convergence horizontal position error dif culty in estimating the phase biases on this combination accurately using only a few Block IIF satellites We hope that in the future the increasing number of modernized satellites will help such bias estimation N 1 Ionosphere Free Phase FIGURES 6 to 8 show the three possible ambiguity estimates using the ionosphere free phase combination with two measurements we assume that the corresponding widelane has already been solved In each case the computed biases allow us to easily retrieve the integer nature of the N 1 ambiguity Application to Triple Frequency PPP The results presented above show that the integer ambiguity nature of phase measurements is conserved for various useful observable combinations and prove the validity of the model Another experiment has been carried out to estimate the impact of ambiguity convergence in the triple frequency context For that in order to maximize the observability of the GPS Block IIF constellation and thus the accuracy of the biases a network of ten stations across Europe has been chosen for the phase biases computation see FIGURE 9 The station REDU in green was the test station to be positioned The test occurred on January 10 2015 around 11 00 UTC At that time four Block IIF satellites were visible simultaneously PRNs 1 3 6 9 for a total of 10 satellites in view The PPP Wizard open source client was used to perform PPP in real time The advantage of this implementation is that it directly follows the uncombined observable formulation described in Equations 5 The strategy for ambiguity resolution is a simple bootstrap approach Convergence of the Widelane Only Solution In this test a PPP solution was performed but only the xing of the widelane ambiguities was implemented As noted in the previous section the wavelength of the widelane ambiguity when the extra widelane ambiguity is solved is about 34 meters so it is expected that all the widelanes can be xed in a very short time Despite the ampli cation factor of about 20 of the equivalent unambiguous phase combination we expect 0 5 10 15 10 09 08 07 06 05 04 03 02 01 00 Time minutes Horizontal position error meters FIGURE 11 All ambiguities triple frequency PPP convergence horizontal position error to obtain an accuracy of about 10 centimeters with such a solution FIGURE 10 shows the convergence time of several PPP runs in this context 16 different runs of ve minutes are superimposed in terms of horizontal position error The extra widelanes are fixed instantaneously the remaining widelanes are xed in about two minutes on average to be below 30 centimeters this is represented by the different sharp reductions of the errors This new configuration available in the triple frequency context is very interesting as it provides an intermediate class of accuracy which converges very quickly and which is suitable for applications that do not demand centimeter accuracy Another interesting aspect of this combination is the gapbridging feature In PPP gap bridging is the functionality that allows us to recover the integer nature of the ambiguities after a loss of the receiver measurements over a short period of time typically a pass through a tunnel or under a bridge This is done usually by means of the estimation of a geometry free combination ionosphere delay estimation during the gap Realistic maximum gap duration in the dual frequency case is about one minute In the triple frequency case the wavelength of the geometry free combination involving the widelane if the extra widelane is xed is 198 meters With such a large wavelength the gaps are much easier to ll and we can safely extend the gap duration to several minutes In addition the widelane combinations are wind up independent so there is no need to monitor a possible rotation of the antenna during the gap as in the dual frequency case Overall Convergence All Ambiguities Another PPP convergence test has been carried out with all ambiguities xing activated four different runs of 15 minutes are superimposed Results are shown in FIGURE 11 The centimeter accuracy is obtained in this con guration within eight minutes which is a signi cant improvement in comparison to the dual frequency case Further improvement of this convergence time is expected with an increase in the number of Block IIF satellites and subsequently GPS IIIA satellites GPS World April 2015 www gpsworld com 48