Improving Ambiguity Resolution using an Ionospheric Differential Correction 71. IntroductionGlobal Positioning System (GPS) is a satellite- based navigation radio system which is used to verifythe position of a location and time in space and earth. The GPS technology has given manyopportunities for geodetic applications. In GPS positioning, ionospheric induced errors could bemeasured, estimated or eliminated depending upon user requirement and availability of theobservables. The influence of ionosphere is one of the main problems in the real-time ambiguityresolution for the carrier phase GPS data in radio navigation. Resolution of the double difference carrier phase ambiguities is the key to precise (cmaccuracy) baseline coordinates from GPS measurements . Generally, most observations for accuratepositioning in the network use dual frequency receivers and these are considered expensive toimplement in developing countries. Only single frequency receivers might be affordable to make therelative measurements . An algorithm has been developed in this research that only requires L1carrier phase measurement . Some methods have been used to determine the systematic effect due toionospheric refraction in the L1 carrier of single frequency GPS receiver. So a good ionospheric modelis essential in order to get unambiguous results or to reduce time to solve the ambiguities . The idea of differential ionospheric modelling was introduced by Webster & Kleusberg . Inaccounting for the effect of the ionosphere using a single-frequency GPS receiver, it is possible to useglobal ionospheric models . Generally, parameter estimation is carried out in three steps: the floatsolution, the integer ambiguity estimation, and fixed solution. Each technique makes use of thevariance-covariance matrix obtained from the float solution step and employs different ambiguitysearch processes at the integer ambiguity estimation step. It was shown that by applying the correctionmodel, the success of ambiguity resolution could be achieved earlier when almost all measurementswere corrected. For positioning, the standard deviation with respect to the local geodetic component ofNorth, East and Up are significantly reduced . The purpose of this work is to improve ambiguity resolution under undisturbed ionosphericconditions in an equatorial region for short baseline to obtain the most precise positioning. The modelcan be used among the single frequency users for differential positioning to reduce the ionosphereerror.2. Differential Ionospheric ModelIonospheric models are usually computed by determining the TEC in the direction of all GPS satellitesin view from a ground GPS network. From this model, there are two main parameters that need to bedetermined: the difference in LOS and TEC. Apart from these, the ratio as a function of elevationangles was examined. The difference in ionospheric induced error  between two stations can beexpanded as: 1 Δtd (TEC ) = = f (TEC ) Ratio ΔLOS ΔLOS Δtd ( β , TEC ) = f (TEC ) (1) f (β )where TEC : total electron content ΔLOS : differential in line of sight β : elevation angle at reference station Δtd : differential delay, in metre f(β) : polynomial coefficient The validation of the modelled differential delay and fitted differential delay are shown in Fig.1. From the figure, the model and the differential delay show approximately the same trend which isthe differential delay at one hour processing.
8 Norsuzila Ya’acob, Mardina Abdullah, Mahamod Ismail and Azami Zaharim Figure 1: Differential delay scaled to L1 of PRN 33. MethodologyIn this study, the effects of initial phase ambiguity at GPS and modelling of ionospheric basecomponents were researched. The stations are shown in Table 1. The station is located at UniversitiTeknologi Malaysia, Johor (1˚33’ 56.934”N, 103˚38’22.429”E), UTMJ, and Kukup, Johor(1˚19’59.791”N, 103˚27’12.354”E), KUKP. Both are located in the equatorial region. Data on 8November 2005 was used. UTMJ was assumed as a reference station and KUKP a mobile station, giving a baseline ofabout 33 km and only the reference station with L1 frequency was used. The GPS data was recorded inuniversal time system (UTC), whereby the sampling interval was 15 seconds and the cut-off elevationmask was 10˚. The local time (LT) was from 11 to 12 a.m.Table 1: RTK and MASS station with North, East and Height Station Lat (N) Lon (E) Height (m) UTMJ 1˚33’56.93” 103˚ 38’22.429’’ 80.44 KUKP 1˚19’59.79” 103˚ 27’12.354’’ 15.429 By applying the model into the GPS phase measurements, it should deliver better ranges. Thesecan be evaluated by examining the above parameters that should give: i. Smaller standard errors of position or baseline components, ii. Resolved ambiguity in shorter period, and iii. Larger variance ratio and smaller reference variance, if the ambiguity is resolved. There are several parameters from the software output that can be examined to evaluate theinfluence of the correction model. These are: i The estimated position of the mobile station ii The standard deviation of position or baseline components iii The ambiguity resolution rate iv The variance ratio and reference variance of the processing solution
Improving Ambiguity Resolution using an Ionospheric Differential Correction 94. ResultA shorter time (less than one hour period from 2:00:00 to 2:59:45) was chosen to see how thecorrection influenced the ambiguity resolution. The observed satellites PRNs are 1, 3, 16 and 19 fromboth stations. The model was evaluated by firstly applying the correction to the PRN 19 measurements,then applying it to the PRN 3, PRN 16, PRN 19 and PRN 1 measurements together.4.1. Fixing the Carrier Phase Integer AmbiguityFloat solution non integer ambiguity estimate is produced when the processing cannot resolve theambiguity. On the other hand, when the processing can resolve the ambiguity to a correct integernumber, it results in a fixed solution. In this study, the ambiguities of the uncorrected data wereresolved with the occupation time of 2:54:30. Two scenarios with different PRNs were studied: with an ionospheric model and without model(the uncorrected data). i. Firstly, the correction was applied to satellite PRN 19 which had elevation angle of about 28 to 54 degrees. Both the ratio and the variance distribution can be controlled by the specific level of confidence, which was set to be at 95%. By applying the correction model to PRN 19, ambiguities were resolved at 02:53:15, which is about 75 seconds earlier. ii. Secondly, ionospheric corrections were applied to PRN 19, 3, 16 and 1 with elevation angles of about 28 to 54 degrees, 56 to 76 degrees, 51 to 28 degrees and 57 to 56 degrees respectively. The ambiguity and baseline component errors of the float solution only show improvement with the correction. The ambiguities were resolved at 02:52:30, which is 120 seconds faster. The improvement can be seen by comparing the variance ratio, reference variance andestimated position errors of the processing after the ambiguities were resolved for satellite PRN 19 forcase 1 as shown in Fig. 2 (a) and (b). The ratio increases while the reference variance decreasesindicating improvements in the processed results. Figure 2: (a) Variance Ratio for PRN 1 (b) Reference Variance Ratio for PRN 19 2 1.8 1.6 V ria c R tio 1.4 a ne a 1.2 1 0.8 0.6 0.4 0.2 0 02:54:00 02:55:00 02:56:00 02:57:00 02:58:00 02:59:00 02:59:45 w/o correction Time [hh:mm:ss] with correction (a)
10 Norsuzila Ya’acob, Mardina Abdullah, Mahamod Ismail and Azami Zaharim w/o correction 20 with correction 19.5 R f r n eV r n e eee c aia c 19 18.5 18 17.5 17 02:54:00 02:55:00 02:56:00 02:57:00 02:58:00 02:59:00 02:59:45 Time [hh:mm:ss] (b) Both the variance ratio and the reference variance are illustrated in Fig. 3 (a) and (b), whichalso show significant improvement for satellite PRN 19, 3, 16 and 1 (case 2). The ratio increases whilethe reference variance decreases indicating the improvement in the processed results. The differencebetween the reference variance without correction and with correction is shown in Fig. 3 (b).Figure 3: (a) Variance Ratio for PRN 19, 3, 16 and 1 (b) Reference Variance Ratio for PRN 19, 3, 16 and 1 (a) (b)
Improving Ambiguity Resolution using an Ionospheric Differential Correction 11Table 2: Ambiguity resolution success rate With Correction Without Correction PRN 19 PRN 3, 16, 19 & 1 02:54:30 02:53:15 02:52:30 Table 2 summarises the ambiguity resolution success rate without and with the correctionapplied. With these 4 satellites (uncorrected data), the ambiguities were resolved with the occupationtime of 02:54:30. By applying the correction model to PRN 19, ambiguities were resolved at 02:53:15,which is 1 minute 15 sec earlier corresponding to uncorrected data and when the correction model wasapplied to PRN 3, 16, 19 & 1, ambiguities were resolved at 02:52:30 which is 1 minute 15 sec earliercorresponding to corrected data with PRN 19 only and two minutes earlier compared to four satellites(uncorrected data). The effectiveness of this new technique has been determined by implementing it into real GPSdata for short baselines. In order to obtain the absolute value of the differential ionospheric delay fromthe measurements, integer ambiguities have to be resolved. Processing software has been used toaccomplish this task, therefore the model can be validated.5. ConclusionIn this study, the results show an improvement in the correction of the differential ionospheric errorover short baselines. By applying the ionospheric model the ambiguity resolution success rate is fastereven when only correcting one satellite seen at low elevation angles. After the ambiguities areresolved, the variance ratio is larger and the reference variances are smaller. This implies goodprocessing results. The model is mostly suitable for short baseline under undisturbed ionospheric conditions overequatorial region. Furthermore, the model can be used among the single frequency users. From themodel differential ionospheric delay in sub-centimetre accuracy can be obtained.AcknowledgementWe are grateful to Jabatan Ukur dan Pemetaan Malaysia (JUPEM) for providing the GPS data. Theauthor would like to express her grateful thanks to Universiti Teknologi Mara (UiTM) for giving theauthor study leave enabling her to conduct the research.
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