Improved Ambiguity Resolution by an Equatorial Ionospheric Differential Correction for Precise Positioning

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1 Improved Ambiguity Resolution by an Equatorial Ionospheric Differential Correction for Precise Positioning NORSUZILA YA ACOB 1, MARDINA ABDULLAH,* MAHAMOD ISMAIL,* AND AZAMI ZAHARIM 3,** 1 Faculty of Electrical Engineering, Universiti Teknologi Mara, Shah Alam, Selangor. MALAYSIA Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia,43600 UKM Bangi, Selangor. MALAYSIA 3 Coordinator, Fundamental Engineering Unit, Universiti Kebangsaan Malaysia,43600 UKM Bangi, Selangor. MALAYSIA * Affiliate fellow, Institute of Space Science, ** Senior fellow, Solar Energy Research Institute, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor. MALAYSIA norsuzilayaacob@yahoo.com, mardina@eng.ukm.my,mahamod@eng.ukm.my, azaminelli@gmail.com Abstract: - Resolving the initial phase ambiguities of GPS carrier phase observations has always been considered an important aspect of GPS processing techniques. The influence of the ionosphere is one of the main problems in ambiguity resolution for carrier phase. In this study we are reviewing the ambiguity resolution problem under the new aspect of using ionospheric models over equatorial region for single frequency over short baseline distance. From the model, we can get differential ionospheric delay in subcentimetre accuracy. This can also be used by a single frequency receivers for a short time in short baselines. Findings show improvements in the correction of the differential ionospheric error over short baselines. The ambiguities were resolved when the variance ratio increased and the reference variances decreased. Key-Words: - ionosphere, differential GPS, ambiguity, single frequency, equatorial, baseline 1 Introduction Global Positioning System (GPS) is a satellitebased navigation radio system which is used to verify the position of a location and time in space and earth. The GPS technology has given many opportunities for geodetic applications. In GPS positioning, ionospheric induced errors could be measured, estimated or eliminated depending upon user requirement and availability of the observables. The influence of ionosphere is one of the main problems in the real-time ambiguity resolution for the carrier phase GPS data in radio navigation. Resolution of the double difference carrier phase ambiguities is the key to precise (cm accuracy) baseline coordinates from GPS measurements [1]. Generally, most observations for accurate positioning in the network use dual frequency receivers and these are considered expensive to implement in developing countries. Only single frequency receivers might be affordable to make the relative measurements []. An algorithm has been developed in this research that only requires L1 carrier phase measurement [3]. Some methods have been used to determine the systematic effect due to ionospheric refraction in the L1 carrier of single frequency GPS receiver. So a good ionospheric model is essential in order to get unambiguous results or to reduce time to solve the ambiguities [4]. The idea of differential ionospheric modelling was introduced by Webster & Kleusberg [5]. In accounting for the effect of the ionosphere using a single-frequency GPS receiver, it is possible to use global ionospheric models [6]. Generally, parameter estimation is carried out in three steps: the float ISSN: ISBN:

2 solution, the integer ambiguity estimation, and fixed solution. Each technique makes use of the variancecovariance matrix obtained from the float solution step and employs different ambiguity search processes at the integer ambiguity estimation step. It was shown that by applying the correction model, the success of ambiguity resolution could be achieved earlier when almost all measurements were corrected. For positioning, the standard deviation with respect to the local geodetic component of North, East and Up are significantly reduced [7]. The purpose of this work is to improve ambiguity resolution under undisturbed ionospheric conditions in an equatorial region for short baseline to obtain the most precise positioning. The model can be used among the single frequency users for differential positioning to reduce the ionosphere error. Differential Ionospheric Model Ionospheric models are usually computed by determining the TEC in the direction of all GPS satellites in view from a ground GPS network. From this model, there are two main parameters that need to be determined: the difference in LOS and TEC. Apart from these, the ratio as a function of elevation angles was examined. The difference in ionospheric induced error [8] between two stations can be expanded as: where 1 t ( TEC) = d = f ( TEC) Ratio LOS LOS td( β, TEC) f ( TEC) f ( β ) = (1) TEC : total electron content LOS : differential in line of sight β : elevation angle at reference station td : 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 is the differential delay at one hour processing. Fig.1: Differential delay scaled to L 1 of PRN 3 3 Methodology In this study, the effects of initial phase ambiguity at GPS and modelling of ionospheric base components were researched. The stations are shown in Table 1. The station is located at Universiti Teknologi Malaysia, Johor ( N, E), UTMJ, and Kukup, Johor ( N, E), KUKP. Both are located in the equatorial region. Data on 8 November 005 was used. UTMJ was assumed as a reference station and KUKP a mobile station, giving a baseline of about 33 km and only the reference station with L1 frequency was used. The GPS data was recorded in universal time system (UTC), whereby the sampling interval was 15 seconds and the cut-off elevation mask was 10. The local time (LT) was from 11 to 1 a.m. Table 1: RTK and MASS station with North, East and Height Height Station Lat (N) Lon (E) (m) UTMJ KUKP ISSN: ISBN:

3 By applying the model into the GPS phase measurements, it should deliver better ranges. These can 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 the influence 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 4 Result A shorter time (less than one hour period from :00:00 to :59:45) was chosen to see how the correction influenced the ambiguity resolution. The observed satellites PRNs are 1, 3, 16 and 19 from both 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 Ambiguity Float solution non integer ambiguity estimate is produced when the processing cannot resolve the ambiguity. On the other hand, when the processing can resolve the ambiguity to a correct integer number, it results in a fixed solution. In this study, the ambiguities of the uncorrected data were resolved with the occupation time of :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 8 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 0:53:15, which is about 75 seconds earlier. ii. Secondly, ionospheric corrections were applied to PRN 19, 3, 16 and 1 with elevation angles of about 8 to 54 degrees, 56 to 76 degrees, 51 to 8 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 0:5:30, which is 10 seconds faster. The improvement can be seen by comparing the variance ratio, reference variance and estimated position errors of the processing after the ambiguities were resolved for satellite PRN 19 for case 1 as shown in Fig. (a) and (b). The ratio increases while the reference variance decreases indicating improvements in the processed results. V a r i a n c e R a ti o R e fe ren c e V a ria n c e (a) (b) Figure : (a) Variance Ratio for PRN 19 (b) Reference Variance Ratio for PRN 19 ISSN: ISBN:

4 Both the variance ratio and the reference variance are illustrated in Fig. 3 (a) and (b), which also show significant improvement for satellite PRN 19, 3, 16 and 1 (case ). The ratio increases while the reference variance decreases indicating the improvement in the processed results. The difference between the reference variance without correction and is shown in Fig. 3 (b). Table : Ambiguity resolution success rate Without Correction With Correction PRN 19 PRN 3, 16, 19 & 1 0:54:30 0:53:15 0:5:30 Reference Variance Variance Ratio (a) (b) Figure 3: (a) Variance Ratio for PRN 19, 3, 16 and 1 (b) Reference Variance Ratio for PRN 19, 3, 16 and 1 Table summarises the ambiguity resolution success rate without and with the correction applied. With these 4 satellites (uncorrected data), the ambiguities were resolved with the occupation time of 0:54:30. By applying the correction model to PRN 19, ambiguities were resolved at 0:53:15, which is 1 minute 15 sec earlier corresponding to uncorrected data and when the correction model was applied to PRN 3, 16, 19 & 1, ambiguities were resolved at 0:5:30 which is 1 minute 15 sec earlier corresponding 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 GPS data for short baselines. In order to obtain the absolute value of the differential ionospheric delay from the measurements, integer ambiguities have to be resolved. Processing software has been used to accomplish this task, therefore the model can be validated. 5 Conclusion In this study, the results show an improvement in the correction of the differential ionospheric error over short baselines. By applying the ionospheric model the ambiguity resolution success rate is faster even when only correcting one satellite seen at low elevation angles. After the ambiguities are resolved, the variance ratio is larger and the reference variances are smaller. This implies good processing results. The model is mostly suitable for short baseline under undisturbed ionospheric conditions over equatorial region. Furthermore, the model can be used among the single frequency users. From the model differential ionospheric delay in subcentimetre accuracy can be obtained. ISSN: ISBN:

5 Acknowledgements We are grateful to Jabatan Ukur dan Pemetaan Malaysia (JUPEM) for providing the GPS data. The author would like to express her grateful thanks to Universiti Teknologi Mara (UiTM) for giving the author study leave enabling her to conduct the research. 7-9, 008 Military Technical College Kobry El-Kobbah,Cairo, Egypt. References: [1] L. Wanninger and T.U Dresden, Improved ambiguity resolution by regional modeling of the ionosphere, Proceeding of ION GPS-95, Palm Springs, Sep. 1-15, 1995, pp [] M.E.Cannon., G. Lachapelle and G Lu, Kinematic ambiguity resolution with a high precision C/A code recever, Department of Geomatic Engineering, University of Calgary, Alberta, Journal of Surveying Engineering, Amer. Soc. Civil Eng. vol. 119, No. 4 (Nov), [3] M. Abdullah and H.J Strangeway, Accurate ionospheric error correction for differential GPS, Proceeding of the 1 th International Conference on Antennas and propagation, Exeter, UK, 003. [4] M. Abdullah, H.J. Strangeways and D.M. A. Walsh, Improving ambiguity resolution rate with an accurate ionospheric differential correction, Journal of Navigation-Cambridge Univ. Press, 6 (1), - accepted for publication, 009. [5] I.Webster and A. Kleusberg, Regional modeling of the ionospheric for single frequency users of the Global Positioning System, Proceedings of the sixth international geodetic symposium on satellite positioning, Columbus, March 199, vol. I, pp [6] R.B. Langley,, Propagation of the GPS signals, in GPS for geodesy, International School, Delft, The Netherlands, 6 march-1 April, Springer- Verlag, New York. [7] Y. Norsuzila, M. Abdullah, M. Ismail and J. Kamaruzaman, Ionospheric Correction and Ambiguity Resolution in DGPS with Single Frequency, J. Applied Physics Research, CCSE, Canada (In Press: The issue of Vol. 1, No., in November 009). [8] Y. Norsuzila, M. Abdullah and M Ismail, The low-latitude ionosphere: modelling of ionospheric effects on relative GPS measurements. 6 th International Conference on Electrical Engineering ICEENG 008, May ISSN: ISBN:

Ionospheric Correction and Ambiguity Resolution in DGPS with Single Frequency

Applied Physics Research November, 9 Ionospheric Correction and Ambiguity Resolution in DGPS with Single Frequency Norsuzila Ya acob Department of Electrical, Electronics and Systems Engineering Universiti