Enhancement of GPS Single Point Positioning Accuracy Using Referenced Network Stations

World Applied Sciences Journal 18 (10): 1463-1474, 2012 ISSN 1818-4952 IDOSI Publications, 2012 DOI: 10.5829/idosi.wasj.2012.18.10.2752 Enhancement of GPS Single Point Positioning Accuracy Using Referenced Network Stations Ahmed E. Ragheb and Ayman F. Ragab Department of Public Works, Faculty of Engineering, Ain Shams University, Cairo, Egypt Abstract: Positioning using e Global Positioning System (GPS) can be performed rough two main techniques which are e Relative Positioning (RP) and Single Point Positioning (SPP). It is well known at e obtainable accuracy using RP is higher an at obtained using SPP. However, it implies e implementation of more an one GPS receiver. Accordingly, SPP is much cheaper and easier an RP. Many researches were devoted to e topic of increasing e accuracy of e SPP rough classical techniques like increasing e leng of e processed session, implementing e precise orbital information instead of e broadcasted one and e effect of turning off e Selective Availability (SA) in May 2000. Here in, e maximum achievable SPP accuracy (using classical techniques) was investigated using GPS real data. A certain test point was assigned in e core of an area of about 120 km x 92 km. Results proved at an accuracy in e order of 3m can be achieved using a session of 3.5 hours by implementing e precise orbital data for e case when e SA turned off. To increase e above achievable SPP accuracy, a new technique is introduced here called Referenced Network Stations (RNS) technique. This technique is based on e establishment of a reference network in e considered area, whose points are precisely determined. The considered reference network used here consists of 9 points wi interspacing ranging from 25-60 km. The SPP of e 9 reference points are determined every 3 minutes along one complete day. Then, e coordinate discrepancies are computed for e 9 reference points, every 3 minutes and stored in one data bank. Thus, e coordinate discrepancies are estimated at e test point, using e constructed data bank and en added to SPP coordinates of e test point to get e final solution for its position. Nine different prediction models were tested to reach at e most reliable one for estimating e coordinate discrepancies at e test point. Results showed at e weighted mean model, which raises e distances to e 7 power, is e superior one for is purpose. A positional accuracy at e test point of only 31 cm was achieved, by e developed RNS technique; using 3 minutes of GPS synchronized data at bo reference points and test point. To generalize e application of e RNS technique, its ability to implement nonsynchronized GPS data at e reference points and e test point was investigated. The performed tests had proved at e two most critical factors are e unification of e time (rough e day) not e date itself between e reference points and e test point as well as e unification of e state of e SA at all points. Processing of 3 minutes of GPS data, collected at e same time but on different dates at bo test and reference points, can yield an accuracy of 36 cm under e condition at e SA was at e same state in bo campaigns. Key words: GPS Single point positioning Positional accuracy Reference Network Stations INTRODUCTION On e oer hand, e achievable positional accuracy using GPS is widely ranging from sub centimeter up to The Global Positioning System (GPS) is rapidly several tens of meters [2]. Such huge difference in replacing most of e traditional surveying techniques. positional accuracy is mainly function of two main factors This is due to e great flexible conditions of operation for which are e type of e used GPS receiver and e e system like its ability to work 24 hours per day, adopted observational technique [3]. Basically, un-necessity of inter-visibility and un-limitation for ere are two main types of GPS receivers which are e separation between surveyed points... etc. e.g. [1]. handheld receivers and geodetic grade receivers. Corresponding Auor: Ahmed Ragheb, Public Works Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt. E-mail: aragheb@link.net. 1463

Handheld GPS receivers observing Coarse Acquisition (C/A) code are generally much lower in positional accuracy and cheaper an geodetic-grade receivers. Positional accuracy of handheld C/A code observing receivers are at e tens of meters level [4], while on e oer hand, geodetic-grade receivers collecting phase measurements produce results wi sub centimeter level accuracy [5]. In e case of using GPS geodetic-grade receivers, two main techniques can be followed which are e Single Point Positioning (SPP) and Relative Positioning (RP). The SPP technique is meant by e process of determining e absolute 3-D coordinates of any point using stand-alone GPS receiver at such point. On e oer hand, e RP is concerned wi e determination of e differences in coordinates, between two or more points, using synchronized GPS observations at all concerned points [6]. This superiority in positional accuracy is due to e fact at e RP technique makes Fig. 1: Concept of SPP and RP use of e spatial correlation of systematic errors between stations to estimate or reduce eir effects in determining This is to pick out e most suitable conditions of e highest positional accuracy [7]. performing e introduced approach. Based on e above discussion it can be stated at, e SPP technique is much easier and has lower Single Point Positioning (SPP) Versus Relative operational cost an e RP technique (as it implies e Positioning (RP): As mentioned above, SPP involves e use of only one GPS receiver). However, RP has a higher use of only a single GPS receiver at one station location accuracy significantly an SPP. This makes it of great to collect data from multiple satellites in order to determine importance in order to increase e achievable positional e location of e receiver, whereas e Relative accuracy raer an SPP. Many researches were devoted Positioning (RP) employs two GPS receivers, to e task of investigating e different ways of simultaneously tracking e same satellites, to determine increasing e accuracy of e SPP technique. Such e difference in coordinates between e two researches investigated e effect of some observational receivers[12]. Figure 1 depicts e main idea of bo SPP and computational parameters on e achievable SPP and RP techniques. accuracy like e used session leng, e geometry of e The collected GPS observations are contaminated by used satellite constellation (expressed by e DOP), e many biases like e satellite and receiver clock errors, effect of turning off e SA etc. Such studies can be tropospheric and ionospheric delays, multipa etc. found in several researches [2, 8-11]. Among all ese These biases are taking place in bo SPP and RP works, e highest achievable positional accuracy using techniques wi e same manner and same magnitude. SPP was in e order of 2 to 3 meters. In is study, many However, e effect of ese biases on e resulted trials will be performed to increase e accuracy of SPP. At positional accuracy is completely different between such first, e classical approaches of increasing e SPP two techniques. This is due to e fact at e RP accuracy will be used rough e investigation of e technique implies a differencing process for e collected effect of ree different parameters on e accuracy of e GPS observations at e considered two stations. This SPP. Such ree parameters are e type of e used differencing process leads to a great reduction in e orbital information, e session leng of e data capture value of e remaining biases, which leads in great process and effect of turning e SA off. The final output reduction of e effect of different GPS biases. Based on of ese ree trials will be considered as e maximum e above discussion it can be stated at, e collected achievable SPP accuracy via classical approaches. At is GPS data using bo SPP and RP techniques are affected stage, e new ought approach to increase e accuracy by GPS biases by e same amount. However, e effect of e SPP will be outlined and tested using e same used of such biases is greatly reduced in e case of RP. A test point. Finally, e different parameters affecting e summary for e magnitude of different GPS biases for efficiency of e proposed approach will be analyzed. bo SPP and RP are listed in Table 1 [10]. 1464

Table 1: Values of different GPS biases for bo SPP and RP techniques Bias magnitude (m) ----------------------------------------- Bias SPP RP Satellite clock 3 0.0 Receiver clock 400 0.0 Tropospheric delay 1.8 0.2 Ionospheric delay 8.2 0.4 Orbital error 2.7 0.0 Multipa 0.6 0.6 Selective Availability 30.0 0.0 Receiver noise 0.3 0.3 By observing Table 1, it can be stated at, many GPS biases are totally removed when implementing e RP technique, whereas oer biases are greatly reduced. The amount of reduction of e biases is inversely proportional to e leng of e processed baseline [13]. In oer words, e RP technique can result in better positional accuracies when applied for relatively short baselines. On e oer hand, RP can lead to bad results in e case of long baselines. This fact can be considered as anoer main motivation behind undertaking e current research to increase e reliability of GPS positional accuracy using SPP to be adopted instead of e RP in e case of long baselines. Increasing e Accuracy of SPP Using Classical Techniques: Many trials were performed to increase e accuracy of GPS SPP. These trials are different among each oer in studying different parameters at affect e accuracy of SPP. However, ey proved at neier e used ionospheric model nor e tropospheric model affect e accuracy of SPP [14]. Moreover, e performed trials proved at e accuracy of SPP is affected mainly by ree different parameters which are e kind of e used orbital data, e leng of e data acquisition session and e cancellation of e Selective Availability (SA). Therefore, before going rough e new ought technique of increasing e accuracy of SPP, ese ree factors should be investigated first to explore e highest possible accuracy of SPP using ese classical approaches. This highest possible accuracy of SPP can en be considered as a reference for e new ought approach. Description of e Used Data: The used GPS data consisted of ten (10) GPS points, covering an area of about 120 km x 92 km. These points are located in Sinai and e western side of Suez Gulf. Figure 2 depicts e location and distribution of e used GPS network. Fig. 2: Used GPS Data The used GPS network is established by e National Research Institute of Astronomy and Geophysics (NRIAG) and it is observed periodically for e purpose of prediction of earquake activity. The data of all points are available in Receiver Independent Exchange (RINEX) format roughout different mons and years. One GPS point was assigned as a test point (indicated by e circle in Figure 2). The adjusted 3-D coordinates of e 10 points are known beforehand rough a network adjustment solution for e whole network. Effect of Increasing e Leng of e Observation Session: It is well known at using a longer session of GPS observations will result in a better positional accuracy. In oer words, GSP positional accuracy is directly proportional to e adopted GPS session leng [3]. However, is increase in positional accuracy is limited, at is increasing e session leng beyond a certain value would not increase e achievable positional accuracy. Accordingly, to investigate e effect of increasing e used session leng, e 3-D coordinates of e indicated test point in Figure 2 are computed several times by varying e used session leng. Every time, e used session leng is increased by 15 minutes up to session lengs of 11 hours were explored. The 3-D coordinates of e test point is computed rough e LEICA Geo Office software package using broad cast orbital information. The used data are collected on August 4, 1999. In is context, for each used session leng, discrepancies are computed between e known reference coordinates of e test point and e computed coordinates using such session leng. These discrepancies are computed as follows: 1465

X = Xref - Xspp (1) Y = Y ref - Y spp (2) Z = Z ref - Z spp (3) (4) 2 2 2 dp = X + Y + Z Where: X ref, Y ref and Z ref = The reference coordinates of e test point X SPP, Y SPP and Z SPP = The 3-D Cartesian coordinates of e test point, estimated in SPP mode X, Y and Z = 3-D components of e coordinate discrepancy vector Fig. 3: Effect of e used session leng on e accuracy = Positional discrepancy of SPP P Based on e above, 44 sets of discrepancies are estimated. The relation between e used session leng and e resulted discrepancies is depicted in Figure 3. Through a quick glance on Figure 3, it can be stated at, increasing e used session leng leads to a significant increase in e accuracy of e SPP. This is valid up to a certain limit. Such limit is indicated in Figure 3 by e vertical dashed line (separating regions A and B). Thus, increasing e session leng increases e accuracy of e SPP (region A). Yet, is increase in accuracy is observed up to about a session leng of 8 Fig. 4: Effect of e used type of orbital information on hours (e vertical dashed line). Beyond is limit, e accuracy of SPP increasing e session leng will not produce any increase in e SPP accuracy (region B). As a conclusion, Effect of Turning off e Selective Availability (SA): using e broadcast orbital information, e best The Selective Availability (SA) was turned off by achievable positional accuracy of SPP reaches e order st e U.S. government on May 1, 2000 [2]. As a of 10 m. result, e accuracy of e SPP is enhanced. To ensure such enhancement, two datasets (collected on Effect of Changing Used Orbital Information: Anoer August 4, 1999) and on e same date in e next year attempt is performed here to increase e accuracy of SPP (after turning e SA off) were processed, while using e by using e precise orbital information instead of e same test point, previous criteria and session leng, broadcasted ones. This precise orbital information was utilizing precise orbital data. Figure 5 summarizes e downloaded from e IGS site [15]. For convenience, e results of is test, showing here only e positional same criteria, data, session leng are used as e discrepancies. previous trial. The obtained results are depicted in Based on Figure 5, it is very evident at, Figure 4. turning e SA off resulted in a significant By observing Figure 4 it can be seen at, enhancement in e accuracy of SPP. This wi e application of e precise orbit instead of enhancement can be noticed in two different forms. e broadcasted orbit, e solution stabled after First, e solution stabilized after shorter time period, about six hours (noticed by e position of e vertical which is about 3.5 hours (denoted by e vertical dashed dashed line). In addition, a positional accuracy in e line). Secondly, after e solution reaches e stability order of 4m can be achieved using e precise orbital level, e final positional accuracy is raised to e level of information. about 3m. 1466

This is e main idea of e proposed technique, which will be introduced in e next section. Basic Idea of e Proposed Technique: The main motivation here is to increase e accuracy of SPP, based on e existence of a reference network surrounding -or in e vicinity of- e point(s) at shall be positioned using SPP. The 3-D adjusted coordinates of e points of is reference network should be known beforehand. After which, all points of such reference network are positioned using SPP. Then, e coordinate discrepancies are computed and stored in a data bank for all e adopted Fig. 5: Effect of turning off e SA on e accuracy of reference stations using equations (1, 2 and 3). At is SPP stage, e coordinate discrepancies or in oer word corrections are estimated at e considered point(s) Closing Remarks Concerning SPP Accuracy Using using e computed discrepancies at e reference Classical Techniques: The above performed ree tests stations. Finally, e final coordinates of e considered clarify e previously known facts concerning e point(s) are computed by adding e estimated accuracy of SPP. However, it was of great importance to corrections to e coordinates obtained via classical SPP perform such tests before going rough e main technique. Based on e above mentioned idea, it can be investigation of increasing e accuracy of SPP, in order stated at, e main factor affecting e efficiency of e to explore e maximum achieved positional accuracy of proposed technique is e reliability of e estimated SPP using classical techniques. The results of e ree discrepancies at e considered point(s). In oer words, tests proved at nowadays, wi e absence of e SA, e degree of dependency of ese discrepancies at e a positional accuracy in e order of 3m can be achieved considered point(s) on ose at e reference points is e using stand-alone GPS receiver by adopting precise main key of is technique. The estimation of e orbital data whilst using a minimum session of 3.5 hours. coordinate discrepancies at e considered point(s) can Of course, neier is accuracy nor e required session be performed using many different prediction techniques. leng is suitable for most of GPS users. Consequently, In e following, e different investigated prediction anoer approach should be established to increase e models will be summarized. efficiency of e SPP. Different Used Prediction Models of Coordinate Increasing e Accuracy of SPP Using Reference Discrepancies: Nine different prediction models are Network Stations (RNS) Technique: As it is well known, investigated, in order to find out e most suitable model. e basic reason behind e higher accuracy of relative The used prediction models are e mean, weighted mean, positioning (RP) when compared to SPP is e nearest neighbor, search radius, triangulation, polynomial minimization of a multitude of biases at affect all GPS model, logarimic trend, power trend and exponential observations, basically due to e differencing process trend. Maematical details of ese prediction models can between e considered stations in e case of RP. In case be found in many researches, e.g. [16, 17]. However, all of SPP, e 3-D coordinates of e considered station are used models are briefly explained in e appendix given at largely affected by ese biases, especially ose who do e end of is research. For any tested prediction model, not have a reliable estimation model. Based on e above each coordinate along wi its corresponding discrepancy discussion and previously performed tests it can be is modeled as a separate variable. Consequently, for each stated at, e 3-D coordinates derived using SPP are one of e applied nine prediction models, ree different largely deviated from e correct values. Such deviations processing meodologies will be performed can be referenced to e various famous GPS biases corresponding to e ree spatial coordinates X, Y and Z. (tropospheric and ionospheric effects, orbital errors In oer words, e X, Y and Z-coordinates of e etc.). However, if a reliable estimation for e deviations reference points are fitted wi e X, Y and Z-coordinate of such 3-D coordinates is performed, e efficiency of discrepancies respectively, using e adopted prediction SPP technique can en be enhanced significantly. model. 1467

Application of Different Prediction Models and Analysis of e Results: Referring to Figure 2, e used GPS data consists of 10 points. The 3-D Cartesian coordinates of ese 10 points are known beforehand. Among ese 10 points, only one point is assigned as e test point. Accordingly, in all e sub-sequent analysis, 9 data points will be involved along wi one central test point. All e 10 points are processed individually, using SPP technique, considering e longest possible session leng (11 hours), while processing precise orbits. The main idea here can be summarized in e following steps: World Appl. Sci. J., 18 (10): 1463-1474, 2012 Estimation of e coordinate discrepancies at e 9 reference stations using equations 1, 2 and 3. Prediction of e ree coordinate corrections at e test point, using e corresponding coordinates and discrepancies at e 9 reference points, using e adopted prediction model. Estimation of e final coordinates of e test point by adding e predicted corrections to its produced SPP coordinates. Accuracy assessment of e applied prediction model by comparing e resulted final coordinates of e test point wi its known precise coordinates. This step is controlled by e computation of e resultant positional discrepancy. The above mentioned nine prediction models are applied. Each one of ese nine prediction models were investigated once except ree models which are e search radius, weighted mean and polynomial model. For each one ese ree models, it is applied several times by varying its order or vicinity range. Concerning e search radius model, radii of 30, 40, 50, 60, 70, 80 and 90 kilometers are used. For e weighted mean model, e distances are weighted using powers started from 1 to 10. Finally, for e polynomial model, polynomials of e st nd rd 1, 2, 3 and 4 orders were explored. This is mainly done in order to find out e most reliable condition of application for each of ese ree models. Figures 6, 7 and 8 summarize e results of e search radius, weighted mean and polynomial models, respectively. By noticing Figures 6, 7 and 8, it can be concluded at, using a search radius of 40 km yields e best results among all examined radii. For e weighted mean technique, weighting e distances by e power 7, gives e most reliable SPP positions for e test point when compared to e oer tested powers. Finally, concerning nd e polynomial model, e 2 order polynomial can be considered as e optimal one at can be used to predict Fig. 6: Results of e search radius prediction model Fig. 7: Results of e weighted mean prediction model Fig. 8: Results of e polynomial prediction model e coordinate corrections at e test point. Based on e results from e latter ree figures, e 40 km search radius, e power 7 for e weighted mean model and e nd 2 order polynomials will be assigned to represent e search radius meod, e weighted mean and polynomial models, respectively. Referring again e nine applied prediction model and after selecting e most reliable configuration for e ree variant models, e results of all nine models are listed in 1468

Table 2: Summary of e results of all tested models Discrepancies (m) ----------------------------------------------------- Prediction Model X Y Z Position Nearest Neighbor 0.39 1.24 0.39 1.36 Mean 1.09 0.55 0.70 1.41 Triangulation 0.88 0.26 0.78 1.20 Logarimic Trend 1.16 0.33 0.76 1.42 Power Trend 1.28 0.2 0.26 1.32 Exponential Trend 1.16 0.31 0.17 1.21 Search Radius (40 km) 0.39 1.24 0.39 1.36 Weighted Mean (Power 7) 0.14 0.18 0.15 0.27 Polynomial (2nd order) 1.11 0.54 0.62 1.38 Fig. 9: Positional discrepancies for e nine tested models Table 2. Also, for simplicity, only e positional discrepancies are depicted in Figure 9 for all nine tested models. Based on Table 2 and Figure 9, it can be seen at, e application of e weighted mean prediction model (wi e power 7) in e estimation of e coordinate discrepancies, using e corresponding discrepancies at e reference points, yields e highest possible positional accuracy. A positional error of few decimeters level is obtained using such technique. Accordingly, e Reference Network Stations (RNS) technique (in its current form) can increase e accuracy of e SPP from 3m (using e classical approaches) to e few decimeters level (0.27m). Effect of e Leng of Processed Data on e Quality of RNS Technique: The above achieved sub-meter accuracy for e SPP, using e developed RNS technique, was based on e implementation of e longest available Fig. 10: Effect of e session leng on e efficiency of e RNS technique session leng (which is 11 hours). Of course, is time span is very long and it is impractical to consider it in any SPP application. The question arises now is "Can is time span be reduced and to which extent?". To answer e above question, e RNS technique is applied many times, using GPS synchronized data of different lengs, applying e most efficient weighted mean prediction model wi 7 power along wi precise orbital data. Data sessions of 11 hours, 1 hour, 15 minutes, 5 minutes, 3 minutes, 2 minutes and 1 minute are used. Results are depicted in Figure 10. Based on Figure 10, it can be seen at, in e introduced RNS technique, e effect of decreasing e leng of e considered session on e resulted positional accuracy is very slight. This is valid up to a session leng of 3 minutes. Considering session lengs shorter an 3 minutes was found to degrade e efficiency of e RNS technique. Based on is, a session leng of 3 minutes can be considered as e optimum session leng for e proposed technique. Note at data sessions of 6 hours and 3.5 hours were also investigated and possessed almost e same results, which is evident here also by e similar accuracy of 11hours and 1 hour data session. Efficiency of e RNS Technique for Non-synchronized Data at Bo Reference Points and Test Point: The introduced RNS technique had proved relatively good results for SPP, even wi session lengs of only 3 minutes. These results were obtained using GPS synchronized data at bo e reference points and e test point. However, it is impractical to apply e RNS technique in its current form. This is due to e simple fact at if a synchronized GPS data is available at bo reference and test points, one should go rough a RP 1469

scenario. Therefore, e main interest of e introduced technique can be expressed by its ability of application for non-synchronized data at bo e reference points and e test point. Two different types of non-synchronicity between reference points and test point should be distinguished here, which are: Type (A) Hour Non-Synchronicity: In is case, GPS data are collected at e reference points and e test point at different time interval (same day but different hour). World Appl. Sci. J., 18 (10): 1463-1474, 2012 Type (B) Date Non-Synchronicity: In is case, GPS data are collected at e reference points and e test point at e same time but in different dates. Based on e above discussion, e efficiency of e RNS technique should be checked for bo types of non-synchronicity. To achieve such a goal, a data bank is constructed for e reference network. Such data bank is constructed using e available 11 hours of GPS data, containing e SPP coordinates of e 9 reference points computed every 3 minutes at e start of each hour, using precise orbital information. Then e 3-D coordinate corrections for e 9 reference points are estimated 11 times for e start of each hour. This data bank will be used now in checking e efficiency of e RNS technique for bo types of non-synchronized GPS data in two different tests. Efficiency of e RNS Technique in Case of Hour Non-Synchronicity: This test is performed to check e reliability of e developed RNS technique when applied on data collected at e reference points at a certain hour and collected at e test point at a different hour (wiin e same day). The SPP coordinates of e test point are estimated using e optimum session leng (which was determined as 3 minutes). These 3 minutes were selected to be e first 3 minutes in e first hour of observations on e same day used for constructing e reference stations data bank (August 4, 1999). Using e established data bank, 11 different sets of coordinate corrections are used in is test, corresponding to e first 3 minutes in each hour of observations. The coordinate discrepancies are estimated at e test point, using e concluded best model (weighted mean wi power 7), using each set of corrections. Consequently, 11 different solutions now exist for e test point. Finally, e positional discrepancy at e test point is computed for each corrections set. Results are depicted in Figure 11. Fig. 11: Efficiency of e RNS technique in case of hourly non-synchronized data By observing Figure 11, it is very evident at, e developed RNS technique failed to get a reliable SPP solution for e test point when an hourly nonsynchronized data is used. This is denoted by e large positional discrepancies obtained in all e tested hours except e first one (positional accuracy=0.31m), which is e only hour having synchronized data. Note at, is test was similarly applied on e first ree minutes of e nd rd, 2, 3.., 11 hour of data of e test point and possessed typical results and conclusions. This expected failure can be simply referenced to e complete un-correlation (independency) between e values of different GPS biases at bo e reference points and e test point, especially multipa due to e effect of sidereal lag [18]. In oer words, for e case of hourly non-synchronized data, different GPS biases will be certainly different in magnitude and behavior at e reference points and e test point. Consequently, e estimation of e coordinate discrepancies at e test point using e corresponding discrepancies at e reference points will not represent e reality. Hence, anoer approach should be followed to enable e application of e RNS technique for GPS nonsynchronized data. Efficiency of e RNS Technique in Case of Date Non-Synchronicity: Here, e efficiency of e RNS technique will be evaluated for date nonsynchronized data at bo e reference points and e test point. This means at e used SPP coordinates of e reference points and e test point are computed using e same 3 minutes of observations but on different dates. Specifically, e coordinate corrections at e reference points are extracted from e prepared data bank (constructed on 1470

Fig. 12: Efficiency of e RNS technique in case of Fig. 13: Efficiency of e RNS technique in case of date date non-synchronized data (Using e data non-synchronized data (Using e data Banks of Bank of 1999) 1999 and 2001) August 4, 1999) for e first ree minutes. Concerning discussion, anoer attempt is made to check e validity e test point, its SPP coordinates are computed, using of e RNS technique for e data collected after turning e same ree minutes, on ree different dates, which e SA off. Anoer correction data bank is constructed are: for e 9 reference points, using e same procedure. The only change here is at e SPP coordinates involved in May 28, 1998 e new data bank are computed using data collected on August 4, 1999 (Same date of e reference points) October 12, 2001 (After turning SA off). The test point September 19, 2000 was processed at e same previous ree dates of Figure 12. However, e first two dates (1998 and 1999) were For every one of e considered ree dates, e SPP processed using e correction data bank of 1999, where coordinates of e test point are computed (using e e ird date (2000) was processed using e new same 3 minutes at e first hour at e reference points). correction data bank (constructed using 2001 data). The same used procedures in e previous test are Results are given in Figure 13. followed to predict e coordinate discrepancies at e By Figure 13, it can be stated at, when updating e test point. Results are summarized in Figure 12. data bank after turning e SA off, e RNS technique Based on Figure 12, two very important notices can succeeded in getting a reliable estimation for e test be observed. First, e RNS technique gets a good result point in SPP mode wi positional accuracy of 0.36m. This for e data collected on May 28, 1998 and of course was also examined on a dataset of e test point after August 4, 1999 using e data bank constructed for e October 12, 2001 and for assurance, possessed e same reference points using August 4, 1999 data. Only a very result. Note here at e consistent results obtained in slight degradation between such two dates is observed in Figure 13 are conditioned by using e appropriate data e resulted positional discrepancy (0.37 m instead of 0.31 bank for each date based on e state of SA. m). Such slight change in e resulted accuracy can be referenced to e change in e ionospheric effect on CONCLUSIONS annual basis. On e oer hand, e RNS failed for e data of September 19, 2000. A positional discrepancy in Based on e performed trials, analysis and obtained e order of 2m can be observed in Figure 12. Such large results, many important conclusions can be extracted discrepancy can be interpreted by e fact at e data concerning e accuracy of SPP using bo classical bank was constructed using e observations of e year approaches and e proposed RNS technique. Such 1999 (Where SA was still on), where as e used data at conclusions can be summarized as follows: e test point was collected where SA was turned off. Therefore, e constructed corrections data bank cannot Considering e broadcast orbital data, e maximum st be used for any GPS data collected after May 1, 2000 achievable positional accuracy using SPP can reach (The date of turning e SA off). Based on e above e order of about 10m by using a session of 8 hours. 1471

Considering e precise orbital data, SPP positional accuracy can reach e order of 4m using a session of 6 hours. Turning e SA off increases e positional accuracy of SPP to about 3m using a session of 3.5 hours. This result is obtained using precise orbital data. The developed RNS technique can improve SPP positional accuracy to e few decimeters level. This technique is based on e estimation of e coordinate corrections at e considered point, using e corresponding discrepancies at some surrounding reference points, using a certain prediction model. In e considered area (which is about 120 km x 92 km), e weighted mean prediction model (wi raising e distances to e 7 power) is e superior one in e RNS technique. For e considered area, e implementation of 9 reference points can yield a positional accuracy for SPP in e order of 27 cm. This result was obtained using 11 hours of synchronized GPS data at bo e reference points and e test point. In e developed RNS technique, a positional SPP accuracy of 31 cm can be obtained using 3 minutes of synchronized GPS data at bo e reference points and e test point. Reducing e session leng below 3 minutes degrades e efficiency of e RNS technique significantly. The application of e RNS technique is based on e construction of a data bank for e considered reference network. Such data bank should contain e coordinate discrepancies between e adjusted coordinates and SPP coordinates of e reference points, obtained every 3 minutes, wiin one complete day. In e RNS technique, coordinate discrepancies at e considered point cannot be interpolated from e corresponding discrepancies, at e reference points, computed at different time (hour) during e day. Interpolating e coordinate discrepancies at e considered point using discrepancies at e surrounding reference points computed at e same time wiin e day but in a different date yields an accuracy of 37 cm for SPP. The appropriate application of e developed RNS technique is based on e implementation of e suitable data base. Such data base should be constructed in e same state of SA (on or off, which is now mainly off) as e considered test point. REFERENCES 1. Fa-Allah, T.F., 2010. A New Approach for Cycle Slips Repairing Using GPS Single Frequency Data. The World Applied Science Journal, 8(3): 315-325. 2. El-Rabbany, A., 2002. Introduction to e Global Positioning System (GPS). Artech House Mobile Communication Series, Boston, London. 3. Hoffmann-Wellenhof, B., H. Lichtenegger and J. Collins, 2001. Global Positioning System - Theory and Practice. 5 Revised Edition, Springer-Verlag, New York. 4. El-Mowafy, A., 2005. Decimeter level mapping using differential phase measurements of GPS handheld receivers. Survey Review, 38(295): 47-57. 5. El-Tokhey, M., A.H. Abd-Elrahman, T.F. Fa-Allah and A.I. Awad, 2011. Preliminary Evaluation of Baseline Relative Accuracies Using L1 Frequency Observations of Navigation-Grade GARMIN Receivers. Journal of Surveying Engineering, 137(1): 26-32. 6. Rabah, M.M., 1998. Enhancing Kinematic GPS Ambiguity Resolution for Medium Baselines Using a Regional Ionospheric Model in Real-Time. Ph.D Thesis, Institute of physical geodesy, Dmstadt University of Technology, Germany. 7. Wubbena, G., M. Schmitz and A. Bagge, 2005. Precise Point Positioning Using State-Space Representation in RTK Networks. Presented at e 18 International Technical Meeting, ION GNSS-05, September 13-16, 2005, Long Beach, California. 8. Beran, T., D. Kim and R.B. Langley, 2003. High precision Single Frequency GPS Point Positioning. Proceedings of ION GPS 2003, Portland, Oregon, pp: 9-12. 9. Bisna, S.B. and R.B. Langley, 2001. High Precision Platform Positioning wi a Single GPS Receiver. Presented at ION GPS 2001, pp: 11-14 September 2001, Salt Lake City, Utah, U.S.A. 10. Leandro, R.F., 2009. Precise Point Positioning wi GPS: A New Approach for Positioning, Atmospheric Studies and Signal Analysis. Ph.D Thesis, Department of Geodesy and Geomatics Engineering, Technical Report No. 267, University of New Brunswick, Fredericton, New Brunswick, Canada. 11. Witchayangkoon, B., 2000. Elements of GPS Precise Point Positioning. Ph.D Thesis, e Graduate School, e University of Maine, 1472

12. Awad, A.I., 2009. Enhancement of e Accuracy of Nearest Neighbor Low Cost GPS Receivers. M. Sc. Thesis, Department of Public Works, Faculty of Engineering, Ain Shams University, Cairo, Egypt. 13. Fa-Allah, T.F., 2004. Accuracy Study of GPS Surveying Operations Involving Long Baselines. Ph.D Thesis, Department of Public Works, Faculty of Engineering, Ain Shams University, Cairo, Egypt. 14. Rehab, K.S., 2008. Performance Study of Wide Area Differential GPS (WADGPS). M Sc. Thesis, Department of Public Works, Faculty of Engineering, Ain Shams University, Cairo, Egypt. 15. IGS, 2011. http://igscb.jpl.nasa.gov/. International GNSS (Global Navigation Satellite System) Service. 16. El-Sheimy, N., 1998. Digital Terrain Modeling. ENGO 573, Lecture Notes, Department of Geomatics Triangulation: Engineering, University of Calgary, Canada. 17. Ghazal, G., T.F. Fa-Allah, S.H. Ibrahim, X A.M. El-Desouky and O.M. Mossa, 2008. Comparison among Different Techniques of Predicting Geoid Undulation. Proceedings of e 7 International Conference on Civil & Architecture Engineering (ICCAE). Military Technical College (MTC), Cairo, Egypt, May 27-29, 2008. 18. Ragheb, A.E., P.J. Clarke and S.J. Edwards, 2007. GPS sidereal filtering: coordinate- and carrier-phaselevel strategies. Journal of Geodesy, 81(5): 325-335. APPENDIX Mean X1+ X2 +... Xn (5) Xcorr = n Where X corr is e Correction in X-Coordinate, calculated as a function in number of network points. Note at similar equations can be written for Y and Z Coordinates for all used prediction models. Weighted Mean PX 1 1+ P2X2 +... PnXn Xcorr = (6) n where P is e weight of each Coordinate correction and can be calculated as follows: 1 P =, where L is e L m distance from each network point to e required test point, while m is e power of is distance starting from 2, 3 8, 9. X corr = X nb, (7) Where X is e X-Correction at e nearest network nb point to e test point. Search Radius: Taking different values for circles radii, where e test point is e center of is circle and us calculating a weighted mean for its correction using equation (6) (for all network points wiin is circle) wi a certain power. Here in is power is taken as e 7 power as agreed upon in page 6. ( X2 X0)( X3 X2) ( X2 X0)( X3 X2) = ( )( ) ( )( ) ( X X ) X2 X1 X3 X2 X2 X1 X3 X2 ( X3 X1)( X1 X3) ( X3 X0)( X1 X3) ( )( ) ( )( ) ( X2 X0 ) X3 X2 X1 X3 X3 X2 X1 X3 ( X1 X0)( X2 X1) ( X1 X0)( X2 X1) ( )( ) ( )( ) ( X2 X0 ) X X X X X X X X corr 1 0 + + 1 3 2 1 1 3 2 1 (8) Where X 1,Y 1, X 2, X 2, X 3, X 3 are e X and Y coordinates of e ree points forming a triangle surrounding e test point, while X is e X-Coordinate of e test point. Note 0 at if more an one triangle is available, en e best solution regarding e test point accuracy is considered. Polynomial Model: ax + b 1 Order nd X 2 Order rd 3 Order 0 2 corr = ax0 + bx0 + c 2 2 ax0 + bx0 + cx0 st nd rd Where in each case of 1, 2 and 3 order Polynomials, e values of a, b, c and d are determined rough least square adjustment using all available network points. Note at, X 0 is e X-Coordinate of e test point substituted by in e previous equation, in order to obtain e correction at is point. Logarimic Trend: X b corr = aln X0 st (9) (10) 1473

Power Trend: Exponential Trend: b X corr = ax 0 X corr bxo e = a (11) (12) Where in e previous ree models, e values of a and b are again determined rough least square adjustment using all available network points. 1474