Improving GPS Surveying Accuracy and Productivity using Continuously Operating Reference Stations (CORS) Infrastructure Ramadan H. Abdel-Maguid Associate Professor Department of Civil Engineering, Faculty of Engineering, Fayoum University, Egypt [email protected]
ﻣﻠﺧص اﻟﺑﺣث ان ﻧظﺎم اﻟرﺻد اﻟﻌﺎﻟﻣﻲ ) (GPSﯾﺳﺗﺧدم ﻓﻲ اﺟزاء ﻣﺧﺗﻠﻔﺔ ﻣن اﻟﻌﺎﻟم ﻟﻠﻛﺛﯾر ﻣن اﻟﺗطﺑﯾﻘﺎت ﻣﺛل ﺷﺑﻛﺎت اﻟرﺑط اﻟﺟﯾودﯾﺳﯾﺔ ،واﻟﺗطﺑﯾﻘﺎت اﻟﻣﺳﺎﺣﯾﺔ واﻟﮭﻧدﺳﯾﺔ ٠وﻟﻘد ﺗم اﻧﺷﺎء اﻟﻌدﯾد ﻣن ﺷﺑﻛﺎت اﻟﻣﺣطﺎت داﺋﻣﺔ اﻟﺗﺷﻐــﯾل ) (CORSﻓﻲ اﻣﺎﻛن ﻋدﯾدة ﻟدﻋم ﻣﺟﺎﻻت اﻟﻣﺳﺎﺣﺔ ﺑﺎﺳﺗﺧدام ﻧظﺎم اﻟرﺻد اﻟﻌﺎﻟﻣﻲ )(GPS وﻣﺟﺗﻣﻊ اﻟﻣﻌﻠوﻣﺎت اﻟﺟﻐراﻓﯾﺔ ٠وﺗﺳﺎھم ھذه اﻟﺷﺑﻛﺎت ﻓﻲ زﯾﺎدة اﻧﺗﺎﺟﯾﺔ اﻟرﺻد ﺑﺗوﻓﯾر ﺗﻛﻠﻔﺔ اﻟرﻓﻊ اﻟﻣﺳﺎﺣﻲ ﺣﯾث ﯾﻣﻛن اﺳﺗﺧدام ﻋدد واﺣد ﻣﺳﺗﻘﺑل ﻟﻼﺷﺎرات ﺑدﻻ ﻣن ﻋدة اﺟﮭزة ﻋﻧد اﺟراء اﻟرﺻد اﻻﺳﺗﺎﺗﯾﻛﻲ واﻟﻛﯾﻧﻣﺎﺗﯾﻛﻲ. وﻗد ﯾﺣﺗﺎج ﻣﺳﺗﺧدﻣﻲ ﺑﯾﺎﻧﺎت ﺷﺑﻛﺎت ﻣﺣطﺎت داﺋﻣﺔ اﻟﺗﺷﻐﯾل ) (CORSاﻟﻲ ﺑﯾﺎﻧﺎت ﺧﺎﺻﺔ ﺑدﻗﺔ ﻗﯾﺎﺳﺎت ارﺻدة ) (GPSوذﻟك ﻻدﻣﺎﺟﮭﺎ ﻣﻊ اﻟﺑﯾﺎﻧﺎت اﻻﺧري اﻟﻣﺟﻣﻌﺔ ﺑواﺳطﺔ اﺟﮭزة ﻣﺳﺗﺧدم اﻟﺑﯾﺎﻧﺎت٠ ﻓﻲ ھذا اﻟﺑﺣث ﻓﻘد ﺗم ﺑﯾﺎن اﻟﺧطوات اﻟﻼزﻣﺔ ﻻﺳﺗﻧﺗﺎج دﻗﺔ ارﺻﺎد ) (GPSاﻟﺗﻲ ﺗم ﺗﺟﻣﯾﻌﮭﺎ ﺑﺎﺳﺗﺧدام ﺷﺑﻛﺎت اﻟﻣﺣطﺎت داﺋﻣﺔ اﻟﺗﺷﻐﯾل ) (CORSﻣﻊ اﻻﺧذ ﻓﻲ اﻻﻋﺗﺑﺎر اﻣﻛﺎﻧﯾﺔ اﺳﺗﺧدام ﻣﺳﺗﺧدم اﻟﺑﯾﺎﻧﺎت ﻻﺟﮭزة وﺑراﻣﺞ ) (GPSﻣﺧﺗﻠﻔﺔ ٠وﻗد اﻋﺗﻣد اﻟﺑﺣث ﻋﻠﻲ ﺗﺟﻣﯾﻊ ﺑﯾﺎﻧﺎت ﻣن ﺷﺑﻛﺔ ﻣﺣطﺎت داﺋﻣﺔ اﻟﺗﺷﻐــﯾل ) (CORSﺑﺗﺎرﯾﺦ ١١اﻛﺗوﺑر ٢٠٠٦وذﻟك ﻟﻌدد ١٨ﻣﺣطﺔ ﺗﻘﻊ ﻓﻲ وﻻﯾﺔ اوھﺎﯾو ﺑﺎﻟوﻻﯾﺎت اﻟﻣﺗﺣد اﻻﻣرﯾﻛﯾﺔ ﺣﯾث ﺗراوﺣت اﻟﻣﺳﺎﻓﺔ ﺑﯾن اﻟﻣﺣطﺔ اﻟﻣﺳﺗﺧدﻣﺔ ﻟﻼﺧﺗﺑﺎر واﻟﻣﺣطﺎت اﻻﺧري ﺑﯾن ٤٩ﻛم ١٣٠ ، ﻛم ٠وﻗد ﺗم دراﺳﺔ ﻣدي ﺗﺄﺛﯾر اﺧﺗﯾﺎر ﻧﻘﺎط واﺷﻛﺎل ﺷﺑﻛﺎت ﻣﺧﺗﻠﻔﺔ ﻋﻠﻲ دﻗﺔ ﺣﺳﺎﺑﺎت اﺣداﺛﯾﺎت اﺣد ﻧﻘﺎط اﻟﺷﺑﻛﺔ ٠وﻛذﻟك ﺗم ذﻛر ﻣﺎﺗوﺻل اﻟﯾﮫ اﻟﺑﺣث ﻣن ﺗوﺻﯾﺎت٠
ABSTRACT Global Positioning System (GPS) is used worldwide for many geodetic controls, surveying and engineering Applications. The recently developed Continuously Operated
____________________________ Associate Professor, Civil Engineering Department, Faculty of Eng., Fayoum Univ., Fayoum , Egypt
433. CERM Vol. (29) No. (2) April, 2007, page 433-449
Reference Stations (CORS) are constructed in many places to support GPS surveys undertaken by the geospatial community. The CORS networks increase GPS positioning productivity by reducing the field survey costs when using one receiver instead of two for traditional differential static and kinematic GPS surveys. The user of CORS data may require information about the reliability measures of CORS data that can be utilized with the data collected by user’s receiver and processing software. In this paper, the procedure to derive the GPS accuracy estimates using CORS data is undertaken into considerations user hardware configuration and processing software. The research studies was undertaken based on CORS data collected on October, 11, 2006 for eighteen CORS stations located in OHIO state, USA. The baseline distances between the estimated tested site and other CORS stations vary between 49 kilometers and 130 kilometers. The impact of using various baseline configurations on the computed GPS coordinates of a known station is tested and analyzed in details. Finally, the paper ends with concluding remarks and recommendations for future GPS networks and surveys based on CORS networks on other places.
Keywords: Global Positioning System (GPS), CORS Networks, Accuracy, Network Analysis
1. Introduction Global Positioning System (GPS) is used worldwide for geodetic control, surveying and engineering applications. Recently, the GPS support effort has been increased using Continuously Operating References Stations (CORS). The CORS networks are comprises of a network of hundreds of GPS base stations whose data are made publicly available through the internet for various applications. One of the most known CORS systems is the national CORS system in the United States that is based on integrated cooperative from various government, academic, commercial, and private organizations (17). In the Arab region, Saudia Arabia established thirteen CORS site to collect GPS data continuously (7). In Egypt, thirty High Accuracy Reference Network (HARN) stations were established with 200 kilometers apart to form the geodetic database with 0.1 ppm accuracy (4). This network is a potential for CORS network. Densification of these stations with 50 kilometers apart is undertaken for National Agriculture Cadastral Network (NACN). 434.
The CORS data are based on GPS carrier phase observations and the data is available in RINEX format. The user of the CORS data can simply download the raw data and combined it with the user’s GPS receiver data. The CORS data, as other GPS data, is inherited by many errors such as: Orbit errors, ionospheric effects, tropospheric effects, multipath effects, measurement resolution (the carrier phase measurement error), ambiguity resolution and accuracy of known control (3). In this paper, the GPS data handling and adjustment using CORS data are presented. The CORS coverage and other accuracy requirements is reviewed in section 2. The GPS network analysis is reviewed in section 3. In section 4, the testing scheme of GPS measurements that downloaded from NGS server (12) is presented. Section 5 presents the results of the GPS data processing of various base stations configurations used to test one of the known CORS stations. Finally, the paper ends with conclusions and recommendations for future research.
2. CORS Coverage and Accuracy Requirements The main components of the CORS systems are: remote GPS reference stations that collect the GPS data, the control station that collect, analyze and distribute the data, and the end users (10). Each GPS reference station includes a dual-frequency GPS receiver, a GPS antenna, and communication equipment. The GPS site requirements for CORS networks are illustrated in details in the literature and can be reviewed for example from Stone (16). The CORS coverage can be selected based on both site requirements and overall network issues such as regional station coverage and site infrastructure robustness. For regional station coverage requirements, the CORS sites can be selected to cover a 80 kilometers around the GPS site. The spacing may be chosen to be dense in urban areas while longer spacing of rural areas (150 kilometers) can be chosen (2, 6). There are many GPS techniques that could be used by the users utilizing CORS networks such as (16): •
Long-session static positioning for geodetic control surveys (centimeter accuracy),
Kinematic travel-path determination (few-decimeter accuracy),
Feature mapping for GIS data collection (meter to sub-meter accuracy).
The obtainable GPS data accuracy using various GPS techniques is represented in Table (1) (18). Performing of GPS surveying utilizing CORS data should be undertaken based on traditional GPS survey guidelines and the maximum recommended distance for GPS surveying applications (14). This means that the distance between the user receiver and the closest reference receiver should be less than 10 kilometers for RTK and 20-30 for rapid static techniques to distance-dependent biases between reference and rover receivers (9). The previous GPS guidelines define the utilization of the CORS networks by the geospatial community. The user can utilize the CORS data in a dynamic and productive manner if the data be collected, resolved, analyzed and utilized properly. The accuracy of CORS baselines itself may run between 1 and 3 cm in horizontal and between 2 and 5 cm in vertical directions (8). The survey accuracy that could be obtained by any user using CORS baselines may be changed based on many factors such as: the number of satellites visible to rover receiver, obstructions, baseline length, multipath, environmental effects, and availability of L1/L2 signals, occupation times, and observation conditions (11).
3. GPS Network Analysis Many of the local GPS surveys are rely on linking of local GPS measurements to existing control points with known positions. The referenced stations of the local surveys can be integrated to national GPS networks using known control stations in an over-constrained adjustment (3). The designing process of such GPS networks is generally based on several operations such as planning, logistical considerations, reconnaissance, field procedures, and office calculation (15). For full utilization of the CORS systems, the GPS local surveys should be tested and evaluated based on various coverage configurations. The evaluation process is undertaken to predict the obtainable level of accuracy using CORS infrastructure. The evaluation of the local surveys collected using such networks involves weighting of control points in adjustment process. The weighting scheme of the used control points should be undertaken with care in case of using control points captured from various GPS network configurations.
The traditional GPS network analysis and surveys standards should initially be fulfilled. Network analysis can be utilized for isolating inherent bad observations using minimally constrained adjustment. Remaining hidden errors will degrade the quality of the least square adjustment (1). Standard requirements for GPS surveys can be demonstrated by fulfilling the minimum requirement of using of three points in the local survey that is connected to at least three known control points in NAD83 to detect any errors in connecting baselines into control stations. When connecting to CORS sites, only two control stations would be required to detect survey errors due to reliability of the CORS sites (3). User Densification Network (UDN) that used in regional densification of the HARN networks is represented in Table (2). Similar guidelines for the orthometric height surveys can be reviewed from (13). Practical considerations concerning dealing with GPS derived elevations should be considered. The GPS derived elevations data are generally affected by many factors such as: limited GPS-measured ellipsoid heights; different ellipsoid reference surfaces; varying geoid models for converting ellipsoid heights to orthometric elevations and antenna heights errors and phase center variation. Therefore the quality of the derived GPS data may be degraded due to such inherited limitations (5). 4. GPS Test Experiment The network to be used as a test bed for this research is a part of a CORS network located in OHIO State, USA (Figure 1). This part of the network was selected due to its dense nature in a well developed geodetic infrastructure environment. The results of the analysis of such networks may help in developing new networks in the Arab region with coarse coverage. The study involves observing eighteen CORS stations. Hourly RINEX files for GPS data collected on October, 11, 2006 are downloaded from the NGS Central Server (12), thinned to a 5 second observation rate and merged into required session durations time. The PDOP values were acceptable. The Ashtech Solutions GPS software, the available software to the author, was used to carry out the network processing. As mentioned above, great care should be taken in the field when dealing with measurement and documentation of the receiver antenna heights. For this research, measurements are related to antenna reference point (ARP) for all CORS base stations. For practical field surveys, reduction of antenna height into proper elevation height is required.
The test experiments involved computing of the tested site named “OHCL”, one of the CORS stations, using single baseline solutions, two baseline solutions up to many baseline solutions. For each category, different baseline configurations are used in the processing of GPS data. The processed baselines range in length from 49.6 kilometers to 130.8 kilometers, with an average length of 90.5 kilometers. The coordinate position accuracy of the known station “OHCL” using various combinations of the surrounding base stations were examined and analyzed using the available software to the author. The coordinates of the reference base stations were held fixed and the station “OHCL” was referenced. Configurations with different baselines were used for several experimental tests. The GPS observation data of 12-hr was collected and a fixed 2 hr was used in many tests. Long lasting observation time between 6 hr and 12 hr is also tested in some cases to ensure achieving millimeter level of accuracy for the tested site. 5. Data Processing and Results The horizontal and vertical variations in the computed position of the test site “OHCL” are calculated. Observations using only one base station lead to 2 centimeter horizontal position accuracy for distances up to 68 kilometers and 2-hr observation session. The vertical accuracy was 5 centimeter for the same distance range and same session duration as shown in Table (3). These results match the pre-estimated accuracy level of the CORS baselines. Improper horizontal residual, when compared with the vertical residual, for the tested station encountered in case (1-4) due to unresolved source of error. Observations using two base stations show that 2 centimeter horizontal position accuracy was not achieved when distances from the “OHCL” station to other stations have higher or varying distances (Table 4). Varying or using longer baseline distances seem to affect both the horizontal and vertical accuracy. Better results as derived from cases (2-10) into (2-13) may be achieved using two stations that lie on a line which almost passing the referenced station “OHCL”. Also unexpected horizontal residuals was obtained in cases (2-3), (2-8) and (2-9). For observation of the test site using three base stations, more accurate horizontal accuracy was achieved while the vertical accuracy does not seem to be achieved (Table 5). Controlling the required vertical accuracy seems to be possible by using longer 438.
sessions duration as illustrated before due to the inherent GPS measured ellipsoidal heights limitations. Better results seem to be achieved using three base stations that constitute a triangle around the test site “OHCL”. The previous remarks concerning the horizontal and vertical accuracies are also valid for four baselines solutions (Table 6). Lower level of accuracy was achieved in case (4.3) due to using longer baseline lengths (range between 68.1 kilometers to 130.8 kilometers) without increasing the session duration time. Also unexpected horizontal residual was obtained in cases (4-3) and this may be due to improper weighting of the control points. Using multi-baseline observation, higher level of accuracy was achieved as shown in Table (7). Better results are derived using only six reference base stations due to using baselines of relatively equal lengths (ranges varies between 49.6 kilometers to 68.6 kilometers) (case 5.3). Multi-baselines solution, using seventeen base stations, is also analyzed to test the inner accuracy of the solution. The processed residuals obtained from the Ashtech software, represent linear relationship with the baseline lengths (Fig. 2). These values are realistic as the errors increase with the increased baseline distances. Residuals for adjusted vectors components versus baseline lengths are shown in Fig. (3) through Fig. (5) and indicate that better accuracies is achieved with “X” component while the lower accuracy with “Z” component. For kinematic solution using the static survey data, the GPS baseline between the reference station and the test station was undertaken to test the stability of kinematic solution. The standard deviations of the overall period were about 3 cm for the horizontal components, and 4 cm for the vertical component when using single baseline solution as shown in Table (8) and Fig. (6). Using many baselines does not improve the stability of the solution significantly as shown in Table (8). This result may be due to dissimilar pattern of errors that affect various baselines calculations using kinematic solution. 6. Conclusions Current and forthcoming GPS infrastructure such as CORS will add great opportunity to the geospatial community as the user will be able to select certain GPS data that assure the required spatial requirements. The user of the CORS data, using his own raw data and processing software, can be able to fully utilized of the available data and be able to get reliable quality estimates of the GPS processing data for the local surveys.
This paper presents the methodology to derive the GPS processing accuracy using several baseline configurations. The results of the study present that the horizontal accuracy of the computed GPS coordinates using single baseline and CORS data was in the level of 2 cm and the vertical accuracy was in the level of 5 cm based on the data captured for 2-hr observation session and the distances between control stations and the test station were up to 68 kilometers. The study reveal that using two base stations for the GPS data processing can not assure getting the required level of accuracy as the baseline distances increase or using baselines with considerable varying distances. Also using three base stations, more accurate horizontal accuracy was achieved while the vertical accuracy does not seem to be achieved. The error, horizontally and vertically, increases with distance from the base station when one or two base stations are used. The horizontal error is essentially un-enhanced with increasing distances up to 78.5 kilometers with three base stations. The concluded statement is restricted to the using fixed 2-hr session duration and the available software to the author. Using multi-baseline observations, high level of accuracy is achieved for both the horizontal and vertical components of the computed GPS coordinates with little effects for increasing the secession duration to 12-hr due to insufficient modeling of the GPS environmental effects and the weighting of control points. Generally, more accurate results seem to be achieved when using baselines with relatively equal lengths and located in a line or around the referenced station. This statement may be due to using homogeneous precision estimates for the reference stations in the adjustment. Therefore, greater errors in the solution may be due to incorrect weighting of the baselines using processing software similar to that used in this research. For kinematic solution using one reference station with the test site, the standard deviations of the overall period were about 3 cm for the horizontal components, and 4 cm for the vertical component. The results do not be enhanced considerably using many baselines in the solution. 7. References 1. Best-Fit Computing, Inc., 2006, “COLUMBUS 3.6 User Manual and Help Files: Chapter Five - Network Adjustment”, website http://www.bestfit.com. 440.
2. Brown, N.; Kealy, A.; Millner, J. and Williamson, I., 2002, “Quality Control and Integrity Monitoring of the Victorian GPS Reference Network”, FIG XXII International Congress, Washington D.C. USA, April 19-26. 3. Craymer, M. R., 1998, “Integration of Local Surveys into the Canadian Spatial Reference System”, Presented at the Public Works and Government Services Canada (PWGSC) Survey Contracting and CACS Seminar, Edmonton, Alberta, February 24, 1998. 4. Dawod, G. M. and Ismail, S. S., 2005, “Enhancing the Integrity of the National Geodetic Data Bases in Egypt ‘, From Pharaohs to Geoinformatics, FIG Working Week 2005 and GSDI-8, Cairo, Egypt April 16-21. 5. Department of Public Works, City of Madison, 2005, “Comparison of GPS Base Station Positions - City of Madison, WI”, Department of Public Works ,Engineering Division,
http://gis.cityofmadison.com/Madison_GPS/ 6. Dollman-Jersey, B., 2002, “MDOT CORS”, website www.ngs.noaa.gov/CORS /CorsPP/forum2002/jersey.ppt. 7. Eren, K., 2005, “The Issues Related to Geoinformation in Developing Countries”, Geo Tech Group. Website http://unstats.un.org/unsd/geoinfo/8unrccaIP32.pdf 8. Fernandez-Falcon, E., 2005 “Pennsylvania GPS - CORS Project”, Penn State Surveying
surv/Cors.htm, website updated on 2005. 9. Hale, M. and Asmussen, H., 2006, “GPSnet / VICpos / MELBpos”, GPS for Cadastral Surveys Workshop, February 2, Melbourne. 10. Harris, R. S., 2002, “Florida Continuous GPS Array: Overview Presentation”, 40th Meeting of the Civil GPS.
summaryrpts/40thmeeting/02Florida40Pres.ppt 11. Mesa County GPS/Surveying, 2002, “CORS / URS GPS Base Station NGS Sanctioned”, website,
Last Updated: 08/02/02 12. National Oceanic and Atmospheric Administration, 2006, “What is CORS? Continuously
http://www.ngs.noaa.gov/CORS accessed on October.
13. National Oceanic and Atmospheric Administration, 2006, “GPS Survey Observations Draft Manual”, NGS website http://www.ngs.noaa.gov/ PROJECTS/ GPSmanual/observations.htm. 14. NCDOT Location and Surveys Manual 6-1, 2002, “Global Positioning System (GPS) Survey Guidelines”,
PRECONSTRUCT/HIGHWAY/location/support/Support_Files/Documents/Manu als/LocationGPS0202.PDF. 15. Saleh, H. A. and Dare, P., 2002, “Heuristic Methods for Designing a Global Positioning System Surveying Network in the Republic of Seychelles”, The Arabian Journal for Science and Engineering, Volume 26, Number 1B. April 2002 16. Stone, W., 2006, “The Evolution of the National Geodetic Survey’s Continuously Operating Reference Station Network and Online Positioning User Service”, National
http://www.ngs.noaa.gov/PUBS_LIB/Evolution_of_CORS_and_OPUS.pdf 17. Washington State Department of Transportation (WSDOT), 2005, “Keeping up with GPS
AdvisoryTeam/ docs/KeepingUp1.pdf 18. Wolf, T., 1999, “Establishing a Multifunctional GPS Base Station for Survey and Resource
Table (1) The obtainable GPS data accuracy using various GPS techniques (after (18) Technique Static (Horiz) Static (Vert) RTK (Horiz) RTK (Vert)
1 sigma ±(5mm+(2ppmXBL)) ±(8mm +(2ppmXBL)) ±(1cm+(2ppmXBL)) ±(2cm+(2ppmXBL))
2 sigma ±(7mm+(2ppmXBL)) ±(1cm +(2ppmXBL)) ±(2cm+(2ppmXBL)) ±(3cm+(2ppmXBL))
Table (2) Network Design Guidelines for UDN Surveys (after 13) Minimum Number of Stations At least 2 HARN stations Maximum Station Spacing < 25 kilometers between UDN stations Required Baselines To adjacent stations Observations per Baseline 2 each, 30 minute observations Sidereal Time Offset Between Repeated No time offset required Observations Fixed-height Tripods Required? No fixed-height tripods required At representative stations in the middle of Acquire Meteorological Data? each observation 30 second epochs, 15 degree elevation Data Acquisition Parameters masks 30 second epochs, 15 degree elevation Data Processing Parameters masks, precise or rapid ephemerides
Table (3) Residuals of “OHCL” station coordinates based on single baseline solutions (Case 1) Case No.
1-1 1-2 1-3 1-4 1-5 1-6 1-7
OHUN - OHCL LEBA - OHCL OHFA - OHCL OHDR - OHCL SIDN – OHCL COLB - OHCL OHPR - OHCL
Distan ce (Km) 51.825 68.617 55.856 68.125 49.622 67.715 49.622
D East (m) 0.002 -0.016 -0.001 0.017 -0.010 0.003 0.006
D North (m) -0.009 0.006 -0.012 -0.012 -0.006 -0.013 -0.001
D Elev. (m) -0.018 0.034 0.017 -0.016 -0.049 0.005 -0.039
Horiz. Error (m) 0.009 0.017 0.012 0.021 0.012 0.013 0.006
Total Error (m) 0.020 0.038 0.021 0.026 0.050 0.014 0.039
Table (4) Residuals of “OHCL” station coordinates based on two baselines solutions (Case 2) Case No.
D East (m)
KNTN – OHCL OHUN - OHCL COLB – OHCL OHUN - OHCL COLB – OHCL OHFA - OHCL LEBA – OHCL OHFA - OHCL LEBA – OHCL OHPR - OHCL OHDR – OHCL OHPR- OHCL OHDR – OHCL SIDN - OHCL OHAL – OHCL SIDN - OHCL KNTN – OHCL OHAL – OHCL KNTN – OHCL LEBA – OHCL OHPR – OHCL OHUN – OHCL COLB – OHCL OHPR – OHCL OHFA – OHCL SIDN – OHCL
78.562 51.825 67.715 51.825 67.715 55.856 68.617 55.856 68.617 66.981 68.125 66.981 68.125 49.622 94.471 49.622 78.562 94.471 78.562 68.617 66.981 51.825 67.715 66.981 55.856 49.622
2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 2-10 2-11 2-12 2-13
D North (m) -0.013
D Height (m) -0.058
Horiz. Error (m) 0.013
Total Error (m) 0.059
Table (5) Residuals of “OHCL” Station coordinates based on three baselines solutions (Case 3) Case No.
COLB KNTN OHUN COLB LEBA OHFA LEBA OHDR OHPR KNTN OHDR SIDN KNTN LEBA OHFA LEBA OHPR OHUN COLB LEBA SIDN OHFA OHPR SIDN
67.715, 78.562, 51.825 67.715, 68.617, 55.856 68.617, 68.125, 66.981 78.562, 68.125, 49.622 78.562, 68.617, 55.856 68.617, 66.981, 51.825 67.715, 68.617, 49.622 55.856, 66.981, 49.622
D East (m)
D North (m)
D Height (m)
Horiz. Error (m)
Total Error (m)
Table (6) Residuals of “OHCL” Station coordinates based on four baselines solutions (Case 4) Case No.
D East (m)
4-1 4-2 4-3
LEBA-OHFA-OHUN-SIDN COLB-LEBA- OHPR-OHUN
-0.007 0.000 -0.004
D North (m) -0.006 -0.005 -0.041
D Height (m)
Horiz. Error (m)
-0.007 -0.015 -0.044
0.009 0.005 0.041
Total Error (m) 0.012 0.016 0.060
Table (7) Residuals of “OHCL” station coordinates based on multiple Baseline solutions (Case 5) Case No.
D East (m) -0.002
Horiz. Error (m)
D Height (m) -0.008
Total Error (m) 0.015
D North (m)
All Baselines (12hr)
All Baselines (2hr)
6 sites (around test site)
Table (8) Residuals of “OHCL” station coordinates based on kinemtaic solution
Single Baseline solution 2 baseline solution
3 baseline solution
4 baseline solution
Value Max Min Aver Stdev Max Min Aver Stdev Max Min Aver Stdev Max Min Aver Stdev
D East (m) 0.016 -0.972 -0.01365 0.031331 0.023 -0.972 -0.01323 0.03153 0.023 -0.972 -0.0132 0.031503 0.023 -0.972 -0.01323 0.03153
D North (m) 0.489 -0.197 0.001096 0.028031 0.489 -0.197 0.000796 0.027806 0.489 -0.197 0.000793 0.027777 0.489 -0.197 0.000796 0.027806
D Height (m) 0.029 -0.506 -0.03732 0.042946 0.029 -0.506 -0.03627 0.043109 0.029 -0.506 -0.03619 0.043095 0.029 -0.506 -0.03626 0.043109
Figure 1: Selected CORS stations located in OHIO, USA
Relationship between processed residuals versus Baseline Length
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
Figure 2: Relationship between processed residuals and baseline lengths. 447.
Residuals for adjusted Vectors (X component) 0.1 Error (m)
0.08 0.06 0.04 0.02 0 -0.02
-0.04 -0.06 -0.08 Distance (m)
Figure 3: Residuals for adjusted vectors components versus baseline lengths Residuals for adjusted Vectors (Y component) 0.1 0.08 Error (m)
0.06 0.04 0.02 0 -0.02
-0.04 -0.06 -0.08 Distance (m)
Figure 4: Residuals for adjusted vectors components versus baseline Lengths Residuals for adjusted Vectors (Z component) 0.2 0.15 Error (m)
0.1 0.05 0 -0.05
-0.1 -0.15 -0.2 Distance (m)
Figure 5: Residuals for adjusted vectors components versus baseline lengths.
Variation in East Coordinates 0.1 0 Error (m)
-0.2 -0.3 -0.4 -0.5 -0.6 Epoch No.
Variation in North Coordinates 0.6
0.4 0.2 0 -0.2 0
-0.4 -0.6 Epoch No.
Variation in Elevation Coordinates 0.1
0 -0.1 0
-0.2 -0.3 -0.4 -0.5 -0.6 Epoch No.
Figure 6: Variations in the computed coordinates of test site using single base kinematic solution