Control Point Positioning Using GPS

Dr Jayanta Kumar Ghosh & Ch. Venkata Appa Rao
Civil Engineering Department
Remote Sensing & Photogrammetric
Engineering Section Indian Institute ofTechnology, Roorkee
Uttaranchal 247 667
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Abstract
GPS technique has been well established as a means for establishment of control points in surveying and mapping. In carrying out this, the absolute coordinates of at least one site have to be known accurately in WGS84 coordinate system. As WGS84 coordinates for a particular site was not known neither it could be derived, in order to establish a reference station, Single Point Positioning technique of GPS has been applied for several hours of observation spanning in three consecutive days and night. The observed value shows precise planimetric position but grossly imprecise in height. However, the study provides some insight on the influence of some variables like a-priori value of parameters, time of observation etc. on result. The paper also discusses the probable sources of errors, precautions to be taken and direction of further study.

Introduction
Control establishment is an important exercise in mapping process. The mapping accuracy is directly based on the accuracy of control network. The control network is formed by a group of points whose position (x,y,z) are known to a high degree of accuracy. Accuracy defines the quality of a control network. The positions of other features of interest are determined with respect to these control points for mapping. To achieve such a high degree of accuracy a reliable and accurate method of surveying is required. Though several techniques are used to properly establish and provide accurate horizontal and vertical control networks, meeting the requirements of the user community, the best technique will be one that provides the control networks with required mapping accuracy at the least cost in time and money.

The GPS (Global Positioning System) is one of the viable systems which meets the requirements of the surveying fraternity all over the globe. It is a space-based all weather radio navigation system. It broadcasts precise, synchronized timing signals to provide precise estimates of position, velocity and time of the antenna location of the system receiver. There are several methods of measurement based on GPS that make possible to take survey measurements from space. The numerous limitations of the terrestrial surveying like requirement of inter-visibility of survey stations, dependability on weather, difficulties in night observations, 3D position parameters etc could be overcome using GPS techniques. These advantages over the conventional techniques coupled with economy in time and cost, accuracy, speed and versatility in operation make GPS the most promising surveying tool of the future. Thus, a great technological revolution is taking place at the development of GPS as it can be used in any conceivable problem under the sky, where the exact position of any object or phenomena involved.

GPS surveying is a relative technique with baseline being “observed” and computed from the reference to rover. As many baseline will often be measured from the same reference station, the choice and reliability of reference station are of particular importance. Thus, the absolute WGS84 coordinates of at least one site have to be known accurately as all measurements in GPS system are depicted in WGS84 coordinate system.

For any precise GPS survey the absolute coordinates of ONE site in a network have to be known in WGS84 to about 10 meters. There are three possibilities for obtaining reliable WGS84 coordinates for one site and these are:
• WGS84 coordinates may be available.
• WGS84 coordinates can be derived from local coordinates using appropriate transform function.
• WGS84 coordinates can be computed by GPS point positioning.
Since, WGS84 coordinates for a particular site is not known neither it could be derived, Single Point Positioning technique of GPS has been applied for several hours of observation spanning in three consecutive days and night.

Methodology – Point positioning
In point positioning, coordinates of the antenna position at an unknown point are sought with respect to the WGS84 reference frame. In this method, the known positions of the tracked GPS satellites (the position of a satellite can be computed from ephemerides) are being used to determine the position of unknown point using single GPS receiver by a method similar to the method of resection used in plane table surveying (Fig. 1).

Fig. 1: Point Positioning of GPS receiver

In this figure, s1, s2, s3 and s4 represent four different satellites (least required) being tracked. The positions of these satellites are referenced to the centre of the earth in the X, Y, Z coordinate frame. The coordinates for s1 are shown as (xs1, ys1, zs1). The coordinates of r, the unknown point, as referenced to the centre of the earth, are assumed to be (xr, yr, zr). The observed code, Prs1, relates the known coordinates of satellite 1 with the unknown coordinates of the receiver using the equation for a line in three-dimensional space. That is,

Prs1 = Ö [(Xs1 - Xr)2 + (Ys1 - Yr)2 + (Zs1 - Zr)2] + error

Thus, from four satellites, four distance equation can be formed leading to computation of the four unknowns (xr, yr, zr and clock bias) can be computed.

Study area
The area of study is the campus of IIT Roorkee. The astronomical coordinates of Roorkee are known to be: 29° 52 002 North, 77° 53 522 East and its height above datum (geoid) is 268 meter.

Location of Control point
Since control point has to meet some specific requirements with special emphasis of its suitability for GPS observation, the choice and reliability of reference station is of particular importance. In taking care of a good site characteristics for GPS observation such as
• A clear view of the sky;
• No obstructions above the cut-off angle (say 15°);
• No reflecting surfaces that could cause multi-path;
• Safe, away from traffic and passers-by;
• Possibility to leave the receiver unattended;
• No powerful transmitters (radio, TV antennas etc.) in the vicinity, a point on the top of a building (the Remote Sensing and Photogrammetric Engineering Section) of Civil Engineering department at IIT Roorkee is found suitable and thus considered as reference station for GPS receiver and subsequently, serves as the control point for this study.
Equipment
The field equipment includes one GPS receiver unit and auxiliary devices such as tripod, tribach, and other ancillary equipment.

Experimental Set up, Data collection and Processing
In view of establishing the control point on the top of building, GPS observation was carried out on absolute position mode, also known as single point positioning. In the absolute positioning mode, single GPS receiver is used to find the coordinates of the antenna position. Steps those were carried out for experimental set up, data collection and processing are as follows:
• Antenna setup: The tripod was set above the control point and then attached the tribach. The leveling and centering was then carried out iteratively before fixing the antenna to the tribach. Other components i.e., sensor, controller, battery etc were then connected.
• Initialisation: A mission was then started to take GPS observation in static survey mode. Before starting to take observation a few input parameters such as the sampling rate, sampling type, cut off elevation angle, project and job name, approximate location (29° 52 002 North, 77° 53 522 East and height 268 meter), height of antenna and antenna offset etc for the point were fed through controller.
• Data collection: The data was collected taken during different sessions spread over three consecutive days/nights as given in Table 1.
• Data processing: The collected data was then dumped from controller to computer. After creating a project, the data was brought and processed within SKI 3.2 post-processing software.
Observation and Result
The observation was taken on April 19, 2001 starting from 17hr 31min 55sec to 26hr 46min 55sec i.e., a duration of 7 hr 15 min starting from early evening to late night. On next day i.e, on April 20, the observation session started at noon (14 hr 31 min 30 sec) and continued till mid-night (24 hr 32min 25 sec) for a duration of 10 hr 12 min 55 sec. On April 21, 2001, there were two sessions for observation- first one from early morning (04hr 38 min 20 sec) to noon (14 hr 31 min 30 sec) for a duration of 09 hr 53 min 10 sec and second one from evening (18hr 47 min 30 sec) to night (21 hr 13 min 05 sec) for a duration of 02 hr 25 min 35 sec. On April 22, the observation session was restricted in early morning only from 03 hr 36 min 35 sec to 05 hr 55 min 15 sec for a duration of 2 hr 18 min 40 sec.

The observed data was processed in SKI 2.3 session wise. Only code data of both bands were used in processing. Broadcast ephemerides were used to compute the position of satellite. Hopfield model was used to take into consideration the delay caused by troposphere but no model was used for ionospheric interference. After processing the data, following results have been obtained:
• The geodetic (WGS 84) Latitude of the station point has been found to be very precise with mean (29° 51 45.5274642 North) and standard deviation (0.479622).
• The geodetic (WGS 84) Longitude of the station point has been found to be very precise with mean (77° 54 0.7782962 East) and standard deviation (0.1705042).
• Mean of the geodetic (WGS 84) heights has been found to be 241.80225 meter with standard deviation 2.79805 meter (In this calculation height found in session 2 is considered as Outlier).
The details of the observation and geodetic coordinates are given in Table 1.

Table 1 Observation Session, Period & Duration and Geodetic coordinates (a-priori and calculated)
SESSION Detail of Observation A-priori Geodetic (WGS84)Co-ordinates of Station point Calculated Geodetic (WGS84)Co-ordinates of Station point
Date (April, 2001) Time Duration Latitude(29° 51'+) Longitude(77° 54'+) Height (m) Latitude(29° 51'+) Longitude(77° 54'+) Height (m)
From To Hr ' " Hr ' " Hr ' " ' " ' "
1 19th 17 31 55 26 46 55 07 15 00 45.7988 0.8375 239.3912 45.79879 0.83757 239.3848
2 20th 14 19 30 24 32 25 10 12 55 45.4908 0.7363 214.2942 44.77643 0.47672 119.0427
3 21st 04 38 20 14 31 30 09 53 10 45.7391 0.7054 235.2110 45.50903 0.89779 243.4658
4 18 47 30 21 13 05 02 25 35 46.0577 0.8414 245.1550 46.05767 0.84139 245.1550
5 22nd 03 36 35 05 55 15 02 18 40 45.4954 0.8380 239.1843 45.4954 0.83801 239.2034

Discussion
The planimetric position of the station point has been observed quite precisely. Assuming the astronomic coordinates (29° 52 002 North, 77° 53 522 East) of the station point as the geodetic coordinates (since, the meridional and prime vertical components of the deflection to vertical are very small, they can be neglected for further consideration of this study), the observed planimetric position of the station point may be considered quite accurate.

However, the observed values for geodetic (WGS 84) height of the station point have been found to be very erratic. The mean calculated height (241.80225 meters) of the point is quite away from the geodetic height (207.6677 meters) [Considering, the geodetic undulation of the station point with reference to WGS 84 ellipsoid is –60.3323 meters and height above datum (geoid) as 268 meters]. It has also been observed that there is a great variation in geodetic height between a-priori and calculated values and depends on the duration of observation as well as on the period of the session. The variation is prominent if the observation session either starts or finishes at afternoon i.e., when the ionospheric disturbances are most severe. It has been also been found that geodetic height increases from its a-priori value as the observation session spreads from morning to early afternoon i.e, ionospheric disturbances changes form stable state to most severe state. And it decreases if the condition gets reverse. The degree of variation is more in case observation taken form most severe disturbance state to stable state of ionosphere. These variations are attributed to the different types of errors involved in GPS observation.

Generally, the position indicated by the GPS at a given time does not coincide with the exact position of the apparatus. In fact, the difference between the coordinate readings and the true values are caused by two types of errors:
• systematic error due to the GPS system itself (receiver noise and resolution offset, receiver hardware offset etc.), which remains the same irrespective of the measurement date and point measured; and
• random error that differs with each measurement, due to atmospheric conditions, muti-path and shadowing effect, presence of water vapor etc.
To obtain accurate geodetic height, single point positioning can not be applied directly. Rather, some other better method may be tried.

Conclusion
GPS system can be used reliably for establishing precise planimetric position of a control point. Thus, planimetric change in position of any object or phenomena can be studied very precisely by single point pointing of GPS receiver. For this no previous information is necessary other than very approximate location of the station point.

Since ionosphere is activated by solar radiation, its disturbances are much more severe on+ GPS observation during the day time than at night. So, GPS data should be preferably be collected at night than during day time, in single point positioning.

A further study can be done on the accuracy of single point positioning by using the precise ephemerides (in calculating the position of satellites).

However, other methods like relative positioning etc may be adopted which minimises the different errors. Moreover, post processing of relative positioning data takes into consideration the phase data of GPS observation and thus, may improve the accuracy of control point location. Local atmospheric models may be adopted to keep atmospheric errors least.

Acknowledgement
The authors are grateful to Dr. P.K.Garg, Coordinator, RSPE section of Civil Engineering Department, IIT Roorkee for providing available facilities and infrastructure and other laboratory staff and helpers for their help and support in carrying out the experiment.

References
• Clark, D, 1968. “Plane and Geodetic Surveying Vol. II”, Constable & Company Ltd., London pp 684.
• Leica GPS- System 300 “Guidelines to Static and Rapid Static GPS Surveying”, May 1995.
• GPS Positioning Guide - Geomatics Canada, Geodetic Survey Division Ottawa, Canada
• Vanicek, p and E.J. Krakiwsky, 1986 . Geodesy: the Concepts, Elsevier Science Publishing Company Ltd pp 697.
• Defense Mapping Agency, 1987. GPS UE Relevant WGS-84 Data Base package, Geoid height approximates in meters.
• Arnaud, M and A. Flori, ”Bias and Precision of Differential Sampling Methods for GPS Positions”, Photogrammetric Engineering and Remote Sensing, Vol. 64, No. 6, June 1998, pp. 597-600.
• Kaplan, E.D., 1996. “Understanding GPS: Principles and Applications”, Artech House, USA pp 554.

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