CHAPTER 2 GPS GEODESY. Estelar. The science of geodesy is concerned with the earth by quantitatively

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1 CHAPTER 2 GPS GEODESY 2.1. INTRODUCTION The science of geodesy is concerned with the earth by quantitatively describing the coordinates of each point on the surface in a global or local coordinate system. The real shape of the earth approximates that of an oblate ellipsoid, which is a solid obtained by rotating an ellipse and is called the Reference Ellipsoid or Spheroid (Leick, 1995). Geodetic investigations are aimed at determining vectorially the coordinates of the real earth surface locations with respect to the origin and surface of this Reference Ellipsoid. Geodetic measurements are made with reference to two points which may be a few kms apart on the earth's surface, coordinates of which have been precisely determined. The line joining these points and forming a baseline is used to constitute a triangle by including a third unknown point whose azimuthal angles from the end points of the base line are measured by theodolites. These two angular measurements, together with the base line length, enable one to calculate the coordinates of the third unknown point and the lengths of the other two sides. Using these other two sides as the next bases for the new triangles, the process is then repeated to cover the whole region with a network of triangles whose vertices can be accurately located (Parkinson et al., 1996). Modern geodetic investigations make use of the same principle, except that the baseline is constituted by positions of a set of 24 specially configured orbiting Global Positioning System (GPS) satellites up in the sky. Satellite 23

2 positions, calculated by using Kepler's laws and periodically updated by the actual tracking to correct any deviations caused by solar radiation pressure are fed to the respective satellites which, in turn, beam that information to the earth with transmission instant. Ground receivers are rigidly positioned at selected locations for accurate coordinate determinations and convert this into Satellite-Receiver Ranges Rjk (distances between the j th receiver and k th satellite) by multiplying the travel time of radio signals (beamed simultaneously at two frequencies of and MHz) with the velocity of light (~ 3X 100 million m/sec) (Leick, 1995). The heart of GPS Geodesy is the unprecedented accuracy of range and thereby coordinates determinations are made possible by the fact that the ruler used is the velocity of light, traveling at the rate of 300 billion mm/sec. The lengths of a single wave at the transmitted frequencies are of the order of 300 mm. Since each cycle consists of 360 degrees which can be accurately made to within 1 degree using modern techniques, it enables one to obtain an accuracy of ~ 3 mm in range determination. This potential accuracy of 3mm is, however, slightly degraded by the effect of the charged Ionosphere and atmosphere in the troposphere, both of which introduce travel time delays due to varying refractive index (Wells, 1989; Hoffmann et al., 1994; Leick, 1995). Fortunately, the former effect can be calculated by exploiting the dispersive (frequency dependent) effect of the ionosphere by making measurements at two different frequencies (dual frequency GPS transmission). Most of the tropospheric effect can be calculated from the ground pressure and humidity by modeling the atmosphere as a 24

3 hydrostatically stabilized medium. A source of inaccuracy stems from the uncertainty in the knowledge of precise satellite coordinates at every instant. However, the International Geodetic Service corrects this shortcoming by calculating refined orbital of GPS satellites by jointly analyzing synchronous data from several hundred permanent GPS stations around the world. This exercise naturally takes time but refined orbital are available for geodetic analysis with a delay of about a fortnight and disseminated for scientific use worldwide through the internet. GPS is widely recognized for the precision measurement of the baseline vector between pairs of receiver antennas. By differencing the carrier phases simultaneously recorded by the receivers, the coordinates of one end of the baseline ( remote or rover site) can be established with respect to the other end ("base" or "reference" site). This is called as interferometry. The phase of fringe pattern is the difference of phases of the interfering waves. In the case of GPS, the differences of the carrier phases measured by two receivers are simply fringe phases (Wells, 1989; Parkinson et al., 1996). GPS carrier-phase measurements are used mostly for positioning, with the coordinates of antenna determined either from post processing of collected data or in real time with the aid of a communication link. However, GPS interferometry can also provide information on the orientation or direction of the baseline connecting the antennas. If these antennas are rigidly mounted on a platform, one can derive information on the platform's attitude ADVANTAGE OF GPS SURVEYS 1. It is three-dimensional, weather independent and site intervisibility is 25

4 not needed. 2. The rapid data processing with quality control is possible with high precision by using common reference system. 3. This is cost effective method which can be operated day and night with a very few skilled personnel. 4. All or any of the following values could be available directly in the field or after post-processing of the GPS data; Latitude, longitude, geodetic height and X, Y, Z Cartesian coordinates; State Plane or Project coordinates; Forward and back geodetic azimuth of the baseline; Geodetic distance or monument to monument slope distance of baselines; Vertical angle from point to point and geodetic azimuth directly between two points MODE OF GPS SURVEYING Planning of GPS survey is most important, regardless of the technique used. Presently the techniques (mode) being used are static, Fast static (rapid static), Kinematic, Pseudo - kinematic (pseudo-static) and Real time kinematic Static mode of GPS surveying This method is used for surveying projects that require high accuracy. In this each receiver logs data at each point continuously for a pre-planned length of time and the duration of data collection depends upon required precision, number of visible satellites, satellite geometry (DOP), type of the receivers (single frequency or dual frequency) and distance between receivers. 26

5 The duration of data collection, however, should be long enough for the post processing software to resolve the integer ambiguity. The modest receivers and processing software are capable of resolving the ambiguity with small amount of data. However, a higher accuracy for the baseline components can be achieved by collecting data for a longer period of time. Collection of data using two or more receivers for a certain period of time is called a session. The slope line between any two antennas is called a baseline vector or simply baseline. If more than two receivers are used, multiple baseline vectors can be determined simultaneously. Most GPS survey projects consist of multiple baselines or networks, and the baselines can be measured individually using only two receivers or several at a time. When the baseline between a known point and a new point is measured, the new point can be used as a known point for other baselines. Unlike in conventional surveys, the accuracy obtainable from networks is independent of the network geometry. Accuracy can be increased by increasing the number of redundant measurements. Redundant measurements are over and above the ones required to determine the coordinates of unknown points. A redundant measurement should also be independent, i.e., a measurement that is not related to or could not be generated from other measurements. In a single session using more than two receivers, there are both independent (non-trivial) and dependent (trivial) baselines. Baselines measured in separate sessions are always independent. In a network of GPS baselines, blunders can be detected by checking the closure of loops formed by connecting independent baselines. If 27

6 the loops are elongated in an east-west direction, a higher accuracy in the position can be obtained (GPS measurements are stronger in north-south direction) and this may taken care of in the beginning. The networks should also have several control points, located at strategic locations in order to strengthen the network. These control points should be preferably above or at least equal to the order of accuracy. The number and locations of control points depend on the size and shape of network (see geometric geodetic accuracy standards and specifications for using GPS relative positioning techniques, Federal Geodetic Control Sub-committee, 1988). Figure 2.1. Glacier surface velocity measurements in fast static mode Fast static mode of GPS surveys Fast Static or Rapid Static was a method developed for dual frequency receivers. The field requirements and procedure for the fast static are same as those for static except for the short session lengths. However, fast static is 28

7 only suitable for low order control surveys, e.g., ground control for photogrammetric mapping and glacier surface velocity measurements (Figure 2.1) Kinematic mode of GPS surveying This is a mode of positioning from a moving platform (i.e., when the antenna is in motion) and used in navigation where usually only a single receiver is used. However, unlike in navigation, the kinematic method is a relative positioning method in which one antenna with a receiver are stationary and other antenna with a receiver moving. When the moving receiver is in constant motion, it is called as continuous kinematic. In most surveying applications, a method called stop-and-go kinematic is used. The stationary receiver, called as the base receiver (Figure 2.2 a), is placed at a known point while a second receiver called as "rover' (Figure 2.2 b) Figure 2.2. (a) Base and (b) Rover during kinematic survey of Gangotri glacier (Kumar et al., 2008) visits all the unknown points. Rover occupies each unknown point for a very 29

8 short time (less than two minutes), hence the term "Stop-and-Go" surveying is used. It is also possible to combine both continuous and stop and go methods in the same survey to operate more than one rover with the same base station. The single most advantage of stop and go surveying is its speed. This method also has following limitations, such as an initialization process to determine the integer biases of at least 4 satellites is needed at the beginning. Secondly, the lock on the four or more satellites must be maintained during the entire survey. For this reason, kinematic GPS surveying is suitable for an area where there are no large over-hanging trees and over-passes or such structures in rover s route. If for any reason a cycle slip occurs, the rover must return to any previous point which had been determined without cycle slip Real time kinematic GPS survey Real time kinematic (RTK) refers to a stop-and-go method where the coordinates of the points are available in real time. Here, a radio communication link is maintained between the base receiver and the rover. The base receiver supplies pseudo-range and carrier phase measurements to the rover which in turn computes its position and display the coordinates. The rover keeps updating coordinates as it moves as long as the lock on satellites is maintained. Kinematic GPS surveying is generally suitable for any type of surveying or mapping. However, for stakeout surveys, RTK is essential. Some RTK receivers have the capability of resolving integer ambiguity and this can only be used with dual frequency receivers. This means that there is no need to maintain the lock on satellites while the rover 30

9 is in motion. With this technique, the integer ambiguity can be resolved while the receiver is still in motion (Blewitt and Lichten, 1992) Pseudo-kinematic (or pseudo-static) survey This is a combination of both static and kinematic methods. It has the speed of kinematic method but there is no need to maintain lock on 4 satellites. However, newer receivers and algorithms can resolve the integer ambiguity much faster. There is a reference (base) receiver and a roving receiver, the former remains at the reference point during the entire survey while the later visits the unknown points (Pant et al., 2008). There is no initialization as in stop and go method. Each point is occupied for 5-10 minutes for baselines of 10 km or less. Each point must be revisited multiple times. Multiple observations at the same site at different times capture different epochs along the satellite's orbit and allow the satellite configuration to change and to resolve the integer ambiguity. This technique is suitable for areas where there are obstructions to signal or the receivers are not equipped with the kinematic software. Pseudo-kinematic is the least precise of all methods but is more productive than static Stop-and-Go and suitable for lower order control such as photogrammetric control etc GPS SEGMENTS The Global Positioning System consists mainly of three segments, the space segment, the control segment and user segment Space segment At altitude of about 20,000 km, space segment contains 24 satellites, in 24 31

10 hours near circular orbits with inclination of orbit 55 0 (Fig. 2.3). The constellation ensures at least 4 satellites in view from any point on the earth at any time for 3-D positioning and navigation on the world wide basis. Three-axis controlled earth pointing satellites continuously transmit navigation and system data comprising predicted satellite ephemeris, clock error etc., on the dual frequency L 1 and L 2 bands Control segment Control segment consists of a master control station, monitor station and upload stations. Major operational tasks of control segment are to estimate satellite ephemeredes and atomic clock behavior to predict the position of satellites, clock drifts and subsequently upload the information to satellites. The monitor stations are transportable shelters with receivers and computers which passively track satellites from the navigation signals. This data is transferred to master control segment for computer processing to provide the best estimates of satellite position, velocity and clock drift relative to the system time. Figure 2.3. Space segment containing GPS satellites 32

11 The data processed there of generate refined information of gravity field influencing the satellite motion, solar pressure parameters, position, clock bias and electronic delay characteristics of ground stations and other observable system influences. Future navigation messages, generated from this are loaded into the satellite memory every day via upload station which has a parabolic antenna, a transmitter and a computer. At present, there are five monitor stations located at Hawaii, Colorado Springs, Ascension Island (South Atlantic Ocean) Diego Garcia (Indian Ocean) and Kwajalein (North Pacific Ocean) (Gouldman et al, 1989) (Figure 2.4). Each station equipped with a precise cesium time standard and receivers that continuously measure pseudoranges to all satellites in view. The pseudoranges are measured every 1.5 seconds and after using the data of ionosphere, they produce 15 minute interval data which is finally sent to the master control station (Hoffmann-Wollenhoff et al., 1992). Figure 2.4.World-wide locations of control segment station (Gouldman et al, 1989) 33

12 User segment The GPS User Segment consists of the GPS receivers and user community. The GPS receivers convert SV signals into position, velocity and time estimates. Four satellites are required to compute the four dimensions of X, Y, Z (position) and Time. The GPS receivers are used for navigation, positioning, time dissemination and other researches. Navigation in three dimensions is the primary function of the GPS. The navigation receivers are made for aircraft, ships, ground vehicles and individuals. Precise positioning is possible by using GPS receivers at reference locations providing corrections and relative positioning data for remote receivers (Leick, 1995; Kaplan, 1996). Surveying, geodetic control and plate tectonic studies are the examples POSITIONING CONCEPTS Various methods of determining the unknown geographic coordinates of the receiver can be used depending upon the information collected by the receiver. Two common methods of position determination are known as pseudo-range positioning and differential carrier phase tracking. These methods can be used with a combination of various mathematical positioning models to determine the unknown geographic coordinates of the receiver (Leick, 1995; Parkinson et al., 1996) Deferential carrier phase tracking Carrier Phase Tracking is accomplished by tracking the fractional phase of the L1 or L2 carrier signals as they arrive at two or more GPS receivers at the same time. The fractional phase of the L1 or L2 carrier signals arriving from 34

13 multiple satellites is tracked over time and is used to infer the distance to each satellite. As the GPS satellites are at far distances, the signals at two receiver locations have essentially the same errors, induced from signal propagation through the ionosphere and troposphere (Figure 2.5). By using differences in the observations of multiple receivers, several errors are removed. This procedure can be done using a single frequency or both the L1 or L2 frequencies (dual frequency). Dual frequency differential carrier phase tracking yields accurate geographic position on the millimeter scale if properly processed (Wells, 1989; Leick, 1995). Figure 2.5. Differential GPS requires that the satellites are observed by two or more receivers at the same time High quality survey grade GPS equipment and advanced processing software are required for differential carrier phase positioning. Since the GPS receivers are at two different locations, it is possible that all the satellites are not 35

14 simultaneously visible to both receiving sites. The equations of mathematical positioning for this method are outside the scope of this thesis, however the topic is thoroughly described in Leick (1995) and Hoffmann-Wellenhof et al. (1997). Figure 2.6. Pseudo-range positioning (p1, p2, p3 and p4) relies on the estimate of the geometric distances between the satellite and receiver Pseudo-range positioning Pseudo-range positioning relies on determining the amount of time it takes for the signal to propagate from the satellite to the receiver. This transmission time is then used to determine the geometrical distance from the receiver to the satellite as depicted in Figure 2.6. Each GPS satellite transmits an unique pseudo-random signal modulated onto the L1 carrier frequency, known as the coarse acquisition (C/A) code. Each GPS receiver contains a copy of the C/A code for each satellite. By 36

15 correlating the signal received from the satellite with one stored in the receiver, the transmission time can be estimated. Once a propagation time is estimated, the geometric distance between GPS receiver antenna and transmitting satellite can also be estimated. The pseudo-range is the apparent propagation time multiplied by the speed of light in a vacuum. Since the satellite and receiver clocks are not synchronized to the same time frame, there is an unknown timing error known as the clock bias. The pseudo-range differs from the actual geometrical distance by the clock bias, propagation delays and other errors including relativistic and doppler effects (Wells, 1989; Hoffmann, et al., 1994; Leick, 1995; Parkinson, et al., 1996,). The pseudo-range for the jth satellites can be expressed as P j = pj + c t + T trop + T ion + T rel + Є. Where P j is the measured pseudo-range, pj is precise geometric distance between the receiver and the jth satellite, c is the speed of light in a vacuum, t is the unknown clock bias, T trop is the signal path delay due to the troposphere, T ion is the signal path delay due to the ionosphere, T rel is the signal delay due to relativistic errors caused by high satellite velocity and Є is an estimate of the noise. A non-linear equation relates to geometric distance between the jth satellite, and unknown positions of receiver (pj = ρ (X j X) 2 + (Y j Y) 2 + (Z j Z) 2, Where (X, Y, Z) are three unknown coordinates of the GPS receiver and (Xj, Yj, Zj) are known coordinates of GPS satellite as transmitted in the ephemeris. A minimum of four satellites must be observed to solve 3 unknown receiver coordinates and receiver clock bias (Wells, 1989; Hoffmann, et al., 1994; Leick, 1995; Parkinson, et al., 1996). 37

16 2.6. ERROR BUDGET IN GPS POSITIONING There are three main error sources in GPS positioning, the satellite, signal propagation and the receiver. Table 2.1 summarizes the error sources and their effects. These errors affecting the resulting position to varying degrees are summarized in Table 2.2. Error Source Satellite Signal Propagation Receiver Variation Effect Clock bias Orbital errors Ionospheric refraction Tropospheric refraction Antenna phase center Clock bias Multipath Table 2.1. Sources of errors in GPS surveying (Hoffman-Wellenhof, 1997) Error Source Ionosphere Troposphere Clock & Ephemeris Receiver Noise Multipath RMS Error (m) Table 2.2. Error sources and their RMS effect on the determined receiver coordinates (Langely, 1997) Satellite errors The satellite coordinates used in determining the geographic coordinates of the receiver are transmitted on the L1 and L2 frequencies along with parameters describing the satellites orbit and time. The orbit along which the satellite travels must be known ahead of time. External effects on the satellite, such as, solar radiation pressure, can shift it out of predicted orbit by as much as 20 m with RMS (root-mean-square) errors of 5m (Langely, 38

17 2000). Each GPS satellite contains four atomic clocks to ensure that a stable timing system is maintained. Although these clocks are extremely accurate, yet they can drift slightly resulting in each satellite s clock not synchronized to each other. These errors in the satellites orbital position and clocks can result in the range of 1 5m in the final geographic position. The International GPS Service (IGS) uses data collected by these sites to determine the true orbital path and the clock drift for each satellite. These are offered at no cost to the GPS community on a variety of time scales. The IGS final orbits are available for download over the internet two weeks after the observation date. Currently, the IGS final orbits have an accuracy of 3 5 cm in the orbital position of satellite and an accuracy of nanoseconds on the satellite clock drift (Heroux et al., 2001). A substantial improvement in the accuracy of the geographic receiver coordinates can be made by re-calculating the receiver coordinates with the new satellite orbit and clock drift Propagation errors GPS satellite signals experience various propagation delays as they travel through the Earth s atmosphere. These errors are mainly due to the ionosphere and troposphere (Langley, 1997). The ionosphere is located approximately 50 km 1000km above the surface, while the troposphere begins at the surface of the Earth and extends up to an altitude of 14 km. the satellites having low elevations with respect to the horizon have higher ionospheric and tropospheric noise components because of the greater amount of time spent in travelling through these two layers. The ionosphere is most active in a region extending approximately 20± on either side of the 39

18 magnetic equator, with high frequency scintillations experienced both in this region and over the poles (Janssen, 2002). Dual-frequency GPS receivers are able to remove the ionospheric effect by using a linear combination of measurements on both frequencies (Janssen et al., 2002) Receiver errors The distance measured by the GPS receiver is the distance between physical phase centers of the receiver and the satellite. However, phase center of the GPS receiver is unstable and gets changes, with the changing direction of the satellite signal (Mader, 2002). The phase center variations can be accounted for by modelling the response of the satellite antenna. The effect of phase center variation is quite small and is not taken into account for our GPS prototypes. A significant amount of receiver error can be generated through a process, known as multipath. This is where the GPS signals are reflected from surface (such as ground surface or buildings) and directed towards the antenna. Because the signal has traveled along a longer path, it appears that the satellite is further away than it actually does. The GPS receivers contain inexpensive quartz oscillators controlling the clocks. By using a relatively inaccurate time keeping method, there is an inherent inaccuracy of the receiver clock resulting in positioning errors. Although an unknown clock drift is accounted and later solved by iterative solution method, it can still incorporate large errors in the resulting position. There are some common errors present in GPS observations which can be eliminated by taking precautions at the time of GPS data generation. 40

19 2.7. GPS SURVEYING CONSIDERATION Visible satellites In order to solve the positioning equations, four or more GPS satellites must be visible to the GPS receiver. For higher latitudes, the geometry of satellite constellation can create difficulty in having enough satellites in view of long periods of time, as the satellites appear low on the horizon. This also makes the satellite orbits susceptible to being blocked by high topography (Figure 2.7), which can be problematic if the GPS receivers are situated in the valleys. Figure 2.7.GPS satellite orbits. The orbital planes of the satellites do not pass directly over the poles Elevation cutoff mask To prevent large errors from the ionospheric and tropospheric delays, satellites below a certain cutoff elevation are usually excluded from being used in the positioning solution. In this work, the satellites at angle of less than 15 0 with respect to the horizon are not incorporated into the solution. 41