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Global Positioning System

Introduction

The GPS program was initiated in 1973 when the United States Air Force, Army, Navy, Marine Corps and Defence Mapping Agency decided to use their combined technical resources to develop a very accurate space-based navigation system. Personnel from these agencies were assembled into the initial cadre of a GPS Joint Program Office and were later joined by a contingent of nine other NATO member nations. The primary justification for the GPS program was military but the number of civilian users and applications are growing daily. GPS provides highly accurate time, velocity and positional data as well as meeting the common radio positioning requirements of a broad spectrum of users. Depending on the mode of use and the equipment used, high precision measurements can be made in geodetic applications. It is therefore utilised in geodetic programmes to supplement and strengthen the databases which are used to build models of the Earth's gravity fields, ocean tides, sea surface topography, orientation, global sea level and ocean circulation. It is especially suitable for high precision short baseline work. GPS is seen as the primary tool of geodesists due to the dramatic improvements in techniques and processing software, availability and economical access to GPS equipment, portability and the benefits of international collaboration.

General System Description

The GPS system comprises three major segments; Space, Control and User segments. Operation of the Space and Control segments is managed by the USAF Space Command and the supporting command for GPS operations is the responsibility of US Air Force Logistics Command (AFLC).

Space Segment

The fully operational space segment was planned to have a constellation of 21 satellites, plus 3 operational spares, in six planes with four satellites per plane. Their orbits are nominally circular with an inclination of about 55 degrees and have a period of 12 hours. Orbital height is approximately 20 200 km. The satellites transmit a spread spectrum signal on two frequencies in the L band, known as Link 1 (L1)=1575.42 MHz and Link 2 (L2)=1227.6 MHz. The L1 signal is modulated with a precision (P) ranging code and a coarse/acquisition (C/A) ranging code, whereas the L2 signal is only modulated with the P-code. All signal components are controlled by atomic clocks which is the key to the system's accuracy. Superimposed on the codes are navigation message data, which includes satellite clock and ephemeris parameters, UTC synchronisation information and satellite signal health data. At present four to eight satellites are visible with an elevation mask of about 15 degrees.

User Segment

User Access

Two methods are used to lower the accuracy of the system.
  1. Selective Availability (SA) SA mainly affects single receiver usage and is achieved primarily by dithering the satellite clock frequency. The transmitted navigation message can also be truncated which denies the user the ability to accurately compute the coordinates of the satellites.
  2. Anti-Spoofing (AS) This feature is invoked randomly to negate potential spoofing (hostile imitation) of PPS users. This ability essentially turns off the P-code or turns on an encrypted Y-code.

Levels of Service

There are two basic levels of service provided by GPS:
  1. Precise Positioning Service (PPS) The PPS can provide 8 metre circular error probable (CEP) positioning and 100 ns (one sigma) UTC time transfers. CEP is defined as the radius of a horizontal circle containing 50 % of all possible position fixes. This service is only available to authorised users and is primarily intended for military users. Access to the PPS is controlled by US Department of Defence (DOD) by invoking SA and AS.
  2. Standard Positioning Service (SPS) This service is specified to produce 100 m horizontal positioning and approximately 337 ns UTC time transfer accuracy.

Users are divided into two categories, those who have access to the PPS and the balance are by default users of the SPS. A PPS-capable GPS receiver has the built-in cryptographic logic which allows cryption/decryption processing with the PPS keys. Normally PPS-capable GPS receiver sets apply PPS encryption/decryption processing for SA and AS functions, although some GPS receivers used in geodetic survey networks operate in a limited PPS mode. With these GPS receivers PPS encryption processing is required only for real-time support of the AS function as the SA decryption functions are taken care of during post-processing.

Control Segment

The control segment consists of one Master Control Station (MCS) at Falcon AFS in Colorado and five monitor stations located at Hawaii, Kwajalein, Diego Garcia, Ascension and the MCS. The MCS collates the tracking data from the monitor stations and calculates the satellite orbit and clock parameters. Three ground control stations which are co-located with the monitor stations at Kwajalein, Diego Garcia and Ascension upload the results as determined by the MCS.

Many other non-military monitor stations contribute to the development of refined orbits and the collection of data for geodynamic research. HartRAO is currently installing a Turbo ROGUE GPS receiver on loan from the Jet Propulsion Laboratory in Pasadena, California. This will allow us to contribute valuable data to the International GPS Service for Geodynamics (IGS) which uses data from a global network of more than fifty stations distributed around the world. Results from the IGS Central Bureau can be found at http://sideshow.jpl.nasa.gov/mbh/global.

GPS Observables

There are two GPS observables which are used to determine position. Lower precision applications such as navigation use pseudo ranges. In geodetic surveying carrier phases are used as it allows high precision.

Pseudo Range

GPS position determination is based on a concept termed time of arrival ranging. A simple example would be to consider the emission of a signal at some precise instant in time t1 from a stationary transmitter. The signal arrives at a receiver some time later, say t2. The time difference t2 - t1 allows the determination of the time of arrival (TOA) value. The range (distance) between receiver and transmitter can be found by multiplying the TOA with the signal propagation speed. When four satellites are observed simultaneously, the (x,y,z) position and receiver clock offset can be found from a single observation. In surveying terminology, this is resection by distance.

The GPS satellites transmit pseudorandom noise (PRN) sequence-modulated radio waves. The PRN codes are predefined strings of binary data which are generated from the satellite clock that serves as the time of transmission encoding for the signals. The transmission of each satellite is unique even if they all transmit on the same frequency. This allows the GPS receiver to differentiate between the signals. This is accomplished by the GPS receiver generating a precise replica PRN sequence which is mixed in the receiver, slewed forward and backwards in time by a code-tracking loop until maximum correlation is achieved. The magnitude of the slewing is the observed TOA value.

The clock in the GPS receiver is not synchronised with the satellite clock, so that the TOA is not directly applicable to the simple example above. The receiver clock has a bias which is found by the data-processor of the GPS receiver set. When the observed TOA is multiplied by the signal propagation delay to find the geometric range, the receiver clock bias is included. This total range is termed a pseudo range (PR) measurement. The measured PRs are affected by the tropospheric and ionospheric propagation delays. The TOA therefore includes both the propagation delay and the clock offset.

A simplified user position determination algorithm would be:

  1. Track PRN sequences from four satellites.
  2. Multiply TOA values by the speed of light to obtain four PR measurements.
  3. Correct PR measurements for ionospheric and tropospheric delays. Add correction for difference between each satellite's clock and GPS system time, effects of relativity, etc. A 50 Hz digital data stream (navigation message) transmitted from the satellites along with their P- and C/A codes contains the necessary information, such as GPS sytem time of transmision, ephemeris and clock data for the particular satellite. Also included are the almanac data for all the satellites, coefficients for the ionospheric delay model and satellite health information to make these adjustments.
  4. Perform a position/time solution by solving the four range equations and compute the (x,y,z) position fix in terms of the WGS-84 coordinate system.

System Accuracy Characteristics

Two important parameters cause the GPS to show statistical accuracy distributions. Firstly, there is the error in the measured PRs and secondly, the accuracy limiting factor due to satellite geometry. These two factors are important as it leads to an understanding of the limitations of GPS and allows prediction of position and time accuracies.

User Equivalent Range Error (UERE)

The error in the determination of the PRs from each satellite is caused by errors in the the prediction of the satellite's orbit, the stability of its clock, errors in the navigation message, ionospheric and tropospheric model errors as well as correlation errors. The UERE is contained in the navigation message and in conjunction with DOP factors enables estimates of the precision in point positioning which can be achieved.

Dilution of Precision (DOP) Factors

The DOP factors are commonly used as a measure of the error contributed by the effect of the geometry of the satellite distribution on the position and time solution. The DOP factors are simple functions of the diagonal elements of the covariance matrix of the adjusted parameters. This description becomes clear when it is realized that the Kalman filter in a GPS receiver contains a matrix of the estimates (the covariance matrix) of the PR errors. The Kalman filter characterizes noise sources resulting from errors in the ionospheric corrections, user clock drift etc, in order to minimise their error introducing effect. It is a recursive (linear combination of previous estimates and present data) mean-square estimator which in a least-squares sense, produces the minimum covariance estimate of the state vector, which includes parameters such as GPS receiver position and time. The error covariance matrix satisfies a Ricatti equation, which is relatively easy to solve using a microprocessor, which in turn facillitates implementation in a GPS receiver. The diagonal of the covariance matrix contains the variances of the position errors and the receiver clock bias error.

A good DOP has a low number (2-3) whereas a bad DOP has a high number. Intuitively, the best possible DOP would be given by one satellite directly overhead and three satellites spaced evenly on the horizon. High DOPs result when the satellites are clustered together or form a line. As the satellite positions are predictable, DOP values can be calculated during the planning stages of a survey to ensure good values. To conclude this section the special types of DOPs are described briefly and their expressions given.

  1. VDOP Vertical DOP. Describes the effect of satellite geometry on height.
  2. HDOP Horizontal DOP. Indicates dilution of precision for horizontal positions.
  3. PDOP Position DOP. Combined vertical-horizontal position value.
  4. TDOP Time DOP. Time dimension effect of geometry.
  5. GDOP Geometric DOP. A composite measure of the vertical-horizontal-time dimensions.

Carrier Phases

Carrier phase measurements are more precise than PR measurements and are used on both short and very long baselines with high precision. The question "what is a carrier phase" is best answered by starting at first principles. The phase observable is the difference in phase between the transmitted carrier wave from the satellite and the receiver oscillator signal at a specified epoch t. The phase of a wave thus only has meaning when it is specified relative to another wave of the same frequency. Once signal acquisition has started the whole number of cycles are counted. The phase measurements are ambiguous and unless the absolute range difference at the initial epoch is determined, the phase measurement only provides the changes in range over the observed period. The initial integer ambiguity depends on the receiver-satellite combination at the initial epoch and remains the same over a particular observing period. This allows the initial and unknown integer ambiguity to be represented by a single bias term. A cycle slip can occur when tracking is interrupted due to blockage of the signals, weak signals or incorrect signal processing due to receiver software failure.

This cycle slip will alter the integer number of cycles, although the fractional phase measurement after reacquisition of the signal will be the same as if the tracking had not been interrupted. Several techniques have been developed to fix cycle slips, such as search techniques, discrete Kalman filtering, optimized Cholesky decomposition and in the case of dual-frequency data in code and carrier, widelaning ambiguity fixing. Fast techniques are very important for real time applications and much research is currently in progress to find better and faster ambiguity resolution methods.

Carrier Phase Precision

In general the vertical component has a greater standard deviation than the horizontal components. This is due to the fact that the vertical component is not as constrained and is more sensitive to errors in tropospheric delay. Precision in the vertical component increases with a larger number of satellites being observed simultaneously as the correlation coefficient between the vertical station coordinate and zenith tropospherical delay decreases. Typical accuracies would be about 10 mm on a global scale and about 1 mm on a local scale. These accuracies are only obtained if advanced processing software is used as well as precise orbit information. The unpredictable behaviour of the time and frequency standards serving as a reference for GPS receivers is the main source of error in a measurement. By the process of differencing, the errors resulting from receiver and satellite clocks can be virtually eliminated. Differencing can be done between receivers, satellites, epochs or a combination of these. Differencing reduces the effect of the ionosphere and troposphere when receivers are close to each other, so that dual-frequency operation is not necessary for short baselines.
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Produced by Ludwig Combrinck 19/02/99, e-mail: ludwig@ludwig.hartrao.ac.za
since 19 February 1999.