## THE GPS TIME & SPATIAL REFERENCE SYSTEMS

To fully understand the operations, as well as the mathematical basis, of GPS it is necessary to know the definition and implementation of the various time and spatial reference systems which are utilised in one form or another:

Spatial or coordinate ("datum") reference systems:

Time reference systems:

### The WGS84 System

World Geodetic System 1984 is defined and maintained by the U.S. National Mapping & Imaging Agency (NMIA), formerly known as the Defense Mapping Agency (DMA), as a global geodetic datum (D.M.A., 1991). It is the datum to which all GPS positioning information is referred by virtue of being the reference system of the Broadcast Ephemeris. (Prior to January 1987, the system in use was WGS72.) The realisation of the WGS84 satellite datum is the catalogue of coordinates of over 1500 geodetic stations (most of them active or past tracking stations) around the world. They fulfil the same function as national geodetic stations, they provide the means by which a position can be related to a datum. WGS84 is an earth-fixed Cartesian coordinate system with:

• Its origin at the earth's centre of mass, the geocentre (for two reasons: the geocentre is the physical point about which the satellite orbits; and it is preferable to any local geodetic datum).
• Its "z-axis" is aligned parallel to the direction of the Conventional Terrestrial Pole (CTP) for polar motion, as originally defined by the Bureau International de l'Heure (BIH), and since 1989 by the International Earth Rotation Service (IERS).
• Its "x-axis" is the intersection of the WGS84 Reference Meridian Plane and the plane of the CTP Equator (the Reference Meridian being parallel to the Zero Meridian defined by BIH/IERS).
• Its "y-axis" completes a right-handed, earth-centred, earth-fixed (ECEF) orthogonal coordinate system, measured in the plane of the CTP Equator, 90 east of the x-axis.

The four defining parameters of the WGS84 ellipsoid are:

• Semi-major axis (a): 6378137m.
• Ellipsoid flattening (f): 1/298.257223563 (derived from the value of the normalised second degree zonal harmonic coefficient of the gravitational field: -484.16685 x 10-6).
• Angular velocity of the earth (w): 7292115 x 10-11 rad/sec.
• The earth's gravitational constant (atmosphere included) (GM): 3986005 x 10-8 m3/sec2.

The relationship between WGS84, as well as other global datums, and local geodetic datums have been determined empirically, and transformation parameters of varying quality have been derived (see SOLER & HOTHEM, 1989; STEED, 1990; and Table -- section1.2.3). Reference systems are periodically redefined, for various reasons, such as when the primary tracking technology changes (for example when the TRANSIT system was superseded by GPS), or if the configuration of ground stations alters radically enough to justify a recomputation of the global datum coordinates. The result is generally a small refinement in the datum definition, and a change in the numerical values of the coordinates. For example, there is a small difference in the definition of WGS84 from TRANSIT and GPS (see Table -- section1.2.3): origin offsets of approximately 10cm in the z-direction and a scale difference of about 0.1ppm.

However, with dramatically increasing tracking accuracies another phenomenon impacts on datum definition and its maintenance: the motion of the tectonic plates across the earth's surface, or "continental drift" as it is often known (it is assumed there is relatively little vertical motion). This motion is measured in centimetres per year, with the fastest rates being over 10cm/year. Nowadays this motion can be monitored and measured to centimetre accuracy, on a global annual-average basis. In 1994 the GPS reference system underwent a subtle change to WGS84(G730) to bring it into the same system as used by the International GPS Service to produce precise GPS ephemerides (section 6.2.3 and section12.2.1).

### The International Terrestrial Reference Frame

The WGS84 system is the most widely used global reference system because it is the system in which the GPS satellite coordinates are expressed in the Navigation Message (section 3.3.3). Other satellite reference systems have been defined but these have mostly been for "scientific" purposes. However, since the mid 1980's, geodesists have been using GPS to measure crustal motion, and to define more precise satellite datums. The latter were essentially by-products of the sophisticated data processing, which included the computation of the GPS satellite orbits. These GPS surveys required coordinated tracking by GPS receivers spread over a wide region during the period of GPS "campaigns". Little interest was shown in these alternative datums until:

• The network of tracking stations evolved into a global one, rather than being concentrated about the region of interest of the GPS campaign.
• The network of tracking stations was maintained on a permanent basis, rather than operating intermittently.
• The scientific community initiated a project to define and maintain a datum at the highest level of accuracy.
• The policy of Selective Availability was announced, whereby the WGS84 datum as realised by the contents of the GPS satellite coordinates and clock parameters within the broadcast Navigation Message could be corrupted.

In 1991, the International Association of Geodesy decided to establish the International GPS Service (IGS) to promote and support activities such as the maintenance of a permanent network of GPS tracking stations, and the continuous computation of the satellite orbits and ground station coordinates (DIXON, 1995; ZUMBERGE et al, 1995). Both of these were preconditions to the definition and maintenance of a new satellite datum independently of the DMA network (used to maintain the WGS datum) and the Control Segment monitor station network used to provide the data for the operational computation of the GPS broadcast ephemerides. After a test campaign in 1992, routine activities commenced at the beginning of 1994. The network now consists of about 40 core tracking stations located around the world, supplemented by more than 100 other stations (some continuously operating, others only intermittently). The precise orbits of the GPS satellites are available from the IGS with several days delay. See section12.2.1 for further details concerning the IGS.

The definition of the reference system in which the coordinates of the tracking stations are expressed and periodically redetermined is the responsibility of the International Earth Rotation Service (IERS). The reference system is now known as the International Terrestrial Reference Frame (ITRF), and its definition and maintenance is dependent on a suitable combination of Satellite Laser Ranging, Very Long Baseline Interferometry and GPS coordinate results. (Increasingly it is the GPS system that is providing most of the data.) Each year a new combination of precise tracking results is performed, and the resulting datum is referred to as ITRFxx, where "xx" denotes the year "epoch". A further characteristic that sets the ITRF series of datums apart from the WGS, is that the definition not only consists of the station coordinates, but also their velocities due to continental and regional tectonic motion. Hence, it is possible to determine station coordinates within the datum, say ITRF96, at some "epoch" such as the year 2000, by applying the velocity information and predicting the coordinates of the station at any time into the future (or the past). The WGS84(G730) reference system is identical to that of ITRF91 at epoch 1994.0.

Such ITRF datums, initially dedicated to geodynamical applications requiring the highest possible precision, have been used increasingly as the fundamental basis for the redefinition of many nations' geodetic datums. For example, the new Australian datum, known as the Geocentric Datum of Australia (MANNING & HARVEY, 1994), is defined as ITRF92 at epoch 1994.0 (section 12.1.5). Of course other countries are free to chose any of the ITRF datums (it is usually the latest), and define any epoch for their national datum (the year of GPS survey, or some reference date in the future, such as the year 2000). Only if both the ITRF datum and epoch are the same, can it be claimed that two countries have the same geodetic datum. Note, the recent redefinition of the WGS84 datum was made in order to bring it into line with this new international approach.

### Time Scales

In order to appreciate the role of time in GPS data analysis it is necessary to review briefly the various time systems involved, and their associated time scales. Some of these definitions are standard and inherent to all space positioning technologies, while others are particular to the GPS system. In general there are three different time systems that are used in space geodesy (KING et al, 1987; LANGLEY, 1991d; SEEBER, 1993):

Dynamical Time is the uniform time scale which governs the motions of bodies in a gravitational field: that is, the independent argument in the Equations of Motion for a body according to some particular gravitational theory, such as Newtonian Mechanics or General Relativity. Atomic Time is time defined by atomic clocks, and is the basis of a uniform time scale on the earth. Sidereal Time is measured by the earth's rotation about its axis, and although sidereal time was once used as a measure of time it is much too irregular by today's standards. Rather, it is a measure of the angular position of a site on the earth with respect to a celestial body (though in keeping with traditional practice, its units are seconds of time rather than seconds of arc). (When the celestial body is the sun, the time scale can also be referred to as Solar Time.) Within each of these broad categories there are specific measures of time, or time scales, that are commonly used in space geodesy and astronomy.

Some time scales have a special importance because they provide the "benchmark" or reference scale within a particular time system. This often occurs by international convention. Often, however, the time scales to which we have access are merely realisations of the "true" or definitive reference time scale (or scales) associated with each time system.

### Calendar Definitions

The Julian Date (JD) defines the number mean solar days (each of which is 86400 SI second in length) elapsed since the epoch 1.5 (midday) January, 4713 B.C. The Modified Julian Date (MJD) is obtained by subtracting 2400000.5 from the JD. (MJD therefore commences at midnight.) The standard epoch for GPS Time (0hr 6 January, 1980) is therefore MJD44244.0.

The date conversions described below are taken from HOFMANN-WELLENHOF et al. (1998), and are valid for the period March 1900 to February 2100. The JD can be computed from the year number Y (a full four digit integer), integer month number M , integer day number D , and the real-valued time in hours H:

 JD = Int[ 365.25y ] + Int[ 30.6001(m+1) ] + D + H / 24 + 1720981.5

where Int denotes the integer part of the number, and:

 y = Y - 1 and m = M + 12 if M 2 y = Y and m = M if M > 2

The reverse conversion is carried out stepwise by first defining the quantities:

 b = Int[ JD + 0.5 ] + 1537 c = Int[ (b - 122.1) / 365.25 ] d = Int[ 365.25c ] e = Int[ (b - d) / 30.6001 ]

The date parameters are then obtained:

 D = b - d - Int[ 30.6001e ] + Frac[ JD + 0.5 ] M = e - 1 - 12.Int[ e / 14 ] Y = c - 4715 - Int[ (7 + M) / 10 ]

where Frac denotes the fractional part of a number.

A further useful relation is between JD and the GPS week number:

 GPSWeek = Int[ (JD - 2444244.5) / 7 ]

The GPS week starts on Saturday midnight (Sunday morning), and runs for 604800 seconds. The "GPS Week Rollover" occurred on the weekend of 21-22 August 1999, when the GPS week number was reset to week 0 ("week zero"). Hence if the week number is greater than 1024, subtract the integer 1024.

© Chris Rizos, SNAP-UNSW, 1999