Using multiple Global Navigation Satellite Systems (GNSS), mainly GPS, Galileo and GLONASS , together provides improved user capability compared to one system alone. However, to enable widespread use and facilitate seamless multi-constellation GNSS high-precision positioning, navigation and timing, a number of significant scientific and technical barriers need to be overcome. In the iNsight project, WP3 aims are specifcally to study and investigate GNSS multi-constellation orbit and clock interoperability, transformation modelling and transformation parameters.

GPS, Galileo, GLONASS and other forthcoming space-based radio-navigation and timing systems, all have their own well-defined spatial geodetic reference frame to represent satellite orbits and users/stations 3-D coordinates. Moreover, each system has its own unique time standard (reference timescale), independent from other systems. This reference timescale is needed to synchronise system’s satellite atomic clocks and generate time-tagged signals. To facilitate seamless multi-constellation GNSS high-precision positioning, navigation and timing one needs to perform:
 
*Inter-frame spatial transformation modelling and parameters estimation: to get the postioning solutions in a common reference frame.
 
*Inter-frame timescale transformation modelling and estimation: to compute the multi-constellation user-to-satellite signals transit time in a common reference timescale and avoid inter-system time offsets/biases.

In WP3 relationships between GNSS geodetic reference frames and reference timescales are investigated and the related frame transformation parameters and reference timescale offsets are derived. For high-accuracy multi-constellation GNSS positioning and navigation these transformations and timescale offsets should be taken into account otherwise the gains from multi-constellation solutions could be impaired. This also helps separate reference frame and timescale effects from other sources of error.

Figures 1 through 4 below depict the reference frame stations and horizontal velocity field for GPS World Geodetic System 84 (WGS-84), Galileo Terrestrial Reference Frame (GTRF), International GNSS Services 2005 (IGS05) and the International Terrestrial Reference Frame 2008 (ITRF2008). In these figures major plate boundaries are shown in green, blue and orange. The velocity vectors in red show direction and magnitude of the plate motion.

Table 1 below gives brief information on GNSS Reference Timescales.

Enhanced GNSS satellite clock modelling and relativistic effects

One of the aims of WP3 is to investigate and model the behaviour of space borne clocks. To define what is meant by clock behaviour it is first important to define clock error. Clock error is simply the difference between the time measurements on one clock with respect to the time measurements on another clock (or some timescale based upon an ensemble of a group of clocks). So in any analysis of clock performance it is essential to have a reference clock (or a reference timescale) against which clock error can be measured. Typically, clock error is changing with time (where time in this instance is defined according to the reference timescale) and it is this time-varying nature of clock errors that we describe as the behaviour of the clock.

The active atomic clock on-board each GNSS spacecraft generates the carrier frequency and allow users to accurately determine the time of transmission of received signals. The problem is that GNSS signals are time-tagged with system time. GPS measurements use GPS Time (GPST) as the reference timescale, Galileo uses Galileo System Time (GST) and Glonass uses Glonass time. These timescales are closely aligned to UTC which is a terrestrial timescale based on clocks on the geoid. As a result, relativistic effects arising from receiver-satellite velocities and gravitational potential differences between a receiver clock on the geoid and a satellite clock cause the satellite clock rates to vary.

The conventional relativistic correction 〖δT〗_rel= -2(r.v)/c^2 uses a simplified point mass Earth gravity model to approximate the gravitational potential differences between the satellite and user. Kouba (2004) showed that the additional inclusion of the gravity oblateness term (J2) when evaluating the geopotential at satellite position introduced periodic errors to the GPS conventional relativistic correction of amplitude 0.1 ns [Kouba, 2004]. Using the latest precise orbit products, detailed Earth Gravity Models (GGM02 up to degree & order 200+ and EGM08, up to degree and order 2000+) and JPL solar system ephemerides we are aiming to describe relativistic effects on spaceborne clock behaviour in a more rigorous way.

One of the standard statistical measures of clock performance is the Allan deviation (ADev) and we use it here to characterise the IGS clock combinations and to determine whether enhanced relativistic clock modelling offers any improvement in our knowledge of spacecraft clock behaviour. The ADev is a measure of frequency stability or equivalently the time drift of a clock but is also useful in identifying any underlying periodic behaviour. The ADev was plotted for the IGS final combined clock products of GPS satellites between 31 October 2010 and 4 December 2010 (see Figure 1 below).

Some interesting observations can be inferred from Figure 1:

• Most GPS satellite clocks have an ADev in the region 〖1*10〗^(-14) for an averaging time of 1 day. This means that if such a clock were perfectly synchronised to GPST at the start of the day the expected time uncertainty at the end of the day would be approximately 0.864 ns.
• The clock combination for the new generation GPS IIF SVN 62 (currently PRN 25) shows the best frequency stability over a 1 day averaging time of 〖5*10〗^(-15).
• Periodic behaviour corresponding to the ~ 12 hours orbital period can clearly be observed in most of the clock combinations at which is unsurprising.

References: Kouba, J. (2004). Improved relativistic transformations in GPS. GPS Solutions, 8, 170-180.