## Implementation of DORIS into Bernese GPS software

The Bernese GPS software has been developed by Astronomical Institute, University of Bern. It is one of the large GNSS data analysis tools for geodetic applications. It is currently in use at more than 200 universities and research institutions worldwide for a large number of applications, including global GNSS data analysis, deformation monitoring in local and regional networks and monitoring of station-specific troposphere parameters. The Bernese GPS software currently supports GPS/GLONASS as well as VLBI and SLR tracking data analysis and developments for the upcoming Galileo system are in progress.

The implementation strategy of the additional tracking technique DORIS was to reduce modifications of the structure of the software and of the processing algorithms to a minimum in order to take maximum profit of the models and algorithms already available for GNSS data analysis. Models describing site displacements and deterministic orbit models can obviously be directly reused. Because DORIS is, as GNSS, a microwave technique, also observation models, e.g. troposphere models or relativistic propagation models, can be used for both techniques in a similar way. This was realized by implementing the classical DORIS Doppler (i.e. the range difference) measurement as two phase measurements, the first at the start, the second at the stop of the DORIS measurement time interval (typically 7, 9 or 10 seconds). Consider the DORIS range rate measurement V as, e.g., available in data files downloaded from the Crustal Dynamics Data Information System (CDDIS) data archive

(1) V = (c/Fb).((Fb – Fs) – D/T)

where Fb and Fs are the beacon and satellite frequency, respectively, D is the cycle count number, T the count integration time interval, and c the velocity of light. The range difference in the count interval may then be written as

(2) Δ Delta = VT = Ρ (t+T) – Ρ(t)

where Ρ is the range including corrections for tropospheric delay, ionospheric phase shift, clock offsets, phase center offset, etc., and t is the start epoch of the count interval. GPS-like carrier phase 'measurements' may then be defined as

(3a) φ(t) = Ρ (t) + A

(3b) φ(t+T) = Ρ (t+T) + A

with an arbitrary constant A that may, in analogy to GNSS, be called 'ambiguity'.

One observable (Eq.1) is then transformed into two phase measurements and one ambiguity, thus leaving the degrees of freedom of the problem unchanged. By forming the difference (Eq.2), the constant A is eliminated. The two 'observations' obtained from a single DORIS observation can be analyzed in exactly the same way as GNSS carrier phase observations: For both the start and stop epochs of the count interval, the observation equations are evaluated in the same way as for GNSS (except for the beacon frequency offset parameters that are present, and the different situation compared to GNSS as the signal is emitted by the ground station and received by the satellite). To make the analogy with GNSS carrier phase data analysis perfect, an ambiguity parameter is set up for each start epoch of the count interval and pre-eliminated again after processing of the 'observation' referring to the stop epoch of the same interval.

The procedure was implemented by writing an interface program that converts DORIS observations, as available from CDDIS, into ionosphere-corrected single-frequency 'observations' at the start and stop of the count interval and storing them in a Bernese-formatted phase observation file. Each observation referring to a start epoch is labeled with a cycle slip flag. This flag then forces the analysis program to pre-eliminate the ambiguity attached to the previous count interval on the same beacon-satellite link (if present) and to introduce a new ambiguity.

As new DORIS-specific parameter type, the beacon frequency offsets were implemented into the main data processing program (GPSEST) as well as into the normal equation stacking program (ADDNEQ2). Models adopting the 2003 IERS Conventions (McCarthy and Petit 2004) for station displacements and gravitational orbit perturbations, as well as troposphere models for microwave frequencies, are already available from the GNSS implementation and can be used for DORIS without further change. For DORIS, however, pass-specific handling of beacon frequency and troposphere parameters had to be implemented since the concept does not exist for GNSS data analysis where a continuous tracking from several GNSS satellites is available. The design allows the Bernese software to process a large station network (with simultaneous observations by one satellite) as well as of several satellites in a single run.