# Our analysis strategy summary

The strategy is described in S. Loyer et al. Zero-difference GPS ambiguity resolution at CNES–CLS IGS Analysis Center

A detailed description is also available at IGS CB.

## Method

We use GINS software for satellites orbit integration and for the computation of one-day NEQ residuals. Daily station positions and daily ERP are solved together from 1-day NEQ systems.

## Measurements models

**Data Preprocessing:** Preprocessing of the GNSS data at the undifferenced and single-difference level to determine cycle slip, remove outliers, and eliminate short passes.

**Basic Observables:**
Undifferenced ionosphere-free linear combination on carrier phase and code (for clocks determination) from IGS network.
GPS : L1/L2
GLONASS : L1/L2
GALILEO : E1/E5a

**Geometric model:**
Ground antenna phase center: absolute elevation-dependent phase center corrections and satellite center of mass offsets and their phase center calibration taken from IGS08.atx.

**Troposphere / Ionosphere:**
Estimation of tropospheric zenital biases (1/2h) and East-North tropospheric gradients (1/day).
Ionospheric first-order effect eliminated by forming the ionosphere-free linear combination of L1 and L2 (or L1/L5 for Galileo)

**Site displacement:**
Short term motion is modelled according to IERS standards.

## Dynamical modelling

**Gravitational forces:**
Earth, Sun, Moon and major planets are taken into account. EIGEN_GL04S_annuel geopotentiel model and tidal variations from FES2004 are used.

**Non gravitational forces:**
Direct solar pressure and albedo.

## Estimated parameters

Initial state vector per satellite, stations coordinates, polar coordinates, troposphere zenithal bias and gradients, clocks, ambiguity and inter-system biases are estimated, as well as a set of empirical acceleration by satellite (1 scale of solar pressure force, 1 Y-bias, periodic terms in the orthogonal plane).

## Ambiguity fixing methodology (GPS only)

The ambiguities are fixed directly on the undifferenced phase measurements. This means that the clocks and all parameters are solved for simultaneously with the ambiguity fixing.

**1 - Wide-lane:**
The first step (as in double difference case) is to fix the widelane ambiguity (ambiguity associated to L2-L1), using the four observables Melbourne-Wubbena combination. This allows the fixing at preprocessing level using only the receiver measurements and a set of satellite biases (Wide-lane Satellite Biases, WSB), which are defined on a daily basis. No geometry modelling (orbits, station coordinates) is needed.
These daily WSB values are available on our ftp site under the name grgxxxxx.wsb and are updated each week.

**2 - Narrow-lane:**
The second step uses the ionosphere-free combinations for phase and pseudo-range. Once the wide-lane ambiguity is known, there is one remaining ambiguity to solve for, associated to an equivalent wavelength of 10.7 cm on the iono-free phase combination (Narrow-lane ambiguity). This ambiguity fixing is performed at zero-difference level, using the complete models and parameterization (orbits, stations coordinates, clocks...).

The Narrow-lane ambiguity are fixed using a bootstrap method applied on the normal equations constructed with the floating solution. The number of ambiguities to solve for is typically 7000, and more than 95% of the phase measurements have a fixed ambiguity at the end of the process.

**Clocks property:**
A consequence is that the associated phase clocks concentrate the complete phase properties of the global network, allowing for example the use of integer valued ambiguities in a PPP problem. As a consequence, they can only take discrete values with a modulo 10.7 cm (see also the Documents section and the Products section).