Incorporating stochastic and clock modeling into global multi-GNSS processing

Short Description

Starting point / motivation

Global navigation satellite systems (GNSS) are integral to a wide array of scientific and commercial applications. Precise orbit determination of satellites in low Earth orbit relies on high-quality GNSS products. Examples of such satellites are those of the Copernicus Earth observation program of the European Union or the satellite gravimetry missions GRACE/GRACE-FO and GOCE.

Numerous ground-based applications also require these products, for example: estimation of terrestrial water storage variations, earthquake monitoring, GNSS reflectometry, tropospheric and ionospheric research, surveying, or civil engineering.

Furthermore, GNSS-derived station coordinates play an important role in the determination of the International Terrestrial Reference Frame. The analysis centers of the International GNSS Service generate such products by processing observations from a global network of ground stations to one or more GNSS constellations.

So far, this kind of processing only incorporates elevation-dependent a priori modeling of observation variances and disregards temporal correlations. Meanwhile, numerous studies have shown the positive impact the incorporation of sophisticated stochastic modeling has on GNSS processing and resulting products.

These studies, however, were usually confined to short time periods and to either baselines, precise point positioning, or small regional networks. So far, there have not been any large-scale investigations regarding the impact of stochastic modeling of observation noise on global GNSS processing.

The stochastic properties of highly stable atomic clocks onboard GNSS satellites or linked to some receivers can also be modeled in this fashion. While studies have shown that this improves the resulting GNSS products, global GNSS processing does not yet commonly utilize stochastic modeling of clock estimates.

Contents and goals

We propose to advance the state of the art of global multi-GNSS processing by incorporating sophisticated stochastic modeling of both observation noise and clock estimates. 


Finding the best parametric description of the observation noise covariance matrix and the stochastic properties of clock estimates is going to be the first step in achieving this goal.

Incorporating these models into the processing chain while preserving the capacity to process large equation systems requires the implementation of a suitable and efficient structure of the normal equations. We further plan to adjust the model coefficients automatically by means of variance component estimation, which is going to result in more realistic noise models.

Our group has a long and successful history of applying stochastic modeling in gravity field determination, where it has improved the accuracy of our widely used ITSG-Grace solutions by 20-40%.

Expected results

We expect a similar improvement for global GNSS processing and are going to assess this by processing a GNSS product time series of at least 10 years. Our plan is to publish this dataset together with all findings and developed methodologies on an open access basis.

The year 2020 will mark the first time of having four systems (i.e., GPS, GLONASS, Galileo, and BeiDou) in full operational capability. Utilizing the various available observation types together in global multi-GNSS processing lends itself to incorporating sophisticated stochastic modeling of the observation noise.

Furthermore, modeling the stochastic properties of clock estimates opens the opportunity to exploit the high and ever increasing quality of onboard satellite clocks. This is especially relevant for the ultra-stable hydrogen masers employed by Galileo.

Project Partners


Graz University of Technology

Contact Address

Graz University of Technology
Rechbauerstraße 12
A-8010 Graz