The ground GNSS tomography – unconstrained approach

The GNSS signal along its more than 20,000 km line of sight is bended, attenuated and delayed. These effects are results of the Earth’s atmosphere, and Sun radiation. Amongst all mentioned effects the one considered in this paper is a signal phase delay in troposphere.This paper presents investigations in the field of GNSS ground tomography, a remote sensing technique able to capture distribution of water vapour partial pressure in the troposphere. In this method, observations are Slant Wet Delays (SWD), the phase delay of GNSS signal due to the presence of water vapour in the troposphere.One of the most important limitation in GNSS tomography is so far mandatory usage of constraints to improve design matrix rank score and in consequence the ability to obtain meaningful troposphere parameters. Solution proposed here is based on combination of SWDs from several consecutive observation epochs to increase rank score. Another important goal is to perform careful selection of singular values in the process of pseudo inverse, to limit the observation noise influence. Three different methods to select singular values are investigated: functional analysis, significant testing and L-curve fitting. The obtained results are validated by means of internal uncertainties propagation, and comparison with external model. With the simulated data the unconstrained stacked GNSS produce reliable results with uncertainties on the level of 0.3hPa in terms of water vapour partial pressure and with mean discrepancies on the level of 0.1hPa. The same measures transform to the 0.03% and 0.01% of relative error on the ground level and 100% and more, above 8 km. Moreover all instabilities inside profiles were resolved properly. The simulations shows that to attain such optimistic results at least 10 observations epoch have to be stacked.

► Stacked differential solution without constraints.
► Functional analysis method most optimal for Truncated SVD.
► Water vapour partial pressure uncertainty 2 sigma 0.5 hPa after 10 stacked epoch.
► Requires multi GNSS constellation.