Estimation of the scale lengths of turbulence from GPS single difference phase observations

<p>Signals from the Global Navigation Satellite System (GNSS) travel through the whole atmosphere and encounter fluctuations of the index of refraction. The long-term variations of the tropospheric refractive index delay the signals, whereas its random variations correlate with the phase measurements. The power spectral density of microwave phase difference can be derived from physical considerations by combining results from the Kolmogorov theory and electromagnetic wave propagation. Four different dominant noise regimes are expected. Their cutoff frequencies can be estimated with the unbiased Whittle Maximum Likelihood estimator; They provide information about the scale lengths of turbulence which are directly linked with the size of the eddies or swirling motion present in the free atmosphere. Dependencies of these parameters with the satellite geometry or the time of the day pave the way for a better comprehension of how tropospheric turbulence acts as correlating GNSS phase observations. The result is less empirical modeling of GNSS phase correlations to improve the positioning results and avoid an overestimation of their precision. We use GPS single differences from 290 m distant antenna positions recorded during two days in 2013 in a common clock experiment at the Physikalisch Technische Bundesanstalt in Braunschweig Germany to explain our methodology, based on adequate filtering of the residuals to mitigate multipath effects.</p>

Codephase center corrections for multi GNSS signals and the impact of misoriented antennas

<p>In absolute positioning approaches, e.g. Precise Point Positioning (PPP), antenna phase center corrections (PCC) have to be taking into account. Beside PCC for carrier phase measurements, also codephase center corrections (CPC) exist, which are antenna dependent delays of the code. The CPC can be split into a codephase center offset (PCO) and codephase center variations (CPV). These corrections can be applied in a Single Point Positioning (SPP) approach, to improve the accuracy in the positioning domain. The CPC vary with azimuth and elevation and are related to an antenna, which is oriented towards north. If the antenna is wrongly oriented, the effect cannot be compensated and wrong corrections will be added to the observations.</p><p>The Institut für Erdmessung (IfE) established a concept to determine CPC for multi GNSS signals, where a robot tilts and rotates an antenna under test precisely around a specific point. Afterwards time differenced single differences are calculated, which are the input to estimate the CPC by using spherical harmonics (8,8). First studies in our working group showed, that an improvement of the position in a SPP are possible, if antenna pattern for the codephase are considering and correctly applied.</p><p>In this contribution, we present the improvement of a SPP and PPP approach by considering CPC for different low cost antennas with multi GNSS signals. Beside the positioning domain, an analysis of the CPC in observation domain, by evaluating the deviations of single differences from zero mean, is performed. Furthermore, we quantify the impact of a disoriented antenna, e.g. oriented in east direction, in the positioning and observation domain by using north oriented CPC. We show, that this impact can be compensating in a post-processing by rotating the antenna pattern. Finally, we present some results of different calibrations, where the antennas are disoriented on the robot and compared to the estimated CPC pattern with the post-processing approach and discussed their impact on the positioning. </p>

Potential of GPS Common Clock Single-differences for Deformation Monitoring

Global satellite navigation systems (GNSS) are a standard measurement device for deformation monitoring. In many applications, double-differences are used to reduce distance dependent systematic effects, as well as to eliminate the receiver and satellites clock errors. However, due to the navigation principle of one way ranging used in GPS, the geometry of the subsequent adjustment is weakened. As a result, the height component is generally determined three times less precisely than the horizontal coordinates. In addition, large correlations between the height and elevation dependent effects exist such as tropospheric refraction, mismodelled phase center variations, or multipath which restricts the attainable accuracy. However, for a kinematic analysis, i. e. for estimating high rate coordinate time series, the situation can be significantly improved if a common clock is connected to different GNSS receivers in a network or on a baseline. Consequently, between-station single-differences are sufficient to solve for the baseline coordinates. The positioning geometry is significantly improved which is reflected by a reduction of the standard deviation of kinematic heights by about a factor 3 underlining the benefits of this new approach. Real data from baselines at the Physikalisch-Technische Bundesanstalt campus at Braunschweig where receivers are connected over 290 m via an optical fiber link to a common clock was analysed.