How Observation Noise impacts the Estimation of Codephase- and Phase-Center Correction with a Robot in the Field

To ensure an accurate and precise position in GNSS applications, phase center corrections (PCC) have to be taken into account. PCC are antenna and frequency dependent correction values. They describe the distance along the line-of-sight direction between the electrical phase center, where the GNSS signal is received, and the antenna reference point. In Melbourne-Wübenna or code-minus-carrier linear combinations, which are often used in highly precise GNSS applications, the codephase of the GNSS signal plays a key role. Similar to the PCC, also correction values for the codephase observation exist, called codephase center corrections (CPC), also known as group delay variations (GDV). The definition of CPC as well as their estimation process with a robot in the field is similar as for PCC.

The team at Institut für Erdmessung is optimizing the established absolute antenna calibration approach for estimating CPC and PCC for multi GNSS signals in terms of repeatability, noise reduction and multipath impact. In this calibration process, an antenna under test (AUT) is precisely tilted and rotated around a fixed point in space by using a robot. A nearby reference station allows the calculation of time differenced single differences (dSD), which are used to estimate absolute CPC and PCC with spherical harmonics of degree and order 8. The pattern quality and also the repeatability of this approach depends, among other effects, on the observation noise of the GNSS signals.

In this contribution, a detailed study about the influence of observation noise on the estimated patterns is presented. To this end, dSD are simulated based on an existing pattern and the robot positioning. The dSD are modified before the estimation process by polluting them with different kind and magnitude of noise. The estimated patterns are compared using e.g. the root-mean-square or the absolute difference between two runs. Our analysis shows, that 18% of the white noise magnitude is reflected in the repeatability of the pattern estimation in terms of absolute differences between two calibration runs.