Site Characterization and Multipath Maps Using Zernike Polynomials

Receiver antenna calibration plays an important role in precise point positioning (PPP). The correct management of the phase center offset and variations (PCV) and multipath effects can drastically improve the estimation of tropospheric parameters and the stability of the position over short measurement sessions. Correction parameters, to compensate for PCV, are usually computed in laboratory on all the geodetic grade antennas, but they are not available for low-cost apparatus; multipath can be partially mitigated by a robot calibration on site but this is an expensive procedure that is rarely adopted. Multipath staking maps (MPS) using carrier phase observation residuals are a cheap and powerful tool to generate site-specific corrections, effective for reducing both near-field and far-field effects. These maps can be generated by gridding multiple residuals falling in a cell of a pre-determined size. In this work, we propose to compute a set of polynomial coefficients of a Zernike expansion from the residuals of a PPP uncombined least-squares adjustment performed by the open-source goGPS processing software; these coefficients can be later used to synthesize corrections of the observations for the next processing of the target station. In contrast with gridding techniques, this approach allows a to generate smoother corrections and allows a limited automatic extrapolation of the correction values in areas of the sky that were not covered by observations in the set of data used in the calibration phase. The results show that the technique is effective in the modelling of multipath and residual phase center variations allowing a drastic reduction of the undifferenced residuals. Zernike polynomials are a sequence of polynomials orthogonal on the unit disk, vastly used in optics but, to our knowledge, never considered for GNSS applications, their symmetric properties and the circular support area makes them an interesting object of investigation for other possible usages in GNSS processing.