A statistical test to determine the minimum threshold for open-loop tracking of GNSS radio-occultation signals

Global Positioning System (GPS) radio occultation (RO) is an atmospheric sounding technique utilizing the change in propagation direction of the GPS signal through the stratified atmosphere. The cumulative effect of this bending is observed as a time-varying excess phase in the received signal. Excess phase and signal amplitude can be inverted to retrieve atmospheric refractivity, pressure, temperature or water vapor profiles. The GNSS-RO technique is now operational on the COSMIC constellation and several other Low Earth Orbiting (LEO) satellites. LEO systems, however, cannot provide dense soundings in a specific area with the very short temporal resolution necessary to observe transient events, such as tropical storms. An airborne RO system has thus been developed for localized GPS-RO campaigns.

RO signals in the lower troposphere can be characterized by rapid phase accelerations and severe signal power fading. These signal dynamics often cause the phase-locked loop in conventional GPS survey receivers to lose lock, limiting the availability of measurements in the lower troposphere. To overcome this problem, the Open-loop (OL) tracking is implemented to a software receiver. In contrast to a conventional tracking loop, OL tracking uses a local carrier phase predicted from a Doppler model to generate a local signal model which can be implemented in both forward and reverse time, operating on pre-recorded intermediate-frequency (IF) GNSS signals. Recent airborne data collected using the GISMOS instrument on HIAPER during the PREDICT campaign and post-processing with OL methods, showed reliable atmospheric profiling down to 0.5 km. In contrast, geodetic dual-frequency receivers, using closed-loop tracking, were only able to acquire data only down to 5 km. The signal to noise ratio (SNR) experienced during this campaign was somewhat limited due to the narrow beam of the antennas employed on both sides of the aircraft. Link analyses, employing models for the antenna gain patters, were used to predict the SNR at both the aircraft position and a COSMIC satellite profile observed in the vicinity. These predictions agreed with the observed SNR for both measurements. SNR may vary considerably for an airborne platform, due to the antenna placement and changes in flight path. We therefore seek to derive a method to set a minimum SNR threshold for obtaining reliable atmospheric profile retrievals from OL processing. Unwrapping is a critical part of OL tracking, in which the modulo-2pi phase extracted from signal is accumulated to produce a smooth, monotonic excess phase time series. Our tracking threshold derives from the assumption that persistent failures in un-wrapping would ultimately limit the inversion of the RO observations to produce a refractivity profile. A previously-derived model relating SNR to probability density of the carrier phase estimate was be applied to derive probabilities for successful and unsuccessful unwrapping decisions. The resulting model enabled us to set a threshold on the minimum SNR (a quantity that can be directly estimated from the RO signal) according to the highest allowable likelihood of unwrapping failure (a specification that can be used to set the reliability of the RO science data product). We plan to present an outline of the derivation of the theory, show the application to the PREDICT airborne data set, and discuss its utility in the quality assurance of RO data.