## 1. Introduction

[2] Radio occultation (RO) by use of the Global Positioning System (GPS) and low Earth orbiting (LEO) satellites has proven to be an accurate technique for remote sensing of the Earth's atmosphere [*Ware et al.*, 1996; *Kursinski et al.*, 1997; *Rocken et al.*, 1997; *Wickert et al.*, 2001; *Hajj et al.*, 2004; *Kuo et al.*, 2004; *Schreiner et al.*, 2007; *Anthes et al.*, 2008; *Foelsche et al.*, 2008]. The observables are the phase and the amplitude of RO signals. They are converted to vertical profiles of ray bending angles and refractivity. The refractivity in the neutral atmosphere is locally related to pressure, temperature and partial pressure of water vapor [*Thayer*, 1974]. Both the bending angle and the refractivity can be assimilated by atmospheric models [*Eyre*, 1994; *Poli*, 2006; *Cucurull et al.*, 2007; *Ringer and Healy*, 2008].

[3] Since the collection of the first GPS RO data in 1995 [*Ware et al.*, 1996] it was found that RO encounters problems in the moist lower troposphere resulting in significant refractivity inversion errors that include biases [*Rocken et al.*, 1997]. Later, it became obvious that these errors are related to the errors of signal tracking by means of the phase-locked loop (PLL) [*Sokolovskiy*, 2001b; *Ao et al.*, 2003; *Beyerle et al.*, 2003; *Beyerle et al.*, 2006] and to propagation effects such as superrefraction [*Sokolovskiy*, 2003; *Xie et al.*, 2006; *Ao*, 2007]. This study is related to resolving the first problem, elimination of the tracking errors in the lower troposphere by applying an alternative tracking technique instead of the PLL.

[4] The complicated structure of refractivity in the moist lower troposphere (related mainly to the complicated structure of humidity) causes multipath propagation, which results in strong random phase and amplitude modulation of the RO signals. The diffracted RO signals propagate deep behind the Earth's limb where they have to be recorded under conditions of low signal-to-noise ratio (SNR). Strong vertical refractivity gradients on top of the moist atmospheric boundary layer result in significant fading of the RO signal amplitude due to defocusing followed by an increase in amplitude at lower heights [*Hajj et al.*, 2004]. An added complication is posed by the 50 Hz navigation data modulation (NDM) [0, *π*] imposed on the phase of GPS signals, which has to be distinguished from the atmosphere-induced modulation (AIM) in order to be removed from the RO signals.

[5] The PLL [*Beyerle et al.*, 2006], which is an optimal tracking technique for single-tone (narrowband) signals under sufficient SNR, has been routinely used in GPS receivers. The PLL extracts the signal phase in real time and projects the expected phase ahead. The projected phase model is used for down conversion of the signal, i.e., shifting its mean frequency close to zero. The down-converted signal is subject to low-pass filtering (integration). Then the residual (unmodeled) phase is extracted and used for updating the phase model for the next sampling interval. Concurrently with the extraction of the phase, the NDM is removed under the assumption that the phase lapse between 50 Hz samples (typical GPS receiver internal sampling rate) induced by AIM is smaller than *π*/2 (half a carrier signal wavelength). Thus, with the removal of the NDM, the phase can be extracted in only 2 quadrants. When the phase lapse due to AIM is larger than *π*/2 or SNR is low, the errors of the phase extraction increase (in particular, these errors include the errors of removal of the NDM, half-cycle slips). As a result, the projection of the phase ahead becomes less accurate. When the difference between the projected and the true frequencies becomes larger than half of the filter bandwidth, the amplitude reduces to noise level, further tracking becomes unstable and, after some time, the receiver declares loss of lock. The results of PLL tracking of RO signals in the moist lower troposphere are sensitive to tunable loop parameters [*Sokolovskiy*, 2001b; *Beyerle et al.*, 2006]. A serious limitation for the PLL is tracking of rising occultations. Sufficient SNR and substantial time, required to lock on the signal emerging from behind Earth's limb, would result in loss of the lowermost part of the RO signal.

[6] Raw sampling of the complex RO signal, i.e., open loop (OL) tracking, is free of the problems discussed above and had previously been applied for RO studies of the planetary atmospheres. The sampling rates applied in those studies, typically, were much higher than required to transfer the information contained in RO signals (for example, 50 and 150 kHz at S and X bands [*Lindal et al.*, 1983]). Application of high sampling rates simplifies signal processing but is neither needed nor efficient for regular GPS RO remote sensing of the Earth's atmosphere because of high data downlink bandwidth requirements. In order to reduce the sampling frequency to the minimal Nyquist-required rate, a novel model-aided OL tracking approach was developed.

[7] The principles of the model-aided OL tracking of RO signals were introduced by *Sokolovskiy* [2001b]. They essentially use the fact that the Doppler frequency shift of the RO signal is related to the arrival angle of the ray at the receiving antenna. This arrival angle is influenced by Earth's atmosphere and, very importantly, its variations decrease with an increase of the distance from the receiver to the limb. For RO observations from LEO, because of large LEO-to-limb separation, the mean Doppler frequency shift caused by all of Earth's atmospheric conditions can be predicted (modeled) with very good accuracy to within 10–15 Hz, without feedback from the RO signal.

[8] In a receiver operating in OL mode, the complex RO signal is down-converted with the frequency model based on a real-time navigation position/velocity/clock solution and a simple bending angle model, then subjected to low-pass (noise) filtering and sampling. According to the Nyquist theorem, the sampling frequency shall not be smaller than the double-sided spread of the signal spectrum (which, in most cases, does not exceed 50 Hz for RO signals recorded from LEO [*Sokolovskiy*, 2001a]). Theoretically, the signal can be sampled at the Nyquist-required rate without any down conversion but with the possibility of spectral aliasing. Then this aliasing can be eliminated by down conversion of the sampled signal in postprocessing. However, practically, this would result in incoherent summation of noise aliased into the sampling band, and thus low SNR. Thus, the purpose of the real-time down conversion of the RO signal in the receiver is entirely noise filtering prior to sampling.

[9] The frequency mismodeling in the receiver does not change the phase of the complex samples (model + residual), but may reduce the SNR. It is important that the signal spectrum remains within the main lobe of the filter response function. In postprocessing, the signal, considered as the sequence of complex samples, is down-converted with a more accurate frequency model than in the receiver. The purpose of this down conversion is to remove the NDM and connect the phase between samples.

[10] The frequency mismodeling in postprocessing, also, does not change the phase of the complex samples, but it may introduce additional errors in the connected phase, i.e., half and full cycle slips. A frequency model based on the postprocessed navigation solution and the bending angle climatology is used only as the first guess. Then this model is further adjusted by determining the mean frequency of the RO signal reconstructed with this model and shifting the mean frequency to zero (this feedback from the whole reconstructed RO signal is different from recursive feedback in real time in PLL). This adjustment makes the results of the postprocessing of OL RO signals independent of the first guess model. This is important, especially, for climate applications.

[11] Six COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate) satellites launched on 15 April 2006 are recording L1 GPS RO signals in OL mode in the lower troposphere (overview of the first results from COSMIC can be found in the work of *Anthes et al.* [2008]). In this study we apply the principles of OL RO signal processing for inversions of the COSMIC OL RO signals at the COSMIC Data Analysis and Archive Center (CDAAC) at the University Corporation for Atmospheric Research (UCAR). We discuss the use of the two frequency models (first guess and adjusted with the use of feedback) in postprocessing of OL RO signals. We also discuss two methods (internal and external) for removal of the NDM [*Sokolovskiy et al.*, 2006]. We demonstrate the difference between the results of these different postprocessing modes based on statistical comparison of the retrieved refractivities in the tropical lower troposphere. Section 2 discusses principles of the processing of OL RO signals. Section 3 demonstrates individual examples of postprocessing OL RO signals. Section 4 discusses the adjustment of the postprocessing model by use of the feedback from the RO signal and compares the inversion results with and without adjustment of the model and with external or internal removal of NDM. Section 5 presents the statistical evaluation of the differences in inversion results obtained with different processing modes. Section 6 summarizes the study.