This section focuses on the structure of post-processing PPP suite in the PANDA software and the data processing procedure for post-processing PPP.
4.4.1
Structure description
Figure 4.2 illustrates the structure of the post-processing PPP suite of the PANDA software. This figure is actually composed of only processing modules and data files. The processing modules include
• Pre-processing. This module includes the software packages teqc (translation, editing, and quality check) developed by UNAVCO (University NAVSTAR Consortium) (Estey and Meertens 1999), clockprep developed by Prof Freymueller at the University of Alaska Fairbanks, cc2noncc developed by Dr Ray at the US National Geodetic Survey (NGS), and turboedit which is based on the pre-processing algorithms by Blewitt (1990). In the PANDA software, teqc is used for RINEX (Receiver INdependent EXchange) formatting in order to avoid software abnormality due to format bugs; clockprep is used to convert
4.4 Post-processing PPP suite 57
RINEX observation files of receiver time into those of GPS time in order to avoid pseudo cycle slips detected by turboedit; cc2noncc is used to convert pseudorange measurements from a cross-correlation receiver to those that are compatible with the modern Y-codeless pseudorange tracking (Dach et al. 2007) in order to keep consistency between clock products and pseudorange measurements; finally, turboedit is used to identify bad measurements and cycle slips in a RINEX observation file.
• Orbit preparation. The module is solely based on sp3orb which transforms SP3 (NGS Standard Product – 3) orbit files into a self-defined binary format. In this manner, the PANDA software can efficiently access the precise orbit products. In addition, the reference frame is changed from an Earth-fixed system into an inertial system through the ERP files. • Least squares adjustment. The module lsq is used to reduce raw measurements and
estimate unknown parameters.
• Posterior residual diagnosis. The module redig is to analyze posterior measurement residuals derived from lsq in order to identify remaining cycle slips and bad measurements. • Double-difference ambiguity resolution. The module arnet is used for network solutions where double-difference ambiguities are formed based on undifferenced ambiguity estimates and ambiguity resolution is then attempted.
• FCB determination. The module defip is used to estimate wide-lane and narrow-lane FCBs based on ambiguity estimates derived from network solutions.
• Ambiguity resolution at a single receiver. The module arsig is used to form single- difference ambiguities between satellites based on undifferenced ambiguity estimates and then apply FCB products in order to recover the integer properties of these single-difference ambiguities.
Moreover, the data files include
• Input data. RINEX ephemerides and measurements, SP3 orbits and ERP files, and RINEX satellite clocks. Broadcast ephemerides are used by turboedit. SP3 orbits, RINEX clocks and ERP files can be freely obtained from the IGS.
• Binary orbits. Intermediate results which are generated by sp3orb.
• RINEX health diagnosis files. Each RINEX file corresponds to a health diagnosis file recording the locations of problematic measurements. It is initially generated by tur- boedit and subsequently updated by redig. RINEX health diagnosis files should accom- pany raw RINEX measurements as input files to lsq.
• Posterior residuals. These are generated by lsq and then input to redig. RINEX health diagnosis files are updated according to the analysis on these residuals.
• Positions, clocks and tropospheric delays. These are the output of lsq. Positions can be daily, sub-daily or epoch-wise estimates. Satellite clocks can also be estimated in a network solution by lsq. Tropospheric delays include ZTDs and horizontal gradients.
• Ambiguities and their optional variance-covariance statistics. These are generated by lsq and are the input of ambiguity resolution. If the variance-covariance statistics are available, ambiguity search by the LAMBDA method can be performed.
• Wide-lane and narrow-lane FCBs. These are estimated in defip. Wide-lane FCBs are daily estimated whereas narrow-lane FCBs can be estimated every 15 minutes or within each satellite-pair pass over a regional network.
• Ambiguity constraints. Double-difference and single-difference integer constraints. These files are the output of ambiguity resolution. They record the combinations of four or two undifferenced ambiguities. These combinations form integer constraints which are
subsequently imposed on the normal equation of lsq in order to achieve ambiguity-fixed solutions.
4.4.2
Processing procedure
This section addresses the processing procedures for post-processing PPP and ambiguity res- olution at a single receiver. The satellite clock determination and double-difference ambiguity resolution are ignored for the brevity of this thesis.
A Post-processing PPP
Post-processing PPP in the PANDA software mainly relies on lsq and redig. Specifically, the procedure for a post-processing ambiguity-float PPP is divided into four steps, namely
1. Build a processing environment. All raw measurements should be put in an independent folder and a work folder has to be created for each project. Afterwards, a number of table files have to be copied into this work folder, mainly including antenna phase center offsets and variations, planetary ephemerides, leap seconds, coefficients for the ocean tide loading model, P1-C1 corrections and satellite states. Moreover, ERP files and satellite clocks need to be copied into the work folder. SP3 orbits can then be transformed into a binary format.
2. Pre-processing. teqc is first used to check the format of raw measurements. clockprep is then applied to all RINEX measurements. cc2noncc should be applied to only cross- correlation receivers and receivers without P1 measurements. Hence, such receivers must be identified before cc2noncc is run. Finally, turboedit is used to generate RINEX health diagnosis files.
3. Estimation. lsq is run at this step. Unknown parameters are estimated and posterior residuals are generated.
4. Residual editing. redig is applied to posterior residuals. Once new bad measurements or new cycle slips are identified, the third step has to be run again. Otherwise, final results can be collected.
B Ambiguity resolution at a single receiver
Ambiguity resolution at a single receiver is performed by running defip and arsig. The processing procedure is
1. A network solution where FCBs are estimated.
(a) Ambiguity-float PPP for a network of reference stations (refer to Section A). (b) Estimate FCBs. defip is applied to all undifferenced ambiguity estimates generated
in the network solution. We can ultimately obtain wide-lane and narrow-lane FCB estimates.
2. Resolve ambiguities at a single receiver by applying FCBs.
(a) Ambiguity-float PPP for a single receiver (refer to Section A).
(b) Ambiguity resolution. arsig employs FCBs to retrieve the integer properties of single- difference ambiguities between satellites at a single receiver. Ambiguity resolution can then be attempted.
4.5 Real-time PPP suite 59
Figure 4.3: Structure of the real-time PPP suite. Meaning of symbols refer to Figure 4.2
(c) PPP by applying integer constraints. lsq is run again and integer-constraint files will be used automatically. Finally, ambiguity-fixed solutions can be achieved.
4.5
Real-time PPP suite
This section focuses on the structure of the real-time PPP suite in the PANDA software and the data processing procedure for real-time PPP.
4.5.1
Structure description
Figure 4.3 illustrates the structure of the real-time PPP suite of the PANDA software. This figure is also composed of only processing modules and data files. The processing modules include
• Pre-processing. Refer to Section 4.4.1. teqc and cc2noncc cannot be used in real time, but adapting them into real-time modules is not a complicated task. turboedit cannot be used and a real-time data screening is embedded into the filter sri (see Section 4.2). Finally, clockprep is not applied because it is not a real-time module. Fortunately, most receivers do not need this processing module.
• Orbit preparation. Refer to Section 4.4.1. Because only predicted satellite orbits are used, according to Table 1.1, we have to update the orbits and ERPs once newer ones are released by the IGS.
• Satellite clock determination. ckdet is based on epoch-differenced data processing, but undifferenced satellite clocks are generated at each epoch. Its efficiency has been illustrated by Ge et al. (2010).
• Square root information filter. This real-time filter is characterized by its high numerical stability (Bierman 1977). Data screening and quality control in real time are embedded into this filter to identify bad measurements and cycle slips. Moreover, real-time ambiguity resolution is also applied to this filter (Geng et al. 2010d). Note that backward smoothing is not allowed in this filter.
• Real-time FCB determination. rtfip is used to estimate only narrow-lane FCBs at a given update rate based on undifferenced ambiguity estimates from a network solution. Note that wide-lane FCBs can be precisely predicted over 24 hours due to their high temporal stability (Ge et al. 2008; Geng et al. 2010d), and hence they are not estimated in rtfip. • Interpolation of atmospheric delays. interp is used to interpolate ionospheric and tro-
pospheric delays for a single receiver from its surrounding reference stations. These interpolated atmospheric delays contribute to accelerating convergences to ambiguity-fixed solutions (refer to Section 3.6).
Moreover, the data files include
• Input data, including RINEX ephemerides and measurements, predicted SP3 orbits and ERP files (refer to Section 4.4.1 and Table 1.1).
• Binary orbits. Refer to Section 4.4.1.
• Real-time satellite clocks. As demonstrated in Section 1.2.2, satellite clocks have to be estimated in real time. It is worth stressing that we should keep consistency between the predicted orbits and the clocks.
• Positions and receiver clocks. These are the output of sri.
• Atmospheric delays. Slant ionospheric delays and tropospheric delays. According to Section 3.4.1, slant ionospheric delays can be estimated with wide-lane measurements (Equation 3.17) after a successful wide-lane ambiguity resolution. In addition, slant tro- pospheric delays are computed with ZTD estimates and posterior carrier-phase residuals. • Interpolated atmospheric corrections. These corrections are generated by interp. If slant atmospheric delays are available at some reference stations, interpolated atmospheric delays can then be computed at a user receiver located inside the coverage of these reference stations. Interpolation methods refer to Dai et al. (2004).
• Ambiguities. At reference stations, undifferenced ambiguity estimates can be output at an interval of a few minutes, for example, rather than every epoch. This can significantly reduce the computation burden of sri.
• Real-time wide-lane and narrow-lane FCBs. Wide-lane FCBs are presumed known whereas narrow-lane FCBs are generated by rtfip. Because narrow-lane FCBs are normally stable over a few tens of minutes, an update rate of a few minutes is usually sufficient. Real-time FCBs are then input to sri for ambiguity resolution.
4.5.2
Processing procedure
This section addresses the processing procedures for real-time PPP, real-time ambiguity resolu- tion at a single receiver and rapid ambiguity resolution with interpolated atmospheric delays. Satellite clock determination in real time by ckdet is ignored for the brevity of this thesis.
A Real-time PPP
Real-time PPP in the PANDA software mainly relies on sri. Specifically, the procedure for a real-time PPP is
4.6 Summary 61
1. Build a processing environment (refer to Section 4.4.2).
2. Satellite clock determination. If real-time satellite clocks are not available, a network of reference stations has to be used to estimate epoch-wise clocks in a real-time manner. 3. Estimation. sri is run for this step. Briefly, raw measurements are preliminarily cleaned
using the Melbourne-W¨ubbena and the geometry-free combination measurements. Undiffe- renced ionosphere-free measurements are then reduced and the filtering is started. Posterior residuals are analyzed to further clean the measurements. Estimates are output at every epoch. Furthermore, ambiguity resolution will be attempted if FCB products are available and rapid re-convergences are started once cycle slips occur.
B Real-time ambiguity resolution
Real-time ambiguity resolution at a single receiver is based on both rtfip and sri. The processing procedure is
1. A network solution where real-time FCBs are estimated. (a) Satellite clock determination. Refer to Section A.
(b) Real-time FCB determination. Ambiguity estimates at all reference stations are input to rtfip. Wide-lane FCBs are presumed known and narrow-lane FCBs are estimated. 2. Single-receiver solution. Refer to Section A.
C Rapid ambiguity resolution with interpolated atmospheric delays
Dense network has to be used if precise atmospheric delays are required. The processing procedure of rapid ambiguity resolution with interpolated atmospheric delays is
1. Determination of satellite clocks and FCBs. Refer to Section A and B.
2. Determination of atmospheric delays at reference stations. By applying known satellite products, slant ionospheric delays are estimated after wide-lane ambiguity resolution and slant tropospheric delays are estimated after narrow-lane ambiguity resolution.
3. Interpolation of atmospheric delays. This is performed by interp. Slant ionospheric and tropospheric delays are separately interpolated for an interested position.
4. Single-receiver solution. Note that ZTD parameters are no longer required and sri does not need to predict ionospheric delays itself.
4.6
Summary
This chapter introduces the PANDA software used and developed in this thesis. The structure, characteristics and capabilities of this software are briefly addressed. Then my contributions to this software are detailed and highlighted. Afterwards, the two software suites for post-processing and real-time PPP are introduced by illustrating their functional modules and processing proce- dures. These can be recognized as a brief manual for the PPP modules of the PANDA software. Most results shown in the subsequent chapters 5, 6 and 7 on ambiguity resolution and rapid convergences are achieved with this software.
Chapter 5
Results on Ambiguity Resolutions
5.1
Introduction
Chapter 2 has introduced the methods recently developed for integer ambiguity resolution at a single receiver, i.e. the FCB- and IRC-based methods (Collins 2008; Ge et al. 2008; Laurichesse et al. 2009c). This thesis adopts the FCB-based method and develops four improvements, i.e. the derivation of undifferenced FCBs, one FCB per satellite-pair pass over a regional area, implementation of real-time ambiguity resolution and constraints from integer double- difference ambiguities, in the PANDA software. This chapter thus assesses the “one FCB estimate per satellite-pair pass” in post-processing PPP with sub-daily and epoch-wise GPS measurements. Three crucial issues, i.e. the rapidity of wide-lane ambiguity resolution, the temporal stabilization of narrow-lane FCBs and the performance of narrow-lane ambiguity resolution, are closely investigated in order to assess real-time ambiguity-fixed PPP. Constraints from integer double-difference ambiguities is highlighted with their contribution to improving position quality of ambiguity-fixed PPP. Finally, a comparison study between the FCB- and IRC-based methods ends this chapter.