measurements in order to rapidly resolve wide-lane ambiguities. Then the resulting precise ionosphere-corrected unambiguous wide-lane measurements are used to tightly constrain and thus significantly accelerate subsequent narrow-lane ambiguity resolution. This method does not rely on the satellite-geometry change, but on the sufficient shrink of the search space for integer candidates. Key issues for this method include the temporal properties of all errors assimilated into ionospheric delay estimates, the predicting strategy for these delays, and the model consistency between estimating ionospheric delays and resolving wide-lane ambiguities.
8.3
Conclusions on the data analysis
8.3.1
One FCB per satellite-pair pass over a regional area
For ambiguity resolution, FCBs are divided into wide-lane and narrow-lane ones. Wide-lane FCBs have good stability over at least several days, even if they are estimated with a global network. However, narrow-lane FCB estimates manifest instability even within 24 hours. This instability is caused by non-hardware-dependent errors, e.g. tropospheric delays, that are assimilated into narrow-lane FCB estimates. Therefore, a narrow-lane FCB estimate contains more than a real hardware bias.
For a global network, Ge et al. (2008) suggested a 15-minute mean to estimate narrow-lane FCBs of high precisions. On the other hand, for a regional network like the EPN, this thesis suggests that narrow-lane FCBs can be precisely estimated once per satellite-pair pass over this network. Tests in this thesis demonstrate that most narrow-lane FCB estimates achieve high precisions of better than 0.1 cycles (3σ). Note that this strategy is developed not because it can outperform the 15-minute mean in the precisions of narrow-lane FCB estimates, but because it produces much fewer, but still sufficiently precise, narrow-lane FCBs for a regional network, thereby improving the efficiency of disseminating FCBs to users.
8.3.2
Post-processing PPP with ambiguity resolution
Ambiguity resolution can significantly improve the positioning quality of sub-daily PPP. Tests on the EPN demonstrate that ambiguity resolution reduces the RMS of differences between hourly and daily position estimates from 3.8, 1.5 and 2.8 cm to 0.5, 0.5 and 1.4 cm for the East, North and Up components for the inside-EPN stations, respectively. The success rate of ambiguity resolution is up to 98.75%. Surprisingly, EPN-based FCB estimates are applicable to ambiguity resolution for outside-EPN stations which can be up to 4000 km away. The RMS statistics are also reduced from 3.7, 1.5 and 3.2 cm in ambiguity-float solutions to 0.6, 0.6 and 2.0 cm in ambiguity-fixed solutions. This finding thus suggests a great advantage of ambiguity-fixed PPP over NRTK.
Note that correct ambiguity resolution does not always lead to an improved positioning accuracy. However, for hourly PPP at inside-EPN stations, the rate of these problematic solutions is greatly reduced from 1.13% to only 0.15% if tropospheric delays are mitigated with accurate a priori values, hence demonstrating that estimating ZTDs is a crucial factor for the occurrence of these problematic solutions.
Sub-daily PPP with more than one hour of measurements can further improve on the hourly PPP. Specifically, the success rate of ambiguity resolution reaches 100.0% and the rate of problematic solutions above falls to 0.7% if three hours of measurements are used. Note that
increasing the observation period from one to three hours minimally reduces the horizontal RMS, but clearly improves the vertical RMS in the ambiguity-fixed solutions.
In addition, the radius of a ring reference network centered on a remote user receiver can affect the performance of ambiguity-fixed kinematic PPP. When the radius is enlarged from 900, 2000 to 3600 km, the RMS statistics of epoch-wise position differences from ground truths are slightly increased from 0.6, 0.5 and 2.6 cm, 0.5, 0.7 and 2.8 cm to 0.8, 1.0 and 3.2 cm for the East, North and Up components respectively. However, the efficiency of ambiguity resolution is negligibly affected by this radius increase.
8.3.3
Real-time PPP with ambiguity resolution
Ambiguity resolution has the potential of leading to PPP-RTK in which PPP provides rapid convergences to the reliable centimeter-level positioning accuracy. It is illustrated that at least 10 minutes of measurements are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to elevations of >30◦
, and over 20 minutes to fix about 90% of those corresponding to elevations of <30◦
. Moreover, several tens of minutes are usually required for a regional network to stabilize a narrow-lane FCB estimate to an accuracy of far better than 0.1 cycles. Within one hour, ambiguity resolution can significantly reduce the RMS of differences between epoch-wise and daily position estimates by an order of magnitude from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. In addition, a globally distributed network of 38 stations can lead to a global PPP-RTK which can guarantee a success rate of over 95% for the ambiguity-fixed epochs.
Therefore, PPP-RTK currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved with at most a few seconds of measurements. However, this PPP-RTK can still be applied to some near-real-time remote sensing applications, such as GPS meteorology and geohazard early warnings.
8.3.4
Integer constraints from double-difference ambiguities
Applying double-difference ambiguity resolution to a PPP-based network solution can improve the accuracy of narrow-lane FCB estimates. In a global network analysis over one year, the RMS of differences for the East component between the daily and IGS weekly estimates is reduced from 2.6 mm in solutions based on original narrow-lane FCBs to 2.2 mm in solutions based on improved narrow-lane FCBs.
8.3.5
Method comparison
Ambiguity-fixed position estimates derived from the FCB- and IRC-based methods are identical in theory. To verify this equivalence, one year of GPS data from a global network of about 350 stations were processed. The mean biases between all daily position estimates derived from these two methods are only 0.2, 0.1 and 0.0 mm, whereas the standard deviations of all position differences are only 1.3, 0.8 and 2.0 mm for the East, North and Up components, respectively. Moreover, the differences of the position repeatabilities are below 0.2 mm on average for all three components. The RMS of the position estimates minus those from the IGS weekly solutions for the FCB-based method differs by below 0.1 mm on average for each component from that for the