Strong demand for low-cost precise positioning exists in the mass market. Carrier-phase differential GNSS (CDGNSS) positioning, accurate to within a few centimeters even on a moving platform, would satisfy this demand were its cost significantly reduced. Low-cost CDGNSS would be a key enabler for many demanding consumer applications.
Centimeter-accurate positioning by CDGNSS has been perfected over the past two decades for applications in geodesy, precision agriculture, surveying and machine control. But mass-market adoption of this technology will demand much lower user cost — by a factor of 10 to 100 — yet still require rapid and accurate position fixing. To reduce cost, mass-market CDGNSS-capable receivers will have to make do with inexpensive, low-quality antennas whose multipath rejection and phase center stability are inferior to those of antennas typically used for CDGNSS.
Moreover, there will be a strong incentive to use single-frequency receivers, whereas almost all receivers used for CDGNSS in surveying and similar applications are multi-frequency. Despite these user-side disadvantages, mass-market precise positioning will be expected to demonstrate convergence and accuracy performance rivaling that of the most demanding current precise positioning applications: Users will be dissatisfied with techniques requiring more than a few tens of seconds to converge to a reliable sub-decimeter solution.
Meeting this challenge calls for innovation targeting both the rover (user) equipment and the reference network. Here we examine the challenge from the point of view of the reference network and offer demonstration results for a low-cost end-to-end system.
The recent trend in precise satellite-based positioning has been toward precise point positioning (PPP), whose primary virtue is the sparsity of its reference network. But standard PPP requires several tens of minutes or more to converge to a sub-10-centimeter 95 percent horizontal accuracy. Faster convergence can be achieved by recasting the PPP problem as one of relative positioning, thereby exposing integer ambiguities to the end user.
This technique, known as PPP-RTK or PPP-AR, is mathematically similar to traditional network real-time kinematic (NRTK) positioning. As the network density is increased, sub-minute or even instantaneous convergence is possible with dual-frequency high-quality receivers. Even single-frequency PPP-RTK is possible, with convergence times of approximately 5 minutes for a 40-kilometer network spacing.
For PPP-RTK and NRTK, convergence time is synonymous with the time required to resolve the integer ambiguities that arise in double-difference (DD) carrier-phase measurements, referred to here as time to ambiguity resolution, or TAR. As reference networks become denser, they can better compensate for spatially-correlated variations in signal delay introduced by irregularities in the ionosphere and, to a lesser extent, in the neutral atmosphere. Improvement is manifest as reduced uncertainty in the atmospheric corrections that the network sends to the user. Reduced uncertainty in the atmospheric corrections is key to reducing TAR.
Prior work has established an analytical connection between uncertainty in the ionospheric corrections (denoted σi ) and TAR. The existing literature does not, however, offer a satisfactory model for the dependence of σι on network density.
The prevailing model is based on single-baseline CDGNSS, which is inapt for PPP-RTK and NRTK. Moreover, prior work does not address the effect of network-side multipath on the accuracy of the corrections data, which becomes increasingly important as low-cost and poorly-sited reference stations are used to densify the network.
Here, we examine the relationship between ionospheric uncertainty and probability of correct ambiguity resolution, and present the results of an empirical investigation of the relationship between network density and the total uncertainty in network correction data. We developed a simple analytical model relating error variance in network corrections to network density. Our analysis and experiments indicate that for rapid TAR in challenging urban environments with low-cost receivers, network density must be significantly increased. We report on the design and deployment of a dense network in Austin, Texas, and demonstrate a new system that taps into the network to provide reliable vehicle lane-departure warning.
