Figure 2: PPP and PPP-AR technology evolution in terms of accuracy versus convergence time.

Essence

Since the dawn of GPS, researchers have worked to improve the accuracy of estimated positioning, navigation and timing (PNT) from the receiver-derived pseudorange, carrier-phase and Doppler measurements. While the pseudorange-based accuracy of standard point positioning (SPP) at the level of 1s to 10s of meters sufficed for most users, carrier-phase-based relative positioning, real-time kinematic (RTK), network RTK (NRTK) and precise point positioning (PPP) measurement processing techniques were developed to provide decimeter-to-centimeter-level PNT under various constraints. Of these approaches, PPP — generally based on the state-space reduction of measurement errors to a single GNSS receiver from a wide area calibration network — has evolved dramatically. Why should readers read this article, as PPP has been around for some two decades? Well, some communities may consider old performance specifications of conventional/classical PPP, a rather niche technology, for static use with post-processing of measurements, resulting in tens of minutes for solution convergence to the decimeter level. However, there have been many performance advances, with more coming, affecting who uses the technology and how.

Figure 1 illustrates the timeline of PPP evolution, from:

1. The development of the original technique in the late 1990s to reduce static GPS network measurement processing load.
2. The removal of GPS Selective Availability (SA), simplifying precise satellite clock prediction.
3. The development of PPP-RTK, in which regional RTK-derived corrections are used to reduce position convergence time and increase accuracy.
4. Successful isolation of PPP GPS dual-frequency carrier-phase ambiguities to increase accuracy.
5. Full multi-constellation, multi-frequency (MCMF) processing to greatly reduce position convergence time.
6. The introduction of GNSS constellation provider corrections. (Individual advances will be discussed in the Elements section.)

From initial scientific uses to becoming the commercial standard in remote areas or regions with limited GNSS terrestrial infrastructure, these research contributions are leading to ubiquitous open sky decimeter to centimeter-level positioning with a range of available corrections, increasing accuracy and reducing initial convergence for more applications.

Essentials

In the late 1990s, to improve positioning accuracy over SPP and avoid the heavy computational burden of network-adjusted relative positioning processing between many receivers, PPP algorithms (detailed in the Elements section) were formulated with undifferenced measurements between tracked satellites and a single receiver (Zumberge et al. 1997). Both pseudorange and carrier-phase measurements are utilized, with the former presenting many decimeter-level references and the latter ambiguous centimeter-level ranging. By filtering continuously tracked measurements over time, decimeter- to centimeter-level positioning is possible, as the state terms, including real-valued estimates of biased carrier-phase ambiguity terms — resulting in tens of minutes to hours of initial convergence time. This approach represents Hatch filtering in the position state rather than the observation domain. Key to PPP is the use of precise satellite orbit and clock estimates derived from a global reference network, which can receive measurements from an entire GNSS constellation. Additionally, to maximize performance, remaining error sources are modeled or estimated. While PPP was initially not as accurate as RTK and, more importantly, took tens of minutes to hours to attain solution convergence, the technique did not have the terrestrial infrastructure constraints of RTK or network RTK, which require reference receivers ~10 km to 15 km and ~75 km away, respectively. Once GPS Selective Availability was turned off in 2000, GPS satellite clock modeling became simpler and more accurate, and scientific and commercial PPP solutions quickly became the standard measurement processing technique for applications requiring decimeter-level accuracy in remote areas or places where it was not economically viable to install (an) RTK base station(s).

In the 2000s, two different approaches were developed to deal with the shortcomings of PPP: PPP-RTK and PPP-AR. In PPP-RTK, state space corrections from a regional NRTK solution are efficiently transmitted and applied as PPP corrections. As NRTK resolves carrier-phase ambiguities and estimates local atmospheric (ionospheric and tropospheric) refraction and reference station position all in a least-squares sense, PPP-RTK can produce centimeter-level positioning in seconds within a reference station network, where stations can be tens to hundreds of kilometers apart. In PPP-AR, the…