The Implementation of Precise Point Positioning: Comparison
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High-precision positioning from Global Navigation Satellite Systems (GNSS) has garnered increased interest due to growing demand in various applications, like autonomous car navigation and precision agriculture. Precise Point Positioning (PPP) offers a distinct advantage over differential techniques by enabling precise position determination of a GNSS rover receiver through the use of external corrections sourced from either the Internet or dedicated correction satellites. However, PPP’s implementation has been challenging due to the need to mitigate numerous GNSS error sources, many of which are eliminated in differential techniques such as Real-Time Kinematics (RTK) or overlooked in Standard Point Positioning (SPP). This paper extensively reviews PPP’s error sources, such as ionospheric delays, tropospheric delays, satellite orbit and clock errors, phase and code biases, and site displacement effects. Additionally, this article examines various PPP models and correction sources that can be employed to address these errors. A detailed discussion is provided on implementing the standard dual-frequency (DF)-PPP to achieve centimeter- or millimeter-level positioning accuracy. This paper includes experimental examples of PPP implementation results using static data from the International GNSS Service (IGS) station network and a kinematic road test based on the actual trajectory to showcase DF-PPP development for practical applications. By providing a fusion of theoretical insights with practical demonstrations, this comprehensive review offers readers a pragmatic perspective on the evolving field of Precise Point Positioning.

  • GNSS
  • precise positioning
  • PPP
  • PPP errors
  • PPP corrections
  • IGS

1. Introduction

The Global Positioning System (GPS) was originally designed to achieve accuracy within a few meters, employing code measurements. At its inception, the designers had not foreseen the prospects for finer precision [1]. The use of GPS carrier-phase measurements to achieve centimeter-level accuracy was first explored by Counselman [2][3]. Because of their short wavelengths, these carrier-phase measurements offer higher precision than their code counterparts. For example, the carrier wavelengths for GPS L1 and L2 frequencies are about 19 cm and 24 cm, respectively. On the other hand, the duration of 1 bit in the GPS coarse/acquisition (C/A) code is 1 μs, corresponding to about 300 m, while 1 bit in the P1 code, which is 10 times faster, corresponds to about 30 m [4].
The Integer Ambiguity (IA) is a paramount challenge for using precise GNSS carrier-phase measurements. The IA is the unknown initial number of full carrier cycles on the path from satellite to receiver. Achieving the desired precision is contingent on resolving this IA [1]. In a broader sense, Differential GPS (DGPS), or DGNSS in general, is engineered to bolster GNSS receiver performance, drawing upon data from one or more strategically positioned reference stations [5]. The core principle of DGNSS is that when the baseline length—defined as the distance between the rover receiver and the reference station—is adequately short (e.g., less than 40 km), certain errors, including atmospheric delays, satellite orbit, and satellite clock errors, become spatially correlated. These correlated errors can then be effectively eliminated using differencing techniques. The Real-Time Kinematics (RTK) is a carrier-phase-based DGNSS technology that provides centimeter-level real-time positioning accuracy [4]. Nonetheless, the overheads associated with reference station setup and the inherent baseline length constraints underscore the limitations of DGNSS.
Introduced in 1997, Precise Point Positioning (PPP) is a technique that facilitates the precise and accurate estimation of a user’s global position using a single GNSS receiver [6]. PPP determines the absolute receiver position, relying exclusively on the rover receiver’s GNSS measurements and a global spectrum of precision correction data. Since PPP must consider all error sources neglected in DGNSS, its pivotal challenge remains the convergence time required for resolving IA to achieve centimeter-level precision [7]. However, the ability of PPP to provide a globally applicable solution via a single receiver has gained significant interest within the research community, leading to ongoing efforts to overcome its limitations [8].
PPP can be applied in many aspects of our daily life. For example, in [9], PPP was integrated with high-end inertial sensors for lane-level autonomous land vehicle navigation on highways. Other papers investigated the integration of PPP with low-cost inertial sensors for land vehicle navigation in GNSS-challenging environments [10][11]. PPP was also applied for precision agriculture [12] and atmospheric monitoring [13]. In [14], PPP with the BeiDou B2b products was used for earthquake monitoring. Several open-source software tools can be used for PPP, such as RTKLIB [15], GAMP [16], PPPH [17], PPPLib [18], raPPPid [19], and PPP-ARISEN [20].

2. Error Sources in PPP

For PPP to attain centimeter-level precision, it is imperative to eliminate or significantly mitigate range errors. Many of these errors, such as the Sagnac effect (attributable to Earth’s rotation), relativistic clock effects, satellite orbit and clock errors, and atmospheric delays, are also prevalent in Standard Point Positioning (SPP), leading to accuracies on the order of several meters [21]. The correction models employed for mitigating the Sagnac effect and relativistic clock errors in SPP equally apply to PPP; therefore, they are not elaborated on in this discussion. Conversely, the broadcast ephemeris data employed in SPP to calculate the atmospheric delays and the errors in satellite position and clock are insufficient for reaching the targeted PPP accuracy. For instance, the GPS Klobuchar’s ionospheric model can correct around 50% rms of the ionospheric error [22]. Other broadcast ionospheric models also provide limited improvement to the positioning accuracy [23]. Therefore, more precise corrections and refined models are required in PPP.

3. PPP Models

PPP exhibits a range of implementation modes contingent upon various determinants, including accessible constellations, management of the ionospheric delays, the decision to fix phase ambiguities, and the number of operational GNSS frequencies. While ionospheric delays are frequently mitigated using IF measurement combinations, leveraging ionospheric corrections sourced from either local or global networks can expedite the convergence of the solution. Concerning ambiguity resolution (AR), the ambiguities might be estimated as float values or as fixed to their integer counterparts. Float PPP remains a prevalent choice, especially for real-time applications, due to the complexity of fixing integer ambiguities within the PPP context. Nevertheless, ambiguity-fixed PPP, or PPP-AR, has the advantages of shorter initial convergence time and improved accuracy, especially in the east direction [7][24]. PPP-RTK is a state-of-the-art technique that combines the complementary characteristics of PPP and RTK to achieve centimeter-level positioning in a short time [25]. Classified by the number of employed GNSS frequencies, implementations encompass single-frequency (SF), dual-frequency, and triple-frequency (TF) PPP. SF-PPP utilizes observations from a single GNSS frequency, which is useful when using low-cost SF GNSS receivers. SF-PPP has the advantages of low-cost hardware and shorter convergence time but to a limited accuracy range of the decimeter to submeter level, especially in the kinematic mode [26][27]. Recently, the availability of DF observations in low-cost GNSS receivers, even smartphones, has grown, reducing the interest in SF-PPP. In TF-PPP, observations from three GNSS frequencies are employed, e.g., GPS L1, L2, and L5. The third frequency’s main contribution is to shorten the convergence time and allow faster ambiguity resolution. Because of this, positioning accuracy can be improved in the short term due to faster convergence, but the contribution to positioning accuracy after convergence will be limited [28]. One limitation of the TF-PPP is that it is still not supported by all GNSS receivers in the market, especially low-cost ones [10].

4. PPP Challenges and Solutions

The experimental results demonstrate the advantage of PPP as a global precise GNSS solution with high accuracy. However, achieving the full potential of PPP requires addressing several challenges. A predominant challenge is the protracted convergence time, often exceeding 20 min in standard DF-PPP, attributed to the time necessary for carrier-phase ambiguity resolution. Multiple factors influence this convergence duration, including the number of visible satellites, satellite geometry, correction product quality, receiver multipath environments, and prevailing atmospheric conditions. Extensive research is underway to expedite PPP convergence, aligning it with the demands of real-time applications. Recent studies have indicated that employing triple-frequency, multiconstellation, and adopting ionospheric corrections instead of IF combinations could potentially shorten PPP convergence time [28][29][30]. Moreover, fixing the integer ambiguities can also reduce the convergence time to some extent compared with the float solution; nonetheless, it necessitates supplementary corrections and more complicated algorithms. A state-of-the-art method that combines the advantages of PPP and RTK and allows faster ambiguity resolution is the PPP-RTK. Another significant challenge for PPP is the performance deterioration or potential inability to provide a solution in challenging GNSS environments like underpasses, within tunnels, or amid towering buildings. Although this limitation is not exclusive to PPP and pervades all GNSS positioning modes, its ramifications are magnified in PPP due to the requisite reconvergence time to reclaim the original precision. This particular constraint is of paramount concern in scenarios like land vehicular navigation. Therefore, the fusion of PPP with other navigation systems is employed to ensure the continuity of the navigation solution and reduce the PPP reconvergence time. Two examples of this fusion are PPP/INS integration [9][11][31] and PPP/INS/Vision/LIDAR integration [32] for navigation in GNSS-challenging environments.

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