To unbiasedly estimate ambiguity-resolved user positional parameters with the carrier-phase ambiguity resolution-enabled precise point positioning (PPP-AR) concept, one needs to combine Global Navigation Satellite Systems (GNSS) measurements with satellite orbit, clock, and bias information computed from an external correction provider. While the provision of such corrections guarantees that the unbiasedness property is preserved in the multi-epoch recursively estimated user parameter solutions, the minimum-variance optimality property of the user-filter is generally lost. This loss is a direct consequence of, first, the violation of the Kalman-filter’s standard assumption of temporally uncorrelated measurements and, second, the negligence of the stochastic properties of the GNSS corrections in the user-filter. Although it has been demonstrated that the temporal correlation of the corrections can be safely ignored under certain conditions [1], the same cannot be said for the correction quality information [2]. The network-derived corrections carry some level of uncertainty, which is typically discarded in post-processing scenarios but can considerably increase in real-time scenarios depending on the dissemination update-rate. In case the uncertainty of the corrections’ prediction error is not captured in the user’s stochastic model, the PPP-AR users will experience performance loss in the form of weaker ambiguity resolution and quality control capabilities, longer positioning convergence times and misleading filter-reported positioning confidence levels, with the degradation becoming more pronounced as the latency increases. The goal of this contribution is to study and quantify the role of the GNSS correction quality information in real-time PPP-AR and to demonstrate practical mitigation solutions for the adverse effects of neglected correctional uncertainty, building on the strategies developed in [3]. With the aid of real-world GPS and Galileo multi-frequency network and user data, it is illustrated that one can leverage limited information by the network-filter’s dynamic model, or use relevant data-driven estimates, to obtain a more representative statistical characterization of the time-predicted correction error. The results will demonstrate that with these practical solutions one is able to obtain improved real-time PPP-AR user performances, not only in terms of ambiguity resolution and positioning convergence, but also in terms of filter-reported positioning confidence levels and outlier detection capabilities.

[1] Psychas, D., Khodabandeh, A. & Teunissen, P.J.G. Multi-epoch PPP-RTK corrections: temporal characteristics, pitfalls and user-impact. J Geod 98, 15 (2024). https://doi.org/10.1007/s00190-024-01823-8

[2] Psychas, D. (2025). How Weight Matrix Misspecifications Drive PPP-RTK User Performances. In: Khodabandeh, A., Verhagen, S. (eds) Navigating the Geodetic Landscape: A Tribute to 45 Years of Excellence. Springer, Cham. https://doi.org/10.1007/978-3-031-99274-2_8

[3] Psychas, D., Khodabandeh, A. & Teunissen, P.J.G. Impact and mitigation of neglecting PPP-RTK correctional uncertainty. GPS Solut 26, 33 (2022). https://doi.org/10.1007/s10291-021-01214-y

Global Navigation Satellite Systems (GNSS) represent one of the most important technologies in several fields due to their capability of providing real-time Positioning, Navigation, Timing (PNT) solutions. By precisely modelling different error sources, the Precise Point Positioning (PPP) technique enables centimetre-level user positioning accuracy worldwide in real time. In support of PPP applications, different real-time services (RTS) are established to provide users with low-latency satellite corrections, including orbits, clocks, and hardware code/phase biases. The latter allow to resolve carrier-phase ambiguities to integers, i.e., further exploiting their millimetre-level precision in what is defined as PPP-Ambiguity Resolution (PPP-AR).

For instance, both Galileo High Accuracy Service (HAS) and BeiDou B2b service were developed to provide in-signal corrections to ground users. Furthermore, different analysis centres of the International GNSS Service (IGS) also generate real-time satellite corrections, which are then provided via internet. However, only a few IGS centres currently provide satellite phase biases necessary for a successful Integer Ambiguity Resolution (IAR) process. Generally, errors introduced by these satellite corrections can negatively impact the ambiguity-fixed solutions. Therefore, both ambiguity “estimation and validation” steps become fundamental for avoiding wrong fixes that might deteriorate the user positioning solution.

In this work, we adopt an uncombined and undifferenced PPP-AR formulation, enabled by the IGS streams of satellite corrections over July 2025. We consider IGS stations in real-time kinematic processing, using IGS streams currently providing phase biases (e.g., Chinese Academy of Science, CAS ), along with ambiguity-fixed kinematic solutions based on IGS final products, e.g., provided by the Center of Orbit Determination in Europe (CODE). The PPP-AR performance is numerically evaluated based on ‘convergence time’ and ‘positioning accuracy’, thus comparing different ambiguity validation approaches using the latest Least-square AMBiguity Decorrelation Adjustment (LAMBDA) 4.0 toolbox implementation.

During the IAR process, wrongly fixed ambiguities might affect the conditional update for the other parameters of interest. This highlights the need for a procedure to control the failure rate of the ambiguity resolution. By a Partial Ambiguity Resolution (PAR), we are able to fix the largest subset of ambiguities with a sufficiently high success rate, however this is a model-driven approach not sensitive to biases introduced by the corrections’ uncertainty. Therefore, an ambiguity validation is needed and made possible by fixed threshold Ratio Test (RT) and the Fixed Failure Rate Ratio Test (FFRT). Both are data-driven approaches that assess the closeness of the integer ambiguity estimates to the corresponding float solution. However, the RT does not provide users with a control over the failure rate leading to potentially unnecessary rejections when the underying model is strong. In contrast, the FFRT adopts a variable threshold computed based on the model providing more control and greater acceptance in weaker models. This contribution analyzes different ambiguity validation methods in PPP-AR solutions based on the real-time IGS-SSR corrections, which are subjected to potentially large errors, whose uncertainty is generally not specified by the provider.

Since the release of Android 7.0 in 2016, raw GNSS measurements tracked by Android smartphones have been accessible to everyone. This allows users to improve position accuracy using their own algorithms and correction data instead of relying on the smartphone's internal calculations. Furthermore, an increasing number of smartphones can now track GNSS signals from multiple constellations on two frequencies, following the release of the first dual-frequency smartphone in 2018. However, smartphone measurements are typically of low quality and difficult to process, as mobile devices usually have simple, cost-effective sensors, chips, and antennas. Consequently, challenges such as outliers, cycle slips, and multipath errors frequently occur.

Precise Point Positioning (PPP) is a well-established positioning technique for multi-frequency GNSS data from geodetic receivers and an excellent approach for smartphone positioning. PPP uses precise satellite products (orbits, clocks, and biases) and complex models to calculate the user's position. This approach enables the development of resilient and flexible algorithms, which is advantageous given the challenging nature of GNSS measurements from smartphones. Additionally, modern services such as the Galileo High Accuracy Service (HAS) and the International GNSS Service's (IGS) real-time service enable PPP applications in real time.

The ongoing research project 'Precise Positioning for Mobile Devices' (PPMD), funded by Aspern Smart City Research GmbH & Co KG (ASCR), aims to develop an open-source Android application performing PPP calculations directly on smartphones to achieve sub-metre accuracy. Based on the algorithms of the open-source PPP software raPPPid, the application utilizes the uncombined PPP model with ionospheric constraint to handle the challenging raw GNSS measurements from smartphones. Furthermore, we explore the potential of using measurements from other smartphone sensors, such as the accelerometer, to support the PPP solution and enhance position accuracy and stability. The Android application allows geodata to be visualised, integrated and managed for use cases such as recording and locating infrastructure objects, guiding individuals and lane-accurate positioning. In this contribution, we present the current status of the application, discuss the challenges posed by ultra-low-cost smartphone equipment, and outline the positioning algorithms and its outcomes.

Positioning, navigation, and timing services of Global Navigation Satellite Systems (GNSS) rely on high-quality orbit and satellite clock correction products. These are regularly provided by various Analysis Centers (ACs) of the International GNSS Service (IGS). Each AC applies its own modeling strategies, reference clocks, and systematic drifts, therefore there is a variety in quality and consistency among orbit and clock products. The GNSS community aims to develop and refine procedures for product combination to address modeling errors and data gaps inherent to individual ACs. The primary objective is to provide users with a consistent and reliable solution, which can be used in Precise Point Positioning (PPP) to achieve global cm-level positioning precision. IGS uses the solutions contributed by multiple ACs to generate combined satellite products for GPS and GLONASS. However, the multi-GNSS clock combination still requires further optimization. This study presents an advanced epoch-wise alignment strategy for combining multi-GNSS clock products. In contrast to the traditional linear transformation used by the IGS, which assumes consistent clock products with linear reference clocks from each AC, the proposed approach addresses situations in which these assumptions cannot be fulfilled. We evaluated the quality of the combined clocks using pairwise AC comparisons, a frequency stability analysis, and PPP results for IGS stations. The epoch-wise alignment effectively mitigates non-linearities in ACs’ clock products, reducing inter-AC dispersion to 0.05 ns. It also stabilizes AC weights and improves agreement for GPS and Galileo blocks by 30–70% over the linear-fit alignment approach. Consequently, PPP solutions using these combined products match or outperform individual ACs’ results. Moreover, our strategy enhances reference frame stability by increasing the parameter repeatability by up to 40% compared to individual ACs. Furthermore, we assessed the impact of integrating Observable-Specific Biases (OSB) from different ACs with our combined products, evaluating their role in enhancing PPP precision.