A multi-tier PPP-RTK positioning method based on correction-product availability

1 Introduction

High-precision positioning is increasingly expected to function as a reliable sensing service rather than as a best-effort algorithmic output (Li et al., 2022; Hamza et al., 2025; Filip and Rispoli, 2024). Intelligent applications, including precision agriculture, smart ports, and automated logistics, operate under dynamically changing environments and operational constraints, in which positioning performance is determined not only by accuracy but also by continuity, timeliness, and robustness (Wang and Geng, 2025; Robustelli et al., 2022; Osman et al., 2026). In practical workflows, different functional modules and task stages impose heterogeneous accuracy requirements: some operations require centimeter-level accuracy, whereas others remain functional with decimeter- or meter-level accuracy, provided that the positioning solution remains stable and available (Osman et al., 2026; Zawieska et al., 2025). From an engineering perspective, enforcing uniformly high accuracy under all operating conditions is neither necessary nor cost-efficient, because high-accuracy positioning depends on external support, including communication links, auxiliary information, and computational resources (Kowalczyk and Hadas, 2024). For positioning services enabled by Precise Point Positioning-Real-Time Kinematic (PPP-RTK), the availability and utilization of service-side correction products therefore become important determinants of the achievable user-side capability. Rather than treating positioning performance as a single fixed level, a service-oriented organization is needed to relate the available correction products to different positioning capabilities and application requirements (Fernandez-Hernandez et al., 2023).

To meet diverse high-precision positioning requirements, a variety of Global Navigation Satellite System (GNSS) techniques have been developed. Precise Point Positioning (PPP) enables absolute positioning without local reference stations by utilizing precise satellite products and advanced error modeling (Gao and Chen, 2004; Kouba and Héroux, 2001); however, it typically suffers from a relatively long convergence period, which limits its responsiveness in real-time operation and after frequent re-initialization (Huang et al., 2026; Chen et al., 2024). In contrast, Real-Time Kinematic (RTK) can deliver rapid centimeter-level positioning once integer ambiguities are resolved; however, its performance degrades with increasing baseline length, and its reliance on dense reference infrastructure and stable bidirectional communication limits scalability for wide-area applications (An et al., 2023a; Hou et al., 2024). PPP-RTK was developed to combine the wide-area flexibility of PPP with the rapid convergence characteristics of RTK by providing service-side correction products to user receivers (An et al., 2023b; Zhang et al., 2025; Teunissen and Khodabandeh, 2015; Cheng et al., 2023). Accordingly, the positioning capability available to a user depends not only on the underlying PPP-RTK model, but also on the correction products that can be received and utilized.

A typical PPP-RTK system comprises a service side and a user side (Teunissen and Khodabandeh, 2015; Zhang et al., 2018) The service side processes observations from a regional reference network to generate satellite-related and atmospheric correction products (Ke et al., 2024; Odijk et al., 2016). The user side applies the available products to accelerate convergence and enable ambiguity resolution for real-time positioning (Wang and Geng, 2023). In conventional GNSS positioning, Single Point Positioning (SPP), PPP, PPP with Ambiguity Resolution (PPP-AR), and PPP-RTK are generally treated as distinct methods (Khodabandeh, 2021). Within the proposed PPP-RTK service architecture, however, the correction products generated at the service side can provide the information required by different user-side positioning configurations. Accordingly, the user-side configuration is organized into SPP, PPP, PPP-AR, and PPP-RTK tiers according to the subset of correction products available to and utilized by the user terminal. This tiered organization provides a service-level interpretation of positioning capability under different correction-product configurations, without altering the conventional definitions of the individual methods. A unified service-oriented formulation that explicitly relates correction-product availability and utilization to tier-specific positioning capability remains limited in the literature (Zhang, 2025).

Beyond the service-level formulation, the practical value of multi-tier PPP-RTK positioning depends on whether tier-specific capability can be implemented and characterized in real time. Although PPP-RTK has been extensively studied, many investigations remain focused on post-processing or software-based evaluations (An et al., 2023a). An operational PPP-RTK service requires the real-time integration of regional-network processing, correction-product generation, data dissemination, and user-side estimation (An et al., 2023b; Hirokawa et al., 2021; Zhang et al., 2024). At the user side, this integration must also accommodate embedded processing resources and practical communication interfaces (Takasu and Yasuda, 2009; Broekman and Gräbe, 2021). Real-time end-to-end implementations that connect a PPP-RTK service platform with an embedded user terminal and quantify tier-specific positioning performance remain limited.

In this study, building on established undifferenced and uncombined (UDUC) PPP-RTK models (Zhang et al., 2018; Zhang et al., 2021; Zhang et al., 2022a; Zha et al., 2021), we develop a multi-tier PPP-RTK positioning method based on correction-product availability. Within the proposed service architecture, user-side positioning configurations are organized into four service tiers, denoted SPP, PPP, PPP-AR, and PPP-RTK, according to the subset of service-side correction products available to and utilized by the user terminal. We further implement an end-to-end real-time system consisting of a PPP-RTK service-side platform and an embedded GNSS positioning device. Under separate correction-product configurations, real-time experiments quantify tier-dependent positioning accuracy and convergence behavior, together with PPP-RTK recovery performance after forced re-initialization. The study provides a service-oriented approach for characterizing the positioning capability achievable with different correction-product configurations. Such a capability-oriented organization is relevant to the continuity objective of GNSS PNT services when externally supplied correction products are subject to availability constraints.

The main contributions of this work are summarized as follows.

• An availability-aware multi-tier PPP-RTK positioning model is established within an existing UDUC PPP-RTK framework. The model defines four tier-specific user-side positioning configurations, denoted SPP, PPP, PPP-AR, and PPP-RTK, according to the service-side correction products available to and utilized by the user terminal. It provides a formal basis for the adaptive configuration of GNSS positioning services under heterogeneous correction-product availability.
• An integrated real-time GNSS positioning service architecture is implemented, linking PPP-RTK service-side correction-product generation and dissemination with an embedded user terminal. The architecture realizes tier-specific positioning configurations within a unified user-side processing framework.
• Real-time experiments conducted under separate correction-product configurations quantify tier-dependent positioning accuracy and convergence behavior, together with PPP-RTK recovery performance after forced re-initialization. The results characterize the positioning capability retained at each evaluated tier and provide empirical evidence relevant to the design of continuity- and resilience-oriented GNSS positioning services.

2 Multi-tier PPP-RTK positioning model based on correction-product availability

A PPP-RTK system comprises a service side and a user side. On the service side, raw GNSS observations collected from a regional reference network are processed to generate network correction products, including satellite-related and atmospheric corrections. On the user side, these correction products are combined with locally collected GNSS observations to support real-time positioning.

This section establishes a multi-tier PPP-RTK positioning model based on correction-product availability. Building on established undifferenced and uncombined (UDUC) PPP-RTK model, the service-side model describes the generation and dissemination of correction products, whereas the user-side model formalizes tier-specific positioning configurations. The user-side configurations are organized into SPP, PPP, PPP-AR, and PPP-RTK tiers according to the subset of service-side correction products available to and utilized by the user terminal. By linking correction-product sets to tier-specific estimation configurations, the model enables a consistent characterization of the positioning capability achievable under different correction-product configurations.

The following subsections present the UDUC observation model, the service-side correction-product model, and the tier-specific user-side positioning configurations. The system architecture and device-level implementation are presented in Section 3.

2.1 UDUC GNSS observation model

We begin with the undifferenced and uncombined (UDUC) GNSS observation equations (Teunissen and Montenbruck, 2017):

E Δ p r , j s = d t r − d t s + m r s τ r s + μ j l r s + d r , j − d j s E Δ ϕ r , j s = d t r − d t s + m r s τ r s − μ j l r s + δ r , j − δ j s + λ j z r , j s (1)

Here, E . denotes the expectation operator; s, r and j the satellite, receiver and frequency indices; Δ p r , j s and Δ ϕ r , j s represent the code and phase observations, respectively, obtained after correcting for the precise receiver–satellite geometric range and other relevant systematic errors; d t r and d t s denote the receiver clock error and the satellite clock error; d r , j and d j s denote the receiver code bias and the satellite code bias; δ r , j and δ j s denote the receiver phase bias and the satellite phase bias; τ r denotes the wet component of the zenith tropospheric delay, which is mapped to the slant direction using a mapping function m r s, while the dry component is assumed to have been corrected; l r s denotes the first-order slant ionospheric delay at the first frequency, which has a coefficient μ j = λ j 2 / λ 1 2, where λ j represents the wavelength corresponding to frequency j; z r , j s denotes the integer ambiguity expressed in cycles and scaled by the wavelength λ j. Note that Equation 1 is based on precise satellite orbit information from external sources. The resulting satellite-orbit effect is accounted for in the corrected code and phase observations.

2.2 Service-side PPP-RTK model and generation of correction products

We consider a regional reference network consisting of n r = 1 , . . . , n ground-based GNSS receivers tracking signals from m s = 1 , . . . , m satellites on f j = 1 , . . . , f frequencies. In this network, the precise positions of all reference receivers are assumed to be known. By exploiting the spatial correlation of ionospheric delays within the region, a UDUC PPP-RTK service model can be formulated as follows (Zhang et al., 2022b):

E Δ p r , j s = d ∼ t r − d ∼ t s + m r s τ ∼ r + μ j l ∼ r s + μ j d ∼ r , G F + d ∼ r , j > 2 − d ∼ j > 2 s E Δ ϕ r , j s = d ∼ t r − d ∼ t s + m r s τ ∼ r − μ j l ∼ r s + δ ∼ r , j − δ ∼ j s + λ j z ∼ r , j s E l ⌢ r s = l ∼ r s − l ∼ 1 s (2)

In Equation 2, l ̑ r s denotes the inter-station single-differenced virtual ionospheric observation. For receivers located within a regional network, the slant ionospheric delays corresponding to the same satellite can be assumed to be approximately identical. Accordingly, the single-differenced ionospheric term is set to zero, while its uncertainty is characterized using a stochastic model. On the right-hand side of the equations, the symbols with the superscript · ∼ indicate estimable parameters rather than their original forms. Detailed definitions and interpretations of these parameters are provided in Table 1. In addition, ionosphere-free . I F and geometry-free . G F combinations are defined in Equation 3 as:

. I F = μ 2 μ 2 − μ 1 . 1 − μ 1 μ 2 − μ 1 . 1 . G F = 1 μ 2 − μ 1 . 2 − . 1 (3)

TABLE 1. Definition of estimable parameters in the PPP-RTK mode.

Based on the PPP-RTK service model, a set of correction products can be estimated, including satellite clock corrections d ∼ t s , satellite code biases d ∼ j > 2 s for the third and higher frequencies, satellite phase biases δ ∼ j s , ionospheric delays l ∼ r s, and tropospheric delays τ ∼ r. These correction products are provided to users in a tier-oriented manner with flexible applicability. On the user side, different positioning tiers are realized by selectively applying available categories of correction information, allowing positioning solutions with different accuracy levels to be configured to accommodate heterogeneous user requirements. This tier-oriented formulation contributes to a reduction in user-side costs, particularly with respect to communication bandwidth and computational burden. Within the proposed model, each positioning tier is associated with a defined subset of correction products and a corresponding user-side estimation configuration. This organization provides a consistent basis for characterizing positioning capability under different correction-product configurations.

2.3 User-side multi-tier PPP-RTK positioning formulation based on correction-product availability

From a modeling perspective, the user side can also be regarded as part of the reference network, and its observation model shares a similar structure with the service-side PPP-RTK model. The primary difference is that user-side positioning requires the additional estimation of receiver position parameters. Under different correction-product configurations, four positioning tiers, namely, SPP, PPP, PPP-AR, and PPP-RTK, are formulated as tier-specific user-side positioning configurations within the unified framework. Unless otherwise stated, the code and phase observations used in the following formulations are defined as in Equation 1 with the satellite-orbit effect already accounted for. The SPP configuration is treated separately using broadcast ephemerides and represents the baseline tier when no service-side correction products are available. Table 2 summarizes the service-side correction products applied in each configuration. The corresponding observation models are presented below.

TABLE 2. Correction-product configurations of the proposed multi-tier PPP-RTK positioning method.

2.3.1 SPP tier: baseline positioning without correction products

When no correction products are available from the service side, the user-side positioning relies solely on broadcast ephemerides and GNSS code observations, based on which an SPP model can be formulated as follows (Birinci and Saka, 2023):

E Δ p u , j s = d t u − d t s + m u s τ u s + μ j l u s + d u , j − d j s (4)

In Equation 4, Δ p u , j s represents the code observations after removal of the approximate receiver–satellite geometric range computed from the approximate receiver position and the satellite position derived from the broadcast ephemerides. The other terms and relevant systematic effects are treated as in Equation 1, where applicable.

2.3.2 PPP tier: positioning with satellite clock corrections

When the user side receives only satellite clock correction products from the service side, a PPP model can be constructed in combination with the broadcast ephemerides, which can be expressed as shown in Equation 5:

E Δ p u , j s + d ∼ t s = e u s Δ x + d ¯ t u + m u s τ ¯ u + μ j l ¯ u s E Δ ϕ u , j s + d ∼ t s = e u s Δ x + d ¯ t u + m u s τ ¯ u − μ j l ¯ u s + λ j z ¯ u , j s (5)

Where terms marked with the subscript ′ u ′, instead of ′ r ′, refer to quantities associated with the user receiver. Δ p u , j s and Δ ϕ u , j s denote the code and phase observations, respectively, after removing the receiver–satellite geometric range computed from the approximate user position and precise satellite orbit information from external sources, and correcting for other relevant systematic errors; d ∼ t s denotes the satellite clock correction product provided by the PPP-RTK service side. On the right-hand side of the equation, the user position is treated as an unknown and linearized as a three-dimensional vector Δ x, projected along the line-of-sight vector e u s; The superscript · ¯ is used to indicate re-parameterized, estimable parameters, with their specific definitions and interpretations summarized in Table 3.

TABLE 3. Definition of estimable parameters in the PPP user mode.

2.3.3 PPP-AR tier: positioning with satellite clock and bias corrections

In addition, when the user side can obtain satellite code bias and satellite phase bias correction products from the service side, in addition to satellite clock corrections, a PPP-AR model can be further constructed in combination with the broadcast ephemerides, as expressed in Equation 6:where d ∼ t s, d ∼ j > 2 s, δ ∼ j s denote the satellite clock correction, satellite code bias correction, and satellite phase bias correction products received from the service side, respectively. The superscript · ^ likewise indicates estimable parameters, whose specific definitions and interpretations are provided in Table 4. All other parameters follow the same definitions as given previously.

E Δ p u , j s + d ∼ t s + d ∼ j > 2 s = e u s Δ x + d ^ t u + m u s τ ^ u + μ j l ^ u s + d ^ u , j > 2 E Δ ϕ u , j s + d ∼ t s + δ ∼ j s = e u s Δ x + d ^ t u + m u s τ ^ u − μ j l ^ u s + δ ^ u , j + λ j z ^ u , j s (6)

TABLE 4. Definition of estimable parameters in the PPP-AR user mode.

2.3.4 PPP-RTK tier: positioning with satellite and atmospheric corrections

Furthermore, when satellite clock corrections, satellite code and phase bias corrections, as well as tropospheric and ionospheric delay corrections estimated on the service side are all applied at the user side, a PPP-RTK user model can be established as shown in Equation 7:

E Δ p u , j s + d ∼ t s + d ∼ j s − m u s τ ∼ c o r s = e u s Δ x + μ j l ∼ u s + μ j d ∼ u , G F + d ∼ u , j > 2 E Δ ϕ u , j s + d ∼ t s + δ ∼ j s − m u s τ ∼ c o r s = e u s Δ x − μ j l ∼ u s + δ ∼ u , j + λ j z ∼ u , j s E l ∼ c o r s = l ∼ u s (7)

Here, l ∼ c o r s and τ ∼ c o r s denote the ionospheric and tropospheric corrections at the user location, respectively, which are obtained through interpolation of the corresponding service-side estimates.

The above tier-specific formulations establish the proposed multi-tier PPP-RTK positioning model, in which correction-product availability defines the user-side estimation configuration and the associated positioning capability. This availability-aware organization provides a theoretical basis for adaptive GNSS positioning service configuration. The practical realization of the model in a PPP-RTK software platform and an embedded positioning device is detailed in the following section.

3 Integrated real-time PPP-RTK service architecture and device implementation

3.1 Overall service architecture

Figure 1 illustrates the integrated real-time PPP-RTK service architecture developed to implement the proposed multi-tier positioning model. At the system level, the architecture comprises a service side and a user side, which are realized by a PPP-RTK service-side platform and a positioning device, respectively. The developed device operates as an integrated GNSS sensing and processing terminal that continuously acquires raw satellite observations and generates real-time positioning information under different correction-product configurations.

On the service side, multiple ground-based reference stations continuously provide raw GNSS observations to the PPP-RTK service-side platform, which serves as the correction-product provisioning component of the integrated service architecture. The platform processes these observations to generate and maintain satellite-related and atmospheric correction products. The correction products are disseminated to user terminals as defined correction-product sets for tier-specific positioning configurations, thereby supporting different levels of positioning capability, as illustrated in Figure 1.

On the user side, the positioning device combines raw GNSS observations with correction products from the service-side platform for real-time positioning. The available correction products determine the operating tier, ranging from SPP to PPP-RTK. All tiers are realized within a unified user-side processing framework and differ in the correction products applied and the associated estimation constraints. Higher tiers use more complete correction information, whereas lower tiers maintain positioning output when some correction products are unavailable. This design supports continuity-oriented GNSS positioning services.

3.2 PPP-RTK software platform architecture

The PPP-RTK software platform forms the service-side core of the integrated GNSS positioning architecture. It receives reference-network observations, generates and manages correction products in real time, and disseminates them to user terminals. These functions provide the correction information required by tier-specific user-side positioning configurations. The platform therefore provides the service-side basis for availability-aware and continuity-oriented GNSS positioning services. Figure 2 illustrates its functional architecture.

The PPP-RTK service-side platform is organized into several functional processing stages, as illustrated in Figure 2.

3.2.1 Data reception and preprocessing

The data-reception and preprocessing stage consists of the NTS-RCV and NTS-EXT modules, which acquire real-time GNSS data streams from regional and external sources and decode them into structured inputs for subsequent processing. NTS-RCV receives raw observations and broadcast ephemerides from the regional reference network, whereas NTS-EXT receives external SSR orbit and clock corrections from the International GNSS Service (IGS). This separation enables the platform to integrate regional network observations with external precise products while retaining flexible data-source management.

3.2.2 Network-based correction estimation

The network-based correction estimation stage is implemented by the NTS-EST module, which performs network-wide parameter estimation using the preprocessed observation data provided by the upstream reception and decoding stage. Based on the estimation results, a set of correction products is generated, including satellite clock corrections, satellite code and phase biases, as well as ionospheric and tropospheric delay corrections. These correction products constitute the core outputs of the service-side PPP-RTK platform and provide the fundamental correction information required to support different positioning tiers on the user side.

3.2.3 Correction encoding and dissemination

The correction encoding and dissemination stage is implemented by the NTS-ENC and NTS-COM modules, which prepare the estimated correction products for delivery to user devices. The NTS-ENC module encodes and compresses the correction products generated by the upstream estimation stage into standardized binary messages to reduce communication bandwidth requirements. The NTS-COM module subsequently delivers the encoded correction messages to user devices through available communication links, including both terrestrial and satellite-based links, thereby ensuring reliable and flexible dissemination of correction information under diverse deployment scenarios.

Beyond the main processing chain, the platform includes auxiliary components for system monitoring, data management, and testing. The NTS-MON module archives raw GNSS observations and generated correction products, supporting service monitoring, data-quality assessment, and offline analysis. The NTS-USR module is a lightweight software component for testing and demonstration. It supports basic decoding and use of correction messages in a software environment, but does not replace the embedded positioning device used on the user side.

3.3 GNSS positioning device design and implementation

Figure 3 shows the prototype of the developed user-side positioning device, including the assembled enclosure and its main internal components. The device serves as the user terminal of the integrated real-time PPP-RTK service architecture. It acquires raw GNSS observations and performs real-time positioning by combining them with correction messages provided by the service-side platform.

3.3.1 Hardware architecture of the positioning device

The developed positioning device adopts a two-board hardware design comprising a main board and an expansion board, as illustrated in Figure 3. At the functional level, the device integrates (Li et al., 2022) GNSS sensing for multi-constellation, multi-frequency observation acquisition (Hamza et al., 2025), communication capabilities for receiving correction messages under different deployment conditions, and (Filip and Rispoli, 2024) an embedded processing unit for real-time data handling and positioning computation.

The GNSS sensing function is implemented using a UM982 full-constellation, multi-frequency GNSS module from Unicore Communications. To support correction delivery under varied communication conditions, the device integrates an EC20 cellular module, an E103 Wi-Fi module, an E72 Bluetooth module, and an HTDM1611 satellite communication module. These interfaces provide terrestrial and satellite channels for accessing service-side correction products. Real-time processing is performed on an MYC-YA157C-V3 core board based on an ARM Cortex-A7 processor.

From an integration perspective, the GNSS module and the EC20 cellular module are placed on the main board and interface with the processing unit through standard serial interfaces, whereas the Wi-Fi, Bluetooth, and satellite communication modules are integrated on the expansion board and connected via board-to-board links. This modular design facilitates flexible integration of sensing and communication capabilities while maintaining stable real-time operation. In addition, the device provides an external DB25 interface for serial output of real-time positioning results.

3.3.2 Embedded positioning algorithm and device operation

The user-side positioning algorithm is embedded in the device and executed on its internal processing unit. The device receives correction messages through terrestrial or satellite communication interfaces and decodes them into the corresponding correction products.

The device combines the recovered correction products with locally collected GNSS observations to generate real-time positioning results. All tier-specific configurations are implemented within a unified processing framework, allowing the device to maintain positioning output at an appropriate tier as correction-product availability changes. This design supports continuity-oriented GNSS positioning services.

4 Experimental setup and data processing

4.1 Experimental setup

Real-time field experiments were conducted using the GNSS PPP-RTK positioning device described in Section 3.3 to evaluate its performance under tier-specific correction-product configurations. The device was deployed on the rooftop of the Navigation Building at the Aerospace Base of the National Time Service Center, Chinese Academy of Sciences.

As shown in Figure 4, a regional reference network was established in central Shaanxi Province to continuously provide GNSS observation data for the service-side PPP-RTK platform. The network consists of 12 ground reference stations, whose GNSS observations were collected at a sampling rate of 1 Hz and processed to generate real-time correction products. The reference network covered an area of approximately 24,500 km², spanning about 225 km in the east-west direction and 155 km in the north-south direction. The average nearest-neighbor inter-station distance was approximately 42 km. These correction products were subsequently delivered to the user-side positioning device throughout the experimental period.

The positioning device was deployed at a fixed rooftop location within the network footprint, in its southern part, approximately 12 km from the nearest reference station. It was equipped with a CNT AT600 GNSS antenna, as shown in Figure 5. The test site provides an open-sky environment suitable for continuous GNSS observation and long-term performance evaluation. During the experimental period, the positioning device was operated continuously and configured to perform user-side positioning under different positioning tiers. The correction products required for PPP-RTK, PPP-AR, and PPP positioning were provided by the PPP-RTK service-side platform described in Section 3.2.

4.2 Test scenarios and experimental design

The experimental design was formulated to systematically evaluate the performance of the positioning device under different positioning tiers, with emphasis on both long-term positioning stability and convergence behavior. Long-term positioning accuracy was assessed using continuous 24-h data sets, which enable the characterization of positioning stability over extended observation periods while accounting for potential temporal variations in GNSS-related error sources.

In contrast, convergence performance was evaluated using multiple independent 1-h sessions, representing practical usage scenarios in which the positioning device may be initialized repeatedly or experience intermittent interruptions. The use of multiple short sessions helps mitigate the influence of individual realizations and provides a more reliable assessment of convergence characteristics. The detailed experimental configurations for each positioning tier are summarized in Table 5.

TABLE 5. Model summary of experimental design for different positioning tiers.

4.3 Data processing strategy and performance metrics

Table 6 summarizes the data processing strategy adopted by the positioning device in the PPP-RTK mode. PPP-RTK represents the highest-accuracy operating mode of the device, in which all correction products estimated on the service side are utilized. The other positioning tiers are implemented as simplified realizations by selectively disabling specific correction terms or estimation constraints according to correction availability. For brevity, these processing strategies are not listed separately. The present implementation and validation are limited to GPS, BDS, and Galileo; extension to GLONASS requires FDMA-specific treatment of inter-frequency biases.

TABLE 6. Data processing strategy of the positioning device in PPP-RTK.

Positioning performance was evaluated using four complementary metrics: positioning accuracy, availability, convergence time, and initialization and recovery performance. Their definitions are summarized in Table 7. Positioning accuracy was evaluated for all tiers; convergence time was evaluated for the PPP-RTK, PPP-AR, and PPP tiers, whereas availability and initialization and recovery performance were evaluated only for the PPP-RTK tier.

TABLE 7. Strategies to evaluate the performance of the positioning device.

The reference coordinates used for performance evaluation were obtained from a static solution computed using 1 week of GNSS data processed with the PRIDE PPP-AR software developed by Wuhan University, which provides high-precision reference positions for accuracy assessment. It should be noted that the performance metrics defined in this section are primarily applied to the PPP-RTK mode, which represents the main operating mode and highest-accuracy configuration of the positioning device. The evaluation of other positioning modes is discussed separately in the subsequent analysis.

5 Results

In this section, the positioning performance of the positioning device under different positioning tiers is evaluated, with particular emphasis on the PPP-RTK mode. The results include positioning accuracy, convergence behavior, availability, and initialization and recovery performance. In addition, the performance differences among the PPP-RTK, PPP-AR, PPP, and SPP modes are analyzed and discussed.

5.1 PPP-RTK positioning performance

In this subsection, the PPP-RTK positioning performance is evaluated in terms of positioning accuracy, availability, and convergence time based on real-time experimental results obtained with the positioning device.

5.1.1 Positioning accuracy

Figure 6 presents the time series of PPP-RTK positioning errors obtained by the developed positioning device over three consecutive days, from DOY 005 to DOY 007 in 2026. For each day, the root-mean-square (RMS) positioning errors remain below 0.6 cm, 0.5 cm, and 1.9 cm in the east, north, and up components, respectively, indicating stable centimeter-level positioning accuracy. In particular, the horizontal positioning accuracy, quantified as the two-dimensional (2D) error in the east–north plane, consistently remains within 1 cm, indicating stable planar positioning performance.

In practical real-time operation, transient effects such as occasional cycle slips, as well as communication latency or short-term interruptions, may lead to reinitialization of the positioning solution. Nevertheless, the positioning device is able to rapidly re-converge to centimeter-level accuracy within a few seconds. During the continuous experiment on DOY 006 in 2026, several re-convergence events were recorded in the device operation logs, occurring at 05:01:20, 13:16:04, 17:20:24, and 20:27:53 GPST. In all cases, the positioning accuracy was restored within a short period after reinitialization.

Table 8 summarizes the positioning accuracy statistics of the positioning device operating in PPP-RTK mode. The table reports the RMS values of positioning errors in the east, north, up, 2D, and three-dimensional (3D) components, computed from the continuous positioning results over the three experimental days. In particular, the 2D and 3D positioning accuracies reach 0.72 cm and 1.78 cm, respectively.

TABLE 8. Positioning accuracy statistics of PPP-RTK.

5.1.2 Availability

Figure 7 shows the cumulative distributions of 2D and 3D positioning errors for the PPP-RTK solution obtained with the positioning device. For the PPP-RTK mode, 99.43% of the epochs exhibit 2D positioning errors below 2.5 cm. The corresponding percentage for 3D positioning errors within 5 cm is 98.80%. These results indicate that, under real-time operating conditions, the PPP-RTK solution maintains high availability when centimeter-level accuracy requirements are applied.

5.1.3 Convergence time

To evaluate the convergence performance of the positioning device in PPP-RTK mode, short-term experiments were conducted over two consecutive days, DOY 008 and DOY 009 in 2026. Six independent PPP-RTK sessions of approximately 1 h were performed each day, resulting in a total of 12 convergence realizations.

Figure 8 illustrates the PPP-RTK positioning error time series for the two test days, showing that centimeter-level positioning accuracy is consistently achieved shortly after initialization. Figure 9 summarizes the convergence times obtained from the 12 independent sessions. All convergence times are within 10 s, with a mean time to convergence of 7.08 s, indicating that the developed positioning device can achieve rapid convergence when operating in PPP-RTK mode under real-time conditions.

5.2 Initialization and recovery performance of PPP-RTK

In this subsection, the recovery performance of the positioning device in PPP-RTK mode is evaluated under repeated hot-restart conditions. In this study, a hot restart refers to a temporary interruption of the correction products provided by the PPP-RTK service-side platform, while GNSS observations remain continuous. The recovery time is defined as the elapsed time from the hot-restart trigger to the first epoch at which a PPP-RTK ambiguity-fixed solution is re-established.

A total of 40 hot-restart events were imposed on the positioning device under real-time operating conditions. For each restart event, the PPP-RTK solution temporarily loses its fixed state and subsequently re-establishes a fixed solution after the correction stream is restored. This experimental design aims to assess the ability of the developed positioning device to maintain accurate positioning performance under repeated interruptions, which commonly occur in challenging real-world environments. The recovery time defined above is evaluated for all restart events to characterize the re-initialization behavior of the device under repeated interruptions.

Figure 10 summarizes the re-acquisition time of the fixed PPP-RTK solution after repeated hot restarts of the developed positioning device. Most restart events recover within 4–5 s, with a mean recovery time of 4.53 s. These results indicate that, after service interruptions and subsequent recovery, the device rapidly re-establishes an ambiguity-fixed PPP-RTK solution, enabling fast re-fixing of integer ambiguities and stable centimeter-level positioning under practical real-time operating conditions.

5.3 Positioning performance under different positioning tiers

In this subsection, the positioning performance across different positioning tiers is evaluated in terms of long-term accuracy and convergence behavior based on real-time experimental results obtained with the positioning device.

5.3.1 Long-term positioning performance across different positioning tiers

Following the evaluation of PPP-RTK as the highest positioning tier, the long-term positioning performance of the remaining tiers is further examined to illustrate the tier-dependent behavior of the positioning device. Figure 11 shows the daily positioning error time series obtained under the PPP-AR, PPP, and SPP modes.

As shown in Figure 11a, when operating in the PPP-AR mode, the root-mean-square (RMS) positioning errors over the full day are 1.51 cm, 0.92 cm, and 4.44 cm in the east, north, and up components, respectively. Although the positioning accuracy is slightly degraded compared to the PPP-RTK mode, centimeter-level accuracy is consistently maintained. Moreover, once convergence is achieved, no evident long-term fluctuations are observed, indicating that ambiguity resolution contributes to improved long-term positioning stability.

When the device operates in the PPP mode, the RMS positioning errors increase to 10.33 cm, 8.99 cm, and 23.57 cm in the east, north, and up components, respectively, as shown in Figure 11b, corresponding to decimeter-level positioning accuracy. It is noted that, even after initial convergence, the positioning errors in the PPP mode exhibit noticeable temporal variations over the day. This behavior is mainly attributed to the fact that, in the PPP mode, only satellite clock corrections provided by the PPP-RTK service side are applied. As summarized in Table 1, the satellite clock corrections provided by the service side absorb information such as the reference receiver clock d t 1, among others, which results in temporal variations in the positioning errors.

In contrast, the SPP mode exhibits meter-level positioning errors throughout the day, as shown in Figure 11c.

Overall, the results reveal a clear tier-dependent degradation in long-term positioning accuracy, from millimeter-level horizontal accuracy in the PPP-RTK mode, through centimeter-level performance in the PPP-AR mode, to decimeter- and meter-level performance in the PPP and SPP modes, respectively, confirming the multi-tier positioning capability of the positioning device under long-term operation.

5.3.2 Convergence behavior across different positioning tiers

In this subsection, the convergence behavior of different positioning tiers is evaluated to characterize the time required to reach a stable positioning solution after initialization. The convergence time is defined in a tier-dependent manner, as described in Section 4.3.

Figure 12 presents the convergence times obtained from six independent short-term experiments for the PPP-AR and PPP modes. For the PPP-AR mode, the convergence times are consistently within a few minutes, with a mean value of 4.27 min, indicating stable and repeatable convergence behavior. In comparison, the PPP mode requires a longer convergence time, with a mean value of 15.98 min, and shows slightly increased variability across different trials. This difference can be attributed to the additional constraints introduced by ambiguity resolution in the PPP-AR mode, which contribute to a faster convergence process.

For the PPP-RTK mode, convergence performance has been evaluated separately in Section 5.1 based on 12 independent short-term sessions, in which convergence is typically achieved within several seconds. Taken together, these results indicate a clear tier-dependent convergence behavior.

5.3.3 Summary of tier-level positioning capability

Table 9 summarizes the positioning capability of the developed device across different positioning tiers, providing an overall view of the achievable long-term accuracy and convergence behavior at each tier.

TABLE 9. Summary of long-term positioning accuracy and convergence behavior of the developed positioning device across different positioning tiers.

At the highest tier, the PPP-RTK mode of the developed device provides millimeter-level horizontal positioning accuracy and centimeter-level three-dimensional accuracy, with convergence typically achieved within several seconds. In PPP-AR mode, the device maintains centimeter-level positioning accuracy; however, due to the absence of atmospheric-related correction products, the convergence time increases to the order of a few minutes. In PPP mode, the achievable positioning accuracy further degrades to the decimeter level, and the convergence time extends to the order of tens of minutes. By contrast, the SPP mode provides only meter-level positioning accuracy.

Notably, the above tier-level positioning performance was evaluated within the unified UDUC PPP-RTK modeling framework adopted in this study. Within the implemented PPP-RTK service architecture, SPP, PPP, PPP-AR, and PPP-RTK were organized as distinct user-side configurations according to the correction products applied at the user terminal. The results characterize the accuracy and convergence behavior associated with these tier-specific configurations.

6 Discussion

The results demonstrate a clear relationship between the correction products applied at the user side and the achievable positioning capability within the implemented PPP-RTK service architecture. Across the evaluated tier configurations, positioning performance varied systematically from PPP-RTK to PPP-AR, PPP, and SPP. The PPP-RTK tier achieved 0.72 cm horizontal RMS accuracy, 1.78 cm three-dimensional RMS accuracy, and a mean convergence time of 7.08 s. The PPP-AR tier converged in 4.27 min, whereas the PPP tier required 15.98 min and provided decimeter-level accuracy. These observations provide empirical support for organizing the system as a multi-tier positioning service under different correction-product conditions.

From a GNSS PPP service perspective, the architecture links service-side correction-product generation and dissemination to tier-specific processing on the positioning device. It therefore provides a practical basis for adaptive GNSS positioning services in near-Earth PNT applications. The forced hot-restart results further indicate rapid restoration of high-tier positioning capability. After 40 interruptions, the device re-established fixed PPP-RTK solutions in 4.53 s on average after the correction stream was restored. By associating correction-product availability with tier-specific user-side processing, the proposed organization supports positioning capabilities that match the information available to the user terminal.

Future work could evaluate the proposed multi-tier PPP-RTK framework in more demanding near-Earth PNT scenarios and further optimize its real-time tier-transition mechanism to improve the adaptability and continuity of GNSS positioning services.

7 Conclusion

Building on established UDUC PPP-RTK models, this study developed a multi-tier PPP-RTK positioning method based on correction-product availability and implemented an end-to-end real-time system comprising a PPP-RTK service-side platform and an embedded GNSS positioning device. Within this architecture, SPP, PPP, PPP-AR, and PPP-RTK are organized as tier-specific user-side configurations according to the service-side correction products applied at the user terminal. The method provides a consistent basis for characterizing GNSS positioning capability under different correction-product conditions.

Real-time experiments with the developed device characterized the positioning capability associated with each tier. The PPP-RTK tier provided millimeter-level horizontal positioning accuracy and centimeter-level three-dimensional accuracy, with convergence typically achieved within several seconds. The PPP-AR tier maintained centimeter-level positioning accuracy, with convergence times consistently within a few minutes. The PPP tier provided decimeter-level positioning accuracy, with convergence on the order of tens of minutes, whereas the SPP tier provided meter-level positioning accuracy. After forced hot restarts, the PPP-RTK tier re-established fixed solutions in 4.53 s on average. Together, these results support the feasibility of the implemented architecture for organizing tier-specific GNSS PPP positioning capabilities and its relevance to continuity- and adaptability-oriented GNSS positioning services in near-Earth PNT applications.

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Footnotes

Edited by: Ke Su, Space Engineering University, China

Reviewed by: Guoqiang Jiao, Beijing Institute of Tracking and Telecommunications Technology, China

Pengyu Hou, Chinese Academy of Sciences (CAS), China