Unlocking More Reliable Multi-GNSS PPP-AR: A Time-Space-Frequency Assessment of Observable-Specific Bias Products

Global Navigation Satellite System precise point positioning with ambiguity resolution (PPP-AR) relies on the accurate treatment of hardware-dependent code and carrier-phase delays originating from satellites and receivers. These delays vary across frequencies and signal channels and can destroy the integer properties of carrier-phase ambiguities if they are not properly corrected. Observable-specific bias (OSB) products address this problem by providing satellite- and signal-specific corrections for raw code and phase observations, enabling users to recover integer ambiguities and flexibly process observations from multiple frequencies and constellations. OSB products have therefore become a critical component of modern multi-GNSS PPP-AR services, with their quality directly affecting ambiguity estimation, validation, fixing, positioning convergence, and solution continuity. However, OSB products may contain discontinuities, abnormal fluctuations, missing data, and structured periodic variations arising from datum definitions, clock-reference conventions, satellite operations, and daily processing procedures. These characteristics are not always fully revealed by evaluating positioning accuracy alone.

Most previous OSB assessments have focused on PPP-AR performance, particularly positioning accuracy after ambiguity fixing. Although such tests demonstrate whether a product can support successful positioning, they provide limited insight into the intrinsic behavior of the bias series. An OSB product may produce acceptable positioning results over a short period while still containing day-boundary jumps, unstable intervals, or periodic variations that affect long-term processing and operational reliability. A more comprehensive assessment is therefore required to characterize the continuity, variability, internal consistency, and spectral behavior of OSB products and to support product screening, quality control, adaptive weighting, anomaly detection, and ambiguity recovery after data interruptions.

In a recently published paper in Advances in Space Research, Ge Ge, Zhetao Zhang, Haijun Yuan, and Huaqing Xu established a unified time-space-frequency framework for the comprehensive evaluation of code and phase OSB products. The framework moves beyond conventional positioning-based validation by examining approximately one year of rapid and final OSB series covering GPS, Galileo, BDS-2, and BDS-3. In the time domain, daily stability tests, box-plot distributions, and peak-to-peak variations are used to reveal discontinuities, fluctuations, and long-term stability. In the spatial domain, standard deviations and Pearson correlation coefficients characterize the dispersion and common variation patterns of OSB series across satellites and signals. In the frequency domain, fast Fourier transform analysis identifies periodic components and structured spectral signatures that cannot be readily distinguished through time-domain inspection alone.

Dr. Zhetao Zhang and his colleagues analyzed OSB products from day of year 060 in 2023 to day of year 060 in 2024. They found that most satellites showed high data availability, although interruptions remained in some series. Rather than smoothing out discontinuities caused by reference changes, daily reinitialization, and other practical processing operations, the research team retained these features so that the evaluated series could reflect actual operational behavior. Their results showed that code OSBs were generally more stable, with relatively limited peak-to-peak variations, whereas phase OSBs exhibited wider ranges, stronger fluctuations, and more visible discontinuities. Dr. Zhang and his colleagues also identified several satellite-specific variations, demonstrating that orbital maneuvers, signal characteristics, and processing events may introduce localized anomalies that require targeted monitoring rather than relying solely on product-wide quality indicators.

The spatial- and frequency-domain analyses conducted by Dr. Zhetao Zhang and his colleagues provided further insight into the internal behavior of OSB products. The team found that phase OSBs showed greater dispersion and more complex relationships than code OSBs. Code-bias series generally exhibited clearer common variation patterns, whereas phase-bias series showed weaker correlations and stronger satellite-, signal-, and processing-dependent characteristics. After reducing the influence of missing data through interpolation, the researchers also identified low-frequency draconitic patterns and periodic components associated with orbital resonance. Distinct spectral peaks appeared in some medium Earth orbit bias series, together with low-frequency harmonics. These findings demonstrate that OSB fluctuations are not purely random but may contain structured and physically meaningful periodic components. By revealing such hidden signatures, the work of Dr. Zhang and his colleagues enables monitoring systems to distinguish recurring behavior from isolated anomalies, abrupt product changes, or processing failures.

The findings of Dr. Zhetao Zhang and his colleagues have direct implications for the development of more reliable multi-GNSS PPP-AR services. Phase OSBs are essential for restoring the integer properties of carrier-phase ambiguities, and undetected jumps or unstable corrections may contaminate ambiguity estimates, delay successful fixing, trigger unnecessary reinitialization, or increase the risk of incorrect validation. The multi-domain indicators proposed by the research team provide complementary tools for addressing these risks: time-domain measures can detect jumps and unstable intervals before ambiguity fixing, spatial-domain measures can support satellite- and signal-specific weighting or screening, and frequency-domain characteristics can separate structured periodic behavior from abnormal events. Together, these capabilities provide a foundation for real-time OSB monitoring, adaptive stochastic modeling, ambiguity management, and automated quality control. Although the study focused on OSB product characteristics rather than directly quantifying positioning improvements, the framework developed by Dr. Zhang and his colleagues establishes a clear connection between product-level quality and PPP-AR performance. More stable, continuous, and well-characterized OSB corrections can improve ambiguity-estimation consistency, reduce unnecessary ambiguity resets, support faster recovery of fixed solutions, and ultimately contribute to shorter convergence times, higher ambiguity-fixing reliability, and more continuous centimeter-level positioning. Overall, the study transforms OSB assessment from a simple positioning-result check into a multi-domain product-quality diagnosis, providing an important methodological foundation for more intelligent OSB selection, monitoring, and adaptive use in next-generation multi-GNSS PPP-AR services.