Robust Statistical and Wavelet-Based Time–Frequency Analysis of Static PPP-RTK Errors Using Low-Cost GNSS Correction Services

This study investigates the horizontal positioning accuracy of a low-cost, multi-frequency GNSS receiver operating in static mode using a newly released PPP-RTK correction service delivering localized corrections. To the authors’ knowledge, this represents one of the first performance evaluations of this service, which optimizes correction data based on the approximate receiver location. The results are compared against those from the previous version of the service, which provided non-localized corrections. Analyses were conducted in both the time and frequency domains, employing robust statistical tools to characterize error behavior. The localized service achieved a mean horizontal error of approximately 0.020 m and a 95% Circular Error Probable (CEP95) of 0.046 m, in line with its declared performance. By contrast, the earlier non-localized service yielded a mean horizontal error of approximately 0.074 m and a CEP95 of 0.124 m under comparable static conditions, confirming the significant improvement achieved by localized corrections. Spectral and wavelet analyses revealed a dominant 33 mHz harmonic in the positioning error, corresponding to the 30 s update period of atmospheric corrections, indicating a periodic influence arising from the correction stream. Continuous wavelet analysis further identified intervals in which this harmonic was absent, during which positioning accuracy improved markedly (CEP95 reduced to 0.019 m). To properly address the non-Gaussian nature of the error distribution, bias-corrected and accelerated (BCa) bootstrap methods were applied to estimate confidence intervals. Overall, the results demonstrate the benefits of localized corrections, while emphasizing the importance of accounting for the temporal structure of correction data in PPP-RTK performance assessments. Future developments will focus on kinematic scenarios and adaptive filtering strategies to mitigate periodic errors induced by correction updates.