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<p>The accurate resolution of integer ambiguity is crucial for Real-Time Kinematic (RTK), with ambiguity validation serving as a pivotal stage. The ratio test based on a fixed threshold (RT) is currently the most widely used test for ambiguity validation. However, the threshold cannot be adjusted in response to variations in GNSS model strength due to its fixed nature. The fixed failure rate ratio test (FFRT) addresses this by adjusting the threshold dynamically according to model strength. However, its statistical accuracy is compromised if the actual observation model does not match the assumed underlying model. This paper contributes by proposing the ML-test, a machine learning (ML)-based test for ambiguity validation, aiming to address the theoretical and practical limitations of traditional statistical tests. ML is adopted to establish a binary classifier, trained using a dataset based on a quad-constellation dual-frequency ionosphere-weighted model in Hong Kong, China. Given the input of the ratio value, lasting epochs, baseline length, ambiguity dimension, PDOP, and TEC provided externally, it can output the binary judgment of the validation (accepted or rejected), unlike the traditional ratio test that determines a threshold. The classifier label is “accepted” if the 3D positioning error with the fixed solution is within 10&#xa0;cm; Otherwise, it is “rejected”. To verify the performance of ML-test, comparative experiments between ML-test, RT, and FFRT are conducted over new days and baselines with the same observation model as the classifier training. The experiments show ML-test and FFRT (with fixed failure rates of 0.01 and 0.001) can reach stable high empirical fix rates compared with RT (<i>C</i> = 1.5, 2, and 3). ML-test can achieve the higher empirical successful-fix rate and the smaller 3D positioning error than FFRT, but it may perform worse than RT (<i>C</i> = 1.5, 2, and 3), revealing its practical limitations. The robustness of ML-test and FFRT under active ionospheric activity has been proved, with ML-test showing the best performance in empirical successful-fix rate and 3D positioning error. ML-test demonstrates advantages in dynamically making validation judgments based on GNSS model strength, with stable performance that ensures a high empirical fix rate while maintaining a sufficiently high empirical successful-fix rate.</p>

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ML-test: validating machine learning for GNSS integer ambiguity resolution in quad-constellation dual-frequency observations of Hong Kong

  • 期刊论文

  • 发表日期：

    2025年6月22日

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  • Yanqing Hou,
  • Yining Shi,
  • Xuan Chen,
  • Xiaojun Duan

摘要

The accurate resolution of integer ambiguity is crucial for Real-Time Kinematic (RTK), with ambiguity validation serving as a pivotal stage. The ratio test based on a fixed threshold (RT) is currently the most widely used test for ambiguity validation. However, the threshold cannot be adjusted in response to variations in GNSS model strength due to its fixed nature. The fixed failure rate ratio test (FFRT) addresses this by adjusting the threshold dynamically according to model strength. However, its statistical accuracy is compromised if the actual observation model does not match the assumed underlying model. This paper contributes by proposing the ML-test, a machine learning (ML)-based test for ambiguity validation, aiming to address the theoretical and practical limitations of traditional statistical tests. ML is adopted to establish a binary classifier, trained using a dataset based on a quad-constellation dual-frequency ionosphere-weighted model in Hong Kong, China. Given the input of the ratio value, lasting epochs, baseline length, ambiguity dimension, PDOP, and TEC provided externally, it can output the binary judgment of the validation (accepted or rejected), unlike the traditional ratio test that determines a threshold. The classifier label is “accepted” if the 3D positioning error with the fixed solution is within 10 cm; Otherwise, it is “rejected”. To verify the performance of ML-test, comparative experiments between ML-test, RT, and FFRT are conducted over new days and baselines with the same observation model as the classifier training. The experiments show ML-test and FFRT (with fixed failure rates of 0.01 and 0.001) can reach stable high empirical fix rates compared with RT (C = 1.5, 2, and 3). ML-test can achieve the higher empirical successful-fix rate and the smaller 3D positioning error than FFRT, but it may perform worse than RT (C = 1.5, 2, and 3), revealing its practical limitations. The robustness of ML-test and FFRT under active ionospheric activity has been proved, with ML-test showing the best performance in empirical successful-fix rate and 3D positioning error. ML-test demonstrates advantages in dynamically making validation judgments based on GNSS model strength, with stable performance that ensures a high empirical fix rate while maintaining a sufficiently high empirical successful-fix rate.