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<p>Satellite code and phase biases are essential for resolving integer ambiguities in precise point positioning–real-time kinematic (PPP–RTK). The undifferenced and uncombined (UDUC) PPP–RTK method simultaneously estimates satellite code and phase biases, making it well-suited for processing multi-frequency global navigation satellite system (GNSS) data. However, limited research has explored whether these estimable satellite biases can serve as observation-specific bias (OSB) corrections that enable user positioning with arbitrarily selected frequencies. In this study, we demonstrate that satellite biases estimable in UDUC PPP–RTK can function as OSB-like corrections, as they can correct the satellite biases of each observation type and enable arbitrary-frequency PPP–RTK, although their analytical expressions differ from conventional OSBs. Unlike conventional code OSBs estimated for each frequency, the OSB-like code corrections are only estimated for the third frequency and above, while these biases for the first two frequencies, defined as pivot frequencies, are constrained to zero. Additionally, the OSB-like phase corrections are directly estimated, containing code biases selected as the datum, whereas conventional phase OSB estimation typically requires the use of previously obtained code OSBs to correct code biases. Despite these differences, the OSB-like corrections enable arbitrary-frequency PPP–RTK user positioning. We categorize user positioning into three cases based on the availability of observations on two, one, or zero pivot frequencies. After applying OSB-like code and phase corrections, we show that while the estimable user parameters differ across these cases, the design matrices remain consistent. This consistency allows us to formulate a unified model for both multi-frequency and single-frequency positioning. To verify this, we collect one-week BDS quad-frequency data from a regional network to estimate OSB-like corrections and perform user positioning. Results show that the OSB-like code and phase corrections achieve centimeter-level precision. These corrections enable ambiguity-resolved positioning with arbitrary single-, dual-, triple-, and quad-frequency observations. Among these, quad-frequency positioning provides the best results, with a time-to-first-fix (TTFF) of 17 epochs and a 3D&#xa0;RMS of 0.042&#xa0;m.</p>

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Satellite biases estimable in undifferenced and uncombined PPP-RTK: can they serve as OSB-like corrections?

  • 期刊论文

  • 发表日期：

    2025年7月27日

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  • Pengyu Hou,
  • Dimitrios Psychas,
  • Baocheng Zhang

摘要

Satellite code and phase biases are essential for resolving integer ambiguities in precise point positioning–real-time kinematic (PPP–RTK). The undifferenced and uncombined (UDUC) PPP–RTK method simultaneously estimates satellite code and phase biases, making it well-suited for processing multi-frequency global navigation satellite system (GNSS) data. However, limited research has explored whether these estimable satellite biases can serve as observation-specific bias (OSB) corrections that enable user positioning with arbitrarily selected frequencies. In this study, we demonstrate that satellite biases estimable in UDUC PPP–RTK can function as OSB-like corrections, as they can correct the satellite biases of each observation type and enable arbitrary-frequency PPP–RTK, although their analytical expressions differ from conventional OSBs. Unlike conventional code OSBs estimated for each frequency, the OSB-like code corrections are only estimated for the third frequency and above, while these biases for the first two frequencies, defined as pivot frequencies, are constrained to zero. Additionally, the OSB-like phase corrections are directly estimated, containing code biases selected as the datum, whereas conventional phase OSB estimation typically requires the use of previously obtained code OSBs to correct code biases. Despite these differences, the OSB-like corrections enable arbitrary-frequency PPP–RTK user positioning. We categorize user positioning into three cases based on the availability of observations on two, one, or zero pivot frequencies. After applying OSB-like code and phase corrections, we show that while the estimable user parameters differ across these cases, the design matrices remain consistent. This consistency allows us to formulate a unified model for both multi-frequency and single-frequency positioning. To verify this, we collect one-week BDS quad-frequency data from a regional network to estimate OSB-like corrections and perform user positioning. Results show that the OSB-like code and phase corrections achieve centimeter-level precision. These corrections enable ambiguity-resolved positioning with arbitrary single-, dual-, triple-, and quad-frequency observations. Among these, quad-frequency positioning provides the best results, with a time-to-first-fix (TTFF) of 17 epochs and a 3D RMS of 0.042 m.