Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. Uncombined Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model
2.1.1. PPP Observation Equations
2.1.2. Uncombined Dual- and Triple-Frequency DCM
- Two receiver clock terms are present in the equation: a pseudorange clock, defined as: and a carrier-phase clock defined as: . This decoupling of the clocks is a consequence of using the DCM, as both terms are biased versions of and , the pseudorange and carrier-phase clocks, respectively. Both state terms are affected by receiver biases, with the carrier-phase clock being affected by the reference satellite’s ambiguity as well, which is discussed in more detail later.
- The ionospheric delay term absorbs the ionosphere-free combination of the receiver pseudorange biases in the form: . When trying to use external ionospheric corrections, either global or regional corrections, the biases have to be separated from the ionospheric delay state term. The biases can be estimated as separate state terms, as long as additional observations of the ionospheric delays are present.
- are the integer single-differenced ambiguities relative to the reference satellite. The single-differencing is performed implicitly without having to explicitly difference the measurements or ambiguities from different satellites. The implicit single-difference is a consequence of the decoupling of the clocks, as the phase measurements lose their datum—typically set by the pseudorange measurements through the receiver clock. The new datum is set by the reference satellite, as its ambiguities are fixed to arbitrary integers and they are not estimated. Doing so not only leads to all ambiguities being single-differenced, but also recovers the datum in the phase measurements, as each frequency’s datum is being set by the reference satellite’s ambiguity on that frequency.
- An interfrequency bias term appears in the third frequency’s pseudorange measurement equation, expressed as: . The term arises from the fact that the other state terms cannot absorb the additional receiver bias that comes with the third pseudorange measurement, as opposed to the first and second frequency receiver pseudorange biases, which are absorbed by the receiver pseudorange clock and ionospheric delay. Ignoring this state term leads to it appearing in the pseudorange residuals, and potentially affecting the estimation of other states.
- Equation (2) also contains two state terms which are specific to the DCM, referred to here as the receiver L2 phase bias , and the receiver L3 phase bias . The two state terms are defined as: and . Both state terms contain receiver biases, as well as the reference satellite’s ambiguities.
2.1.3. Reference Satellite and Multi-GNSS Considerations
2.2. Data and Processing
3. Results
3.1. Performance Comparison with Dual-, Triple-, and Mixed Dual-/Triple-Frequency Processing
3.2. Mixed Dual-/Triple-Frequency Performance Analysis
3.3. Kinematic Automotive Data Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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State Term Dependency (One Per …) | Measurement Type | Frequency Band | ||||||
---|---|---|---|---|---|---|---|---|
Receiver | Constellation | Satellite | Code | Phase | 1 | 2 | 3 | |
Receiver coordinates | X | X | X | X | X | X | ||
Wet tropospheric delay | X | X | X | X | X | X | ||
Receiver pseudorange clock | X | X | X | X | X | |||
Receiver carrier-phase clock | X | X | X | X | X | |||
Receiver L2 phase bias | X | X | X | |||||
Receiver L3 phase bias | X | X | X | |||||
Receiver IFB | X | X | X | |||||
Slant ionospheric delay | X | X | X | X | X | X | ||
L1 ambiguity | X | X | X | |||||
L2 ambiguity | X | X | X | |||||
L3 ambiguity | X | X | X |
Parameter | Strategy |
---|---|
Receiver coordinates | Kinematic mode: estimated with process noise equivalent to 100 km/h |
Static mode: estimated as constants | |
Receiver reference coordinates | IGS SINEX positions |
Receiver code and phase clocks | Estimated as white noise processes |
Receiver L2 and L3 phase biases and IFB | Estimated as white noise processes |
Tropospheric delay | Dry: GMF model and mapping function [29]. |
Wet: estimated as a random walk process with process noise of 0.05 mm/ | |
Ionospheric delays | Estimated as white noise processes |
Ambiguities | Estimated as constants on each continuous arc |
Elevation angle cut-off | 7 |
Satellite orbits and clocks | Corrected for using CNES ultra-rapid products [30] |
Code and phase biases | Corrected for using CNES ultra-rapid observable-specific bias (OSB) products |
Weighting strategy | Elevation dependent weighting: with equal to |
0.3 m and 0.003 m for the pseudorange and carrier-phase measurements, | |
respectively, and being the elevation angle. a and b were determined | |
based on a residual and measurement quality analysis. |
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Naciri, N.; Bisnath, S. Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model. Remote Sens. 2021, 13, 3768. https://doi.org/10.3390/rs13183768
Naciri N, Bisnath S. Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model. Remote Sensing. 2021; 13(18):3768. https://doi.org/10.3390/rs13183768
Chicago/Turabian StyleNaciri, Nacer, and Sunil Bisnath. 2021. "Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model" Remote Sensing 13, no. 18: 3768. https://doi.org/10.3390/rs13183768
APA StyleNaciri, N., & Bisnath, S. (2021). Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model. Remote Sensing, 13(18), 3768. https://doi.org/10.3390/rs13183768