Using Multi-Antenna Trajectory Constraint to Analyze BeiDou Carrier-Phase Observation Error of Dynamic Receivers
<p>The main experimental steps (A means static antennae, B means dynamic antennae).</p> "> Figure 2
<p>Installation diagram of antennae and rotating platform (A means static antennae, B means dynamic antennae).</p> "> Figure 3
<p>Procedure for calibrating coordinates and relative positions.</p> "> Figure 4
<p>Calculate the valid precise relative positioning results.</p> "> Figure 5
<p>The contents of the multiple testing.</p> "> Figure 6
<p>The method of improving the success rate of precise relative positioning.</p> "> Figure 7
<p>Diagram of bi-normal distribution.</p> "> Figure 8
<p>The experimental scene and equipment. (<b>a</b>) The rotating platform and four dynamic receiver antennae. (<b>b</b>) Static receiver antennae.</p> "> Figure 9
<p>The histogram of cycle slips at B1I and B3I.</p> "> Figure 10
<p>The fitting envelop curve of the cycle-slips histogram with the mixture of Gaussian distribution.</p> "> Figure 11
<p>The change trend of cycle-slip frequency and measurement observations with SNR.</p> "> Figure 12
<p>The relationship among cycle-slip incidence, SNR, and orbit.</p> "> Figure 13
<p>Fitting curve of the carrier-phase measurement error distribution and Gaussian distribution.</p> "> Figure 14
<p>Envelope of bi-normal distribution.</p> "> Figure 15
<p>Variation of the carrier-phase measurement error STD with SNR and orbit.</p> ">
Abstract
:1. Introduction
2. Determination Method of Carrier Phase Cycle-Slip and Measurement Error
2.1. Experimental Scheme Design
- (a)
- Installing the equipment and collecting data. Install four antennae on a rotating platform of the same radius as the dynamic antennae, at intervals of 90° (as shown at the top of Figure 2), and installed two static antennae not far away. Collect data as needed for calibration and in the calculation of dynamic results.
- (b)
- Calibrating coordinates and relative positions. Calibrate the exact position of the static antennae and the relative positioning relationships between the dynamic antennae, and then calculated the motion trajectories of the antennae. After obtaining the above parameters, set the platform set to rotate at a uniform speed and began collecting data. The calibration method and contents are shown in Figure 3.
- (c)
- Calculating precise and effective relative positioning results. Calculate the relative position of each dynamic antenna relative to the static antennae according to the collected data. In addition, since the orientation of the rotation axis of the rotating platform is fixed, when the body coordinate system of the rotating platform is defined, the real position of all dynamic antennae can be described by an azimuth parameter (similar to yaw angle). The schematic diagram is shown in Figure 4.
- (d)
- Multiply test to ensure the accuracy of the positioning results. Error analysis requires sufficiently accurate positioning data as reference. Even for ultra-short baselines, there will be some epochs without a solution or with a wrong solution in long-term data, which is unfavorable to error analysis. In order to obtain reliable reference results, multiple testing is required for the positioning results at each time point.
- (i)
- Comparing the positioning results with antennae trajectories. If the deviation is too large (for example, horizontal deviation: >5 cm or the elevation deviation: >7 cm), we discarded it.
- (ii)
- The relative positioning results from the dynamic antennae to the two static antennae need to be checked by a closure error test. Theoretically, the sum of the baseline vectors from the dynamic antenna to the two static antennae and the baseline vector of the two static antennae should be zero. Therefore, the position of the dynamic antennae can be considered accurate only when the sum of the three baseline vectors is lower than the given threshold in three-dimensional space (for example, 3D threshold = 8 cm).
- (iii)
- According to the positioning results, the azimuth of platform rotation can be calculated, and the positioning results corresponding to the azimuth with excessive deviation should be discarded.
2.2. Using a Multi-Antennae Trajectory Constraint to Improve the Success Rate of Precision Relative Positioning in the Post-Processing Mode
2.2.1. Geometric Constraints Aided Ambiguity Searching
2.2.2. Interpolation Calculation and Secondary Processing
- (a)
- Take the interpolated antenna position as the initial position, and then solve the float ambiguity calculation equation.
- (b)
- Use LAMBDA to search the fixed ambiguity solution. As the initial value is more accurate, the success rate of this step will increase.
- (c)
- Integrate the results of other antennae to obtain the accurate position.
2.3. Using the Mixture of Gaussian Distribution to Model Carrier-Phase Cycle Slips
2.4. Using the Bi-Normal Distribution to Model Carrier Phase Measurement Error
3. Experimental Results and Analysis
3.1. The Effect of Geometric Constraints-Aided Ambiguity Searching
3.2. The Result of Interpolation Calculation and Secondary Processing
3.3. Cycle-Slip Characteristics of the Dynamic Receiver
3.3.1. The Distribution Characteristics of Cycle Slips
3.3.2. The Relationship between Cycle-Slip Incidence and SNR
3.4. Carrier-Phase Measurement-Error Characteristics Analysis
3.4.1. Distribution of Carrier-Phase Measurement Error
3.4.2. Relationship among Carrier Phase Measurement Error and Orbit
4. Conclusions
5. Patents
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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System | Solvable Epoch | Traditional Method | Geometric Constraints Method | Satellite Number (Min) | Satellite Number (Max) |
---|---|---|---|---|---|
GPS | 9409 | 9108 | 9338 | 5 | 9 |
GPS + BDS | 9414 | 9332 | 9310 | 21 | 27 |
Steps | A1B1/A2B1 | A1B2/A2B2 | A1B3/A2B3 | A1B4/A2B4 |
---|---|---|---|---|
Move to static precise relative positioning | 4,319,319/4,319,644 | 4,319,688/4,320,046 | 4,318,656/4,319,033 | 4,318,900/4,319,280 |
Closure error test | 4,316,937 | 4,316,677 | 4,316,478 | 4,316,870 |
Integrated processing | 4,319,191 | |||
Interpolation processing | 4,324,975 (increased 5784 epochs) | |||
Secondary processing | 4,325,669/4,325,803 | 4,325,595/4,325,786 | 4,325,634/4,325,800 | 4,325,577/4,325,723 |
Closure error test | 4,324,550 | 4,324,531 | 4,324,575 | 4,324,383 |
Integrated processing | 4,325,062 | |||
Interpolation processing | 4,325,400 (increased 338 epochs) |
Interval | B1I | B3I | Interval | B1I | B3I |
---|---|---|---|---|---|
≤−40 | 878 | 650 | (0, 5) | 9178 | 18,486 |
(−40, −35] | 0 | 78 | [5, 10) | 1235 | 7541 |
(−35, −30] | 0 | 67 | [10, 15) | 398 | 3565 |
(−30, −25] | 5 | 221 | [15, 20) | 213 | 1887 |
(−25, −20] | 4 | 150 | [20, 25) | 141 | 1173 |
(−20, −15] | 10 | 110 | [25, 30) | 106 | 753 |
(−15, −10] | 46 | 51 | [30, 35) | 43 | 636 |
(−10, −5] | 348 | 229 | [35, 40) | 73 | 432 |
(−5, −0) | 5523 | 19,781 | ≥−40 | 1563 | 4275 |
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Xiong, C.; Li, Q.; Wang, D.; Wu, J. Using Multi-Antenna Trajectory Constraint to Analyze BeiDou Carrier-Phase Observation Error of Dynamic Receivers. Sensors 2021, 21, 6930. https://doi.org/10.3390/s21206930
Xiong C, Li Q, Wang D, Wu J. Using Multi-Antenna Trajectory Constraint to Analyze BeiDou Carrier-Phase Observation Error of Dynamic Receivers. Sensors. 2021; 21(20):6930. https://doi.org/10.3390/s21206930
Chicago/Turabian StyleXiong, Chenyao, Qingsong Li, Dingjie Wang, and Jie Wu. 2021. "Using Multi-Antenna Trajectory Constraint to Analyze BeiDou Carrier-Phase Observation Error of Dynamic Receivers" Sensors 21, no. 20: 6930. https://doi.org/10.3390/s21206930