Design and Development of an Automatic Layout Algorithm for Laser GNSS RTK
Abstract
:1. Introduction
2. GNSS Laser RTK Calculation Principle
2.1. IMU RTK Measurement Principles
2.2. Laser Beam and Motor Assembly System Calibration
2.3. The Angle of Inclination of the Centering Rod in Any State
2.4. Principle of Motor Rotation Angle Calculation
- Plane is the horizontal plane, and plane is an inclined plane.
- OA represents the rotation axis of the alignment pole in any state, with its direction vector.
- Point is the intersection perpendicular to OA through the laser rotation point, with a known length r.
- A circle with radius r centered at a point lies on a plane .
- Point P is the point to be laid out with known specific coordinates; a perpendicular from point P to the plane intersects at point .
- Point K is the intersection of and the laser rotation radius, where intersects with at point K.
- Through point , tangents from point to are drawn at points U and V, and perpendiculars from points U and V to plane intersect at points M and N, respectively.
3. Example Verification
- Obtain the RTK phase center coordinates and the coordinates of the point to be laid out based on the RTK attitude, with related data shown in Table 1.
- 2.
- After initialization, the IMU attitude (in radians) is expressed as follows:
- 3.
- Coordinates of the pole tip and point are shown in Table 2.
- 4.
- Center the rod shaft unit vector .
- 5.
- 6.
- Coordinates of points and are shown in Table 5.
- 7.
- The values for the horizontal motor angle and the vertical motor tilt angle are as follows, with relevant data shown below, see Table 6:
4. Error Analysis
4.1. Effect of Laser Rotation Point Error
- (1)
- , , , and the average error obtained is (Figure 9).
- (2)
- , , , and the average error obtained is (Figure 10).
- (3)
- , , , and the average error obtained is (Figure 11).
- (4)
- , , , and the average error obtained is (Figure 12).
- (1)
- , , , and the average error obtained is (Figure 13).
- (2)
- , , , and the average error obtained is (Figure 14).
- (3)
- , , , and the average error obtained is (Figure 15).
- (4)
- , , , and the average error obtained is (Figure 16).
4.2. Effect of Motor Rotation Error
- (1)
- With m′ = 0.02°, the average error is (Figure 18).
- (2)
- With , the average error is (Figure 19).
5. Experimental Analysis
Network Continuous Operational Reference System Was Used for RTK Layout
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Nair, P.; Abd Sukor, S. A Review on Application of Global Positioning System in Construction Industry. Prog. Eng. Appl. Technol. 2022, 3, 249–259. [Google Scholar]
- Li, X.; Huang, J.; Li, X.; Shen, Z.; Han, J.; Li, L.; Wang, B. Review of PPP–RTK: Achievements, challenges, and opportunities. Satell. Navig. 2022, 3, 28. [Google Scholar] [CrossRef]
- Li, X.; Ge, M.; Dai, X.; Ren, X.; Fritsche, M.; Wickert, J.; Schuh, H. Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. J. Geod. 2015, 89, 607–635. [Google Scholar] [CrossRef]
- Chang, G.; Xu, T.; Wang, Q.; Li, S.; Deng, K. GNSS attitude determination method through vectorisation approach. IET Radar Sonar Navig. 2017, 11, 1477–1482. [Google Scholar] [CrossRef]
- Janos, D.; Kuras, P. Evaluation of Low-Cost GNSS Receiver under Demanding Conditions in RTK Network Mode. Sensors 2021, 21, 5552. [Google Scholar] [CrossRef]
- Hamza, V.; Stopar, B.; Ambrozic, T.; Turk, G.; Sterle, O. Testing Multi-Frequency Low-Cost GNSS Receivers for Geodetic Monitoring Purposes. Sensors 2020, 20, 4375. [Google Scholar] [CrossRef] [PubMed]
- He, H.; Li, J.; Yang, Y.; Xu, J.; Guo, H.; Wang, A. Performance assessment of single- and dual-frequency BeiDou/GPS single-epoch kinematic positioning. GPS Solut. 2014, 18, 393–403. [Google Scholar] [CrossRef]
- Tian, Y.; Ge, M.; Neitzel, F. Particle filter-based estimation of inter-frequency phase bias for real-time GLONASS integer ambiguity resolution. J. Geod. 2015, 89, 1145–1158. [Google Scholar] [CrossRef]
- Dabove, P. The usability of GNSS mass-market receivers for cadastral surveys considering RTK and NRTK techniques. Geod. Geodyn. 2019, 10, 282–289. [Google Scholar] [CrossRef]
- Qiu, H. Application and accuracy analysis of GNSS-RTK technology in data acquisition. J. Comput. Electron. Inf. Manag. 2023, 10, 21–23. [Google Scholar]
- Shang, R.; Gao, C.; Gan, L.; Zhang, R.; Gao, W.; Meng, X. Multi-GNSS Differential Inter-System Bias Estimation for Smartphone RTK Positioning: Feasibility Analysis and Performance. Remote Sens. 2023, 15, 1476. [Google Scholar] [CrossRef]
- Kim, H.; Hyun, C.-U.; Park, H.-D.; Cha, J. Image Mapping Accuracy Evaluation Using UAV with Standalone, Differential (RTK), and PPP GNSS Positioning Techniques in an Abandoned Mine Site. Sensors 2023, 23, 5858. [Google Scholar] [CrossRef] [PubMed]
- Kim, K.; Choi, J.; Chung, J.; Koo, G.; Bae, I.-H.; Sohn, H. Structural displacement estimation through multi-rate fusion of accelerometer and RTK-GPS displacement and velocity measurements. Measurement 2018, 130, 223–235. [Google Scholar] [CrossRef]
- Zhang, X.; Li, X.; Li, P. GNSS precision single-point positioning technology and application progress. Acta Geod. Cartogr. Sin. 2017, 46, 1399–1407. [Google Scholar]
- Odolinski, R.; Teunissen, P.J.G. Best integer equivariant estimation: Performance analysis using real data collected by low-cost, single- and dual-frequency, multi-GNSS receivers for short- to long-baseline RTK positioning. J. Geod. 2020, 94, 91. [Google Scholar] [CrossRef]
- Dai, Q.; Sui, L.; Wang, L.; Zeng, T.; Tian, Y. An efficiency algorithm on Gaussian mixture UKF for BDS/INS navigation system. Geod. Geodyn. 2018, 9, 169–174. [Google Scholar] [CrossRef]
- Zhou, W.-D.; Cai, J.-N.; Sun, L.; Shen, C. Time–space difference based GPS/SINS ultra-tight integrated navigation method. Measurement 2014, 58, 87–92. [Google Scholar] [CrossRef]
- Liu, J.; Feng, Z.; Yang, L.; Mannan, A.; Khan, T.; Zhao, Z.; Cheng, Z. Extraction of Sample Plot Parameters from 3D Point Cloud Reconstruction Based on Combined RTK and CCD Continuous Photography. Remote Sens. 2018, 10, 1299. [Google Scholar] [CrossRef]
- Ren, Y.; Wang, Z. A Novel Scene Matching Algorithm via Deep Learning for Vision-based UAV Absolute Localization. In Proceedings of the 2022 International Conference on Machine Learning, Cloud Computing and Intelligent Mining (MLCCIM), Xiamen, China, 5–7 August 2022; pp. 211–218. [Google Scholar]
- Niu, X.; Chen, Q.; Zhang, Q.; Zhang, H.; Niu, J.; Chen, K.; Shi, C.; Liu, J. Using Allan variance to analyze the error characteristics of GNSS positioning. GPS Solut. 2014, 18, 231–242. [Google Scholar] [CrossRef]
- Liu, K.; Tang, S.; Zhang, Y.; Li, H.; Lv, F. Tilt RTK attitude solving based on complementary filtering algorithm. Sci. Technol. Eng. 2022, 22, 10402–10408. [Google Scholar]
- Gao, K.; Ren, S.; Yi, G.; Zhong, J.; Wang, Z. An Improved ACKF/KF Initial Alignment Method for Odometer-Aided Strapdown Inertial Navigation System. Sensors 2018, 18, 3896. [Google Scholar] [CrossRef] [PubMed]
- Chen, Q.; Lin, H.; Guo, R.; Niu, X. Rapid and accurate initial alignment of the low-cost MEMS IMU chip dedicated for tilted RTK receiver. GPS Solut. 2020, 24, 119. [Google Scholar] [CrossRef]
- Gallo, E.; Barrientos, A. Long-Distance GNSS-Denied Visual Inertial Navigation for Autonomous Fixed-Wing Unmanned Air Vehicles: SO(3) Manifold Filter Based on Virtual Vision Sensor. Aerospace 2023, 10, 708. [Google Scholar] [CrossRef]
- Hua, T.; Pei, L.; Li, T.; Yin, J.; Liu, G.; Yu, W. M2C-GVIO: Motion manifold constraint aided GNSS-visual-inertial odometry for ground vehicles. Satell. Navig. 2023, 4, 13. [Google Scholar] [CrossRef]
- Chang, L.; Li, J.; Chen, S. Initial Alignment by Attitude Estimation for Strapdown Inertial Navigation Systems. IEEE Trans. Instrum. Meas. 2015, 64, 784–794. [Google Scholar] [CrossRef]
- Dai, J.S. Rodrigues formula variations, quaternion conjugation and intrinsic connections. Mech. Mach. Theory 2015, 92, 144–152. [Google Scholar] [CrossRef]
- Singh, A.; Chaturvedi, P. Error Propagation. Reson 2021, 26, 853–861. [Google Scholar] [CrossRef]
Point Name | X (m) | Y (m) | Z (m) |
---|---|---|---|
A | 2,797,820.603 | 430,599.348 | 150.500 |
P | 2,797,820.786 | 430,599.133 | 148.706 |
Point Name | X (m) | Y (m) | Z (m) |
---|---|---|---|
2,797,820.888 | 430,599.488 | 148.702 | |
2,797,820.587 | 430,599.315 | 150.436 |
Point Name | Point Data |
---|---|
2,797,820.517 | |
430,598.999 | |
150.400 |
Point Name | Point Data |
---|---|
0.325 | |
81°51′14.0″ | |
Point Name | X (m) | Y (m) | Z (m) |
---|---|---|---|
U | 2,797,820.560 | 430,599.355 | 150.486 |
V | 2,797,820.645 | 430,599.330 | 150.498 |
Location | Horizontal Motor Angle Value | Vertical Motor Angle Value |
---|---|---|
U | ||
V |
Point Name | X (m) | Y (m) | Z (m) |
---|---|---|---|
P1 | 2,798,011.193 | 431,052.745 | 154.008 |
P2 | 2,798,009.418 | 431,062.020 | 154.012 |
P3 | 2,798,019.385 | 431,067.850 | 154.024 |
P4 | 2,798,018.965 | 431,054.765 | 154.028 |
Point Name | X (m) | Y (m) |
---|---|---|
P5 | 2,798,013.516 | 431,053.557 |
P6 | 2,798,011.330 | 431,055.442 |
P7 | 2,798,011.012 | 431,058.822 |
P8 | 2,798,012.405 | 431,061.685 |
P9 | 2,798,014.713 | 431,057.192 |
P10 | 2,798,016.503 | 431,054.846 |
P11 | 2,798,016.026 | 431,059.975 |
P12 | 2,798,018.573 | 431,062.162 |
P13 | 2,798,016.304 | 431,063.395 |
P14 | 2,798,017.618 | 431,065.343 |
P15 | 2,798,013.902 | 431,064.398 |
Point Name | X (m) | Y (m) |
---|---|---|
P5 | 2,798,013.520 | 431,053.574 |
P6 | 2,798,011.314 | 431,055.448 |
P7 | 2,798,011.022 | 431,058.809 |
P8 | 2,798,012.416 | 431,061.697 |
P9 | 2,798,014.71 | 431,057.209 |
P10 | 2,798,016.516 | 431,054.835 |
P11 | 2,798,016.01 | 431,059.971 |
P12 | 2,798,018.559 | 431,062.17 |
P13 | 2,798,016.321 | 431,063.391 |
P14 | 2,798,017.626 | 431,065.327 |
P15 | 2,798,013.895 | 431,064.383 |
Point Name | X (m) | Y (m) |
---|---|---|
P5 | 2,798,013.527 | 431,053.561 |
P6 | 2,798,011.323 | 431,055.451 |
P7 | 2,798,011.020 | 431,058.831 |
P8 | 2,798,012.412 | 431,061.694 |
P9 | 2,798,014.704 | 431,057.184 |
P10 | 2,798,016.509 | 431,054.856 |
P11 | 2,798,016.019 | 431,059.965 |
P12 | 2,798,018.565 | 431,062.17 |
P13 | 2,798,016.295 | 431,063.404 |
P14 | 2,798,017.612 | 431,065.353 |
P15 | 2,798,013.909 | 431,064.408 |
Number | Conventional Inertial Navigation RTK | Laser Inertial Navigation RTK | ||||
---|---|---|---|---|---|---|
(m) | (m) | (m) | (m) | (m) | ||
1 | −0.004 | −0.017 | 0.017 | −0.011 | −0.004 | 0.012 |
2 | 0.016 | −0.006 | 0.017 | 0.007 | −0.009 | 0.011 |
3 | −0.01 | 0.013 | 0.016 | −0.008 | −0.009 | 0.012 |
4 | −0.011 | −0.012 | 0.016 | −0.007 | −0.009 | 0.011 |
5 | 0.003 | −0.017 | 0.017 | 0.009 | 0.008 | 0.012 |
6 | −0.013 | 0.011 | 0.017 | −0.006 | −0.01 | 0.012 |
7 | 0.016 | 0.004 | 0.017 | 0.007 | 0.01 | 0.012 |
8 | 0.014 | −0.008 | 0.016 | 0.008 | −0.008 | 0.011 |
9 | −0.017 | 0.004 | 0.018 | 0.009 | −0.009 | 0.013 |
10 | −0.008 | 0.016 | 0.018 | 0.006 | −0.01 | 0.012 |
11 | 0.007 | 0.015 | 0.017 | −0.007 | −0.01 | 0.012 |
m | 0.017 | 0.012 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Tang, J.; Sun, X.; Lu, X.; Jia, J.; Tang, S. Design and Development of an Automatic Layout Algorithm for Laser GNSS RTK. Sensors 2024, 24, 5857. https://doi.org/10.3390/s24175857
Tang J, Sun X, Lu X, Jia J, Tang S. Design and Development of an Automatic Layout Algorithm for Laser GNSS RTK. Sensors. 2024; 24(17):5857. https://doi.org/10.3390/s24175857
Chicago/Turabian StyleTang, Jiazhi, Xuan Sun, Xianjian Lu, Jiguang Jia, and Shihua Tang. 2024. "Design and Development of an Automatic Layout Algorithm for Laser GNSS RTK" Sensors 24, no. 17: 5857. https://doi.org/10.3390/s24175857