Road Tests of the Positioning Accuracy of INS/GNSS Systems Based on MEMS Technology for Navigating Railway Vehicles
"> Figure 1
<p>Users of radio navigation systems.</p> "> Figure 2
<p>Global Navigation Satellite System (GNSS) signal obscuration in urban area.</p> "> Figure 3
<p>Requirements for positioning system accuracy and availability in rail transport compared to other navigation types. Own study based on: [<a href="#B37-energies-13-04463" class="html-bibr">37</a>,<a href="#B57-energies-13-04463" class="html-bibr">57</a>,<a href="#B58-energies-13-04463" class="html-bibr">58</a>,<a href="#B59-energies-13-04463" class="html-bibr">59</a>,<a href="#B61-energies-13-04463" class="html-bibr">61</a>,<a href="#B62-energies-13-04463" class="html-bibr">62</a>].</p> "> Figure 4
<p>Testing electrical connections of the measurement equipment (<b>a</b>) and a plate with measurement equipment assembled on a passenger car (<b>b</b>).</p> "> Figure 5
<p>Geometric relationships between the tested devices mounted on the measurement platform.</p> "> Figure 6
<p>Division of the route into test sections.</p> "> Figure 7
<p>Variability in the two-dimensional (2D) position errors recorded by the VN-200 and VN-300 devices as a function of the route length when travelling at speeds of 40 km/h, 80 km/h and 100 km/h along section no. 1.</p> "> Figure 8
<p>Variability in the two-dimensional (2D) position errors recorded by the VN-200 and VN-300 devices as a function of the route length when travelling at speeds of 40 km/h, 80 km/h and 100 km/h along section no. 4.</p> "> Figure 9
<p>Variability in one-dimensional (1D) position errors recorded by the VN-200 and VN-300 devices as a function of the route length when travelling at speeds of 40 km/h, 80 km/h and 100 km/h along section no. 3.</p> "> Figure 10
<p>Variability in two-dimensional (2D) and three-dimensional (3D) position errors recorded by the VN-200 and VN-300 devices as a function of the route length when travelling at increased speeds (100–120 km/h) along section no. 7.</p> ">
Abstract
:1. Introduction
- —measurement error of the navigation parameter (pseudorange),
- —geometric coefficient of the system’s accuracy, depending on the spatial distribution of GNSS satellites used in relation to the user (Dilution of Precision).
2. Materials and Methods
2.1. Navigation Requirements for Rail Transport
- Experimental assessment of the positioning accuracy of INS/GNSS equipment with one or two GNSS antennas, as a function of availability of satellite signals depending on the type of development (terrain with and without field obstacles).
- Experimental assessment of the positioning accuracy of INS/GNSS equipment fitted with one or two GNSS antennas, as a function of variable train speed (40–120 km/h). It will answer the question of what extent an increase in the speed of an object results in a decrease in positioning accuracy.
2.2. Measurement Equipment
- The tests need to be carried out on long straight sections of a dual carriageway.
- Constant measurement speed needs to be ensured by using cruise control.
- The measurements need to be taken early in the morning (Sunday) to benefit from reduced traffic of other road users that could make it necessary to change lane or speed.
- Software for forecasting the number of available GNSS satellites needs to be used to determine the test time. Such software allowed the selection of a period in which the Horizontal Dilution of Precision (HDOP) value did not exceed 2.
- Reference—consisting of two Trimble R10 receivers using GNSS network positioning, in real-time at 10 Hz, allowing to determine the three-dimensional (3D) position with simultaneous use of four GNSS systems (GPS/GLONASS/BDS/Galileo). The antennas of both GNSS receivers are placed symmetrically in relation to the platform’s axis, which significantly facilitates the subsequent calculation of coordinates and determination of momentary errors of the tested devices. They were mounted on tripods, which also significantly facilitated their assembly. The predictable positioning accuracy of the reference system was 1 cm (RMS).
- Measurement—consisting of two independently operated VN-200 and VN-300 systems. The VN-200 consisted of an INS device and a single GNSS antenna, whereas the VN-300 system used an INS device and two GNSS antennas. All elements were mounted in the platform axis and symmetrically with respect to the reference system (Trimble R10 receivers), which significantly facilitated future calculations (Figure 4). Mobile phones were also tested in the study but they are not the subject of this paper.
2.3. Measurement Method
- GPS time (s),
- —rotation about the lateral axis (°),
- —rotation about the vertical axis (°),
- —rotation about the longitudinal axis (°),
- —geodetic latitude (°),
- —geodetic longitude (°),
- —height above the surface of the World Geodetic System 1984 (WGS 84) ellipsoid (m).
- Universal Time Coordinated (UTC) (s),
- —northing in the PL-2000 system (m),
- —easting in the PL-2000 system (m),
- —height above the surface of the WGS 84 ellipsoid (m).
- —scale factor (-),
- —ellipsoid normal (radius of curvature perpendicular to the meridian) (m),
- —meridian arc length from the equator to the arbitrary latitude (B) (m),
- —distance between the point and the central meridian (rad),
- —longitude of the central meridian (°).
- —first eccentricity (-).
- —point coordinates lying on the line connecting the R1 and R2 receivers at the moment of observation t,
- —slope of the line connecting the R1 and R2 receivers at the moment of observation t,
- —y-intercept of the line connecting the R1 and R2 receivers at the moment of observation t.
- —point coordinates lying on the axis of platform symmetry at the moment of observation t,
- —slope of the axis of platform symmetry at the moment of observation t,
- —y-intercept of the axis of platform symmetry at the moment of observation t.
- —actual distance calculated along the platform’s longitudinal symmetry axis between the AV and rVN points,
- —momentary lateral inclination of the platform recorded by the VectorNav device at the moment of observation t.
3. Results and Discussion
3.1. Test Sections
- Assessment of the positioning accuracy of the VN-200 and VN-300 systems on a route without buildings and GNSS signal obscurations.
- Assessment of the positioning accuracy of the VN-200 and VN-300 systems on a route in a densely developed area causing GNSS signal obscurations.
- Assessment of the positioning accuracy of the VN-200 and VN-300 systems as a function of vehicle speed, in undeveloped areas without GNSS signal obscurations.
- Section no. 1 was located between the Stadion Energa Gdańsk and the entrance to the road tunnel under the Martwa Wisła river from the Letnica district. It was about 1.85 km long. The measurement passage consisted of long straight segments (several hundred metres) through areas with a small number of obstructions, which included a drawbridge over a rail track (about 100 m long) and a roundabout over the lane (about 150 m long). Section no. 5 lies almost on the same route as section no. 1, but it was oriented in the opposite direction (towards the Stadion Energa Gdańsk). Sections no. 1 and 5 were located parallel to each other and separated by a 4-metre wide strip separating roadways.
- Section no. 2 was located between the entrance to the road tunnel under the Martwa Wisła river from the Letnica district and the exit from Third Millennium John Paul II Bridge towards the Teofila Lenartowicza Street. It was about 2.5 km long. The measurement passage consisted of two segments: a large circular arc (about 1 km long) and a straight section (about 1.5 km long). The area around the route was free of any terrain obstructions such as buildings or trees. Section no. 4 lies almost on the same route as section no. 2, but it was oriented in the opposite direction (towards the road tunnel under the Martwa Wisła river). Sections no. 2 and 4 were located parallel to each other and separated by a 4-metre wide strip separating roadways.
- Section no. 3 starts under Third Millennium John Paul II Bridge and runs along Teofila Lenartowicza Street. It was about 800 m long. The measurement passage consisted of circular arches with a large turning angle. The third tested section ran through numerous obstructions, which included: a bridge, multi-storey buildings, trees and shrubs with heights not exceeding 5 m.
- Section no. 6 was located near the roundabout at Trasa Słowackiego between sections no. 1 and 5. It consisted of an arch with a large turning angle, and the area around it was free of any obstructions.
- Section no. 7 was the last tested route located between the road tunnel under the Martwa Wisła river and the intersection of Generała Józefa Hallera Avenue with the Trasa Słowackiego, about 2 km long. The measurement passage consisted of long straight segments (several hundred metres) around which there were practically no obstructions, with the exception of small allotment houses and shrubs. This section was selected to determine the impact of increased vehicle speeds (reaching over 120 km/h) on the positioning accuracy of INS/GNSS systems.
3.2. Analysis Results for a Route without GNSS Obstructions (Sections No. 1 and 5)
3.3. Analysis Results for a Route without GNSS Obstructions (Sections No. 2 and 4)
3.4. Analysis Results for a Densely Developed Route with GNSS Obstructions (Sections No. 3 and 6)
3.5. Analysis Results from Testing of Positioning Accuracy of VectorNav Systems as a Function of Vehicle Speed
3.6. Cumulative Results
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Specht, C. GPS System; Publishing House of the Bernardinum: Pelplin, Poland, 2007. (In Polish) [Google Scholar]
- Forssell, B. Radionavigation Systems; Artech House: Norwood, MA, USA, 2008. [Google Scholar]
- Specht, C.; Weintrit, A.; Specht, M. A History of Maritime Radio-navigation Positioning Systems Used in Poland. J. Navig. 2016, 69, 468–480. [Google Scholar] [CrossRef] [Green Version]
- Czaplewski, K.; Goward, D. Global Navigation Satellite Systems—Perspectives on Development and Threats to System Operation. TransNav Int. J. Mar. Navig. Saf. Sea Transp. 2016, 10, 183–192. [Google Scholar] [CrossRef] [Green Version]
- Specht, M.; Szmagliński, J.; Specht, C.; Koc, W.; Wilk, A.; Czaplewski, K.; Karwowski, K.; Dąbrowski, P.S.; Chrostowski, P.; Grulkowski, S. Analysis of Positioning Methods Using Global Navigation Satellite Systems (GNSS) in Polish State Railways (PKP). Sci. J. Marit. Univ. Szczec. 2020, 62, 26–35. [Google Scholar] [CrossRef]
- Chen, Q.; Zhang, Q.; Niu, X. Estimate the Pitch and Heading Mounting Angles of the IMU for Land Vehicular GNSS/INS Integrated System. IEEE Trans. Intell. Transp. Syst. 2020, 1–13. [Google Scholar] [CrossRef]
- Elsheikh, M.; Abdelfatah, W.; Noureldin, A.; Iqbal, U.; Korenberg, M. Low-cost Real-time PPP/INS Integration for Automated Land Vehicles. Sensors 2019, 19, 4896. [Google Scholar] [CrossRef] [Green Version]
- Li, T.; Zhang, H.; Gao, Z.; Niu, X.; El-sheimy, N. Tight Fusion of a Monocular Camera, MEMS-IMU, and Single-frequency Multi-GNSS RTK for Precise Navigation in GNSS-challenged Environments. Remote Sens. 2019, 11, 610. [Google Scholar] [CrossRef] [Green Version]
- Zhang, Q.; Chen, Q.; Niu, X.; Shi, C. Requirement Assessment of the Relative Spatial Accuracy of a Motion-constrained GNSS/INS in Shortwave Track Irregularity Measurement. Sensors 2019, 19, 5296. [Google Scholar] [CrossRef] [Green Version]
- EC; GSA. Galileo—Open Service—Service Definition Document; Version 1.1; EC: Brussels, Belgium; GSA: Prague, Czech, 2019.
- PNT IAC of the Central Research Institute of Machine Building. Global Navigation Satellite System Glonass Open Service Performance Standard (GLONASS OS PS), 2.2 ed.; PNT IAC of the Central Research Institute of Machine Building: Korolev, Russia, 2020. [Google Scholar]
- SCIO. China’s BeiDou Navigation Satellite System; SCIO: Beijing, China, 2016. [Google Scholar]
- U.S. DoD. Global Positioning System Standard Positioning Service Performance Standard, 4th ed.; U.S. DoD: Arlington County, VA, USA, 2008.
- EC-DG Enterprise and Industry. EGNOS Data Access Service (EDAS) Service Definition Document; Version 2.2; EC-DG Enterprise and Industry: Brussels, Belgium; Luxembourg City, Luxembourg, 2019. [Google Scholar]
- EC-DG Enterprise and Industry. EGNOS Open Service (OS) Service Definition Document; Version 2.3; EC-DG Enterprise and Industry: Brussels, Belgium; Luxembourg City, Luxembourg, 2017. [Google Scholar]
- EC-DG Enterprise and Industry. EGNOS Safety of Life (SoL) Service Definition Document; Version 3.3; EC-DG Enterprise and Industry: Brussels, Belgium; Luxembourg City, Luxembourg, 2019. [Google Scholar]
- Specht, C.; Pawelski, J.; Smolarek, L.; Specht, M.; Dąbrowski, P. Assessment of the Positioning Accuracy of DGPS and EGNOS Systems in the Bay of Gdansk Using Maritime Dynamic Measurements. J. Navig. 2019, 72, 575–587. [Google Scholar] [CrossRef] [Green Version]
- U.S. DoT.; FAA. Global Positioning System Wide Area Augmentation System (WAAS) Performance Standard, 1st ed.; U.S. DoT.: Washington, DC, USA; FAA: Washington, DC, USA, 2008.
- Li, G.; Geng, J. Characteristics of Raw Multi-GNSS Measurement Error from Google Android Smart Devices. GPS Solut. 2019, 23, 90. [Google Scholar] [CrossRef]
- Liu, W.; Shi, X.; Zhu, F.; Tao, X.; Wang, F. Quality Analysis of Multi-GNSS Raw Observations and a Velocity-aided Positioning Approach Based on Smartphones. Adv. Space Res. 2019, 63, 2358–2377. [Google Scholar] [CrossRef]
- Paziewski, J. Recent Advances and Perspectives for Positioning and Applications with Smartphone GNSS Observations. Meas. Sci. Technol. 2020, 31, 091001. [Google Scholar] [CrossRef]
- Paziewski, J.; Crespi, M. High-precision Multi-constellation GNSS: Methods, Selected Applications and Challenges. Meas. Sci. Technol. 2020, 31, 010101. [Google Scholar] [CrossRef]
- Specht, C.; Szot, T.; Dąbrowski, P.; Specht, M. Testing GNSS Receiver Accuracy in Samsung Galaxy Series Mobile Phones at a Sports Stadium. Meas. Sci. Technol. 2020, 31, 064006. [Google Scholar] [CrossRef]
- Dziewicki, M.; Specht, C. Position Accuracy Evaluation of the Modernized Polish DGPS. Pol. Marit. Res. 2009, 16, 57–61. [Google Scholar] [CrossRef]
- FSA. System of Differential Correction and Monitoring Interface Control Document, 1st ed.; FSA: Moscow, Russia, 2012. [Google Scholar]
- Krasuski, K.; Ćwiklak, J. Accuracy Analysis of Aircraft Position at Departure Phase Using DGPS Method. Acta Mech. Autom. 2020, 14, 36–43. [Google Scholar] [CrossRef]
- Przestrzelski, P.; Bakuła, M.; Galas, R. The Integrated Use of GPS/GLONASS Observations in Network Code Differential Positioning. GPS Solut. 2017, 21, 627–638. [Google Scholar] [CrossRef] [Green Version]
- Specht, C.; Smolarek, L.; Pawelski, J.; Specht, M.; Dąbrowski, P. Polish DGPS System: 1995–2017—Study of Positioning Accuracy. Pol. Marit. Res. 2019, 26, 15–21. [Google Scholar] [CrossRef] [Green Version]
- Bakuła, M.; Przestrzelski, P.; Kaźmierczak, R. Reliable Technology of Centimeter GPS/GLONASS Surveying in Forest Environments. IEEE Trans. Geosci. Remote Sens. 2015, 53, 1029–1038. [Google Scholar] [CrossRef]
- Krasuski, K.; Savchuk, S. Determination of the Precise Coordinates of the GPS Reference Station in of a GBAS System in the Air Transport. Commun. Sci. Lett. Univ. Zilina 2020, 22, 11–18. [Google Scholar] [CrossRef]
- Paziewski, J.; Sieradzki, R.; Baryla, R. Multi-GNSS High-rate RTK, PPP and Novel Direct Phase Observation Processing Method: Application to Precise Dynamic Displacement Detection. Meas. Sci. Technol. 2018, 29, 091001. [Google Scholar] [CrossRef]
- Siejka, Z. Validation of the Accuracy and Convergence Time of Real Time Kinematic Results Using a Single Galileo Navigation System. Sensors 2018, 18, 2412. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Specht, M.; Specht, C.; Wilk, A.; Koc, W.; Smolarek, L.; Czaplewski, K.; Karwowski, K.; Dąbrowski, P.S.; Skibicki, J.; Chrostowski, P.; et al. Testing the Positioning Accuracy of GNSS Solutions during the Tramway Track Mobile Satellite Measurements in Diverse Urban Signal Reception Conditions. Energies 2020, 13, 3646. [Google Scholar] [CrossRef]
- Kelner, J.M.; Ziółkowski, C.; Nowosielski, L.; Wnuk, M. Local Navigation System for VTOLs Used on the Vessels. In Proceedings of the IEEE/ION Position, Location and Navigation Symposium, Savannah, GA, USA, 11–14 April 2016. [Google Scholar]
- Kelner, J.M.; Ziółkowski, C.; Nowosielski, L.; Wnuk, M. Reserve Navigation System for Ships Based on Coastal Radio Beacons. In Proceedings of the IEEE/ION Position, Location and Navigation Symposium, Savannah, GA, USA, 11–14 April 2016. [Google Scholar]
- Spilker, J.J., Jr.; Axelrad, P.; Parkinson, B.W.; Enge, P. Global Positioning System: Theory and Applications; AIAA: Reston, VA, USA, 1996; Volume I. [Google Scholar]
- EC. European Radio Navigation Plan; Version 1.1; EC: Luxembourg City, Luxembourg, 2018. [Google Scholar]
- IALA-AISM. IALA World Wide Radio Navigation Plan, 2nd ed.; IALA-AISM: Saint Germain en Laye, France, 2012. [Google Scholar]
- Dąbrowski, P.S.; Specht, C.; Felski, A.; Koc, W.; Wilk, A.; Czaplewski, K.; Karwowski, K.; Jaskólski, K.; Specht, M.; Chrostowski, P.; et al. The Accuracy of a Marine Satellite Compass under Terrestrial Urban Conditions. J. Mar. Sci. Eng. 2020, 8, 18. [Google Scholar] [CrossRef] [Green Version]
- Naus, K.; Waz, M. Precision in Determining Ship Position Using the Method of Comparing an Omnidirectional Map to a Visual Shoreline Image. J. Navig. 2016, 69, 391–413. [Google Scholar] [CrossRef] [Green Version]
- Almeida, C.; Franco, T.; Ferreira, H.; Martins, A.; Santos, R.; Almeida, J.M.; Carvalho, J.; Silva, E. Radar Based Collision Detection Developments on USV ROAZ II. In Proceedings of the OCEANS 2009-EUROPE, Bremen, Germany, 11–14 May 2009. [Google Scholar]
- Droeschel, D.; Schwarz, M.; Behnke, S. Continuous Mapping and Localization for Autonomous Navigation in Rough Terrain Using a 3D Laser Scanner. Robot. Auton. Syst. 2017, 88, 104–115. [Google Scholar] [CrossRef]
- Huang, L.; Chen, S.; Zhang, J.; Cheng, B.; Liu, M. Real-time Motion Tracking for Indoor Moving Sphere Objects with a LiDAR Sensor. Sensors 2017, 17, 1932. [Google Scholar] [CrossRef]
- Noureldin, A.; Karamat, T.B.; Georgy, J. Fundamentals of Inertial Navigation, Satellite-based Positioning and their Integration; Springer: Berlin/Heidelberg, Germany, 2013. [Google Scholar]
- Barton, A.; Volna, E. Control of Autonomous Robot Using Neural Networks. In Proceedings of the 14th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2016), Rhodes, Greece, 9–25 September 2016. [Google Scholar]
- Jo, J.; Tsunoda, Y.; Stantic, B.; Liew, A.W.-C. A Likelihood-based Data Fusion Model for the Integration of Multiple Sensor Data: A Case Study with Vision and Lidar Sensors. In Robot Intelligence Technology and Applications 4. Advances in Intelligent Systems and Computing; Kim, J.H., Karray, F., Jo, J., Sincak, P., Myung, H., Eds.; Springer: Cham, Switzerland, 2017; Volume 447, pp. 489–500. [Google Scholar]
- Specht, C.; Dąbrowski, P.; Dumalski, A.; Hejbudzka, K. Modeling 3D Objects for Navigation Purposes Using Laser Scanning. TransNav Int. J. Mar. Navig. Saf. Sea Transp. 2016, 10, 301–306. [Google Scholar] [CrossRef]
- Chen, Q.; Niu, X.; Zhang, Q.; Cheng, Y. Railway Track Irregularity Measuring by GNSS/INS Integration. Navig. J. Inst. Navig. 2015, 62, 83–93. [Google Scholar] [CrossRef]
- Chen, Q.; Niu, X.; Zuo, L.; Zhang, T.; Xiao, F.; Liu, Y.; Liu, J. A Railway Track Geometry Measuring Trolley System Based on Aided INS. Sensors 2018, 18, 538. [Google Scholar] [CrossRef] [Green Version]
- Gao, Z.; Ge, M.; Li, Y.; Shen, W.; Zhang, H.; Schuh, H. Railway Irregularity Measuring Using Rauch–Tung–Striebel Smoothed Multi-sensors Fusion System: Quad-GNSS PPP, IMU, Odometer, and Track Gauge. GPS Solut. 2018, 22, 1–14. [Google Scholar] [CrossRef]
- Jiang, Q.; Wu, W.; Jiang, M.; Li, Y. A New Filtering and Smoothing Algorithm for Railway Track Surveying Based on Landmark and IMU/Odometer. Sensors 2017, 17, 1438. [Google Scholar] [CrossRef]
- Jiang, Q.; Wu, W.; Li, Y.; Jiang, M. Millimeter Scale Track Irregularity Surveying Based on ZUPT-aided INS with Sub-decimeter Scale Landmarks. Sensors 2017, 17, 2083. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Kurhan, M.B.; Kurhan, D.M.; Baidak, S.Y.; Khmelevska, N.P. Research of Railway Track Parameters in the Plan Based on the Different Methods of Survey. Nauka Prog. Transp. 2018, 2, 77–86. [Google Scholar] [CrossRef] [Green Version]
- Li, Q.; Chen, Z.; Hu, Q.; Zhang, L. Laser-aided INS and Odometer Navigation System for Subway Track Irregularity Measurement. J. Surv. Eng. 2017, 143, 04017014. [Google Scholar] [CrossRef]
- Koc, W.; Specht, C.; Szmaglinski, J.; Chrostowski, P. A Method for Determination and Compensation of a Cant Influence in a Track Centerline Identification Using GNSS Methods and Inertial Measurement. Appl. Sci. 2019, 9, 4347. [Google Scholar] [CrossRef] [Green Version]
- Specht, C.; Koc, W.; Chrostowski, P. Computer-aided Evaluation of the Railway Track Geometry on the Basis of Satellite Measurements. Open Eng. 2016, 6, 125–134. [Google Scholar] [CrossRef] [Green Version]
- GLA. GLA Radio Navigation Plan; GLA: Harwich-London, UK, 2007. [Google Scholar]
- SMA. Swedish Radio Navigation Plan, Policy and Plans; SMA: Norrköping, Sweden, 2009. [Google Scholar]
- U.S. DoD. 2019 Federal Radionavigation Plan; U.S. DoD: Springfield, VA, USA, 2019.
- GSA. Report on Rail User Needs and Requirements; Version 1.0; GSA: Prague, Czech, 2018. [Google Scholar]
- IHO. IHO Standards for Hydrographic Surveys, 5th ed.; Special Publication No. 44; IHO: Monte Carlo, Monaco, 2008. [Google Scholar]
- Specht, M. Method of Evaluating the Positioning System Capability for Complying with the Minimum Accuracy Requirements for the International Hydrographic Organization Orders. Sensors 2019, 19, 3860. [Google Scholar] [CrossRef] [Green Version]
- Gajderowicz, I. Map Projections: Basics; Publishing House of the University of Warmia and Mazury in Olsztyn: Olsztyn, Poland, 2009. (In Polish) [Google Scholar]
- Deakin, R.E.; Hunter, M.N.; Karney, C.F.F. The Gauss-Krüger Projection. In Proceedings of the 23rd Victorian Regional Survey Conference, Warrnambool, Australia, 10–12 September 2010. [Google Scholar]
- Kadaj, R.J. Polish Coordinate Systems. Transformation Formulas, Algorithms and Softwares. Available online: http://www.geonet.net.pl/images/2002_12_uklady_wspolrz.pdf (accessed on 28 August 2020).
- NovAtel Positioning Leadership. GPS Position Accuracy Measures. Available online: https://www.novatel.com/assets/Documents/Bulletins/apn029.pdf (accessed on 28 August 2020).
- Szot, T.; Specht, C.; Specht, M.; Dabrowski, P.S. Comparative Analysis of Positioning Accuracy of Samsung Galaxy Smartphones in Stationary Measurements. PLoS ONE 2019, 14, e0215562. [Google Scholar] [CrossRef]
- Van Diggelen, F. GNSS Accuracy—Lies Damn Lies and Statistics. GPS World 2007, 18, 27–32. [Google Scholar]
- Whelan, B.; Taylor, J. Precision Agriculture for Grain Production Systems; CSIRO Publishing: Clayton, Victoria, Australia, 2013. [Google Scholar]
Requirements | Measures of Minimum Performance Criteria to Meet Requirements | |||||
---|---|---|---|---|---|---|
Accuracy (2DRMS) | Availability | Continuity | Integrity | TTA | Coverage * | |
Positive Train Control (PTC) | 1 m | 99.9% | N/A | 2 m | 6 s | Railroad right of way in all 50 states and District of Columbia. |
Track Defect Location (TDL) | 0.3 m | 99.9% | N/A | 0.6 m | 30 s | Railroad right of way in all 50 states and District of Columbia. |
Automated Asset Mapping (AAM) | 0.2 m | 99.9% | N/A | 0.4 m | 30 s | Railroad right of way in all 50 states and District of Columbia. |
Surveying | 0.02 m | 99.7% | N/A | 0.04 m | 30 s | Railroad right of way in all 50 states and District of Columbia. |
Bridge and tectonic monitoring for bridge safety | 0.002 m | 99.7% | N/A | 0.004 m | 30 s | Railroad right of way in all 50 states and District of Columbia. |
Telecommunications timing | 340 nsec | 99.7% | N/A | 680 nsec | 30 s | All 50 states and District of Columbia. |
Application | Accuracy (2σ) | Availability | Integrity | SIL | TTA | Category |
---|---|---|---|---|---|---|
Cold movement detection | HNSE < 1 m | High | Very high | 4 | TTA < 10 s | Safety relevant |
Level crossing protection | 1 m < HNSE < 10 m | High | Very high | 4 | TTA < 10 s (TBC) | Safety relevant |
Train integrity and train length monitoring | 1 m < HNSE < 10 m (TBC) | High | Very high | 4 | 10 s < TTA < 30 s | Safety relevant |
Track identification | ACTE < 1.9 m | High | Very high | 2–4 | 10 s < TTA < 30 s | Safety relevant |
Odometer calibration | HNSE < 1 m | High | Low | TBD | TTA < 10 s | Non safety relevant |
Door control supervision | 1 m < HNSE < 10 m | High | High | TBD | 10 s < TTA < 30 s | Safety relevant |
Door control supervision in ATO | HNSE < 1 m | High | High | 2 | 10 s < TTA < 30 s | Safety relevant |
Trackside personnel protection | 1 m < HNSE < 10 m | High | High | TBD | 10 s < TTA < 30 s | Safety relevant |
Management of emergencies | 1 m < HNSE < 5 m | High | High | TBD | 10 s < TTA < 30 s | Non safety relevant |
Infrastructure surveying | 0.01 m < HNSE < 1 m | Low | Low/High | TBD | TTA ≥ 30 s | Liability relevant |
Location of GSM reports | 1 m < HNSE < 100 m | Low | High | TBD | TTA ≥ 30 s | Liability relevant |
Gauging surveys | 0.01 m < HNSE < 1 m | Low | Very high | TBD | TTA ≥ 30 s | Liability relevant |
Structural monitoring | 0.01 m < HNSE < 1 m | Low | Low | TBD | TTA ≥ 30 s | Liability relevant |
Fleet management | HNSE ≥ 10 m | High | Low | TBD | TTA ≥ 30 s | Liability relevant |
Cargo monitoring | HNSE ≥ 10 m | High | Low | TBD | TTA ≥ 30 s | Liability relevant |
Energy charging | HNSE ≥ 10 m | High | Low | TBD | TTA ≥ 30 s | Liability relevant |
Infrastructure charging | HNSE ≥ 10 m | High | High | TBD | TTA ≥ 30 s | Liability relevant |
Hazardous cargo monitoring | 1 m < HNSE < 10 m | High | High | TBD | 10 s < TTA < 30 s | Liability relevant |
Passenger information | HNSE < 100 mALTE < 5 m | 95% | N/A | TBD | N/A | Non-safety and non-liability relevant |
Parameter | VN-100 | VN-200 | VN-300 |
---|---|---|---|
IMU | Yes | Yes | Yes |
Magnetic heading | Yes | Yes | Yes |
INS | Yes | Yes | Yes |
GNSS compass | No | No | Yes |
Navigation Parameter | VN-100 | VN-200 | VN-300 |
---|---|---|---|
Range (heading, roll) | ±180° | ±180° | ±180° |
Range (pitch) | ±90° | ±90° | ±90° |
Static accuracy (heading, GPS compass) | - | - | 0.3° RMS |
Static accuracy (heading, magnetic) | 2° RMS | 2° RMS | - |
Static accuracy (pitch/roll) | 0.5° RMS | 0.5° RMS | 0.5° RMS |
Dynamic accuracy (heading, true inertial) | 2° RMS | 0.3° RMS | 0.3° RMS |
Dynamic accuracy (pitch/roll) | 1° RMS | 0.1° RMS | 0.1° RMS |
Static accuracy (pitch/roll, after dynamic alignment) | - | 0.1° RMS | 0.1° RMS |
Angular resolution | <0.05° | <0.05° | <0.05° |
Angular repeatability | <0.2° | <0.1° | <0.1° |
Horizontal position accuracy | - | 2.5 m RMS | 2.5 m RMS |
Horizontal position accuracy (w/SBAS) | - | 2 m RMS | 2 m RMS |
Vertical position accuracy | - | 5 m RMS | 5 m RMS |
Vertical position accuracy (w/barometric pressure sensor) | - | 2.5 m RMS | 2.5 m RMS |
Position resolution | - | 1 mm | 1 mm |
Velocity accuracy | - | ±0.05 m/s | ±0.05 m/s |
Velocity resolution | - | 1 mm/s | 1 mm/s |
Output rate (IMU data) | 800 Hz | 800 Hz | 800 Hz |
Output rate (navigation data) | 400 Hz | 400 Hz | 400 Hz |
Accuracy Measure | Dimension | Probability | Definition |
---|---|---|---|
RMS | 1D | 68% | The root mean squared error calculated for φ, λ or h. |
DRMS | 2D | 63–68% | The distance root mean squared error calculated for φ, λ, (h). |
3D | |||
2DRMS | 2D | 95–95% | Twice the DRMS. |
3D | |||
CEP | 2D | 50% | The radius of circle centred at the true position, containing the position estimate with probability of 50%. |
SEP | 3D | 50% | The radius of sphere centred at the true position, containing the position estimate with probability of 50%. |
R68 | 2D | 68% | The radius of circle (sphere) centred at the true position, containing the position estimate with probability of 68%. |
3D | |||
R95 | 2D | 95% | The radius of circle (sphere) centred at the true position, containing the position estimate with probability of 95%. |
3D |
Statistics of Position Error | Section No. 1 | Section No. 5 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
V = 40 km/h | V = 80 km/h | V = 100 km/h | V = 40 km/h | V = 80 km/h | V = 100 km/h | |||||||
VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | |
Number of measurements | 154 | 74 | 52 | 140 | 73 | 48 | ||||||
RMS (h) | 6.88 m | 0.32 m | 5.34 m | 0.37 m | 5.01 m | 0.62 m | 6.88 m | 0.32 m | 5.34 m | 0.37 m | 5.01 m | 0.62 m |
DRMS (2D) | 3.61 m | 1.54 m | 2.83 m | 1.19 m | 2.28 m | 1.19 m | 3.61 m | 1.54 m | 2.83 m | 1.19 m | 2.28 m | 1.19 m |
2DRMS (2D) | 7.22 m | 3.07 m | 5.65 m | 2.37 m | 4.57 m | 2.38 m | 7.22 m | 3.07 m | 5.65 m | 2.37 m | 4.57 m | 2.38 m |
DRMS (3D) | 7.77 m | 1.57 m | 6.05 m | 1.24 m | 5.51 m | 1.34 m | 7.77 m | 1.57 m | 6.05 m | 1.24 m | 5.51 m | 1.34 m |
CEP (2D) | 3.42 m | 1.54 m | 2.87 m | 1.14 m | 2.27 m | 1.14 m | 3.42 m | 1.54 m | 2.87 m | 1.14 m | 2.27 m | 1.14 m |
R68 (2D) | 4.10 m | 1.57 m | 3.09 m | 1.19 m | 2.53 m | 1.16 m | 4.10 m | 1.57 m | 3.09 m | 1.19 m | 2.53 m | 1.16 m |
R95 (2D) | 4.58 m | 1.85 m | 3.44 m | 1.28 m | 3.11 m | 1.42 m | 4.58 m | 1.85 m | 3.44 m | 1.28 m | 3.11 m | 1.42 m |
SEP (3D) | 8.01 m | 1.56 m | 5.88 m | 1.21 m | 5.12 m | 1.26 m | 8.01 m | 1.56 m | 5.88 m | 1.21 m | 5.12 m | 1.26 m |
R68 (3D) | 8.22 m | 1.60 m | 6.61 m | 1.25 m | 6.84 m | 1.38 m | 8.22 m | 1.60 m | 6.61 m | 1.25 m | 6.84 m | 1.38 m |
R95 (3D) | 9.90 m | 1.87 m | 8.06 m | 1.39 m | 8.24 m | 1.48 m | 9.90 m | 1.87 m | 8.06 m | 1.39 m | 8.24 m | 1.48 m |
Statistics of Position Error | Section No. 2 | Section No. 4 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
V = 40 km/h | V = 80 km/h | V = 100 km/h | V = 40 km/h | V = 80 km/h | V = 100 km/h | |||||||
VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | |
Number of measurements | 220 | 103 | 84 | 237 | 111 | 93 | ||||||
RMS (h) | 5.43 m | 0.33 m | 8.63 m | 0.78 m | 8.57 m | 0.85 m | 3.98 m | 0.36 m | 6.00 m | 0.52 m | 6.93 m | 0.76 m |
DRMS (2D) | 2.44 m | 1.14 m | 3.15 m | 1.27 m | 2.57 m | 1.05 m | 3.17 m | 0.82 m | 2.19 m | 0.82 m | 2.22 m | 0.76 m |
2DRMS (2D) | 4.87 m | 2.29 m | 6.31 m | 2.53 m | 5.14 m | 2.11 m | 6.33 m | 1.64 m | 4.37 m | 1.65 m | 4.44 m | 1.53 m |
DRMS (3D) | 5.95 m | 1.19 m | 9.19 m | 1.49 m | 8.94 m | 1.35 m | 5.08 m | 0.90 m | 6.38 m | 0.97 m | 7.28 m | 1.08 m |
CEP (2D) | 2.39 m | 1.12 m | 3.42 m | 1.25 m | 2.79 m | 0.97 m | 2.89 m | 0.79 m | 1.90 m | 0.81 m | 2.07 m | 0.74 m |
R68 (2D) | 2.62 m | 1.18 m | 3.62 m | 1.31 m | 2.96 m | 1.13 m | 3.10 m | 0.84 m | 2.30 m | 0.88 m | 2.31 m | 0.79 m |
R95 (2D) | 3.39 m | 1.46 m | 3.95 m | 1.46 m | 3.13 m | 1.35 m | 4.59 m | 1.06 m | 3.30 m | 1.02 m | 3.20 m | 0.85 m |
SEP (3D) | 6.01 m | 1.12 m | 9.29 m | 1.31 m | 9.62 m | 1.20 m | 4.68 m | 0.87 m | 7.04 m | 0.95 m | 7.93 m | 1.08 m |
R68 (3D) | 6.79 m | 1.21 m | 9.62 m | 1.60 m | 10.02 m | 1.32 m | 5.37 m | 0.95 m | 7.26 m | 1.05 m | 8.65 m | 1.12 m |
R95 (3D) | 7.84 m | 1.57 m | 10.57 m | 1.96 m | 10.74 m | 1.91 m | 8.61 m | 1.17 m | 8.00 m | 1.26 m | 8.90 m | 1.19 m |
Statistics of Position Error | First Series | Second Series | Third Series | |||
---|---|---|---|---|---|---|
VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | |
Number of measurements | 96 | 80 | 100 | |||
RMS (h) | 5.10 m | 0.34 m | 6.04 m | 0.22 m | 5.22 m | 0.91 m |
DRMS (2D) | 2.59 m | 0.99 m | 2.75 m | 0.95 m | 2.42 m | 0.94 m |
2DRMS (2D) | 5.18 m | 1.97 m | 5.49 m | 1.91 m | 4.84 m | 1.88 m |
DRMS (3D) | 5.72 m | 1.04 m | 6.63 m | 0.98 m | 5.75 m | 1.31 m |
CEP (2D) | 2.34 m | 1.05 m | 2.76 m | 0.97 m | 2.34 m | 0.88 m |
R68 (2D) | 2.56 m | 1.08 m | 2.87 m | 1.03 m | 2.64 m | 1.01 m |
R95 (2D) | 4.25 m | 1.15 m | 3.49 m | 1.13 m | 3.04 m | 1.20 m |
SEP (3D) | 5.35 m | 1.09 m | 6.02 m | 1.02 m | 4.77 m | 1.32 m |
R68 (3D) | 5.57 m | 1.14 m | 7.15 m | 1.07 m | 5.33 m | 1.38 m |
R95 (3D) | 9.68 m | 1.29 m | 9.69 m | 1.14 m | 10.42 m | 1.57 m |
Statistics of Position Error | 1st Series | 2nd Series | ||
---|---|---|---|---|
VN-200 | VN-300 | VN-200 | VN-300 | |
Number of measurements | 41 | 75 | ||
RMS (h) | 5.52 m | 0.41 m | 4.84 m | 0.62 m |
DRMS (2D) | 1.62 m | 1.48 m | 2.40 m | 1.35 m |
2DRMS (2D) | 3.24 m | 2.95 m | 4.80 m | 2.69 m |
DRMS (3D) | 5.76 m | 1.53 m | 5.41 m | 1.48 m |
CEP (2D) | 1.30 m | 1.30 m | 2.37 m | 1.28 m |
R68 (2D) | 1.60 m | 1.52 m | 2.55 m | 1.54 m |
R95 (2D) | 2.57 m | 2.24 m | 3.23 m | 1.85 m |
SEP (3D) | 4.54 m | 1.47 m | 5.30 m | 1.44 m |
R68 (3D) | 6.63 m | 1.53 m | 5.96 m | 1.70 m |
R95 (3D) | 8.91 m | 2.29 m | 8.03 m | 1.98 m |
Statistics of Position Error | V = 120 km/h | |
---|---|---|
VN-200 | VN-300 | |
Number of measurements | 102 | |
RMS (h) | 7.57 m | 0.76 m |
DRMS (2D) | 3.36 m | 1.04 m |
2DRMS (2D) | 6.71 m | 2.07 m |
DRMS (3D) | 8.28 m | 1.28 m |
CEP (2D) | 3.46 m | 0.98 m |
R68 (2D) | 3.79 m | 1.04 m |
R95 (2D) | 3.98 m | 1.32 m |
SEP (3D) | 8.39 m | 1.09 m |
R68 (3D) | 9.14 m | 1.27 m |
R95 (3D) | 9.65 m | 1.77 m |
Statistics of Position Error | 1st Lap | 2nd Lap | 3rd Lap | |||
---|---|---|---|---|---|---|
VN-200 | VN-300 | VN-200 | VN-300 | VN-200 | VN-300 | |
Number of measurements | 888 | 516 | 377 | |||
RMS (h) | 5.33 m | 0.37 m | 6.63 m | 0.58 m | 6.73 m | 0.81 m |
DRMS (2D) | 2.80 m | 1.16 m | 2.62 m | 1.13 m | 2.43 m | 0.99 m |
2DRMS (2D) | 5.60 m | 2.33 m | 5.24 m | 2.26 m | 4.85 m | 1.98 m |
DRMS (3D) | 6.02 m | 1.22 m | 7.13 m | 1.27 m | 7.15 m | 1.28 m |
CEP (2D) | 2.54 m | 1.02 m | 2.48 m | 1.07 m | 2.38 m | 0.89 m |
R68 (2D) | 2.90 m | 1.15 m | 2.90 m | 1.19 m | 2.68 m | 1.05 m |
R95 (2D) | 4.52 m | 1.63 m | 3.74 m | 1.80 m | 3.16 m | 1.35 m |
SEP (3D) | 5.57 m | 1.05 m | 7.06 m | 1.14 m | 7.11 m | 1.19 m |
R68 (3D) | 6.97 m | 1.22 m | 7.96 m | 1.26 m | 8.51 m | 1.30 m |
R95 (3D) | 8.91 m | 1.76 m | 9.91 m | 1.96 m | 10.36 m | 1.73 m |
© 2020 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 (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Specht, M.; Specht, C.; Dąbrowski, P.; Czaplewski, K.; Smolarek, L.; Lewicka, O. Road Tests of the Positioning Accuracy of INS/GNSS Systems Based on MEMS Technology for Navigating Railway Vehicles. Energies 2020, 13, 4463. https://doi.org/10.3390/en13174463
Specht M, Specht C, Dąbrowski P, Czaplewski K, Smolarek L, Lewicka O. Road Tests of the Positioning Accuracy of INS/GNSS Systems Based on MEMS Technology for Navigating Railway Vehicles. Energies. 2020; 13(17):4463. https://doi.org/10.3390/en13174463
Chicago/Turabian StyleSpecht, Mariusz, Cezary Specht, Paweł Dąbrowski, Krzysztof Czaplewski, Leszek Smolarek, and Oktawia Lewicka. 2020. "Road Tests of the Positioning Accuracy of INS/GNSS Systems Based on MEMS Technology for Navigating Railway Vehicles" Energies 13, no. 17: 4463. https://doi.org/10.3390/en13174463