(46-2) 14 * << * >> * Russian * English * Content * All Issues

The methodology for obtaining nonlinear and continuous three-dimensional topographic data using inertial and optical measuring instruments of unmanned ground systems
P. Musa 1, I. Purwanto 1, D.A. Christie 1, E.P. Wibowo 1, R. Irawan 2

Faculty of Computer Science and Information Technology, Gunadarma University,
Faculty of Industrial Technology, Gunadarma University,
Indonesia, Jl. Margonda Raya No.100, Pondok Cina, Kecamatan Beji, Kota Depok, Jawa Barat 16424

 PDF, 2343 kB

DOI: 10.18287/2412-6179-CO-915

Pages: 280-297.

Full text of article: English language.

Topography is the study of an area on the earth's surface. This term relates to the land's slope or contour, which is the interval of elevation differences between two adjacent and parallel contour lines. Topography generally presents a three-dimensional model of object surface relief and an identification of land or hilly areas based on horizontal coordinates such as latitude and longitude, and vertical position, namely elevation. The topography is essential information that must be provided in the execution of building or road construction based on the ground contour. The problem which is the ground contour which can provide visualization topography as a three-dimensional (3D) condition of the ground contour is not normal (non-linear). Another problem is that the traditional measurement techniques with wheel rotation only measure distances and cannot represent the trajectory of the ground contour in 3D. The proposed in-depth evaluation of orientation estimation results in the topography accuracy level. This methodology consists of several processes; Inertia and orientation of an object, Distance measurement, Terrestrial topocentric – Euclidean transformation, and Topography visualization. This research designed a prototype and proposed a new visualization method of the ground contours to reconstruct a topography map between three algorithms; Direct Cosine Matrix-3D Coordinate, Madgwick-3D Coordinate, and Complementary Filter. The methodology was tested and evaluated intensively by direct observation at three measurement locations with different difficulty levels. As a result, the Direct Cosine Matrix-3D Coordinate is able to visualize the ground contours by reconstructing a topography map much better than other methods.

topography maps, visualization of a three-dimensional (3D), ground contour, inertia, distance measurement, direct cosine matrix, madgwick algorithms.

Musa P, Purwanto I, Christie DA, Wibowo EP, Irawan R. The methodology for obtaining nonlinear and continuous three-dimensional topographic data using inertial and optical measuring instruments of unmanned ground systems. Computer Optics 2022; 46(2): 280-297. DOI: 10.18287/2412-6179-CO-915.

The work was fully funded and supported by Gunadarma University, Indonesia.


  1. Subaweh MB, Wibowo EP. Implementation of Pixel Based Adaptive Segmenter method for tracking and counting vehicles in visual surveillance. Int Conf on Informatics and Computing (ICIC) 2016: 1-5. DOI: 10.1109/IAC.2016.7905679.
  2. Rostianingsih S, Gunadi K. Pemodelan Peta Topografi ke Objek Tiga Dimensi. Jurnal Informatika University Petra Kristian 2004; 5(1): 14-21. DOI: 10.9744/informatika.5.1.pp.14-21.
  3. Jenks GF, Steinke T, Buchert B, Armstrong L. Illustrating the concepts of the contour symbol, interval, and spacing via 3-D maps. J Geog 1971; 70(5): 280-288. DOI: 10.1080/00221347108981640.
  4. Yu C, Lee J, Munro-Stasiuk MJ. Extensions to least-cost path algorithms for roadway planning. Int J Geogr Inf Sci 2003; 17(4): 361-376. DOI: 10.1080/1365881031000072645.
  5. Wibowo EP, Talita AS, Iqbal M, Mutiara AB, Lu CK, Meriaudeau F. An improved calibration technique for polarization images. IEEE Access 2019; 7: 28651-28662. DOI: 10.1109/ACCESS.2019.2900538.
  6. Purwanto I, Wibowo EP, Christie DA, Musa P, Harahap RK, Irawan R. Comparative performance evaluation of direction cosine matrix and madgwick’s as 3D orientation estimation algorithm. ICIC Express Letter 2021; 15(4): 409-420.
  7. Doh N, Choset H, Chung W. Accurate relative localization using odometry. Conf on Robotics and Automation 2003; 2: 1606-1612. DOI: 10.1109/robot.2003.1241824.
  8. Jin Y, Toh HS, Soh WS, Wong WC. A robust dead-reckoning pedestrian tracking system with low cost sensors. Int Conf on Pervasive Computing and Communications (PerCom) 2011: 222-230. DOI: 10.1109/PERCOM.2011.5767590.
  9. Fathurrochman D, Musa P, Wimananda DD, Lestari OB. Remote sensing system of odometry and telemetry data in real-time. 3rd Int Conf on Informatics and Computing (ICIC) 2018: 1-6. DOI: 10.1109/IAC.2018.8780484.
  10. Fadlillah HM, Musa P, Wimananda DD. Heading correction in rocket flight system using odometry trajectory information. 3rd International Conference on Informatics and Computing (ICIC) 2018. DOI: 10.1109/IAC.2018.8780428.
  11. 11 Best measuring wheels of 2021 reviewed. Source: <https://cdn.architecturelab.net/wp-content/uploads/2020/03/Best-Measuring-Wheels-3.jpg>.
  12. Iafolla L, Filipozzi M, Freund S, Zam A, Rauter G, Cattin PC. Proof of concept of a novel absolute rotary encoder. Sens Actuator A Phys 2020; 312: 112100. DOI: 10.1016/j.sna.2020.112100.
  13. Ključanin S. Inspire specifications in the service of making a topographic map. Geodetski List 2020; 74(4): 373-387.
  14. Rusmanto A. Pedoman Geoparsial Kebijakan Satu Peta [In Indonesian]. Badan Informasi Geospasial 2018. Source: <https://portalksp.ina-sdi.or.id/Buku_Pedoman_Geoportal%20KSP.pdf>.
  15. Nurwadjedi N, Rosalina L, Wibisono Y. Membangun Satu Peta Untuk Penataan Ruang [In Indonesian]. Seminar Nasional Geomatika 2019; 3: 157-166. DOI: 10.24895/sng.2018.3-0.946.
  16. Kluykov AA, KrylovVI. Space geodesy: Past, present and future. To the 50th anniversary of the first set of students MIIGAiK on specialty "Space Geodesy" [In Russian]. Geodezy and Cartography 2019; 80(3): 48-56. DOI: 10.22389/0016-7126-2019-945-3-48-56.
  17. Savinikh VP, Krasnorylov II, Shlapak VV. Training engineers of space geodesy in the MIIGAiK [In Russian]. Geodezy and Cartography 2014; (5): 30-34. DOI: 10.22389/0016-7126-2014-887-5-30-34.
  18. Makarov AP, Chibunichev AG, Poliakova EV. Application of robotic system for obtaining information about the area. ISPRS Archives 2020; XLIII-B2-2020: 611-616. DOI: 10.5194/isprs-archives-XLIII-B2-2020-611-2020.
  19. Liu T, Xu P, Zhang S. A review of recent advances in scanned topographic map processing. Neurocomputing 2019; 328: 75-87. DOI: 10.1016/j.neucom.2018.02.102.
  20. Islami N. The use of online media and topography map in the topic of landslide natural disaster, advanced earth physics course. International Journal of Educational Best Practices 2019; 3(2): 1-9. DOI: 10.31258/ijebp.v3n2.p1-9.
  21. Pawlus P, Reizer R, Wieczorowski M. A review of methods of random surface topography modeling. Tribol Int 2020; 152: 106530. DOI: 10.1016/j.triboint.2020.106530.
  22. Arraigada M, Partl M. Calculation of displacements of measured accelerations, analysis of two accelerometers and application in road engineering. Swiss Transport Research Conference 2006: I-II, 3-30.
  23. Doumiati M, Victorino A, Charara A, Lechner D. Estimation of road profile for vehicle dynamics motion: Experimental validation. American Control Conference 2011: 5237-5242. DOI: 10.1109/acc.2011.5991595.
  24. Cariow A, Cariowa G, Majorkowska-Mech D. An algorithm for quaternion-based 3D rotation. Int J Appl Math Comput Sci 2020; 30(1): 149-160. DOI: 10.34768/amcs-2020-0012.
  25. Corrales-Rodrigáñez C. Rotations and units in quaternion algebras. J Number Theory 2012; 132(5): 888-895. DOI: 10.1016/j.jnt.2011.12.009.
  26. Sarabandi S, Thomas F. A survey on the computation of quaternions from rotation matrices. J Mech Robot 2019; 11(2): JMR-18-1163. DOI: 10.1115/1.4041889.
  27. Chudá H. Universal approach to derivation of quaternion rotation formulas. MATEC Web of Conferences 2019; 292: 01060. DOI: 10.1051/matecconf/201929201060.
  28. Terzakis G, Lourakis M, Ait-Boudaoud D. Modified Rodrigues parameters: An efficient representation of orientation in 3D vision and graphics. J Math Imaging Vis 2018; 60(3): 422-442. DOI: 10.1007/s10851-017-0765-x.
  29. Hamilton WR. Theory of quaternions. Proceedings of the Royal Irish Academy (1836-1869) 1844; 13(48): 1-16. Source: <https://www.jstor.org/stable/20489494>.
  30. Griffin S. Quaternions: Theory and applications (Mathematics research developments). Nova Science Publishers Inc; 2017.
  31. Xu FN, Wang B, Deng ZC, Li QJ, Wei Y. Attitude control of targets captured by tethered space robots based on the quaternion theory. Appl Math Mech 2017; 38(12): 1309-1318. DOI: 10.21656/1000-0887.380168.
  32. Ramasubramani V, Glotzer SC. rowan: A Python package for working with quaternions. J open source softw 2018; 3(27): 787. DOI: 10.21105/joss.00787.
  33. Vince J. Calculus for computer graphics. Springer International Publishing; 2019.
  34. Bektaş DemIrcI B, Aghayev N. On geometric applications of quaternions. Turkish J Math 2020; 44(4): 1289-1303. DOI: 10.3906/MAT-1907-120.
  35. Baek J, Jeon H, Kim G, Han S. Visualizing quaternion multiplication. IEEE Access 2017; 5: 8948-8955. DOI: 10.1109/ACCESS.2017.2705196.
  36. Novelia A, O’Reilly OM. On geodesics of the rotation group SO(3). Regul Chaotic Dyn 2015; 20(6): 729-738. DOI: 10.1134/S1560354715060088.
  37. Bennett A, Kindratenko V. Quaternion C++ class. Source: <www.ncsa.illinois.edu/People/kindr/emtc/quaternions/>.
  38. Lee D, Pernicka H. Vision-based relative state estimation using the unscented kalman filter. Int J Aeronaut Space Sci 2011; 12(1): 24-36. DOI: 10.5139/IJASS.2011.12.1.24.
  39. Zivan Y, Choukrouny D. Dual quaternion kalman filters for spacecraft relative navigation. AIAA Guidance, Navigation, and Control Conference 2018: 1-29. DOI: 10.2514/6.2018-1347.
  40. Na Y, Bang H, Mok SH. Vision-based relative navigation using dual quaternion for spacecraft proximity operations. Int J Aeronaut Space Sci 2019; 20(4): 1010-1023. DOI: 10.1007/s42405-019-00171-8.
  41. Razgus B, Mooij E, Choukroun D. Relative navigation in asteroid missions using dual quaternion filtering. J Guid Control Dyn 2017; 40(9): 2151-2166. DOI: 10.2514/1.G002805.
  42. Chelnokov YN. Inertial navigation in space using the regular quaternion equations of astrodynamics. Mechanics of Solids 2019; 54(2): 157-168. DOI: 10.3103/S0025654419030063.
  43. Musa P, Christie DA, Wibowo EP. An implementation of direction cosine matrix in rocket payload dynamics attitude monitoring. Int Conf on Informatics and Computing (ICIC) 2016: 271-276. DOI: 10.1109/IAC.2016.7905728.
  44. Fernández JRM, Junco AH. Design and implementation of an Attitude and Heading Reference System (AHRS) using Direction Cosine Matrix. Revista Cubana de Ciencias Informáticas 2017; 11(1): 15-28.
  45. Tuck K. Implementing auto-zero calibration technique for accelerometers. Freescale Semiconductor Inc; 2007. Source: <https://forum.pololu.com/uploads/default/original/2X/7/7f6a6201387635b3597e5b19cdb692250e0e3260.pdf>.
  46. Li Q, Griffiths JG. Least squares ellipsoid specific fittin. Proc Geometric Modeling and Processing 2004: 335-340. DOI: 10.1109/gmap.2004.1290055.
  47. Shenoi BA. Introduction to digital signal processing and filter design. Hoboken, New Jersey: John Wiley and Sons Inc; 2005.
  48. Premerlani W, Bizard P. Direction cosine matrix imu: Theory. Diy Drone Usa 2009; 13-15. Source: <https://owenson.me/build-your-own-quadcopter-autopilot/DCMDraft2.pdf>.
  49. Wang Y. Rajamani R. Direction cosine matrix estimation with an inertial measurement unit. Mech Syst Signal Process 2018; 109: 268-284. DOI: 10.1016/j.ymssp.2018.02.038.
  50. Madgwick SOH. An efficient orientation filter for inertial and inertial/magnetic sensor arrays. 2010. Source: <https://www.samba.org/tridge/UAV/madgwick_internal_report.pdf>.
  51. Albab AN, Rahmawati E, Yantidewi M, Sucahyo I, Firmansyah RR. Control position of mobile robot based on odometry method and PID controller. J Phys: Conf Ser 2020; 1491(1): 1-7. DOI: 10.1088/1742-6596/1491/1/012039.
  52. Krakiwsky AJ, Wells DE. Coordinate systems in geodesy. Department of Geodesy and Geomatics Engineering, University of New Brunswick 1971. Source: <http://www2.unb.ca/gge/Pubs/LN16.pdf>.
  53. Altamimi Z, Gross R. Geodesy. In Book: Springer handbook of global navigation satellite systems. New York: Springer; 2017: 1039-1061. DOI: 10.1007/978-3-319-42928-1_36.
  54. Ormeling F. Cartography. The ideal and its history. Int J Cartogr 2021: 1-4. DOI: 10.1080/23729333.2021.1890343.
  55. Węgrzyn M, Mościcka A. CityGuideTour Toruń – tourist application using augmented reality. Geodesy Cartogr 2017; 66(2): 317-331. DOI: 10.1515/geocart-2017-0018.
  56. Marino L, Cicirello A. Experimental investigation of a single-degree-of-freedom system with Coulomb friction. Nonlinear Dyn 2020; 99: 1781-1799. DOI: 10.1007/s11071-019-05443-2.
  57. Jiang J, Newman ST, Zhong RY. A review of multiple degrees of freedom for additive manufacturing machines. Int J Comput Integr Manuf 2021; 34(2): 195-211. DOI: 10.1080/0951192X.2020.1858510.
  58. Friedman JH, Bentley JL, Finkel RA. An algorithm for finding best matches in logarithmic expected time. ACM Trans Math Softw 1977; 3(3): 209-226. DOI: 10.1145/355744.355745.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20