Skip to main content
Log in

Nonlinear filtering for map-aided navigation. Part 1. An overview of algorithms

  • Published:
Gyroscopy and Navigation Aims and scope Submit manuscript

Abstract

A map-aided navigation method is considered. The main features of this method are discussed; an overview of the algorithms used to solve navigation problems is given. Considerable attention is focused on the algorithms based on the use of nonlinear filtering, which make it possible to not only formulate and solve the problem of algorithm design, but also provide a background for accuracy analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Nygren, I., Terrain navigation for vehicles, Dissertation, Sweden: Stockholm Royal Institute of Technology, 2005. 270 p.

    Google Scholar 

  2. Karlsson, R. and Gustafsson, F., Bayesian surface and underwater navigation, IEEE Trans. Signal Processing, 2006. vol. 54 (11), pp. 4204–4213.

    Article  MathSciNet  Google Scholar 

  3. Berdyshev, V.I. and Kostousov, V.B., Ekstremal’nye zadachi i modeli navigatsii po geofizicheskim polyam (Extremal Problems and Models of Navigation by Geophysical Fields), Ekaterinburg: UrO RAN, 2007.

    Google Scholar 

  4. Teixeira, F., Terrain-aided navigation and geophysical navigation of autonomous underwater vehicles: PhD 1 Ji-Thesis, Instituto Superior Técnico Universidade Técnica de Lisboa, 2007. 177 p.

    Google Scholar 

  5. Richeson, J.A., Gravity gradiometer aided inertial navigation within non-GNSS environments: Dissertations, USA Washington: University of Maryland, 2008. 438 p.

    Google Scholar 

  6. Antyufeev, V.I., Bykov, V.N., Grichanyiuk, A.M., Krayushkin, V.A., and Gakhov, R.P., Primenenie printsipov radiometrii v korrelyatsionno-ekstremal’nykh sistemakh navigatsii letatel’nykh apparatov (Applying the Principles of Radiometry in Correlation-Extremal Navigation Systems of Aircraft), Moscow: Fizmatlit, 2009.

    Google Scholar 

  7. Veremeenko, K.K., Zheltov, S.Yu., Kim, N.V., Sebryakov, G.G., and Krasil’shchikov, M.N., Sovremennye informatsionnye tekhnologii v zadachakh navigatsii i navedeniya bespilotnykh manevrennykh letatel’nykh apparatov (Modern Information Technologies in Problems of Navigation and Guidance of Maneuverable Unmanned Aerial Vehicles), Krasil’shchikov, M.N. and Serebryakov, G.G., Eds., Moscow: Fizmatlit, 2009.

  8. Syryamkin, V.I. and Shidlovskii, V.S., Korreliatsionnoekstremal’nye radionavigatsionnye sistemy (CorrelationExtremal Radionavigation Systems), Tomsk: Izd. Tomskogo universiteta, 2010.

    Google Scholar 

  9. Carreno S., Wilson, P., Ridao, P., and Petillot, Y, Asurvey on terrain based navigation for AUVs, OCEANS 2010 MTS/IEEE, 2010. pp. 1–7.

    Chapter  Google Scholar 

  10. Pavlov, B.V., Volkovitskii, A.K., and Karshakov, E.V. Low frequency electromagnetic system of relative navigation and orientation, Gyroscopy and Navigation, July, 2010, vol. 1, no. 3, pp. 201–208.

    Article  Google Scholar 

  11. Afzal, M.H., Use of Earth’s magnetic field for pedestrian navigation: Dissertation, Canada: University of Calgary, 2011. 247p.

    Google Scholar 

  12. Shcherbinin, V.V., Postroenie invariantnykh korreliatsionno-ekstremal’nykh sistem navigatsii i navedeniya letatel’nykh apparatov (Design of Invariant Correlation-Extremal Navigation and Guidance Systems of Aircraft), Moscow: MGTU im. N.E. Baumana, 2011.

    Google Scholar 

  13. Meduna, D.K., Terrain relative navigation for sensorlimited systems with application to underwater vehicles: Dissertation, USA: Stanford University, 2011. 183 p.

    Google Scholar 

  14. Beloglazov, I.N., Kazarin, S.N., and Kos’yanchuk, V.V., Obrabotka informatsii v ikonicheskikh sistemakh navigatsii, navedeniia i distantsionnogo zondirovaniya mestnosti (Information Processing in the Iconic Systems of Guidance, Navigation and Earth Remote Sensing), Moscow: Fizmatlit, 2012.

    Google Scholar 

  15. Shockley, J.A., Ground vehicle navigation using magnetic field variation: PhD thesis, Air Force Institute of Technology, Ohio, 2012. 186 p.

    Google Scholar 

  16. Klyueva, S.F. and Zav’yalov, V.V., Sintez algoritmov batimetricheskikh sistem navigatsii (Designing Algorithms for Bathymetric Navigation Systems), Vladivostok: Morskoi gos. universitet, 2013.

    Google Scholar 

  17. Davidson, P., Algorithm for autonomous personal navigation systems: Dissertation, Finland: Tampere University of Technology, 2013. 95 p.

    Google Scholar 

  18. Toropov, A.B., Filtering algorithms in problems of marine navigation system position error correction with using nonlinear measurements, Cand. Sci. Dissertation, St. Petersburg: GNTs RFTsNII Elektropribor, 2013. 147 p.

    Google Scholar 

  19. Dhzandzhgava, G.I., Gerasimov, G.I., and Avgustov, L.I., Navigation and homing by spatial geophysical fields, Izvestiya Yuzhnogo Federal.Universiteta, Engineering Sciences, 2013. no. 3 (140) pp. 74–83.

    Google Scholar 

  20. Medvedev, G.A., and Tarasenko, V.P., Veroyatnostnye metody issledovaniya ekstremal’nykh system (Probabilistic Methods for Studying Extreme Systems), Moscow: Nauka, 1967.

    Google Scholar 

  21. Kozubovskii, S.F., Korreliatsionno-ekstremal’nye sistemy: Spravochnik (Correlation-Extreme Systems: Reference Book), Kiev: Naukova dumka, 1973.

    Google Scholar 

  22. Beloglazov, I.N. and Tarasenko, V.P., Korreliatsionnoekstremal’nye sistemy (Correlation-Extreme Systems), Moscow: Sov. radio, 1974.

    Google Scholar 

  23. Alekseev, V.I., Korikov A.M., Polonnikov, R.I., and Tarasenko, V.P., Ekstremal’naya radionavigatsiya (Extremal Radio Navigation), Polonnikov, R.I. and Tarasenko, V.P., Eds., Moscow: Nauka, 1978.

  24. Chigin, G.P., Simulation of an optimal correlation system, Izv. AN SSR. Tekhnicheskaya kibernetika, 1978, no. 2, pp. 182–192.

    Google Scholar 

  25. Rzhevkin, V.A., Autonomous navigation using local maps, Zarubezhnaya radioelektronika, 1981, no. 10, pp. 3–28.

    Google Scholar 

  26. Silaev, A.I., Stefanov, V.A., and Chigin, G.P., Combined estimation algorithm in correlation-extremal navigation systems, Izvestiya ANSSSR. Tekhnicheskaya kibernetika, 1984, no. 6, pp. 12–16.

    Google Scholar 

  27. Baklitskii, V.K., Bochkarev, A.V., and Mus’yankov, M.P., Metody fil’tratsii signalov v korrelyatsionno-ekstremal’nykh sistemakh (Methods of Filtering Signals in Correlation-Extreme Systems), Moscow: Radio i svyaz, 1986.

    Google Scholar 

  28. Shcherbatyuk, A.F., Searchless correlation-extreme correction algorithms for vehicle position correction using the field relief, Sb. Korrektsiya v navigatsionnykh sistemakh i sistemakh orientatsii ISZ (Correction in Satellite Navigation and Orientation Systems), Moscow: Izd. MGU, 1986. pp. 40–48.

    Google Scholar 

  29. Buimov, A.G., Korrelyatsionno-ekstpemal’naya obrabotka izobrazhenii (Correlation-Extreme Image Processing). Tomsk: Izd. Tomskogo universiteta, 1987.

    Google Scholar 

  30. Chigin, G.P., Using a field of reference lines in extreme navigation problems, Izvestiya Academii Nauk. Teoriya i sistemi upravleniya, 1998. no. 2, pp. 161–172.

    Google Scholar 

  31. Solunin, V.L., Gursky, B.G. and Spirin, E.P., Correlation-extremal systems for aircraft high accuracy navigation and computer diagnostics of complicated faults, Giroskopiya i Navigatsiya, 2005, no. 2, pp. 56–61.

    Google Scholar 

  32. Kosyachenko, S.A. and Naumov, A.I., Algorithms for searching the global extremum of the search algorithm functional of a correlation-extreme navigation system with simultaneous estimation of position and velocity errors, Materialy X konferentsii molodykh uchenykh “Navigatsiya i upravlenie dvizheniem” (Proceedings of the 10th Conference of Young Scientists “Navigation and Motion Control”), 2008. pp. 395–402.

    Google Scholar 

  33. Beloglazov, I.N., Kazarin S.N., Merkulov V.A., and Naumov, A.I., Accuracy estimation of the reference information for terrain aided navigation systems, Informatsionno-izmeritel’nye i upravlyayushchie sistemy, 2010, vol. 8, no. 4, pp. 9–14.

    Google Scholar 

  34. Stepanov, O.A. and Toropov, A.B., Sequential Monte Carlo methods for terrain-aided navigation, Izv. vuzov. Priborostroenie, 2010, vol. 53, no. 10, pp. 49–54.

    Google Scholar 

  35. Scherbinin, V.V., Shevtsova, E.V., Vasil’eva, Yu.S., and Chizhevskaya, O.M., Functioning methods and algorithms of color vision-based correlation-extremal aircraft navigation system, Gyroscopy and Navigation, 2013. vol. 4, no. 1, pp 39–49.

    Article  Google Scholar 

  36. Volkovitsky, A.K., Karshakov, E.V., Moilanen, E.V., and Pavlov B.V., Integration of magnetic gradiometer correlation-extremal and inertial navigation systems, Proc. 19th Saint-Petersburg International Conference on Integrated Navigation Systems, 2012. pp. 182–184.

    Google Scholar 

  37. Stepanov, O.A., Sokolov, A.V., Toropov, A.B., Vasil’ev, V.A., and Krasnov, A.A., Selecting informative trajectories in the problem of correlation-extreme navigation with account for the errors of map and sensors, Materialy XXIX konferentsii pamyati vydayushchegosya konstruktora giroskopicheskikh priborov N.N. Ostryakova (Proceedings of the 29th Conference in Memory of N.N. Ostryakov), St. Petersburg, 2014. pp. 217–225.

    Google Scholar 

  38. Miller, R., Correlation radio electronic system for aircraft and spacecraft, Elektronika, 1961. no. 50.

  39. Hinrichs, R., Advance terrain correlation techniques, IEEE, PLAN’S-76, 1976, pp. 76–89.

    Google Scholar 

  40. Hessel, A. and Eckle, W., Precision navigation updating by means of digital area correlation, Journal of Navigation, vol. 30, no. 2, 1977. pp. 296–30.

    Article  Google Scholar 

  41. Reed, C.G. and Hogan, J., Range correlation guidance for cruise missiles, IEEE Trans. Aerospace and Electr. Sys., 1979. vol. AES-15, no. 4, pp. 547–555.

    Article  Google Scholar 

  42. Bialecke, E.P. and Lewis, R.C., A digital terrain correlation system for tactical aircraft, Proc. IEEE /AIAA Digital Avionics Systems Conference, Seattle, 1983.

    Google Scholar 

  43. Boozer, D.D. and Fellerhoff, J.R., Terrain aided navigation test results in the AFIT/F-16 Aircraft, Navigation, 1988, vol. 35, no. 2, pp. 161–175.

    Article  Google Scholar 

  44. Lux, D. and Eibert, D.M, ISS-A combined terrain topography reference navigation system, IEEE, PLAN’S-90, 1990. pp. 470–473.

    Google Scholar 

  45. Boozer, D.D., Terrain referenced navigation, Aerospace Navigation Systems, 1995. pp. 152–157.

    Google Scholar 

  46. Hollowell, J., Heli/SITAN: A Terrain referenced navigation algorithm for helicopters, IEEE PLAN’S-90, 1990. pp. 616–625.

    Google Scholar 

  47. Henley, A.J., Terrain aided navigation: current status, techniques for flat terrain and reference data requirements, IEEE PLAN’S-90, 1990. pp. 608–615.

    Google Scholar 

  48. Priestley, N., Terrain referenced navigation, PLAN’S90, 1990. pp. 482–489.

    Google Scholar 

  49. Snyder, F.B., Baird, C.A., and Beierle, L.M., Terrain aided altitude computations on the AFTI/F-16, PLAN’S-90, 1990. pp. 474–481.

    Google Scholar 

  50. Johnson, N., Tang, W., and Howell, G., Terrain aided navigation using maximum a posteriori estimation, PLAN’S-90, 1990. pp. 464–46.

    Google Scholar 

  51. Bar-Gill, A., Ben-Ezra, P., and Bar-Itzhack, I.Y., Improvement of terrain-aided navigation via trajectory optimization, IEEE Trans. on Control Syst. Tech., 1994, vol. 2, no. 4, pp. 336–342.

    Article  Google Scholar 

  52. Enns, R. and Morrell, D., Terrain-aided navigation using the Viterbi algorithm, Joumal of Guidance Control and Dynamics, 1995, vol. 18, no. 6, pp. 1444–1449.

    Article  Google Scholar 

  53. Massa, D.E., Terrain-relative navigation for autonomous underwater vehicles: Dissertation. USA, Massachusetts Institute of Technology, 1997. 147 p.

    Google Scholar 

  54. Bachmann, A. and Williams, S.B., Terrain aided underwater navigation: A deeper insight into generic Monte Carlo localization, Australian Conference on Robotics and Automation 2003 (ACRA) 2003, pp. 1–7.

    Google Scholar 

  55. Metzger, J., Meister, O., and Trömmer. G.F., Covariance estimation for terrain referenced navigation with a comparison technique, Proc. the ION 60th Annual Meeting 2004, pp. 571–580.

    Google Scholar 

  56. Campbell, J., de Haag, M.U., and van Graas, F., Terrain referenced navigation using airborne LAser SCAnner (ALASCA): Preliminary flight test results, Proc. 60th Annual Meeting of The Institute of Navigation, 2004. pp. 671–678.

    Google Scholar 

  57. Metzger, J., Trömmer, G.F., Kreutz, P., and Taddiken, B., Acquisition and tracking improvement by an enhanced comparison based terrain referenced navigation method, Proc. ION 61st Annual Meeting, June 27–29, 2005. pp. 970–975.

    Google Scholar 

  58. Carlstrom, J. and Nygren, I., Terrain navigation of the Swedish AUV62f vehicle, International Symposium on UUST05, Durham, 2005. www.ee.kth.se/php/modules/publications/reports/2005/IR-S3-SB-0560.pdf.

    Google Scholar 

  59. Oliveira, P., MMAE terrain reference navigation for underwater vehicles using eigen analysis, Proc. 44th IEEE Conference on Decision and Control and the European Control Conference, 2005. pp. 5468–5473.

    Chapter  Google Scholar 

  60. Meduna, D.K., Rock, S.M., and McEwen, R., AUV terrain relative navigation using coarse maps, Unmanned Untethered Submersible Technology Conference, 2009. pp. 1–11.

    Google Scholar 

  61. Morice, C., Veres, S., and McPhail, S., Terrain referencing for autonomous navigation of underwater vehicles, Oceans, 2009. pp. 1–7.

    Google Scholar 

  62. Leines, M.T. and Raquet, M.T., Terrain referenced navigation using SIFT features in LiDAR range-based data, Proc. 2015 International Technical Meeting of the Institute of Navigation, 2015. pp. 239–250.

    Google Scholar 

  63. Nordlund, P-J. and Gustafsson, F., Recursive estimation of three-dimensional aircraft position using terrain-aided positioning, IEEE International Conference on Acoustics Speech and Signal Processing, 2002. pp. 1121–1124.

    Google Scholar 

  64. May, M.B., Gravity navigation, IEEE PLAN’S-78, 1978. pp. 212–218.

    Google Scholar 

  65. D’Appolito, J.A., Griffiths, B.E., and Healy, R.D., Gravity navigation performance analysis using the optimal linear correlation technique, IEEE PLAN’S-80, 1980. pp. 101–105.

    Google Scholar 

  66. Andreev, V.D., Ivanishcheva, E.I., and Popov, E.I., Pribory i metody obrabotki graviinertsial’nykh izmerenii (On the theory of gravi-inertial systems), 1984. pp. 98–109.

    Google Scholar 

  67. Gleason, D.M., Passive airborne navigation and terrain avoidance using gravity gradiometry, Journal of Guidance Control and Dynamics, 1995, no. 6, pp. 1450–1458.

    Article  Google Scholar 

  68. Lowrey, J. III and Shellenbarger, J.C., Passive navigation using inertial navigational sensors and maps, Naval Engineering Journal, 1997. pp. 245–24.

    Google Scholar 

  69. Moryl, J., Rice, H., and Shinners, S., The universal gravity module for enhanced submarine navigation, Proc. IEEE, Position Location and Navigation Symposium, 1998. pp. 324–331.

    Google Scholar 

  70. Timney, T.E., Mayhall, R.E., and Lowrey, J. III, Bounding the errors of the marine inertial navigator by employing an array of algorithms encompassed in the triad passive navigation (TPN) software, Proc. of Position Location and Navigation Symposium, 2000. pp. 193–200.

    Google Scholar 

  71. Wang, F., Wen, X., and Sheng, D., Observability analysis and simulation of passive gravity navigation system, Journal of Computers, 2013. vol. 8, n. 1. pp. 248–255.

    Google Scholar 

  72. Smoller, Yu.L., Yurist, S.Sh., Fedorova, I.P., Bolotin, Yu.V., Golovan, A.A., Koneshov, V.N., Hewison, W., Richter, T., Greenbaum, J., Young, D., and Blankenship, D., Using airborne gravimeter GT2A in polar areas, IAG Symposium on Terrestrial Gravimetry: Static and Mobile Measurements. St. Petersburg, Russia, 2013.

    Google Scholar 

  73. Krasnov, A.A., Sokolov, A.V., and Elinson, L.S., A New air-sea gravimeter of the Chekan series, Gyroscopy and Navigation, 2014, no. 3, pp. 181–185.

    Article  Google Scholar 

  74. Peshekhonov, V.G., Sokolov, A.V., Elinson, L.S., and Krasnov, A.A., A new air-sea gravimeter: development and test results, Proc. 22nd Saint-Petersburg International Conference on Integrated Navigation Systems, 2015. pp. 193–199.

    Google Scholar 

  75. Mikhlin, B.Z., Seleznev, V.P., and Seleznev A.V., Geomagnitnaya navigatsiya (Geomagnetic Navigation), Moscow: Mashinostroenie, 1976.

    Google Scholar 

  76. Gur’ev, I.S., daptivnye magnitometricheskie sistemy kontrolya prostranstvennogo polozheniya (Adaptive magnetometric attitude control systems), Moscow: Energoatomizdat, 1985.

  77. Tyren, C., Magnetic terrain navigation, 5th International Symposium on Unmanned Untethered Submersible Technology, 1987, vol. 5, pp. 245–256.

    Google Scholar 

  78. Kiselev, S.K., Extremal correlative navigation over a field of magnetic anomalies of stretched reference points, Journal of Computer and Systems Sciences International, 1997, vol. 36, no. 6, pp. 887–892.

    MATH  Google Scholar 

  79. Goldenberg, F., Geomagnetic navigation beyond the magnetic compass, Proc. IEEE/ION PLANS 2006, pp. 684–694.

    Google Scholar 

  80. Frassl, M. et. al., Magnetic maps of indoor environments for precise localization of legged and non-legged locomotion, RSJ International Conference on Intelligent Robots and Systems (IROS), Japan, 2013. pp. 913–920.

    Google Scholar 

  81. Shockley, J.A. and Raquet, F., Navigation of ground vehicles using magnetic field variations, Journal of the Institute of Navigation, 2014, vol. 61, no. 4, pp. 237–252.

    Article  Google Scholar 

  82. Canciani, A.J. and Raquet, F., Absolute positioning using the Earth’s magnetic anomaly field, Proc. 2015 International Technical Meeting of the Institute of Navigation, 2015. pp. 265–278.

    Google Scholar 

  83. Klass, Ph.J., New guidance technique being tested, Àviation Week and Space Technology, 1974. vol. 100, no. 8.

  84. Reed, C.G. and Hogan, J., Range correlation guidance for cruise missiles, IEEE Trans. Aerospace and Electr. Sys., 1979. vol. AES-15, no. 4, pp. 547–555.

    Article  Google Scholar 

  85. Golden, J.P., Terrain contour matching (TERCOM): A cruise missile guidance aid, SPIE: Image Processing for Missile Guidance, 1980, vol. 238, pp. 10–18.

    Google Scholar 

  86. Longenbaker, W.E., Terrain-aided navigation of an unpowered tactical missile using autopilot-grade sensors, Journal of Guidance, Control and Dynamics, 1984. vol. 7, no. 2, pp. 175–182.

    Article  Google Scholar 

  87. French, R.L., Land Vehicle Navigation and Tracking. Global Positioning System: Theory and Applications, Parkinson, B.W. Ed., 1996. vol. II, pp. 275–301.

    Google Scholar 

  88. Dmitriev. S.P., Stepanov, O.A., and Koshaev, D.A., Map matching for automobile navigation. GIM International. The World Magazine for Geomatics, 2000, vol. 14, no. 7, pp. 69–71.

    Google Scholar 

  89. Dmitriev, S P., Stepanov, O.A., Rivkin, B.S., Koshaev, D.A., and Chung, D., Synthesis and analysis of mapmatching algorithm for car navigation systems, Institute of Navigation 55th Annual Meeting. Navigational Technology for the 21st Century, 1999. pp. 505–514.

    Google Scholar 

  90. Stepanov, O.A., Land Navigation Systems. State and Prospects, Giroskopiya i Navigatsiya, 2005, no. 2, pp. 95–121.

    Google Scholar 

  91. Sholokhov, A.V. and Liventsev V.A., Comparative analysis of methods for constructing correction algorithms for terrestrial navigation systems by digital road maps, Measurement Techniques, 2007. vol. 50, no. 3, pp. 276?281.

    Google Scholar 

  92. Davidson, P., Collin, J., and Takala, J., Application of particle filters to a map-matching algorithm, Gyroscopy and Navigation, 2011, vol. 3, pp. 46–58.

    Google Scholar 

  93. Gustafsson, F. et al., Navigation and tracking of roadbound vehicles using map support, In: Handbook of Intelligent Vehicles, Eskandarian, A., Ed., London: Springer, 2012. pp. 397–434.

    Chapter  Google Scholar 

  94. Gilleeron, P.Y., Spassov, I., and Merminod, B., Indoor navigation enhanced by map-matching, European Journal of Navigation, 2005, vol. 3, no. 3, pp. 6–13.

    Google Scholar 

  95. Ascher, C.C., Kessler, C., Wankerl, M., and Trömmer, G.F., Dual IMU indoor navigation with particle filter based map-matching on a smartphone, Proc. International Conference on Indoor Positioning and Indoor Navigation, 2010.

    Google Scholar 

  96. Kinsey, J.C., Eustice, R.M., and Whitcomb, L.L., A survey of underwater vehicle navigation: Recent advances and new challenges, Proc. 7th Conf. on Maneuvering and Control of Marine Craft (MCMC’2006), 2006.

    Google Scholar 

  97. Stutters L., Liu, H., Tiltman, C., and Brown, D.J., Navigation technologies for autonomous underwater vehicles, IEEE Transactions on Systems Man and Cybernetics Part C: Applications and Reviews, 2008. 38 (4), pp. 581–589.

    Article  Google Scholar 

  98. Paull, L., Saeedi, S., Seto, M. and Li, H., AUV navigation and localization: A review, IEEE Journal of Oceanic Engineering, 2014. 39(1), pp. 131–149.

    Article  Google Scholar 

  99. Bergem, O., Bathymetric navigation of autonomous underwater vehicles using a multibeam sonar and a Kalman filter with relative measurement covariance matrices: Dissertation, Norway: University of Trondheim, 1993. 162 p.

    Google Scholar 

  100. Beloglazov, I.N., Optimal filtering in correlationextreme systems using images of terrain, Izv. AN SSSR. Tekhnicheskaya kibernetika, 1977, no. 2, pp. 185–191.

    MathSciNet  Google Scholar 

  101. Stepanov, O.A., Ultimate overlapping accuracy of Gaussian images, Avtometriya, 1990, no. 5, pp. 16–22.

    Google Scholar 

  102. Stepanov, O.A., Optimal solution of the problem of object coordinates refinement in the correlationextremum navigation systems in using field information in the form of a frame, Avtometriya, 1994, no. 2, pp. 18–27.

    Google Scholar 

  103. Bevington, J.E. and Martila, C.A., Precision aided navigation using SAR and digital map data, PLAN’S90, 1990. pp. 490–496.

    Google Scholar 

  104. Gasilov, V.P. and Kostousov, V.B., Identification of the parameters of object motion by processing the image of external information field, Izv. AN SSSR. Tekhnicheskaya kibernetika, 1994. no. 3, p. 78.

    Google Scholar 

  105. Boreiko, A.A., Vorontsov, A.V., Kushnerik, A.A., and Shcherbatyuk, A.F., Image processing algorithms for solving some problems of control and navigation autonomous underwater vehicles, Podvodnye issledovaniya i robototekhnika, 2010, no. 1, pp. 29–39.

    Google Scholar 

  106. Stepanov, O.A., Osnovy teorii otsenivaniya s prilozheniyami k zadacham obrabotki navigatsionnoi informatsii (Fundamentals of the Estimation Theory with Applications to the Problems of Navigation Information Processing), Part 1, Vvedenie v teoriyu otsenivaniya (Introduction to the Estimation Theory), St. Petersburg: TsNII Elektropribor, 2010.

    Google Scholar 

  107. Beisner, H.M., Arbitrary path magnetic navigation by recursive nonlinear estimation, Navigation, 1969, vol. 16, no. 3, pp. 271–278.

    Article  Google Scholar 

  108. Krasovskii, A.A., Optimal filtering in the theory of correlation-extreme systems, Izv. AN SSSR. Tekhnicheskaya kibernetika, 1976, no. 3, pp. 155–160.

    Google Scholar 

  109. Hostetler, L.D., A Kalman approach to continuous aiding of inertial navigation systems using terrain measurements, Proc. Milwaukee Symp. Automat. Computation Contr., 1976. pp. 305–309.

    Google Scholar 

  110. Dmitriev, S.P. and Shimelevich, L.I., Nelineinye zadachi obrabotki navigatsionnoi informatsii: Obzor (Nonlinear Problems of Navigation Data Processing), Leningrad: TsNII Rumb, 1977.

    Google Scholar 

  111. Andreas, R.D., Hostetler, L.D., and Beckman, R., Continuous Kalman updating of an inertial navigation system using terrain measurements, NAECON’78, vol. 3.

  112. Krasovskii, A.A,, Beloglazov, I.N., and Chigin, G.P., Teoriya korrelyatsionno-ekstremal’nykh navigatsionnykh sistem (Theory of Correlation-Extreme Navigation Systems), Moscow: Nauka, 1979.

    Google Scholar 

  113. Sheives, T.S. and Andreas, R.D., An alternate approach for terrain-aided navigation using parallel kalman filters, Tech. Rep. SAND79-2198. Sandia Nat. Lab., Albuquerque, NM, 1979.

    Google Scholar 

  114. Beloglazov, I.N., Ermilov, A.S., and Karpenko, G.I., Recursive searching estimation and design of algorithms for extremum correlation navigation systems, Automation and Remote Control, 1979, vol. 40, no. 7, pp. 1001–1010.

    MATH  Google Scholar 

  115. Dmitriev, S.P., Shimelevich, L.I., A generalized Kalman filter with repeated linearization and its use in navigation over geophysical fields, Automation and Remote Control, 1978. vol. 39. no. 4, pp. 505–509.

    MATH  Google Scholar 

  116. Hostetler, L.D., and Andreas, R.D., Nonlinear Kalman filtering techniques for terrain-aided navigation, IEEE Trans. Automat. Control, 1983. vol. AC-28, no. 3, pp. 315–323.

    Article  Google Scholar 

  117. Mealy, G.L. and Tang, W., Application of multiple model estimation to a recursive terrain height correlation system, IEEE Trans. Automat. Contr., 1983. vol. AC-28, no. 3, pp. 323–331.

    Article  Google Scholar 

  118. Beloglazov, I.N., Dzhandzhgava, G.I., and Chigin, G.P., Osnovy navigatsii po geofizicheskim polyam (Basics of Navigation on Geophysical Fields), Moscow: Nauka, 1985.

    Google Scholar 

  119. Stepanov, O.A., Priblizhennye metody analiza potentsial’noi tochnosti v nelineinykh zadachakh obrabotki navigatsionnoi informatsii (Approximate Methods for the Analysis of Potential Accuracy in Nonlinear Problems of Navigation Information Processing), Leningrad: TsNII Rumb, 1986.

    Google Scholar 

  120. Dmitriev, S.P., Vysokotochnaya morskaya navigatsiya (High-Precision Marine Navigation), St. Petersburg: Sudostroenie, 1991.

    Google Scholar 

  121. Stepanov, O.A., Metody otsenki potentsial’noi tochnosti v korrelyatsionno-ekstremal’nykh navigatcsionnykh sistemakh (Methods for Estimating Potential Accuracy in Correlation-Extreme Navigation Systems), St. Petersburg: TsNII Elektropribor, 1993.

    Google Scholar 

  122. Stepanov, O.A., Primenenie teorii nelineinoi fil’tratsii v zadachakh obrabotki navigatsionnoi informatsii (Application of Nonlinear Filtering Theory for Processing Navigation Information), St. Petersburg: Elektropribor, 1998.

    Google Scholar 

  123. Bergman, N., Ljung L., and Gustafsson., F., Point mass filter and Cramer-Rao bound for terrain-aided navigation, IEEE Conference on Decision and Control, San Diego, 1997.

    Google Scholar 

  124. Bergman, N., Recursive Bayesian Estimation. Navigation and Tracking Applications, Sweden Linkoping: Linkoping University, 1999.

    Google Scholar 

  125. Kalman, R.E., A new approach to linear filtering and prediction problems, Trans. ASME J. Basic Eng., 1960. 82 (Series D), pp. 35–45.

    Article  Google Scholar 

  126. Stratonovich, R.L., Conditional Markov Processes and their Application to the Theory of Optimal Control, New York: Elsevier, 1968.

    MATH  Google Scholar 

  127. Kushner, H.J., Dynamical equations of optimal nonlinear filtering, J. Differential Equations, 1967, vol. 3, pp. 179–199.

    Article  MATH  MathSciNet  Google Scholar 

  128. Jazwinski, A.H., Stochastic Process and Filtering Theory, New York: Academic Press, 1970.

    Google Scholar 

  129. Gelb, A., Applied Optimal Estimation, Cambridge: M.I.T. Press, 1974.

    Google Scholar 

  130. Magill, D.T., Optimal adaptive estimation sampled stochastic processes, IEEE Trans. Automat. Contr., 1965. vol. AC-IO, no. 4, pp. 434–439.

    Article  MathSciNet  Google Scholar 

  131. Lainiotis, D.G. Optimal adaptive estimation: Structure and parameter adaptation, IEEE Trans. Automat. Contr., 1971, vol. 16, pp. 160–170.

    Article  MathSciNet  Google Scholar 

  132. Bucy, R.S. and Senne, K.D., Digital synthesis of nonlinear filters, Automatica, 1971. no. 7(3), pp. 287–298.

    Article  MATH  Google Scholar 

  133. Alspach, D.L. and Sorenson, H.W., Recursive Bayessian estimation using Gaussian sum approximation, Automatica, 1971, vol. 7, no. 4, pp. 465–479.

    Article  MATH  MathSciNet  Google Scholar 

  134. Lainiotis, D.G., Partitioning: A unifying framework for adaptive systems, I: Estimation, II: Control, IEEE Trans., 1976. vol. 64, no. 8. I. Estimation, pp. 1126–1140. II: Control, pp. 1182–1198.

    MathSciNet  Google Scholar 

  135. Beloglazov, I.N., Recurrence-search estimation, Doklady ANSSSR, 1977. vol. 236, no. 2.

  136. Kramer, S.C. and Sorenson, H.W., Recursive Bayesian estimation using piecewise constant approximations, Automatica, 1988. 24(6), pp. 789–801.

    Article  MATH  MathSciNet  Google Scholar 

  137. Yarlykov, M.S. and Mironov, M.A., Markovskaiya teoriya otsenivaniya sluchainykh protsessov (Markov theory of random process estimation), Moscow: Radio i svyaz’, 1993.

    Google Scholar 

  138. Stepanov, O.A., Kalman filtering: Past and present. An outlook from Russia. (On the occasion of the 80th birthday of Rudolf Emil Kalman), Gyroscopy and Navigation, 2011, vol. 2, no. 2, pp. 99–110.

    Article  Google Scholar 

  139. Zaritskii, V.S., Svetnik, V.B., and Shimelevich, L.I., Monte Carlo technique in problems of optimal data processing, Automation and Remote Control, 1975, vol. 12, pp. 95–103.

    MathSciNet  Google Scholar 

  140. Berkovskii, N.A. and Stepanov, O.A., Error of calculating the optimal Bayesian estimate using the Monte Carlo method in nonlinear problems, Journal of Computer and Systems Sciences International, 2013. vol. 52, n. 3. pp. 342–353.

    Article  MATH  MathSciNet  Google Scholar 

  141. Van Trees, H.L., Detection, Estimation, and Modulation Theory, Part I, New York: Wiley, 1968.

    Google Scholar 

  142. Koshaev, D.A. and Stepanov, O.A., Application of the Cramer-Rao inequality in the problems of nonlinear estimation, Journal of Computer and Systems Sciences International, 1997, vol. 36, no. 2, pp. 220–227.

    MATH  Google Scholar 

  143. Tichavsky, P., Muravchik, C., and Nehorai. A. Posterior Cramer-Rao bounds for discrete-time nonlinear filtering, IEEE Transactions on Signal Processing, 1998, no. 46, pp. 1386–1398.

    Article  Google Scholar 

  144. Simandl, M., Kralovec, J., and Tichavsky, P., Filtering predictive and smoothing Cramer-Rao bounds for discrete-time nonlinear dynamic systems, Automatica, 2001, no. 37, pp. 1703–1716.

    Article  MATH  MathSciNet  Google Scholar 

  145. Van Trees, H.L. and Bell, K.L., Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking, Wiley-IEEE Press, 2007.

    Book  MATH  Google Scholar 

  146. Karlsson, R., Gustafsson, F., and Karlsson, T., Particle filtering and Cramer-Rao lower bound for underwater navigation, IEEE International Conference on Acoustics Speech and Signal Processing, 2002. pp. 65–68.

    Google Scholar 

  147. Stepanov, O.A., Koshaev, D.A., and Motorin, A.V., Designing models for signals and errors of sensors in airborne gravimetry using nonlinear filtering methods, Proc. of the 2015 International Technical Meeting of the Institute of Navigation, ITM 2015, California, pp. 279–284.

    Google Scholar 

  148. Stepanov, O.A. and Toropov, A.B., Nonlinear filtering in map-aided navigation. Par. 2. Current trends in algorithm design, Gyroscopy and Navigation, 2016. no. 1 (in press).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to O. A. Stepanov.

Additional information

Published in Giroskopiya i Navigatsiya, 2015, No. 3, pp. 102–125

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepanov, O.A., Toropov, A.B. Nonlinear filtering for map-aided navigation. Part 1. An overview of algorithms. Gyroscopy Navig. 6, 324–337 (2015). https://doi.org/10.1134/S2075108715040148

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2075108715040148

Keywords

Navigation