A.B. Borzov1, Yu.A. Sidorkina2, S.V. Mikaelyan3, A.V. Kolesnikov4, D.A. Vlasenko5

1–5 Bauman Moscow State Technical University (Moscow, Russia)

The article considers the determination of the potentially achievable accuracy of estimating corrections to the navigation coordinates of the reference inertial navigation system using correlation-extreme algorithms (map-matching method) for the geomagnetic field (geomagnetic navigation) based on the non-Bayesian approach using the Cramer–Rao Lower Bound for sensors the module and components of the magnetic field induction vector. The feasibility of using sensors of vector components, module and a combination of both types of magnetic field induction meters for navigation purposes is analyzed.

The use of the Cramer–Rao Lower Bound makes it possible to estimate the potentially achievable accuracy without implementing the navigation algorithm itself, which significantly reduces the amount of calculations compared to the approach based on statistical tests, and allows us to take into account the influence of disturbing factors in a more convenient form. It is demonstrated that for correlation-extremal systems (map-matching method), the lower boundary of Cramer–Rao characterizes fairly accurately the achievable accuracy of navigation definitions. At the same time, this approach makes it possible to detect areas of the geomagnetic field where greater or lesser navigation accuracy is provided, which can be used as initial information for planning the trajectory of movement through the correction area in order to maximize the total effect of increasing the accuracy of navigation corrections.

It is shown that the magnetic induction vector component sensor with the same measurement noise as the magnetic induction vector module sensor makes it possible to obtain coordinate determinations with approximately 2,5 times greater accuracy. However, taking into account the accuracy characteristics of currently available sensors, it has been demonstrated that the error of a system with a fluxgate vector meter will be significantly higher than with a quantum sensor of the magnetic induction module.

It is concluded that the use of a combined meter begins to have a noticeable effect on the accuracy of location determination only when the standard deviation of the errors of the module sensor and the sensor components of the induction vector are values of the same order. It is shown that the currently available combination of a quantum sensor of the induction vector module and a ferrosonde vector magnetometer is inefficient – it is preferable to use a quantum sensor of the module, however, as available SQUID magnetometers become available, the combined meter can become effective in terms of significantly improving the accuracy of the development of navigation definitions.

1. Krasovskiy A.A., Beloglazov I.N., Chigin G.P. Teoriya korrelyatsionno – ekstremal'nykh navigatsionnykh sistem. M.: Nauka. 1979. [in Russian]
2. Beloglazov I.N., Dzhandzhgava G.I., Chigin G.P. Osnovy navigatsii po geofizicheskim polyam. M.: Nauka. 1985. [in Russian]
3. Dzhandzhgava G.I., Avgustov L.I. Navigatsiya po geopolyam. Nauchno-metodicheskie materialy. M.: OOO «Nauchtekhlitizdat». 2018. [in Russian]
4. Karshakov E.V., Pavlov B.V., Tkhorenko M.Yu., Papusha I.A. Perspektivnye sistemy navigatsii letatel'nykh apparatov s ispol'zovaniem izmereniy potentsial'nykh fizicheskikh poley. Giroskopiya i navigatsiya. 2021. T. 29. № 1 (112). S. 32–51. DOI 10.17285/0869-7035.0055. [in Russian]
5. Peshekhonov V.G. Vysokotochnaya navigatsiya bez ispol'zovaniya informatsii global'nykh navigatsionnykh sputnikovykh sistem. Giroskopiya i navigatsiya. 2022. T. 30. № 1 (116). S. 3–11. [in Russian]
6. Vyaz'min V.S., Golovan A.A., Papusha I.A., Popelenskiy M.Yu. Informativnost' izmereniy vektornogo magnitometra i global'nykh modeley magnitnogo polya Zemli dlya korrektsii BINS letatel'nogo apparata. Sb. materialov XXIII Sankt-Peterburgskoy mezhdunar. konf. po integrirovannym navigatsionnym sistemam. SPb: AO «Kontsern «TsNII «Elektropribor». 2016. S. 340–344. [in Russian]
7. Stepanov O.A., Nosov A.S., Toropov A.B. Navigatsionnaya informativnost' geofizicheskikh poley i vybor traektoriy v zadache utochneniya koordinat s ispol'zovaniem karty. Izvestiya TulGU. Tekhnicheskie nauki. 2018. № 5. S. 74–92. [in Russian]
8. Kopytenko Yu.A., Petrova A.A., Avgustov L.I. Analiz informativnosti magnitnogo polya zemli dlya avtonomnoy global'noy navigatsii. Fundamental'naya i prikladnaya geofizika. 2016. T. 9. № 4. [in Russian]
9. Stepanov O.A., Toropov A.B. Metody nelineynoy fil'tratsii v zadache navigatsii po geofizicheskim polyam. Ch. 1. Obzor algoritmov. Giroskopiya i navigatsiya. 2015. № 3 (23). C. 102–125. [in Russian]
10. Stepanov O.A. Priblizhennye metody analiza potentsial'noy tochnosti v nelineynykh navigatsionnykh zadachakh. Leningrad.: TsNII «Rumb». 1986. [in Russian]
11. Balakrishnan A.V. Teoriya fil'tratsii Kalmana. M.: Mir. 1988. [in Russian]
12. Stepanov O.A. Osnovy teorii otsenivaniya s prilozheniyami k zadacham obrabotki navigatsionnoy informatsii. Ch. 1. Vvedenie v teoriyu otsenivaniya. Izd. 3-e, ispravl. i dop. SPb.: AO «Kontsern «TsNII «Elektropribor». 2017. [in Russian]
13. Stepanov O.A., Sokolov A.I., Dolnakova A.S. Analiz potentsial'noy tochnosti otsenivaniya parametrov sluchaynykh protsessov v zadachakh obrabotki navigatsionnoy informatsii. Materialy XII Vseross. soveshchaniya po problemam upravleniya. M: IPU im. V.A. Trapeznikova RAN, 16–19 iyunya 2014. S. 3730–3740. [in Russian]
14. Volkovitskiy A.K., Karshakov E.V., Kharichkin M.V. Sistema aeromagnitnoy s"emki anomaliy magnitnogo polya. Datchiki i sistemy. 2007. № 8. S. 17– 21. [in Russian]
15. Karshakov E.V., Tkhorenko M.Yu., Pavlov B.V. Aeromagnitnaya gradientometriya i ee primenenie v navigatsii. Problemy upravleniya. 2016. № 2. S. 72–80. [in Russian]
16. Foley C.P., Tilbrook D.L., Leslie K.E., Binks R.A. and etc. Geophysical exploration using magnetic gradiometry based on HTS SQUIDs. IEEE Trans. Appl. Supercond. 2001. № 11 (1). P. 1375–1378.
17. Stolz R., Zakosarenko V., Schulz M., Chwala A. and etc. Magnetic full-tensor SQUID gradiometer system for geophysical applications, Leading Edge, 2006. № 25. P. 178–180.
18. Schiffler M., Queitsch M., Stolz R., Chwala A. and etc. Calibration of SQUID vector magnetometers in full tensor gradiometry systems. Geophys. J. Int. 2014. № 198. P. 954–964.