The Basis and Theoretical Model of Earth Gravity Field Navigation and Positioning

The irregularity of the earth's shape and the non-uniformity of density lead to different gravity fields at various points of the earth, which are expressed as a function of spatial position (longitude, latitude, height). Therefore, during navigation, the submersible can collect the gravity data of the route through the gravity measuring instrument, match it with the pre stored gravity data, obtain the current positioning information of the submersible, and then correct the position error accumulated by the inertial navigation system. Gravity assisted navigation system in the process of measuring gravity field data, the submersible does not need to be exposed to or close to the water surface, and the measuring instrument does not need to send or receive external signals to the outside. The system can carry out passive and covert navigation and positioning, and the submersible can still achieve the purpose of autonomous covert navigation in the special case of satellite and radio positioning system failure or damage. With the development of gravity measurement instruments and space measurement technology [Chen et al. in Advances in Earth Sciences. 16:1–13, 2001], it has become a reality to obtain gravity data quickly and accurately all over the world, which makes the mapped gravity aided navigation system have the ability to correct ins accumulated position error. There are mainly two representative systems of the charted gravity assisted navigation system, both developed by Bell aerospace, namely, the gravity gradient navigation system developed in 1990 and the gravity assisted inertial navigation system developed in 1991. The gravity assisted positioning system can be divided into four main parts: inertial navigation system, gravity measurement instrument, digital gravity reference map and matching positioning algorithm. The performance difference of each part has an important impact on the performance of the gravity assisted positioning system. Gravity model (benchmark map) is the basis of gravity assisted positioning. Whether the description of gravity model is accurate, whether the gravity features contained are rich, and whether the resolution meets the requirements will affect the performance of gravity assisted positioning system. Based on the external gravity model J2 gravity field model, this chapter discusses the calculation method of normal gravity on the surface of rotating ellipsoid, and establishes a small depth underwater three-dimensional gravity field model and the corresponding underwater inertial navigation system INS combined model, which provides a basic theoretical method for the application of gravity assisted positioning system.