Research On Representation Of Geomagnetic Field Using Poisson Wavelet On The Sphere

As a passive autonomous navigation technique, geomagnetic navigation method has good performance in hiding itself, high navigation accuracy and low cost. It meets the future demand of navigation technique, and will be widely used. The research on representation of geomagnetic field, which is the preparative work for geomagnetic navigation, is also one of the factors which have an effect on performance of geomagnetic navigation. So it is of scientific and practical importance.The main research of this thesis is representing geomagnetic field using Poisson wavelet on the sphere. These wavelets can be interpreted as multipolar sources which are situated in the Earth, and they can overcome the drawbacks that spherical harmonics analysis has when observation data are sparsely distributed or only cover a local zone.First, the methods of the representing geomagnetic field are summed up. By analyzing the basic theories of spherical harmonics, the drawbacks of representing geomagnetic field using spherical harmonics are listed.Secondly, by analyzing the definition, basic properties of Poisson wavelet on the sphere and its basic theories of representing geomagnetic field, three key problems are pointed out to be solved. The implementation of wavelet frames results from a discretization of the continuous wavelet transform in space and scale. We use one kind of partition method of near-equal on spherical facet and associate each generation of positions with the corresponding scale. To overcome the difficulties of implementation of wavelet frames in higher generation of positions, a data-driven approach is used, and a generalized cross validation (GCV) technique is involved to determine the corresponding scale. The problem of finding optimal coefficients of the wavelet is a regularization problem. A method based on Tikhonov regularization is suggested to solve this kind of problem. The parameters of additional constraints which can eliminate the overfitted solutions are under discussion.Finally, we adopted the methods above to representing the main geomagnetic field, regional geomagnetic field and regional magnetic anomaly field. The results prove the advantages of representing geomagnetic field using Poisson wavelet on the sphere.