关键词: 仿射变换, 地磁匹配, 平方差算法, 相关性原则, 迭代, 数值求解

Abstract:

For the problem that the positioning error of inertial navigation system accumulated with time, a geomagnetic matching positioning algorithm based on affine transformation is proposed. The correlation constraint between the matched trajectory and the measured geomagnetic field eigenvalue is established by the square difference algorithm. The constraint function is expanded and discretized by Taylor, and the affine transformation model is introduced. The constraint function is transformed into a multivariate index function of the displacement, angle and contraction error of the curve. According to the relativity principle, the geomagnetic matching problem is transformed into solving nonlinear equations. The iterative and numerical method in Mathematica is used to solve the nonlinear equations. The obtained solutions are input into MATLAB for matching and positioning. Experiments show that the final registration point of the matched track differs from the end point of the real track by 293.3 m, and the longitude and latitude errors between the matched track and the real track are 0.003° and 0.000 4° respectively, which verifies the feasibility of the proposed algorithm.

Key words: affine transformation, geomagnetic matching, squared difference algorithm, relevance principle, iteration, numerical solution