A robust geomagnetic matching algorithm based on l1 norm

The outliers in geomagnetic measured data can seriously impact the geomagnetic matching results and greatly affect the geomagnetic matching efficiency. A geomagnetic matching algorithm which has anti-outlier ability and can adjust the displacement, heading and zoom errors is investigated in this paper. Firstly, L1 norm is introduced for robust estimation. Secondly, by combining the affine transformation, the correlate criterion and the Taylor series expansion for geomagnetic information, a mathematical expression of the displacement, heading and zoom errors is obtained. Thirdly, according to L1 norm weight function and the mathematical expression, the robust target function is acquired. Then the geomagnetic matching problem is converted to the solutions of nonlinear equations to minimize the function. Finally, Broyden iteration is applied to implement the novel algorithm. Simulation results show that the matching error of the novel algorithm is decreased to 31.08% to the conventional iterative contour matching algorithm when the outlier is 31nT. Meanwhile, the position error of the novel algorithm is 0.0195° while the conventional iterative contour matching algorithm fails to match when the outlier is 310nT.