An Optimized Two-Step Magnetic Correction Strategy by Means of a Lagrange Multiplier Estimator with an Ellipsoid Constraint

Abstract

The geomagnetic field is as fundamental a constituent of passive navigation as Earth’s gravity. In cases where no other external attitude reference is available, for the direct heading angle estimation by a typical magnetic compass, a two-step optimized correction algorithm is proposed to correct the model coefficients caused by hard and soft iron nearby. Specifically, in Step 1, a Levenberg-Marquardt (L-M) fitting estimator with an ellipsoid constraint is applied to solve the hard magnetic coefficients. In Step 2, a Lagrange multiplier estimator is used to deal with the soft magnetic iron circumstance. The essential attribute of “the two-step” lies in its eliminating the coupling effects of hard and soft magnetic fields, and their mutual interferences on the pure geomagnetic field. Under the conditions of non-deterministic magnetic interference sources with noise, the numerical simulation by referring to International Geomagnetic Reference Field (IGRF), and the laboratory tests based upon the turntable experiments with Honeywell HMR3000 compass (Honeywell, Morristown, NJ, USA) conducted, the experimental results indicate that, in the presence of the variation of multi-magnetic interferences, the RMSE (Root Mean Square Error) value of the estimated total magnetic flux density by the proposed two-step estimator falls to 0.125 μT from its initial 2.503 μT, and the mean values of the heading angle error estimates are less than 1°. The proposed solution therefore, exhibits ideal convergent properties, fairly meeting the accuracy requirements of non-tactical level navigation applications.

Keywords

• two-step optimized correction
• ellipsoid constraint
• non-deterministic magnetic interferences
• L-M fitting
• Lagrange multiplier estimator