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

Area of Science:

• Geophysics
• Navigation Systems
• Signal Processing

Background:

• The geomagnetic field is crucial for passive navigation when other references are unavailable.
• Magnetic compasses are susceptible to errors caused by hard and soft iron interference.
• Accurate heading angle estimation is vital for navigation applications.

Purpose of the Study:

• To propose a novel two-step optimized correction algorithm for magnetic compasses.
• To address and correct model coefficients affected by hard and soft iron.
• To improve the accuracy of direct heading angle estimation in the presence of magnetic interference.

Main Methods:

• A two-step algorithm combining Levenberg-Marquardt (L-M) fitting and Lagrange multiplier estimation.
• Step 1: L-M fitting with ellipsoid constraint for hard magnetic coefficients.
• Step 2: Lagrange multiplier estimation for soft magnetic iron interference.

Main Results:

• The algorithm effectively eliminates coupling effects between hard and soft magnetic fields.
• Numerical simulations using International Geomagnetic Reference Field (IGRF) and laboratory tests were conducted.
• Root Mean Square Error (RMSE) for magnetic flux density reduced from 2.503 μT to 0.125 μT.
• Mean heading angle error estimates were below 1° under multi-magnetic interference.

Conclusions:

• The proposed two-step algorithm demonstrates ideal convergent properties.
• The solution meets accuracy requirements for non-tactical navigation.
• This method enhances the reliability of magnetic compasses in challenging environments.