Trust-Region Solver of a Nonlinear Magnetometer Disturbance Estimation Problem

Earth geomagnetic field provides very important information for autonomous navigation. However, in practice, magnetometer measurements are easily distorted by outer disturbances, as shown in the right diagram. In a recent study, the real-time magnetometer disturbance estimation problem has been solved via a constrained nonlinear programming for better underwater navigation accuracy. However, the employed interior-point optimizer will require considerable computational resources and cannot always guarantee optimality during optimization updates. This paper further investigates this problem and refines the solution by introducing the trust-region method. The challenge of the designed approach mainly falls into finding out the feasible regions of the possible solutions. Geometric analysis and algebraic elimination methods are taken into account to give globally optimal solutions to the trust-region solver. Experimentations are conducted to verify the correctness of the proposed method. Moreover, it is also confirmed that the trust-region technique can continuously and accurately propagate so that high-frequency dynamic magnetic disturbances can be efficiently estimated.