# Complex Environmental Geomagnetic Matching-Assisted Navigation Algorithm Based on Improved Extreme Learning Machine

## TL;DR

This paper introduces a new navigation algorithm using optimized machine learning to improve positioning accuracy in environments where satellite signals are unreliable.

## Contribution

The novel contribution is the NGO-ELM algorithm, which optimizes ELM with an improved Northern Goshawk Optimization method for geomagnetic matching.

## Key findings

- The INGO-ELM model achieves positioning with average absolute errors of 6.38 m (latitude), 6.43 m (longitude), and 0.0137 m (altitude).
- INGO-ELM is significantly faster and more accurate than other models like ELM, XGBoost, and BP.
- The model maintains robustness even when noise is introduced into the input data.

## Abstract

In complex environments where satellite signals may be interfered with, it is difficult to achieve precise positioning of high-speed aerial vehicles solely through the inertial navigation system. To overcome this challenge, this paper proposes an NGO-ELM geomagnetic matching-assisted navigation algorithm, in which the Northern Goshawk Optimization (NGO) algorithm is used to optimize the initial weights and biases of the Extreme Learning Machine (ELM). To enhance the matching performance of the NGO-ELM algorithm, three improvements are proposed to the NGO algorithm. The effectiveness of these improvements is validated using the CEC2005 benchmark function suite. Additionally, the IGRF-13 model is utilized to generate a geomagnetic matching dataset, followed by comparative testing of five geomagnetic matching models: INGO-ELM, NGO-ELM, ELM, INGO-XGBoost, and INGO-BP. The simulation results show that after the airborne equipment acquires the geomagnetic data, it only takes 0.27 µs to obtain the latitude, longitude, and altitude of the aerial vehicle through the INGO-ELM model. After unit conversion, the average absolute errors are approximately 6.38 m, 6.43 m, and 0.0137 m, respectively, which significantly outperform the results of four other models. Furthermore, when noise is introduced into the test set inputs, the positioning error of the INGO-ELM model remains within the same order of magnitude as those before the noise was added, indicating that the model exhibits excellent robustness. It has been verified that the geomagnetic matching-assisted navigation algorithm proposed in this paper can achieve real-time, accurate, and stable positioning, even in the presence of observational errors from the magnetic sensor.