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.

To address the decline in measurement accuracy of magnetometers due to process errors and environmental interference, as well as the insufficient robustness of traditional calibration algorithms under strong interference conditions, this paper proposes an ellipsoid fitting algorithm based on Dynamic Adaptive Elite Particle Swarm Optimization (DAEPSO). The proposed algorithm integrates three enhancement mechanisms: dynamic stratified elite guidance, adaptive inertia weight adjustment, and inferior particle relearning via Lévy flight, aiming to improve convergence speed, solution accuracy, and noise resistance. First, a magnetometer calibration model is established. Second, the DAEPSO algorithm is employed to fit the ellipsoid parameters. Finally, error calibration is performed based on the optimized ellipsoid parameters. Our simulation experiments demonstrate that compared with the traditional Least Squares Method (LSM) the proposed method reduces the standard deviation of the total magnetic field intensity by 54.73%, effectively improving calibration precision in the presence of outliers. Furthermore, when compared to PSO, TSLPSO, MPSO, and AWPSO, the sum of the absolute distances from the simulation data to the fitted ellipsoidal surface decreases by 53.60%, 41.96%, 53.01%, and 27.40%, respectively. The results from 60 independent experiments show that DAEPSO achieves lower median errors and smaller interquartile ranges than comparative algorithms. In summary, the DAEPSO-based ellipsoid fitting algorithm exhibits high fitting accuracy and strong robustness in environments with intense interference noise, providing reliable theoretical support for practical engineering applications.

Data-driven learning optimization, which considers optimization as a means to perform end-to-end learning, is an emerging methodology used to solve large-scale learning and continuous control tasks. These methods provide mathematically tractable solutions with inherent interpretability, but their training can be inefficient due to the need to differentiate through the optimization problem and to solve gradient information in every training iteration. To address this issue, we propose a novel learning algorithm called Efficient Differentiable Model Predictive Control (EDMPC), which significantly improves computational efficiency by integrating an optimization-driven inference step within the backpropagation process. More concretely, we derive an analytical gradient of the trajectory from the optimal problem relative to the tunable parameter, enabling significant acceleration of the end-to-end learning procedure. This gradient can be solved by a standard optimizer in a recursive form, which then provides the direction for parameter updates. An unmanned aerial vehicle control task was conducted to demonstrate the effectiveness of EDMPC in controlling complex dynamic systems. The results indicate that the proposed EDMPC method exhibits superior efficiency in the learning process and accuracy in the control process.