Traditional geomagnetic vector matching methods are mainly based on a certain correlation criterion to filter the optimal track, that the optimal track selection function is single and unable to distinguish the nonlinear mapping of the geomagnetic field and geographical position. Since the geomagnetic matching process is similar to pattern recognition, a vector pattern recognition matching method based on a probabilistic neural network (PNN) is proposed to realize geomagnetic navigation. The neural network input is geomagnetic vector elements, and the genetic algorithm is used to optimize the PNN’s smooth parameter to classify better. The comparison of VICCP, VMAGCOM and the proposed method is carried out in simulation in two kinds of areas with significant and insignificant geomagnetic features. Simulation results show that the proposed method has the highest matching rates of 94% and 100% in two kinds of regions. The matching accuracy is also significantly better than traditional algorithms. The experiment is carried out to verify the effectiveness and robustness of the proposed method at last.

During the geomagnetic vector navigation, there are three attitude angles required for coordinate transformation in the process of geomagnetic vector elements’ calculation. However, the yaw angle provided by inertial navigation system (INS) has accumulated error which is inevitable and will seriously reduce navigation accuracy. An improved geomagnetic navigation method based on two-component gradient weighting (TCGW) is proposed in this paper. The horizontal and vertical geomagnetic components can be calculated with roll angle and pitch angle based on the implicit trigonometric theorem in the process of coordinate transformation. And the gradient weights are used as the coefficients to improve the accuracy and universality. The simulations based on four typical types have been performed, and the Monte Carlo simulation results indicated that the proposed method has higher matching accuracy than traditional vector ICCP (VICCP) method. Furthermore, the airborne navigation experiments have been carried out to verify the accuracy and effectiveness of the proposed method.

The high-precision magnetic anomaly reference map is a prerequisite for magnetic navigation and magnetic target detection. However, it is difficult to reflect the detailed characteristics of magnetic anomaly changes by using conventional data interpolation and reconstruction in the areas where magnetic anomaly gradients vary drastically and the distribution of magnetic survey lines is sparse. To solve the problem, an improved variogram of the Kriging interpolation method is proposed to improve the spatial resolution of magnetic anomaly feature. This method selects the spherical variogram model and uses the third power of the lag distance to fit the trend of magnetic anomalies. Meanwhile, the second power of the lag distance is introduced to solve the problem of under-fitting between the lag distance and the value of the variation function near the origin of the sparse variogram graph of measured data. Hyperparameter $\lambda$ is introduced to compensate for the unbalance caused by the introduction of quadratic lag in the spherical variogram model. The results of several sets of simulated and measured data show that the interpolation accuracy of the proposed method is improved by 30–50% compared with the traditional Gaussian, spherical, and exponential models in the region where the magnetic anomaly gradient changes drastically, and the proposed model provides an effective way to build a high-precision magnetic anomaly reference map of the complex magnetic background under the condition of sparse survey lines.

The traditional geomagnetic matching navigation method is based on the correlation criteria operations between measurement sequences and a geomagnetic map. However, when the gradient of the geomagnetic field is small, there are multiple similar data in the geomagnetic database to the measurement value, which means the correlation-based matching method fails. Based on the idea of pattern recognition, this paper constructs a two-stage neural network by cascading a probabilistic neural network and a non-fully connected neural network to, respectively, classify geomagnetic vectors and their feature information in two steps: “coarse screening” and “fine screening”. The effectiveness and accuracy of the geomagnetic vector navigation algorithm based on the two-stage neural network are verified through simulation and experiments. In simulation, it is verified that when the geomagnetic average gradient is 5 nT/km, the traditional geomagnetic matching method fails, while the positioning accuracy based on the proposed method is 40.17 m, and the matching success rate also reaches 98.13%. Further, in flight experiments, under an average gradient of 11 nT/km, the positioning error based on the proposed method is 39.01 m, and the matching success rate also reaches 99.42%.

Under dynamic conditions, when the measured magnetic field is projected onto the sensitive axis of the fluxgate magnetometer, it will show strong dynamic characteristics, resulting in errors or delayed interpretation of the measured physical process. Considering the dynamic characteristics of the three-axis fluxgate magnetometer, this paper proposes a series dynamic compensator based on system identification to carry out system identification and modeling of the dynamic characteristics of the three-axis fluxgate magnetometer and proposes a system parameter calculating method based on hybrid optimization of the genetic algorithm and the simulated annealing algorithm (GA-SA). With these methods, not only can the parameter optimization process effectively avoid falling into the local optimal, but they can also greatly improve the search efficiency and shorten the time of solving the optimal solution. Thus, the full-space search ability of the algorithm is improved, and the accuracy of the dynamic magnetic measurements is improved to the maximum extent. The simulation results of the step signal show that the response time is reduced to 18.22% of the pre-compensation time. The standard signal test results of the step signal and sinusoidal signal, respectively, show that the response time of the step signal is reduced to 5.5% and, in the 0.01–10 Hz frequency band, the maximum attenuation decreases from 0.24% to 0.10%, and the phase difference is less than −0.5°. Moreover, the experimental results of the geomagnetic dynamic measurements show that the dynamic compensated data are mostly close to the real geomagnetic field values. In addition, the standard deviation errors are reduced from 95.30/277.35/108.51 nT to 3.41/2.36/2.75 nT in three geomagnetic vector components. The results of this work show the ability of dynamic measurement accuracy improvement of fluxgate magnetometers and are useful for geomagnetic dynamic measurement and related applications.

In aeromagnetic detection and geomagnetic navigation, the reference geomagnetic maps usually need to be continued to different altitudes. Traditionally, the geomagnetic field upward continuation is stable. Nevertheless, the downward continuation is instable near the magnetic source and sensitive to the high-frequency noise. To address the problem, this article proposes a recursive truncated Taylor expansion (RTTE) downward continuation method for geomagnetic field. This method models the geomagnetic field in the vertical direction. The coefficients of the model are calculated based on the harmonicity of the geomagnetic field to ensure stability; a recursive process is implemented to extend its effect under a large continuation distance. To demonstrate the effectiveness of the proposed method, this paper compares the effects of the traditional Landweber iteration method and the proposed method using simulation data and real measured data. Under real measurement conditions, the MAE and RMSE of the proposed RTTE method are 0.1878 nT and 0.3184 nT, respectively, representing a reduction of 90.33% and 95.75% compared to the Landweber iteration method. The results show that the proposed RTTE method significantly improves the continuation accuracy compared with traditional methods, providing support for geomagnetic navigation and aeromagnetic exploration.