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In this paper, we investigate the algorithms for traversal exploration and path coverage of target regions using multiple agents, enabling the efficient deployment of a set of agents to cover a complex region. First, the original multi-agent path planning problem (mCPP) is transformed into several single-agent sub-problems, by dividing the target region into multiple balanced sub-regions, which reduces the explosive combinatorial complexity; subsequently, closed-loop paths are planned in each sub-region by the rapidly exploring random trees (RRT) algorithm to ensure continuous exploration and repeated visits to each node of the target region. On this basis, we also propose two improvements: for the corner case of narrow regions, the use of geodesic distance is proposed to replace the Eulerian distance in Voronoi partitioning, and the iterations for balanced partitioning can be reduced by more than one order of magnitude; the Dijkstra algorithm is introduced to assign a smaller weight to the path cost when the geodesic direction changes, which makes the region division more “cohesive”, thus greatly reducing the number of turns in the path and making it more robust. The final optimization algorithm ensures the following characteristics: complete coverage of the target area, wide applicability of multiple area shapes, reasonable distribution of exploration tasks, minimum average waiting time, and sustainable exploration without any preparation phase.

Magnetic anomaly detection is an effective method for detecting ferromagnetic targets. The practical application of target detection by measuring the magnetic gradient has been confirmed in many studies, and its suppression of background noise has been widely recognized. However, the variation of the unidirectional magnetic field gradient is very small in a short distance, and the amplitude of the signal is also affected by the direction of the target’s magnetic moment and the shaking of the sensor platform itself. These make it difficult to extract the signal from complex background interference. In order to solve these problems, this paper is devoted to use the variation of three axial magnetic gradients in the geomagnetic coordinate system caused by the presence of magnetic target (we call it full magnetic gradient) to construct the magnetic anomaly characteristic of the target. A set of orthonormal basis functions is further derived to linearly describe this characteristic, which improves the signal-to-noise ratio (SNR) of the signal from the perspective of signal energy. The present work main contribution is to propose a full magnetic gradient orthonormal basis function (FMG-OBF) method to effectively characterize magnetic anomaly of magnetic targets. Compared with the traditional one-direction magnetic gradient orthonormal basis function method, the SNR of this method is greatly improved, and it is not affected by a change in the target magnetic moment’s direction nor by the shaking of the sensor carrier platform. Therefore, it has great value in the practical application of aeromagnetic detection.

In performing the detection and tracking of ferromagnetic targets or magnetic anomaly detection, a magnetometer array or magnetic gradiometer is often used to suppress environmental background magnetic field interference and improve measurement accuracy. Increasing the distance between the magnetometers is beneficial to improving the signal-to-noise ratio(SNR) of the magnetometer gradiometer, but the mismatching error of the magnetometer array affects the measurement accuracy of the magnetic gradient tensor and the positioning accuracy of the ferromagnetic target. In order to calibrate the mismatch error of a magnetometer array, the mounting position and orientation of each magnetometer must be accurately measured. When the magnetometer installation array is too large, the commonly used calibration methods are difficult to implement because it is difficult to make such a large rigid support, optical systems or robot. This paper reports a method that uses two coils and an excitation current source to generate a test magnetic field, after which methods of modulation demodulation and phase-locked filtering are used to suppress the ambient magnetic field interference. The output of each magnetometer is recorded, and the Particle Swarm Optimization (PSO) algorithm is employed to calculate the mounting position and orientation of each magnetometer. After theoretical analysis, computational simulation, and experimental verification, the results showed that the position measurements in a range of 2.4 m × 2.4 m were accurate to within 0.05 m and the orientation measurements were accurate to within 0.03 radians. The average relative positioning error was less than 1.7%. By designing larger coils and current sources, the needs of larger arrays can be satisfied as long as the same SNR is maintained.