The existing magnetic target localization methods are greatly affected by the geomagnetic field and exist approximation errors. In this paper, a two-point magnetic gradient tensor localization model is established by using the spatial relation between the magnetic target and the observation points derived from magnetic gradient tensor and tensor invariants. Based on the model, the equations relating to the position vector of magnetic target are constructed. Solving the equations, a new magnetic target localization method using only a two-point magnetic gradient tensor and no approximation errors is achieved. To accurately evaluate the localization accuracy of the method, a circular trajectory that varies in all three directions is proposed. Simulation results show that the proposed method is almost error-free in the absence of noise. After adding noise, the maximum relative error percentage is reduced by 28.4% and 2.21% compared with the single-point method and the other two-point method, respectively. Furthermore, the proposed method is not affected by the variation in the distance between two observation points. At a detection distance of 20 m, the maximum localization error is 1.86 m. In addition, the experiments also verify that the new method can avoid the influence of the geomagnetic field and the variation in the distance, and achieve high localization accuracy. The average relative error percentage in the y-direction is as low as 3.78%.

The performance of time-critical systems depends heavily on time synchronization accuracy. Therefore, it is crucial to have a synchronization method that can achieve high time synchronization accuracy. In this paper, we propose a new underlying transmission architecture and new synchronization messages. On the basis of these, aiming at the time error problem of the slave clock, we propose an enhanced time synchronization method based on new synchronization messages. Furthermore, we evaluate the performance of the enhanced time synchronization method on the OMNeT++ simulator. In addition, we compare the impact of different crystal oscillator accuracies and different crystal oscillator frequencies on time synchronization accuracy, respectively. Simulation results show that the time offset is at most ±1 clock period using the enhanced time synchronization method. We realize the purpose of timing the master clock and the slave clock by counting the period of the clock signal. Therefore, we needed to round down the time count to an integer. This is the reason why −1 and 1 appear at the same time. When the crystal oscillator frequency used is 80 MHz, the system can achieve a time synchronization accuracy of ±12.5 ns; that is, a nanosecond-level time synchronization accuracy can be achieved. With the reduction of the crystal oscillator accuracy of the slave clock, the synchronization accuracy of ±1 clock period can still be achieved. With the increase in the crystal oscillator frequency, the time synchronization accuracy that can be achieved also improves. The method proposed in this paper provides a new way of thinking and has certain guiding significance for improving the time synchronization accuracy of time-critical systems.

Magnetic anomaly detection (MAD) technology based on the magnetic gradient tensor (MGT) has broad application prospects in fields such as unexploded ordnance detection and mineral exploration. The difference approximation method currently employed in the MGT measurement system introduces measurement errors. Designing reasonable geometric structures and configuring optimal structural parameters can effectively reduce measurement errors. Based on research into differential MGT measurement, this paper proposes three simplified planar MGT measurement structures and provides the differential measurement matrix. The factors that affect the design of the baseline distance of the MGT measurement system are also theoretically analyzed. Then, using the magnetic dipole model, the error analysis of the MGT measurement structures is carried out. The results demonstrate that the planar cross-shaped structure is optimal, with the smallest measurement error, only 3.15 × 10⁻¹⁰ T/m. Furthermore, employing the control variable method, the impact of sensor resolution constraints, noise level, target magnetic moment, and detection distance on the design of the optimal baseline distance of the MGT measurement system is simulated and verified. The results indicate that the smaller the target magnetic moment, the farther the detection distance, the lower the magnetometer resolution, the greater the noise, and the greater the baseline distance required. These conclusions provide reference and guidance for the construction of the MGT measurement system based on triaxial magnetometers.

Precision time synchronization methods are critical for maintaining event order and data consistency among nodes in distributed measurement and control systems. However, microsecond-level time synchronization precision is no longer sufficient to meet the demand. As the number of devices increases, the time synchronization precision tends to degrade. This study proposes a high-precision progressive time synchronization method. The method integrates a progressive time synchronization approach with a clock frequency compensation algorithm, effectively mitigating the exponential growth of time offsets caused by an increasing number of devices. The algorithm was validated through simulation experiments and the construction of a test system. Experimental results demonstrate that, under conditions of an 80 MHz crystal oscillator frequency and a 13.11 ms sending interval, the maximum time offset between the fifth-hop slave clock and the master clock is only 70 ns. This nanosecond-level time synchronization method is capable of meeting the high-precision synchronization requirements of future distributed measurement and control systems.

The Scalar Triangulation and Ranging (STAR) method has broad application prospects in magnetic anomaly detection (MAD) due to its unique advantages of high real-time performance and insensitivity to high-mobility magnetic sensing platforms. However, the intrinsic asphericity error limits its performance for localization accuracy. This paper introduces the normalized source strength (NSS) instead of tensor contraction and proposes a novel magnetic dipole localization method without asphericity error. First, an explicit closed-form localization formula is derived based on the NSS. Then, to improve noise immunity, an objective function is constructed based on the relation between NSS and position parameters to optimize the linear localization results. To evaluate the localization effect of the method comprehensively and accurately, an omnidirectional simulation analysis model is established. The results demonstrate that the proposed method has high localization accuracy, high real-time performance, strong noise resistance, and is less affected by misalignment errors. Finally, the field experiments are conducted. Experimental results indicate that, at a detection distance of 2.11 m, the average localization error of the proposed method on the latitude trajectory is only 0.119 m, which is reduced by 40.8%, 17.9%, and 11.2% compared with the traditional STAR method, Wang’s STAR method, and Lin’s STAR method, respectively.

Leak detection and localization of liquid or gas is of great significance to avoid potential danger and reduce the waste of resources. Leak detection and localization methods are varied and uniquely suited to specific application scenarios. The existing methods are primarily applied to conventional pressurized pipelines and open areas, and there are few methods suitable for multi-grid spaces. In this paper, a gas diffusion model applied to multi-grid space is constructed, and a method for leak detection and localization using the concentration gradient of characteristic gas is proposed according to the prediction behavior. The Gaussian plume model is selected due to its advantages of simplicity and the interpretation of gas diffusion behavior is closer to reality; the expression of the improved model is also obtained. To verify the correctness of the model and the applicability of the localization method, taking the coolant leakage in the circuit system as an example, three experiments with different source strengths were repeated. The fitting correlation coefficients between the gas concentration data of the three experiments and the model are 0.995, 0.997 and 0.997, respectively. The experimental results show that the model has a strong correlation with the real plume behavior, and it is reasonable to use the gas concentration gradient for the localization of the leak source. This study provides a reference for future research on the leak detection and localization of gas- or liquid-containing volatile substances in a complex multi-grid space.