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.

The bus network is widely used in industrial automation and avionics systems due to its many advantages. Network reliability is an important indicator of the bus network design and analysis. However, the widely used reliability evaluation method is not capable of dealing with the bus network. In this paper, we model the bus network without redundancy and the bus network with redundancy, propose the algorithms to calculate the two-terminal reliability and the k-terminal reliability of the bus network with redundancy, and verify the effectiveness of the algorithms in three scenarios. The experimental results show that when the reliability of the link reaches 0.9, the two-terminal reliability of the bus network with redundancy of six terminal nodes, eight terminal nodes, and ten terminal nodes is 40.95%, 52.17%, and 61.26% higher than that of the bus network without redundancy, respectively; k-terminal reliability is 61.26%, 74.58%, and 83.32% higher than that of the bus network without redundancy, respectively. The bus network with redundancy increases the communication paths for data exchange between devices, and has higher reliability than the bus network without redundancy. The algorithms proposed in this paper provide an effective solution for the reliability evaluation of the bus network. It perfects the reliability evaluation system of the network with different topology architectures.INDEX TERMS Minimal path sets, minimal cut sets, reliability evaluation, Sum-of-Disjoint Products, the bus networks.