Metal-$\mu$hemispherical resonant gyros (M-$\mu$HRGs) are widely used in highly dynamic navigation systems in extreme environments due to their high accuracy and structural stability. However, the effect of temperature variations on the capacitance characteristics of M-$\mu$HRGs has not been fully investigated, which is crucial for optimizing the performance of the gyro. This study aims to systematically analyze the effect of temperature on the static and dynamic capacitances of M-$\mu$HRGs. In this study, an M-$\mu$HRG structure based on a 16-tooth metal oscillator is designed, and conducted simulation experiments using non-contact capacitance measurement method and COMSOL Multiphysics 6.2 finite element simulation software in the temperature range of 233.15 K to 343.15 K. The modeling analysis of the static capacitance takes into account the thermal expansion effect, and the results show that static capacitance remains stable across the measured temperature range, with minimal effect from temperature. The dynamic capacitance exhibits significant nonlinear variations under different temperature conditions, especially in the two end temperature intervals (below 273.15 K and above 313.15 K), where the capacitance values show local extremes and fluctuations. In order to capture this nonlinear behavior, the experimental data were smoothed and fitted using the LOESS method, revealing a complex trend of the capacitance variation with temperature. The results show that the M-$\mu$HRG has good capacitance stability in the mid-temperature range, but its dynamic performance is significantly affected at extreme temperatures. This study provides a theoretical reference for the optimal design of M-$\mu$HRGs in high- and low-temperature environments.

Aiming at the problem of a lack of positioning satellites and no available beacons in underground space, an injected ground electrode current field signal localization method is proposed. An extremely low-frequency current field signal is applied to two pairs of electrodes inserted into the earth to form a ground current field underground, and the ground electrode current field signal detected at the detection end is used for localization, which can effectively provide reference localization for the underground space when the satellite positioning fails. On this basis, considering that the ground electrode current field signal is susceptible to the influence of the geological structure, electromagnetic interference, and the complexity of the propagation path during underground transmission, which results in the signal showing strong non-stationary characteristics, it is difficult for the traditional time–frequency analysis method to accurately extract stable and reliable positioning characteristics. In order to improve the signal-processing accuracy and robustness, this paper introduces fractional Fourier transform (FRFT) to process the detected signals, and focuses the signal energy more effectively under the optimal order. In order to verify the effectiveness of the localization method, several experiments on the localization of ground electrode current field signals are carried out in the underground space. The experimental results show that, in the positioning environment of more than 10,000 square meters, the average positioning error is 6.896 m. The application of this method will provide a solid technical support for life rescue in underground space, provide the ‘last protection’ for rescue, and complete the life chain of emergency first aid, which has an important application prospect and practical value.

To address the issue of weak geoelectric current field signals that are severely affected by noise and cannot be directly used for geological structure analysis in injected geoelectric current field detection technology, this study proposes a complete ensemble empirical mode decomposition with adaptive noise and improved wavelet thresholding collaborative denoising (CEEMDAN-IWT) method to enhance the interpretation accuracy of geoelectric current signals. The method performs signal decomposition through CEEMDAN and selects the effective intrinsic mode function (IMF) components based on the variance contribution criterion for preliminary denoising. It then combines the improved wavelet thresholding function for further fine denoising and reconstruction, obtaining high signal-to-noise ratio (SNR) electrical data. Simulation and real-world data validation show that in a simulation experiment with an initial SNR of −5 dB, the method improves the $SNR$ to 18.65 dB, and the SNR enhancement is superior to traditional methods under various noise intensities. In practical applications, the normalized cross-correlation (NCC) between the denoised signal and the original injected signal reaches as high as 0.9254, significantly outperforming traditional methods. At the same time, it balances the preservation of signal features with noise suppression, offering significant application value for improving the reliability of injected geoelectric current field detection data.

Aiming to solve the problems of communication interruption caused by the collapse of underground space, this study constructs a strong penetration information transmission system and proposes a centroid localization method based on the received signal strength indication (RSSI) in an underground space ground electrode current field. This is applicable to localization in underground space such as subways, mines, tunnels, etc., as well as under the environment of collapse. First, the propagation characteristics of the ground current field signal in underground space are analyzed, and the attenuation model of the ground current field signal is constructed by combining the RSSI ranging method. On this basis, an improved weighted centroid localization algorithm is introduced to improve the localization accuracy and reliability by optimizing the algorithm parameters to cope with the fluctuations and instabilities generated in the signal propagation process. The experimental results show that the proposed localization method achieves an average positioning error of 7.47 m in an underground environment of 10,000 square meters, which is 32.32% less compared with the weighted centroid localization algorithm, and 62.74% less compared with the traditional centroid localization algorithm. This method presents a positioning technology that operates independently in underground spaces, overcoming the limitation of traditional wireless positioning systems, which rely on external transmission links. Its application will provide crucial technical support for life-saving operations in underground environments, acting as the ‘last line of defense’ in rescue missions. By completing the emergency response chain, it will enhance disaster rescue capabilities, offering substantial practical value and promising prospects.

As the core component of the all-metal micro resonant gyroscope, the structural parameters and form and position errors of the resonator significantly influence its vibration characteristics, and consequently, the accuracy of the gyroscope. By establishing the finite element model of an ideal hemispherical resonator and optimizing the meshing method, we refined the frequency difference to 0.1 Hz, enhancing the accuracy of the simulation model. Through finite element simulation, we examined the impact of various structural parameters and processing errors on the natural frequencies of each mode. We analyzed how form and position errors, including shell thickness error, central axis error, equatorial plane error, and edge rectangular tooth position error, affect the frequency splitting of the resonator. We provided optimization suggestions for the structural parameters, ensuring frequency splitting variations of less than 1 Hz. Theoretical modeling and simulation analysis indicated that the primary factors influencing the vibration modes and frequency splitting are the rectangular tooth structure and shell thickness. Following the optimized parameters, the frequency splitting of the All-Metal Micro Resonant Hemisphere was reduced by an order of magnitude to 14 Hz, demonstrating that these optimized conditions can significantly enhance the resonator’s performance.