Temperature fluctuations seriously damage the performance of resonant accelerometers. Two approaches have been proposed in this paper to address this problem. In structural design, electrostatic softening spring is utilized to modulate the external acceleration on the frequency of resonator’s anti-phase modal without any stress transmission, and thus improve the thermal robustness of the accelerometer. In control circuit, continuous ring-down technique is employed for real-time quality factor (utilized as a virtual thermometer) monitoring, which attenuates measuring hysteresis and improves the precision of temperature compensation. A prototype is implemented to verify the proposed approaches. Experiments show that this accelerometer is insensitive to stress and has better performance of temperature compared with vibration beam resonant accelerometer. The bias stability of acceleration output was improved from 35.2mg to 0.08mg with real-time quality factor compensation ranging from −40°C to +40°C.

For the purpose of direct angle measurement with high accuracy, this paper focuses on the gain self-calibration of operating modes of MEMS disk gyroscope, when it works in the rate-integration mode. The difference of C/V conversion gain, quality factor and front-end amplifier’s gain of gyroscope operating modes will lead to the total gain difference, which causes angle error. Although one-time manual calibration can temporarily reduce the influence of gain difference, environmental factors (e.g. temperature) will interfere with the calibration results. In this paper, a novel self-calibration method is proposed, which detects the gain difference of gyroscope operating modes in real time and compensates it without adding additional circuits. This method is verified using a digital signal processing platform, and the angle dependent bias (ADB) error is reduced from 18 degrees to 2 degrees.

Due to material mismatch, silicon differential resonant accelerometers (SDRA) experience unpredictable thermal stress that is challenging to account for. An SDRA with a stress-isolated frame that is co-faced with the sensitive structural layer is shown in this study. Analytical construction is used to create the stress transmission model of SDRA, which incorporates the equivalent stiffness of a stress-isolated frame. It offers a technique to balance the scale factor of the device with thermal stress resistance. Then, from -40°C to 85°C, the proposed SDRA devices’ temperature behavior with and without a stress-isolated frame were examined theoretically, numerically, and experimentally. The measured temperature sensitivities of the device with the stress-isolated structure were around -1.15Hz /°C, 0.19mg/°C, and 37.23ppm /°C for the frequency, bias, and scale factors, respectively. The bias instability of the novel device is 0.72μg. Under the identical experimental conditions, each of these metrics outperformed the device without stress isolation by one to two orders of magnitude, demonstrating the efficiency of the novel stress-isolated structure.

Toward the objective of eliminating the angle error and rate threshold of the rate integrating gyroscope (RIG) caused by stiffness asymmetry, a novel in-run automatic mode-matching method is presented in this paper. Although other manual mode-matching methods can reduce the stiffness asymmetry temporarily, the environmental factors will interfere the manual calibration. Combined with virtual rotation, the processing circuits obtain the resonant frequencies of RIG operation modes and a controller is used to reduce the frequency difference. Meanwhile, an innovative method is proposed for RIG angle error analysis, avoiding the drawbacks of the traditional analysis methods. An FPGA based platform using a MEMS disk resonator is tested and the angle error is reduced to 1 degree compared with the manual calibration result 6.1 degrees.

The inversion of Ground-Penetrating Radar data is beneficial for studying the subsurface media distribution, especially for the root system and their environment. Emerging GPR inversion models focus on constructing a direct mapping from radar wave B-Scan image to permittivity distribution. They not only rely on the diversity of the dataset, but also hard to specify the effects of electromagnetic wave propagation properties. These make it difficult to accurately recover complex underground scenes. Addressing the above issues, this paper proposes a radar wave inversion model based on the embedded velocity field (Velocity Field Inversion UNet, VFIUNet), which utilizes the estimated global velocity information within the detection domain to reconstruct the subsurface permittivity distribution from B-Scan data. First, the propagation velocity of radar wave in the detection domain is estimated through self-focusing FK migration. Then, an embedded physical velocity field inversion model based on the multi-scale transformation module was designed, which integrates the prior velocity field and the collected B-Scan data to estimate the difference in permittivity distribution. Finally, the parameters of the VFIUNet are optimized with the hybrid loss function (including L2 and SSIM) and the root scene radar wave dataset. Comparative studies with existing inversion models exhibit that inversion models based on a priori velocity information provide better performance in the permittivity distribution reconstruction. The predictions of numerical experiments and in situ root detection indicate that the permittivity, shapes, and positions of the subsurface media could be restored by the proposed inversion model with high accuracy. Accurate GPR inversion would facilitate the three-dimensional reconstruction of subsurface root scenes.