This paper investigates the pull-in dynamics of single-sided and double-sided parallel-plate (SSPP and DSPP) structures employed in MEMS devices for acceleration measurement. A lumped electromechanical model considering a variable damping coefficient and external acceleration is developed for studying their pull-in dynamical behavior. The critical pull-in displacement and pull-in voltage for both parallel-plate structures operated with external acceleration are derived based on the static and dynamical analysis of the proposed model, which are in good agreement with the experimental results. The derived closed-form solutions are shown to be capable of predicting the pull-in behavior of both parallel-plate structures in an overdamped system. Two MEMS parallel-plate structures exhibit distinct pull-in characteristics due to their distinct configurations. The commonly used SSPP structure for MEMS devices is shown to have a relatively linear response to the external acceleration in terms of the critical pull-in displacement and pull-in voltage. However, the DSPP structure exhibits much larger yet nonlinear sensitivity of both the critical pull-in displacement and the critical pull-in voltage to a small range of external acceleration, which has the potential of developing high-sensitivity accelerometers whenever the sensitivity nonlinearity is compensated. Moreover, the effects of pressure are characterized for both DSPP and SSPP devices, which affects the difference between the critical static and dynamic pull-in voltages. The SSPP structure is shown to have the critical pull-in voltage proportional to the logarithmic magnitude of the pressure, while that of the DSPP structure do not vary linearly with respect to the logarithmic magnitude of the pressure.

The inter-satellite relative navigation method—based on radio frequency (RF) range and angle measurements—offers good autonomy and high precision, and has been successfully applied to two-satellite formation missions. However, two main challenges occur when this method is applied to multi-microsatellite formations: (i) the implementation difficulty of the inter-satellite RF angle measurement increases significantly as the number of satellites increases; and (ii) there is no high-precision, scalable RF measurement scheme or corresponding multi-satellite relative navigation algorithm that supports multi-satellite formations. Thus, a novel multi-satellite relative navigation scheme based on inter-satellite RF range and angle measurements is proposed. The measurement layer requires only a small number of chief satellites, and a novel distributed multi-satellite range measurement scheme is adopted to meet the scalability requirement. An inter-satellite relative navigation algorithm for multi-satellite formations is also proposed. This algorithm achieves high-precision relative navigation by fusing the algorithm and measurement layers. Simulation results show that the proposed scheme requires only three chief satellites to perform inter-satellite angle measurements. Moreover, with the typical inter-satellite measurement accuracy and an inter-satellite distance of around 1 km, the proposed scheme achieves a multi-satellite relative navigation accuracy of ~30 cm, which is about the same as the relative navigation accuracy of two-satellite formations. Furthermore, decreasing the number of chief satellites only slightly degrades accuracy, thereby significantly reducing the implementation difficulty of multi-satellite RF angle measurements.

The phase modulation and demodulation technique is widely used in resonant optical gyroscopes to accurately detect resonance frequencies, which directly affect gyro sensitivity. In order to overcome the influences of the system phase fluctuations, an in-phase and quadrature (IQ) demodulation technique is introduced for a resonant micro-optic gyroscope (RMOG). The phase fluctuations in the RMOG are measured, and their influence on the demodulation slope at the resonance point is compared between the traditional sinusoidal demodulation and the IQ demodulation both theoretically and experimentally. It can be concluded that the output of the proposed IQ demodulation is not affected by any phase fluctuations. The demodulation slope is always at its maximum value, thus improving the signal-to-noise ratio of the detection system. By using the IQ demodulation technique, a random walk coefficient of $0.5°/\surd \mathrm{h}$ is carried out. A long-term bias stability of 9°/h is successfully observed, which is improved by a factor of 1.6 compared with that obtained using the traditional phase-sensitive sinusoidal demodulation technique.

This paper proposes two methods to mitigate the zero bias of noncommensurate sampling based code-tracking loops to significantly improve the pseudonoise ranging accuracy. For the compensation-based method, a set of algorithms is developed to directly calculate the zero bias which is then removed from the range measurement. For the compensation-free method, a special category of sampling ratios are selected such that the zero bias is self-cancelled. Simulations validate the effectiveness of the proposed methods.

The waveguide-type ring resonator (WRR) is the key rotation-sensing element in a resonant micro-optic gyroscope (RMOG). A universal model used to analyze both the polarization characteristics of the WRR and corresponding temperature-related polarization error in the RMOG is presented. It indicates that the polarization problem stems from the excitation of two polarization states within the WRR. Unequal variations of incident lights on the cavity in the two directions can cause bias errors at the RMOG output. With the application of different silica WRRs to the RMOG, the polarization errors are tested and verify the theoretical results. Finally, a segment of tilted waveguide gratings with Brewster’s angle is fabricated on the silica waveguide within the cavity. The measured polarization extinction ratio of the output light from the WRR is as high as 35.2 dB. The corresponding temperature dependence of the polarization error is theoretically reduced to 0.0019 (°/s)/°C, which indicates that temperature control is sufficient for a tactical grade RMOG.

This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young’s modulus was developed via Lagrange’s equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rotation of the principal axis of the 2θ mode pair, leading to modal coupling and the degradation of gyroscopic sensitivity. While both anisotropic Young’s modulus and nonideal deep trench verticality affect the frequency difference between two vibration modes, they have little contribution to deflecting the principal axis of the 2θ mode pair. However, the 4θ variations in the width of both the ring and the supporting beams cause modal coupling to occur and the degenerate 2θ mode pair to split in frequency. To aid the optimal design of MEMS ring-based gyroscopic sensors that has relatively high robustness to fabrication tolerance, a geometrical compensation based on the developed model is demonstrated to identify the geometries of the ring and the suspension.