A self-centering and stiffness-controlled MEMS accelerometer.

This paper presents a high-performance MEMS accelerometer with a DC/AC electrostatic stiffness tuning capability based on double-sided parallel plates (DSPPs). DC and AC electrostatic tuning enable the adjustment of the effective stiffness and the calibration of the geometric offset of the proof mass, respectively. A dynamical model of the proposed accelerometer was developed considering both DC/AC electrostatic tuning and the temperature effect. Based on the dynamical model, a self-centering closed loop is proposed for pulling the reference position of the force-to-rebalance (FTR) to the geometric center of DSPP. The self-centering accelerometer operates at the optimal reference position by eliminating the temperature drift of the readout circuit and nulling the net electrostatic tuning forces. The stiffness closed-loop is also incorporated to prevent the pull-in instability of the tuned low-stiffness accelerometer under a dramatic temperature variation. Real-time adjustments of the reference position and the DC tuning voltage are utilized to compensate for the residue temperature drift of the proposed accelerometer. As a result, a novel controlling approach composed of a self-centering closed loop, stiffness-closed loop, and temperature drift compensation is achieved for the accelerometer, realizing a temperature drift coefficient (TDC) of approximately 7 µg/°C and an Allan bias instability of less than 1 µg.

Simulation of, Optimization of, and Experimentation with Small Heat Pipes Produced Using Selective Laser Melting Technology.

With the development of microsatellite technology, the heat generated by onboard components is increasing, leading to a growing demand for improved thermal dissipation in small satellites. Metal powder additive manufacturing technology offers the possibility of customizing and miniaturizing heat pipes to meet the specific requirements of small satellites. This article introduces a small-scale heat pipe designed using selective laser melting (SLM) technology. The heat pipe's material, structure, and internal working fluid were determined based on mission requirements. Subsequently, the SolidWorks 2021 software was used for heat pipe modeling, and the ANSYS 2021R2 finite element analysis software was employed to simulate the heat transfer performance of the designed heat pipe, confirming its feasibility. The heat pipe's structure was optimized using multi-objective regression analysis, considering various structural parameters, such as the channel diameter, vapor chamber height, and narrow gap width. The simulation results demonstrate that the optimized heat pipe achieved a 10.5% reduction in thermal resistance and an 11.6% increase in equivalent thermal conductivity compared to the original heat pipe. Furthermore, compared to conventional metal heat-conducting rods, the optimized heat pipe showed a 38.5% decrease in thermal resistance and a 62.19% increase in equivalent thermal conductivity. The heat pipe was then fabricated using a 3D printer (EOS M280), and a vacuum experimental system was established to investigate its heat transfer characteristics. The experimental results show that the heat pipe operated most efficiently at a heating power of 20 W, reached its maximum heat transfer capacity at 22 W, and had an optimal fill ratio of 30%. These results highlight the excellent performance of the heat pipe and the promising application prospects for SLM technology in the field of small satellites.

Combined Temperature Compensation Method for Closed-Loop Microelectromechanical System Capacitive Accelerometer.

This article describes a closed-loop detection MEMS accelerometer for acceleration measurement. This paper analyzes the working principle of MEMS accelerometers in detail and explains the relationship between the accelerometer zero bias, scale factor and voltage reference. Therefore, a combined compensation method is designed via reference voltage source compensation and terminal temperature compensation of the accelerometer, which comprehensively improves the performance over a wide temperature range of the accelerometer. The experiment results show that the initial range is reduced from 3679 ppm to 221 ppm with reference voltage source compensation, zero-bias stability of the accelerometer over temperature is increased by 14.3% on average and the scale factor stability over temperature is increased by 88.2% on average. After combined compensation, one accelerometer zero-bias stability over temperature was reduced to 40 µg and the scale factor stability over temperature was reduced to 16 ppm, the average value of the zero-bias stability over temperature was reduced from 1764 µg to 36 µg, the average value of the scale factor stability over temperature was reduced from 2270 ppm to 25 ppm, the average stability of the zero bias was increased by 97.96% and the average stability of the scale factor was increased by 98.90%.

Research on a Method to Improve the Temperature Performance of an All-Silicon Accelerometer.

This paper presents a novel method for the performance of an all-silicon accelerometer by adjusting the ratio of the Si-SiO2 bonding area, and the Au-Si bonding area in the anchor zone, with the aim of eliminating stress in the anchor region. The study includes the development of an accelerometer model and simulation analysis which demonstrates the stress maps of the accelerometer under different anchor-area ratios, which have a strong impact on the performance of the accelerometer. In practical applications, the deformation of the comb structure fixed by the anchor zone is influenced by the stress in the anchor region, causing a distorted nonlinear response signal. The simulation results demonstrate that when the area ratio of the Si-SiO2 anchor zone to the Au-Si anchor zone decreases to 0.5, the stress in the anchor zone decreases significantly. Experimental results reveal that the full-temperature stability of zero-bias is optimized from 133 µg to 46 µg when the anchor-zone ratio of the accelerometer decreases from 0.8 to 0.5. At the same time, the full-temperature stability of the scale factor is optimized from 87 ppm to 32 ppm. Furthermore, zero-bias full-temperature stability and scale factor full-temperature stability are improved by 34.6% and 36.8%, respectively.

Precision Joint RF Measurement of Inter-Satellite Range and Time Difference and Scalable Clock Synchronization for Multi-Microsatellite Formations.

The rapid development of multi-satellite formations requires inter-satellite radio frequency (RF) measurement to be both precise and scalable. The navigation estimation of multi-satellite formations using a unified time reference demands the simultaneous RF measurement of the inter-satellite range and time difference. However, high-precision inter-satellite RF ranging and time difference measurements are investigated separately in existing studies. Different from the conventional two-way ranging (TWR) method, which is limited by its reliance on a high-performance atomic clock and navigation ephemeris, asymmetric double-sided two-way ranging (ADS-TWR)-based inter-satellite measurement schemes can eliminate such reliance while ensuring measurement precision and scalability. However, ADS-TWR was originally proposed for ranging-only applications. In this study, by fully exploiting the time-division non-coherent measurement characteristic of ADS-TWR, a joint RF measurement method is proposed to obtain the inter-satellite range and time difference simultaneously. Moreover, a multi-satellite clock synchronization scheme is proposed based on the joint measurement method. The experimental results show that when inter-satellite ranges are hundreds of kilometers, the joint measurement system has a centimeter-level accuracy for ranging and a hundred-picosecond-level accuracy for time difference measurement, and the maximum clock synchronization error was only about 1 ns.

An Efficient Algorithm for Infrared Earth Sensor with a Large Field of View.

Infrared Earth sensors with large-field-of-view (FOV) cameras are widely used in low-Earth-orbit satellites. To improve the accuracy and speed of Earth sensors, an algorithm based on modified random sample consensus (RANSAC) and weighted total least squares (WTLS) is proposed. Firstly, the modified RANSAC with a pre-verification step was used to remove the noisy points efficiently. Then, the Earth's oblateness was taken into consideration and the Earth's horizon was projected onto a unit sphere as a three-dimensional (3D) curve. Finally, the TLS and WTLS were used to fit the projection of the Earth horizon. With the help of TLS and WTLS, the accuracy of the Earth sensor was greatly improved. Simulated images and on-orbit infrared images obtained via the satellite Tianping-2B were used to assess the performance of the algorithm. The experimental results demonstrate that the method outperforms RANSAC, M-estimator sample consensus (MLESAC), and Hough transformation in terms of speed. The accuracy of the algorithm for nadir estimation is approximately 0.04° (root-mean-square error) when Earth is fully visible and 0.16° when the off-nadir angle is 120°, which is a significant improvement upon other nadir estimation algorithms.

Polarization error in resonant micro-optic gyroscope with different waveguide-type ring resonator structures.

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.

Suppressing backscattering noise of a resonant fiber optic gyroscope using coherent detection.

This paper provides a novel, to the best of our knowledge, method for suppressing backscattering noise of a resonant fiber optic gyroscope (RFOG) with a coherent detection technique. The light from the fiber ring resonator is mixed with a reference beam rather than being demodulated directly in traditional configurations, generating a coherent signal with a radio frequency. The central frequencies of the two reference lights used for the clockwise and counterclockwise waves are different to avoid the effect of backscattered waves. Besides, a common phase modulation is applied on the two counter-propagating waves to eliminate the parasitic effect due to the residual amplitude modulation in the phase modulator. Two demodulation schemes for the rotation rate detection from the coherent signals are then proposed and demonstrated, with performance on noise suppression tested. One is the beat-frequency demodulation, and the other is the self-mixing demodulation technique. The influence of backscattering intensity is reduced from 270°/h to 3°/h and 0.05°/h with the two demodulation techniques, respectively, showing a full suppression of backscattering noise.

Resonant fiber optic gyroscope using a reciprocal modulation and double demodulation technique.

A resonant fiber optic gyroscope (RFOG) using a reciprocal modulation and double demodulation technique based on a single laser source is proposed and demonstrated. The effect of the residual amplitude modulation of the phase modulator is well suppressed thanks to the reciprocal modulation and demodulation. On this basis, the backscattering noise is also eliminated by the double demodulation process. The long-term bias stability of the RFOG is successfully improved to 0.2°/h for a test time of 45 hours.

Effects of Structural Dimension Variation on the Vibration of MEMS Ring-Based Gyroscopes.

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.

An Efficient and Robust Star Identification Algorithm Based on Neural Networks.

A lost-in-space star identification algorithm based on a one-dimensional Convolutional Neural Network (1D CNN) is proposed. The lost-in-space star identification aims to identify stars observed with corresponding catalog stars when there is no prior attitude information. With the help of neural networks, the robustness and the speed of the star identification are improved greatly. In this paper, a modified log-Polar mapping is used to constructed rotation-invariant star patterns. Then a 1D CNN is utilized to classify the star patterns associated with guide stars. In the 1D CNN model, a global average pooling layer is used to replace fully-connected layers to reduce the number of parameters and the risk of overfitting. Experiments show that the proposed algorithm is highly robust to position noise, magnitude noise, and false stars. The identification accuracy is 98.1% with 5 pixels position noise, 97.4% with 5 false stars, and 97.7% with 0.5 Mv magnitude noise, respectively, which is significantly higher than the identification rate of the pyramid, optimized grid and modified log-polar algorithms. Moreover, the proposed algorithm guarantees a reliable star identification under dynamic conditions. The identification accuracy is 82.1% with angular velocity of 10 degrees per second. Furthermore, its identification time is as short as 32.7 miliseconds and the memory required is about 1920 kilobytes. The algorithm proposed is suitable for current embedded systems.

Multi-Satellite Relative Navigation Scheme for Microsatellites Using Inter-Satellite Radio Frequency Measurements.

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.

Signal processing improvement of passive resonant fiber optic gyroscope using a reciprocal modulation-demodulation technique.

A resonant fiber optic gyroscope (RFOG) based on the reciprocal phase modulation-demodulation technique is proposed and demonstrated. The residual amplitude modulation induced error of the phase modulator, and the effect of laser frequency noise are all suppressed thanks to the reciprocity of the proposed signal processing scheme. Compared with the past separate modulation-demodulation RFOG, the angular random walk is improved by a factor of 15 times from 0.08°/√h to 0.0052°/√h, and the bias stability is improved from 0.3°/h to 0.06°/h.

Synchronous in-phase and quadrature demodulation technique for resonant micro-optic gyroscope.

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°/√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.

An Improved Phase-Robust Configuration for Vibration Amplitude-Phase Extraction for Capacitive MEMS Gyroscopes.

This paper presents for the first time an improved algorithm for vibration amplitude-phase information extraction of capacitive microelectromechanical systems (MEMS) gyroscopes. Amplitude and phase information resulting from the improved algorithm is insensitive to the phase variation of an interface capacitance-voltage (CV) circuit, thus both long time drift of the gyroscope and bias instability have been improved. Experimental results show that both the phase and amplitude information extracted using this improved algorithm is insensitive to phase variation of CV circuit which is in accordance with theory. Bias instability using this improved configuration is 0.64°/h, which is improved two times more than the configuration using traditional double-side-band (DSB) demodulation configuration, and 4.3 times more than the configuration using single-side-band (SSB) demodulation, respectively. Allan deviation analysis shows that the slow varying drift term using D&S configuration is effectively reduced due to its robustness to CV phase variation compared to test results using DSB or SSB configuration.

Short fiber resonant optic gyroscope using the high-frequency Pound-Drever-Hall technique.

Optical gyros are attractive angular rotation sensors based on the Sagnac effect. The phase modulation technique is adopted to detect the weak resonant frequency shift induced by the Sagnac effect, which determines the detection sensitivity of the gyros. The Pound-Drever-Hall (PDH) modulation is a mature laser frequency stabilization technique that is widely recognized. A resonant optic gyro equipped with a short and high-finesse fiber ring resonator employing the high-frequency PDH modulation technique is proposed and demonstrated. The modulation index and frequency are optimized to maximize the slope of the demodulation curve. Compared with the low-frequency modulation, the high-frequency PDH modulation increases the slope of the demodulation curve by a factor of 1.23 and achieves an extra 15.8 dB of laser frequency noise suppression. The bias stability of the gyro output is improved from 9.6°/h to 8°/h, and the equivalent lock-in frequency accuracy increases 12 dB.

Single-polarization fiber-pigtailed high-finesse silica waveguide ring resonator for a resonant micro-optic gyroscope.

A new record for high-finesse silica waveguide ring resonators (WRRs), to the best of our knowledge, is demonstrated experimentally. The achieved finesse and resonant depths of the silica WRR with a length of 7.9 cm and a diameter of 2.5 cm are 196.7% and 98%, respectively. In addition, the silica WRR chip is coupled with single-polarization fiber to improve the polarization extinction ratio (PER) and, thus, to reduce the polarization error. With the application of this high-finesse and high-PER WRR to the resonant micro-optic gyroscope (RMOG), a bias stability of 0.004°/s is observed over a 1 h timeframe. To the best of our knowledge, this is the first RMOG reported in the open literature that can sense the earth's rotation rate (15°/h).

Measurement of the reflection and loss of the hybrid air-core photonic-bandgap fiber ring resonator.

A fiber ring resonator is the key element in a resonant fiber optic gyroscope (RFOG). Both reflection and loss characteristics can severely decrease the accuracy of the RFOG. This paper first implements optical frequency domain reflectometry (OFDR) to measure the reflection and loss coefficients of the hybrid air-core photonic-bandgap fiber (PBF) ring resonator. Compared with the traditional measurement method of the resonant curve, OFDR can clearly distinguish the two junctions between the air-core PBF and the solid-core fiber. The measured reflection coefficients at the two splicing points are 1.77% and 2.65%, respectively. The excess losses are 2.28 dB and 3.22 dB, respectively. Thus, the measurement of the junctions in the fiber ring resonator is realized.

Resonant fiber optic gyro based on a sinusoidal wave modulation and square wave demodulation technique.

New developments are made in the resonant fiber optic gyro (RFOG), which is an optical sensor for the measurement of rotation rate. The digital signal processing system based on the phase modulation technique is capable of detecting the weak frequency difference induced by the Sagnac effect and suppressing the reciprocal noise in the circuit, which determines the detection sensitivity of the RFOG. A new technique based on the sinusoidal wave modulation and square wave demodulation is implemented, and the demodulation curve of the system is simulated and measured. Compared with the past technique using sinusoidal modulation and demodulation, it increases the slope of the demodulation curve by a factor of 1.56, improves the spectrum efficiency of the modulated signal, and reduces the occupancy of the field-programmable gate array resource. On the basis of this new phase modulation technique, the loop is successfully locked and achieves a short-term bias stability of 1.08°/h, which is improved by a factor of 1.47.

Effect of Fresnel reflections in a hybrid air-core photonic-bandgap fiber ring-resonator gyro.

A novel hybrid polarization-maintaining (PM) air-core photonic bandgap fiber (PBF) ring resonator is firstly demonstrated by using a conventional solid-core PM fiber optical coupler formed by splicing a section of PM air-core PBF into the resonator. Due to Fresnel reflections exist at the two junctions between the air-core PBF and the solid-core fiber, the forward output signal of this hybrid ring resonator is the normal resonant curve with the superposition of the lightwaves that experienced even numbers of Fresnel reflections and the backward output signal is composed of lightwaves that experienced odd numbers of Fresnel reflections. Rigorous derivations of the forward and backward output signals are given out. The biggest resonant depth and finesse of the hybrid air-core PBF ring resonator predicted are 0.352 and 6.3 respectively by assuming a splice loss of 1.8 dB per junction. These predictions are finally confirmed by testing both the forward and backward output signals of the hybrid ring resonator. With the countermeasures against the influences of the odd numbers of Fresnel reflections, a bias stability of 0.007°/s is successfully demonstrated in a hybrid PM air-core PBF ring-resonator gyro.