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.

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.

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.

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.

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.

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.

Reducing polarization-fluctuation induced drift in resonant fiber optic gyro by using single-polarization fiber.

A novel hybrid single-polarization (SP) fiber ring resonator is demonstrated by using a polarization-maintaining coupler formed by splicing a section of SP fiber into the resonator. The SP fiber selectively eliminates the unwanted resonance by introducing high loss for the unwanted eigenstates of polarization in the resonator. The calculated result shows that this hybrid SP resonator is a good candidate for a tactical-grade performance gyro with a high environmental temperature stability. The experiment shows that the desired resonance in the resonator can keep an excellent stability in a wide temperature range, thus the temperature-dependent polarization-fluctuation drift in the resonant fiber optic gyro is sufficiently suppressed. As a result, a random walk coefficient of 0.08°/√h and a typical bias stability below 0.3°/h for an integration time of 300 s have been carried out.

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.

Double closed-loop resonant micro optic gyro using hybrid digital phase modulation.

It is well-known that the closed-loop operation in optical gyros offers wider dynamic range and better linearity. By adding a stair-like digital serrodyne wave to a phase modulator can be used as a frequency shifter. The width of one stair in this stair-like digital serrodyne wave should be set equal to the optical transmission time in the resonator, which is relaxed in the hybrid digital phase modulation (HDPM) scheme. The physical mechanism for this relaxation is firstly indicated in this paper. Detailed theoretical and experimental investigations are presented for the HDPM. Simulation and experimental results show that the width of one stair is not restricted by the optical transmission time, however, it should be optimized according to the rise time of the output of the digital-to-analogue converter. Based on the optimum parameters of the HDPM, a bias stability of 0.05°/s for the integration time of 400 seconds in 1 h has been carried out in an RMOG with a waveguide ring resonator with a length of 7.9 cm and a diameter of 2.5 cm.

Laser frequency noise induced error in resonant fiber optic gyro due to an intermodulation effect.

For the first time, a significant noise source in the resonant fiber optic gyroscope (RFOG) called intermodulation induced error is proposed and deeply analyzed in this paper. The intermodulation error is produced by the laser frequency noise at even multiples of the modulation frequency due to an intermodulation effect, which will seriously limit the random noise performance of the RFOG. Experiments are designed and conducted to verify and measure the intermodulation induced error in the RFOG. The experimental results confirm the existence of intermodulation error, and fit well with the theory. As for the design of the RFOG, light sources with a narrow intrinsic linewidth and a high modulation frequency are preferable to achieve a high rotation-rate sensitivity.

Resonant micro-optic gyro using a short and high-finesse fiber ring resonator.

A novel hybrid integrated scheme is proposed for a high-performance resonant micro-optic gyro (RMOG), which requires a low-loss micro-ring resonator for mass production. A new record for the RMOG is established experimentally with a short fiber ring resonator and an integrated signal detecting and processing circuit. The finesse of the short fiber ring resonator with a length of 60 cm and a diameter of 4.77 cm is as high as 202, and the theoretical sensitivity of the RMOG is better than 0.3°/h assuming the average optical intensity at the photodetector is 1 mW. The 60 cm long spliceless micro-ring resonator is experimentally proved to be sufficient for a tactical-grade RMOG. An angle random walk coefficient of 0.64°/√h and a typical bias stability below 9.6°/h for the integration time of 50 s are successfully demonstrated using an innovative open-loop approach for an operation time of 1600 s.

Eliminating bias drift error in lock-in frequency for a resonant fiber optic gyro.

The accuracy of the resonant frequency servo loop is a major concern for high-performance operation of a resonant fiber optic gyro. This is usually resolved by adopting the central frequency of the laser source to track the resonance of the optical fiber ring resonator in one direction. However, the drift of the resonant frequency arising from resonator temperature fluctuation must be eliminated to maintain this accuracy. The traditional proportional integral (PI) frequency servo loop cannot address this issue very well. For instance, a bias error as large as tens or even hundreds of degrees/hour has been observed at the demodulated output of a resonant frequency servo loop. In this paper, we propose a method to eliminate this bias error by adding a double integral term in the traditional PI-based resonant frequency servo loop. We demonstrate that the double integral term can precisely track the linear resonant frequency drift, evidenced by our experimentally achieved close-to-zero bias error of -0.0009 deg/h at the demodulated output of the resonant frequency servo loop.

Reduction of optical Kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique.

As a type of main optical error source in the resonant micro-optic gyro (RMOG), the optical Kerr-effect brings a nonzero bias to the output of the RMOG. The light-intensity fluctuations are interpreted as the cause. To eliminate the drifts due to the optical Kerr-effect, the intensities of the clockwise (CW) and counterclockwise (CCW) lightwaves circulating in the resonator should be equal at all times. Through theoretical analysis and experimental investigation, a linear relationship between the second-harmonic demodulated signal and the light-intensity input to the resonator is demonstrated for the sinusoidally phase modulated RMOG. Both our numerical simulation and experimental verification are carried out, which, for the first time to the best of our knowledge, demonstrate that the second-harmonic demodulated signal can be used as a feedback error signal to reduce both the input-intensity mismatch between the CW and CCW lightwaves and their intensity fluctuations. By applying the light-intensity feedback loop to the closed-loop RMOG, the light-intensity fluctuations are reduced to 2.7×10⁻5, down from 5.86%. As a result, the optical-Kerr effect induced error is effectively reduced.