Search Results (20)

Space-based gravitational wave missions such as LISA, Taiji, and Tianqin rely on the time-delay interferometry (TDI) technique to observe low-frequency signals such as Galactic binaries (GBs), massive black-hole binaries, and extreme-mass-ratio inspirals. Among these sources, resolving the large population of GBs poses a central challenge for data analysis. In this work, we present GBSIEVER-C, a pipeline implemented in C and parallelized using OpenMP (Open Multi-Processing), along with a range of additional algorithmic optimizations, including a fast implementation of second-generation TDI response modeling. It builds upon the previous MATLAB-based pipeline that demonstrated competitive performance on LISA Data Challenge (LDC) data. To the best of our knowledge, GBSIEVER-C is the first pipeline to address the GB resolution problem using second-generation TDI data. We apply it to the GB dataset in Taiji Data Challenge (TDC) that contains 30 million GBs. Compared with our previous results on LDC data, it achieves improved source resolution, residual suppression, and parameter-estimation accuracy. These gains are consistent with the enhanced sensitivity expected from Taiji’s longer arm length. Although validated on Taiji data, the pipeline is fully compatible with LISA and similar mission configurations, and supports both single-detector and multi-detector network analyses. Full article

The high-precision gravitational reference sensor, which hosts a heavy test mass (TM) surrounded by electrodes with a relatively large gap, is crucial in all high-sensitivity drag-free sensors. Consequently, a dedicated locking mechanism is needed to securely hold the TM during the launch phase. After reaching the intended orbit, the TM is released to a free-falling state and subsequently captured by electrostatic actuation, which demands that the transferred momentum and angular momentum to the TM do not exceed ${10}^{-5}\mathrm{kgm}/\mathrm{s}$ and ${10}^{-7}{\mathrm{kgm}}^2/\mathrm{s}$, respectively. This paper introduces a three-level structural design of the locking-and-release mechanism. In order to investigate the release requirement, a pendulum system has been developed for on-ground testing. The mock-up of the TM is entirely consistent with the size and mass of TianQin TM, and the dual-sided release tips constrain the TM and then rapidly retract simultaneously, after which the transferred momentum and angular momentum are estimated from the free oscillations as $0.38\left(21\right)\times {10}^{-5}\mathrm{kgm}/\mathrm{s}$ and $0.15\left(14\right)\times {10}^{-7}{\mathrm{kgm}}^2/\mathrm{s}$ with a preload force of 0.3 N. This proposes a feasible scheme for validating the release mechanism conducting impulse testing for the TianQin project. Full article

We present a Fisher information matrix study of the parameter estimation precision achievable by a class of future space-based, “mid-band”, gravitational wave interferometers observing monochromatic signals. The mid-band is the frequency region between that accessible by the Laser Interferometer Space Antenna (LISA) and ground-based interferometers. We analyze monochromatic signals observed by the TianQin mission, gLISA (a LISA-like interferometer in a geosynchronous orbit) and a descoped gLISA mission, gLISA_d, characterized by an acceleration noise level that is three orders of magnitude worse than that of gLISA. We find that all three missions achieve their best angular source reconstruction precision in the higher part of their accessible frequency band, with an error box better than ${10}^{-10}$ sr in the frequency band [${10}^{-1},10$] Hz when observing a monochromatic gravitational wave signal of amplitude $h_0={10}^{-21}$ that is incoming from a given direction. In terms of their reconstructed frequencies and amplitudes, TianQin achieves its best precision values in both quantities in the frequency band [${10}^{-2},4\times {10}^{-1}$] Hz, with a frequency precision ${\sigma }_{f_{gw}}=2\times {10}^{-11}$ Hz and an amplitude precision ${\sigma }_{h_0}=2\times {10}^{-24}$. gLISA matches these precisions in a frequency band slightly higher than that of TianQin, [$3\times {10}^{-2},1$] Hz, as a consequence of its smaller arm length. gLISA_d, on the other hand, matches the performance of gLISA only over the narrower frequency region, [$7\times {10}^{-1},1$] Hz, as a consequence of its higher acceleration noise at lower frequencies. The angular, frequency, and amplitude precisions as functions of the source sky location are then derived by assuming an average signal-to-noise ratio of 10 at a selected number of gravitational wave frequencies covering the operational bandwidth of TianQin and gLISA. Similar precision functions are then derived for gLISA_d by using the amplitudes resulting in the gLISA average SNR being equal to 10 at the selected frequencies. We find that, for any given source location, all three missions display a marked precision improvement in the three reconstructed parameters at higher gravitational wave frequencies. Full article

Low-frequency seismic vibrations extremely limit the performance of ground simulation facilities for space-borne gravitational wave detections, which need to be substantially suppressed. Active vibration systems are thus required. However, the tilt-translation coupling of inertial sensors strongly limits the performance of vibration isolation platforms in the low frequency range, which requires a precise measurement of the low-frequency tilt signal. This study compares two methods for the tilt signal measurement: the differential-mode method and the direct method. The differential-mode method estimates tilt signals by analyzing differential motion between two inertial sensors, while the direct method utilizes an interferometric tilt sensor (ITS) which consists of a suspended rotational beam system and an interferometer for the readout. Experimental results show that ITS achieves a lower noise floor. Its noise floor is dominated by the thermal-mechanical noise below 0.25 Hz and the readout noise of the interferometer above 0.25 Hz. The findings highlight the potential of ITS for improving the performance of vibration isolation platforms in the low-frequency range. Full article

Space-based gravitational wave detection uses an equilateral triangular satellite constellation with inter-satellite laser heterodyne interferometry to measure displacement variations caused by gravitational waves. Inter-satellite laser communication is critical for data transmission, redundancy and clock synchronization, which suppresses clock noise and enhances detection sensitivity. This integrated approach ensures precise gravitational wave information extraction, supporting the high-accuracy requirements of space-based observatories. This study focuses on the modeling and simulation of inter-satellite laser communication for space-based gravitational wave detection. Based on the data-transmission requirements of such systems, the principles of inter-satellite laser communication are analyzed. The research includes the selection of pseudo-random noise (PRN) codes, the signal scheme design and the development of the mathematical models for signal transmission. A simulation model is subsequently constructed in Simulink to evaluate the system. The simulation results confirm the accuracy of the model’s functionalities, including spreading, phase modulation, noise addition, phase demodulation and despreading. Additionally, the model achieves a data-transmission rate of 62.5 kbps with a bit error rate (BER) better than ${10}^{-6}$ when the modulation index exceeds $3.4\times {10}^{-3}$, meeting the requirements for inter-satellite laser communication in space-based gravitational wave detection. Full article

Lunar laser retroreflectors are a crucial target for lunar laser ranging (LLR). During LLR operations at all lunar laser ranging stations, the considerable distance between the Earth and the Moon makes it impossible to visually identify the position of the lunar laser retroreflectors within the camera’s field of view (FOV). Typically, we use the camera to observe various lunar surface features illuminated by sunlight, and then we align the telescope with the corresponding area for accurate positioning. Based on lunar digital elevation model (DEM) data and INPOP19a planetary ephemeris, our research presents an illumination model for the lunar terrain around the lunar laser retroreflectors, suitable for the 1’ camera FOV constraint at the TianQin laser ranging station. The illumination model is linked to universal time coordinated (UTC) time and DEM data. By inputting the UTC time, the illumination conditions of the terrain surrounding the five lunar laser retroreflectors can be determined for that specific time. The terrain surrounding the Apollo 15 and Lunokhod 2 retroreflectors exhibits distinctive terrain features under illumination, making them easier to locate compared to other retroreflectors. This illumination model provides a better solution to the problem of aligning laser ranging stations to lunar laser retroreflectors. Full article

The scale factor serves as a ruler for converting raw phase measurements into physical displacements and significantly impacts the preprocessing of data from the Laser Ranging Interferometer (LRI) in laser ranging systems. In the current GRACE Follow-On (GRACE-FO) mission for low–low tracking gravity satellites, most of the existing LRI scale factor estimation algorithms heavily rely on cross-calibration between instantaneous/biased ranges from the Ka-Band Ranging Interferometer (KBR) and the LRI. However, due to the nonlinearity of the objective function (which includes terms involving the product of scale and time shifts), the scale factor estimation may absorb errors from timing noise. Moreover, future gravity missions or gravity detection tasks may no longer incorporate KBR ranging instruments. To address these challenges, this paper proposes an energy-based method for scale factor estimation using inter-satellite baseline solutions. Comparative analysis indicates that the proposed method effectively disentangles two parameters in the objective function and can be applied in scenarios where KBR data are unavailable, demonstrating promising prospects for practical application. The experimental results show that when the KBR validation residuals are lower than 0.8 mm, the SYSU LRI1B V01 products exhibit residuals below the payload design accuracy thresholds in the frequency band of 2 mHz to 0.1 Hz. Additionally, the stability of the scale factors obtained from the baseline can reach 10⁻⁷. Although this is still below the required precision of better than 10⁻⁸ for the laser frequency stability in next-generation gravity satellites, advancements in orbit determination technology and the enhanced stability of GPS receivers offer potential for future precision improvements. Currently, this method appears suitable for roughly extracting the scale factor as a stochastic mean over several months or serving as a backup validation strategy for future missions, but it is not well suited to measure day-to-day variations. Full article

This article explores novel in-orbit drag-free technology that can be utilized for deep space detection scientific missions. In this study, we considered a two-test-mass drag-free method and analyzed the design of the drag-free and attitude control system for the TianQin mission. The entire control system was comprehensively designed, including an actuator allocation design and controllers for two test masses and one spacecraft, with a total of 18 degrees of freedom. Furthermore, stability analysis was conducted. Based on our design, numerical analysis and simulations were performed assuming geocentric orbit conditions in the TianQin mission, confirming the feasibility of this aerospace engineering concept. The versatility of the design allows for its application to scientific observations across various disciplines by modifying the structure of the simulation environment, and consequently, the approach discussed in this study holds significant practical implications for effectively accomplishing deep space observation tasks. Full article

During the operation of space gravitational wave detectors, the constellation configuration formed by three satellites gradually deviates from the ideal 60° angle due to the periodic variations in orbits. To ensure the stability of inter-satellite laser links, active compensation of the breathing angle variation within the constellation plane is achieved by rotating the optical subassembly through the telescope pointing mechanism. This paper proposes a high-performance robust composite control method designed to enhance the robust stability, disturbance rejection, and tracking performance of the telescope pointing system. Specifically, based on the dynamic model of the telescope pointing mechanism and the disturbance noise model, an H_∞ controller has been designed to ensure system stability and disturbance rejection capabilities. Meanwhile, employing the method of an H_∞ norm optimized disturbance observer (HODOB) enhances the nonlinear friction rejection ability of the telescope pointing system. The simulation results indicate that, compared to the traditional disturbance observer (DOB) design, utilizing the HODOB method can enhance the tracking accuracy and pointing stability of the telescope pointing system by an order of magnitude. Furthermore, the proposed composite control method improves the overall system performance, ensuring that the stability of the telescope pointing system meets the 10 nrad/Hz^1/2 @0.1 mHz~1 Hz requirement specified for the TianQin mission. Full article

Tilt-to-length coupling, a non-constant systematic error source caused by satellite attitude variations, has been observed in the laser ranging signals of the GRACE Follow-On mission. This error can be corrected by certain calibration maneuvers performed regularly in orbit. In this paper, we introduce an alternative approach to tilt-to-length coupling estimation for a laser ranging interferometer in future gravity missions, using the ranging signals without any specific calibration maneuvers, which allows daily estimation. An analytical model of laser ranging signals is derived. The tilt-to-length estimation is performed under different conditions using the least squares method as well as the simulated data. The pointing angle noise is found to be the most significant limiting factor. When the pointing angle noise is below $0.3\mathsf{\mu }{\mathrm{rad}/\mathrm{Hz}}^{1/2}$, the RMS of the estimation error is below 4 nm, much better than the tilt-to-length error of GRACE Follow-On. In the case of low pointing angle noise, the estimation error of an under 1.5 m offset between the center of mass and the interferometer reference point is not obviously different from the case with only a 0.5 mm offset, which provides installation flexibility for the laser ranging interferometer. Full article

The presence of strong ambient vibrations could have a negative impact on applications such as high precision inertial navigation and tilt measurement due to the vibration rectification error (VRE) of the accelerometer. In this paper, we investigate the origins of the VRE using a self-developed MEMS accelerometer equipped with an area-variation-based capacitive displacement transducer. Our findings indicate that the second-order nonlinearity coefficient is dependent on the frequency but the VRE remains constant when the displacement amplitude of the excitation is maintained at a constant level. This frequency dependence of nonlinearity is a result of several factors coupling with each other during signal conversion from acceleration to electrical output signal. These factors include the amplification of the proof mass’s amplitude as the excitation frequency approaches resonance, the nonlinearity in capacitance-displacement conversion at larger displacements caused by the fringing effect, and the offset of the mechanical suspension’s equilibrium point from the null position of the differential capacitance electrodes. Through displacement transducer and damping optimization, the second-order nonlinearity coefficient is greatly reduced from mg/g${}^2$ to $\mathsf{\mu }$g/g${}^2$. Full article

Satellite laser ranging (SLR) is the space geodetic technique with the highest degree of range, measuring precision and distances right down to the millimeter level. Thanks to the improvement of SLR station layouts and the advance of SLR technology, in recent years, more research has been conducted to determine Global Navigation Satellite System (GNSS) satellite orbits using SLR data. The primary goal of this contribution is to investigate the accuracy of BeiDou Navigation-3 (BDS-3) Satellite precise orbit determination (POD) using solely SLR data, as well as explore the impact of various factors on that accuracy. Firstly, we used actual SLR data to make the POD for BDS-3 satellites, and the POD accuracy was positively connected with the orbital arc lengths. The 9-day median root mean square (RMS) in radial (R), along-track (T), and cross-track (N) directions were estimated at 4.7–8.2, 22.1–35.2, and 27.4–43.8 cm, respectively, for comparison with WUM precise orbits. Then, we explored the impact of SLR observations and stations on POD accuracy. For 9-day orbital arc lengths, five station or 20 observation arcs may offer an orbit with a 1 m precision. Six to eight stations or 30–35 observation arcs allow an improved orbit accuracy up to approximately 0.5 m. Furthermore, we examined how measurement errors and orbit modeling errors affect the SLR-only POD accuracy using simulated SLR data. For orbital arc lengths of 9 days, each cm of random error leads to a 9.3–11.0 cm decrease in orbit accuracy. The accuracy of an orbit is reduced by 10.1–15.0 cm for every 1 cm of systematic error. Moreover, for solar radiation pressure (SRP) errors, the effect of POD accuracy is 20.5–45.1 cm, respectively. Full article

In order to meet the position and attitude requirements of spacecrafts and test masses for gravitational-wave detection missions, the attitude-orbit coordination control of multiple spacecrafts and test masses is studied. A distributed coordination control law for spacecraft formation based on dual quaternion is proposed. By describing the relationship between spacecrafts and test masses in the desired states, the coordination control problem is converted into a consistent-tracking control problem in which each spacecraft or test mass tracks its desired states. An accurate attitude-orbit relative dynamics model of the spacecraft and the test masses is proposed based on dual quaternions. A cooperative feedback control law based on a consistency algorithm is designed to achieve the consistent attitude tracking of multiple rigid bodies (spacecraft and test mass) and maintain the specific formation configuration. Moreover, the communication delays of the system are taken into account. The distributed coordination control law ensures almost global asymptotic convergence of the relative position and attitude error in the presence of communication delays. The simulation results demonstrate the effectiveness of the proposed control method, which meets the formation-configuration requirements for gravitational-wave detection missions. Full article

This study proposes a three-spacecraft formation reconfiguration strategy of minimum fuel for space gravitational wave detection missions in the high Earth orbit (10⁵ km). For solving the limitations of measurement and communication in long baseline formations, a control strategy of a virtual formation is applied. The virtual reference spacecraft provides a desired relative state between the satellites, which is then used to control the motion of the physical spacecraft to maintain the desired formation. A linear dynamics model based on relative orbit elements’ parameterization is used to describe the relative motion in the virtual formation, which facilitates the inclusion of J₂, SRP, and lunisolar third-body gravity effects and provides a direct insight into the relative motion geometry. Considering the actual flight scenarios of gravitational wave formations, a formation reconfiguration strategy based on continuous low thrust is investigated to achieve the desired state at a given time while minimizing interference to the satellite platform. The reconfiguration problem is considered a constrained nonlinear programming problem, and an improved particle swarm algorithm is developed to solve this problem. Finally, the simulation results demonstrate the performance of the proposed method in improving the maneuver sequence distribution and optimizing maneuver consumption. Full article

A distributed six-degree-of-freedom (6-DOF) cooperative control for multiple spacecraft formation is investigated considering parametric uncertainties, external disturbances, and time-varying communication delays. Unit dual quaternions are used to describe the kinematics and dynamics models of the 6-DOF relative motion of the spacecraft. A distributed coordinated controller based on dual quaternions with time-varying communication delays is proposed. The unknown mass and inertia, as well as unknown disturbances, are then taken into account. An adaptive coordinated control law is developed by combining the coordinated control algorithm with an adaptive algorithm to compensate for parametric uncertainties and external disturbances. The Lyapunov method is used to prove that the tracking errors converge globally asymptotically. Numerical simulations show that the proposed method can realize cooperative control of attitude and orbit for the multi-spacecraft formation. Full article