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The GRACE Follow-On satellite mission measures distance variations between its two satellites in order to derive monthly gravity field maps, indicating mass variability on Earth on a scale of a few 100 km originating from hydrology, seismology, climatology and other sources. This mission hosts two ranging instruments, a conventional microwave system based on K(a)-band ranging (KBR) and a novel laser ranging instrument (LRI), both relying on interferometric phase readout. In this paper, we show how the phase measurements can be converted into range data using a time-dependent carrier frequency (or wavelength) that takes into account potential intraday variability in the microwave or laser frequency. Moreover, we analyze the KBR-LRI residuals and discuss which error and noise contributors limit the residuals at high and low Fourier frequencies. It turns out that the agreement between KBR and LRI biased range observations can be slightly improved by considering intraday carrier frequency variations in the processing. Although the effect is probably small enough to have little relevance for gravity field determination at the current precision level, this analysis is of relevance for detailed instrument characterization and potentially for future more precise missions.

Spacecraft formation flying (SFF) in highly elliptical orbit (HEO) has attracted a great deal of attention in many space exploration applications, while precise guidance, navigation, and control (GNC) technology—especially precise ranging—are the basis of success for such SFF missions. In this paper, we introduce a novel K-band microwave ranging (MWR) equipment for the on-orbit verification of submillimeter-level precise ranging technology in future HEO SFF missions. The ranging technique is a synchronous dual one-way ranging (DOWR) microwave phase accumulation system, which achieved a ranging accuracy of tens of microns in the laboratory environment. The detailed design and development process of the MWR equipment are provided, ranging error sources are analyzed, and relative orbit dynamic models for HEO formation scenes are given with real perturbations considered. Moreover, an adaptive Kalman filter algorithm is introduced for SFF relative navigation design, incorporating process noise uncertainty. The performance of SFF relative navigation while using MWR is tested in a hardware-in-the-loop (HIL) simulation system within a high-precision six degrees of freedom (6-DOF) moving platform. The final range estimation errors from MWR using the adaptive filter were less than 35 μm and 8.5 μm/s for range rate, demonstrating the promising accuracy for future HEO formation mission applications.

The Gravity Recovery and Climate Experiment (GRACE) satellite mission has provided global long-term observations of mass transport in the Earth system with applications in numerous geophysical fields. In this paper, we targeted the in-orbit performance of the GRACE key instruments, the ACCelerometers (ACC) and the MicroWave ranging Instrument (MWI). For the ACC data, we followed a transplant approach analyzing the residual accelerations from transplanted accelerations of one of the two satellites to the other. For the MWI data, we analyzed the post-fit residuals of the monthly GFZ GRACE RL06 solutions with a focus on stationarity. Based on the analyses for the two test years 2007 and 2014, we derived stochastic models for the two instruments and a combined ACC+MWI stochastic model. While all three ACC axes showed worse performance than their preflight specifications, in 2007, a better ACC performance than in 2014 was observed by a factor of 3.6 due to switched-off satellite thermal control. The GRACE MWI noise showed white noise behavior for frequencies above 10 mHz around the level of 1.5×10−6 m/Hz. In the combined ACC+MWI noise model, the ACC part dominated the frequencies below 10 mHz, while the MWI part dominated above 10 mHz. We applied the combined ACC+MWI stochastic models for 2007 and 2014 to the monthly GFZ GRACE RL06 processing. This improved the formal errors and resulted in a comparable noise level of the estimated gravity field parameters. Furthermore, the need for co-estimating empirical parameters was reduced.

In this study, submillimeter level accuracy K-band microwave ranging (MWR) equipment is demonstrated, aiming to verify the detection of the Earth’s gravity field (EGF) and digital elevation models (DEM), through spacecraft formation flying (SFF) in low Earth orbit (LEO). In particular, this paper introduces in detail an integrated BeiDou III B1C/B2a dual frequency receiver we designed and developed, including signal processing scheme, gain allocation, and frequency planning. The receiver matched the 0.1 ns precise synchronize time-frequency benchmark for the MWR system, verified by a static and dynamic test, compared with a time interval counter synchronization solution. Moreover, MWR equipment ranging accuracy is explored in-depth by using different ranging techniques. The test results show that MWR achieved 40 μm and 1.6 μm/s accuracy for ranging and range rate during tests, using synchronous dual one-way ranging (DOWR) microwave phase accumulation frame, and 6 μm/s range rate accuracy obtained through a one-way ranging experiment. The ranging error sources of the whole MWR system in-orbit are analyzed, while the relative orbit dynamic models, for formation scenes, and adaptive Kalman filter algorithms, for SFF relative navigation designs, are introduced. The performance of SFF relative navigation using MWR are tested in a hardware in loop (HIL) simulation system within a high precision six degree of freedom (6-DOF) moving platform. The final estimation error from adaptive relative navigation system using MWR are about 0.42 mm (range/RMS) and 0.87 μm/s (range rate/RMS), which demonstrated the promising accuracy for future applications of EGF and DEM formation missions in space.

Nowadays, indoor positioning using ultra-wideband (UWB) signals is actively being developed with the aim of implementing existing ideas and solutions, improving their performance, and searching for new measurement schemes. This paper proposes an approach to estimating the distance between wireless nodes by measuring radio signal propagation time using UWB chaotic radio pulses and UWB transceivers. This type of signal is a simple and practically interesting alternative to radio carriers of other types of UWB signals, which are based on packets of pulses (usually ultra-short pulses). The practical interest is caused by the noise-like nature of chaotic radio pulses, as well as their immunity to multipath fading and ease of generation. The aim of this work is to analyze such a system and identify the fundamental limitations inherent in the proposed approach. This paper describes a wireless system for measuring the signal propagation time based on the envelope of chaotic radio pulses using the SS-TWR (Single-Sided Two-Way Ranging) method. A difference scheme is used to determine the range. The characteristics of the proposed system are studied experimentally. The factors related to the threshold scheme for determining the time of arrival of a radio signal that introduce a systematic error into the measurement results are revealed, and approaches to correcting their influence are proposed.

Micrometre level ranging accuracy between satellites on-orbit relies on the high-precision calibration of the antenna phase center (APC), which is accomplished through properly designed calibration maneuvers batch estimation algorithms currently. However, the unmodeled perturbations of the space dynamic and sensor-induced uncertainty complicated the situation in reality; ranging accuracy especially deteriorated outside the antenna main-lobe when maneuvers performed. This paper proposes an on-orbit APC calibration method that uses a reinforcement learning (RL) process, aiming to provide the high accuracy ranging datum for onboard instruments with micrometre level. The RL process used here is an improved Temporal Difference advantage actor critic algorithm (TDAAC), which mainly focuses on two neural networks (NN) for critic and actor function. The output of the TDAAC algorithm will autonomously balance the APC calibration maneuvers amplitude and APC-observed sensitivity with an object of maximal APC estimation accuracy. The RL-based APC calibration method proposed here is fully tested in software and on-ground experiments, with an APC calibration accuracy of less than 2 mrad, and the on-orbit maneuver data from 11–12 April 2022, which achieved 1–1.5 mrad calibration accuracy after RL training. The proposed RL-based APC algorithm may extend to prove mass calibration scenes with actions feedback to attitude determination and control system (ADCS), showing flexibility of spacecraft payload applications in the future.

The use of ultra-wideband (UWB) signals for local positioning is very attractive for practice, because such signals have the potential to provide centimeter precision. In this paper, we consider wireless ranging (distance measurement) and positioning, using one of the kinds of UWB signals, i.e., chaotic radio pulses, which are noise-like signals with no constant shape. The distance measurement is based on an assessment in the receiver of the power of UWB chaotic radio pulses emitted by the transmitter. A new method for estimating their power and its experimental implementation is proposed and described. Experimental layouts of the transmitter and receiver and the principles of their operation are described. To determine the main features of this method under real signal propagation conditions, full-scale indoor measurements were carried out, and statistical estimates of the accuracy were made. We present the results of experimental testing of the proposed approach for positioning the emitter relative to a system of anchors in an office space 6 × 6.5 m2 in the mode of measuring object coordinates on a line and on a plane. The mean absolute error (MAE) of distance measurement (1D) was 25 cm, and the root mean squared error (RMSE) was 39 cm. When positioning on a plane (2D), the MAE of coordinate estimation was 34 cm and the RMSE was 42 cm. The proposed distance measurement method is intended for use in wireless UWB transceivers used in wireless sensor networks.

Early works 1 and recent advances in thin-film lithium niobate (LiNbO 3 ) on insulator have enabled low-loss photonic integrated circuits 2 , 3 , modulators with improved half-wave voltage 4 , 5 , electro-optic frequency combs 6 and on-chip electro-optic devices, with applications ranging from microwave photonics to microwave-to-optical quantum interfaces 7 . Although recent advances have demonstrated tunable integrated lasers based on LiNbO 3 (refs. 8 , 9 ), the full potential of this platform to demonstrate frequency-agile, narrow-linewidth integrated lasers has not been achieved. Here we report such a laser with a fast tuning rate based on a hybrid silicon nitride (Si 3 N 4 )–LiNbO 3 photonic platform and demonstrate its use for coherent laser ranging. Our platform is based on heterogeneous integration of ultralow-loss Si 3 N 4 photonic integrated circuits with thin-film LiNbO 3 through direct bonding at the wafer level, in contrast to previously demonstrated chiplet-level integration 10 , featuring low propagation loss of 8.5 decibels per metre, enabling narrow-linewidth lasing (intrinsic linewidth of 3 kilohertz) by self-injection locking to a laser diode. The hybrid mode of the resonator allows electro-optic laser frequency tuning at a speed of 12 × 10 15  hertz per second with high linearity and low hysteresis while retaining the narrow linewidth. Using a hybrid integrated laser, we perform a proof-of-concept coherent optical ranging (FMCW LiDAR) experiment. Endowing Si 3 N 4 photonic integrated circuits with LiNbO 3 creates a platform that combines the individual advantages of thin-film LiNbO 3 with those of Si 3 N 4 , which show precise lithographic control, mature manufacturing and ultralow loss 11 , 12 . A frequency-tunable laser based on a hybrid silicon nitride and lithium niobate integrated photonic platform has a fast tuning rate and could be used for optical ranging applications.

The transition to chaos is ubiquitous in nonlinear systems ranging from fluid dynamics and superconducting circuits to biological organisms. Optical systems driven out of equilibrium such as lasers and supercontinuum generation exhibit chaotic states of light with fluctuations in both amplitude and phase and can give rise to Levy statistics, turbulence and rogue waves. Spatiotemporal chaos also occurs in continuous-wave-driven photonic-chip-based Kerr microresonators, where it is referred to as chaotic modulation instability. Such modulation instability states have generally been considered impractical for applications, in contrast to their coherent-light-state counterparts, which include soliton or dark-pulse states. Here we demonstrate that incoherent and chaotic states of light in an optical microresonator can be harnessed to implement unambiguous and interference-immune massively parallel coherent laser ranging by using the intrinsic random amplitude and phase modulation of the chaotic comb lines. We utilize 40 distinct lines of a microresonator frequency comb operated in the modulation instability regime. Each line carries >1 GHz noise bandwidth, which greatly surpasses the cavity linewidth, and enables to retrieve the distance of objects with centimetre-scale resolution. Our approach utilizes one of the most widely accessible microcomb states, and offers—in contrast to dissipative Kerr soliton states—high conversion efficiency, as well as flat optical spectra, and alleviates the need for complex laser initiation routines. Moreover the approach generates wideband signal modulation without requiring any electro-optical modulator or microwave synthesizer. Viewed more broadly, similar optical systems capable of chaotic dynamics could be applied to random-modulation optical ranging as well as spread-spectrum communication, optical cryptography and random number generation.The intrinsic random amplitude and phase modulation of 40 distinct lines of a microresonator frequency comb operated in the modulation instability regime are used to realize massively parallel random-modulation continuous-wave light detection and ranging, without requiring any electro-optical modulator or microwave synthesizer.

An ultrafast microwave ranging method based on optically generated frequency-modulated microwave pulses is proposed in this study. The theoretical analysis demonstrated that nanosecond-scale linear frequency modulation microwave pulse can be obtained by femtosecond laser interference under the condition of unbalanced dispersion, which can be used to achieve a high temporal resolution of the displacement change in the measurement by the principle of frequency modulation continuous wave (FMCW) radar. The proof-of-principle experiment successfully measured the displacement change with an error of 2.5 mm and a range of 0.6 m, with a response time of 468 ns. Compared to existing microwave ranging technologies, the temporal resolution was improved by two orders of magnitude, which greatly improves the temporal resolution of distance measurement in the field of microwave FMCW radar.