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 $\mathsf{\mu }$m and 8.5 $\mathsf{\mu }$m/s for range rate, demonstrating the promising accuracy for future HEO formation mission applications.

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 $\mathsf{\mu }$m and 1.6 $\mathsf{\mu }$m/s accuracy for ranging and range rate during tests, using synchronous dual one-way ranging (DOWR) microwave phase accumulation frame, and 6 $\mathsf{\mu }$m/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 $\mathsf{\mu }$m/s (range rate/RMS), which demonstrated the promising accuracy for future applications of EGF and DEM formation missions in space.

In this study, analytical results are obtained for fuel-optimal spacecraft formation maneuver, including initialization and reconfiguration. The method consists of two stages. The first is parameterization of the problem and a new form of the problem is developed for simplicity. Second, the out-of-plane and in-plane maneuver are studied with the help of a useful inequality introduced and proved, the lower bound of the fuel consumption and the corresponding constraints of the control forces are derived and obtained. The result shows that the minimum total fuel consumption depends on the relative size parameters, and that the existence of optimal control algorithms depends upon the initial conditions. Numerical simulation of application proved the validity and efficiency of the proposed method, which can also be utilized in the maneuver of PCF.

With the support of the national nature science foundation, the Academy of Space Electronic Information Technology is developing a novel compact spaceborne GNSS receiver, referred to as the HiSGR (High Sensitivity GNSS Receiver). This receiver can operate effectively in the full range of Earth orbiting missions, from LEO (Low Earth Orbit) to geostationary and beyond. Improved signal detection algorithms are used in the signal process section of the HiSGR and an inertial sensor is used for GNSS/INS ultra tight coupled design, which makes the acquisition process fast and provides improved tracking performance for weaker GPS signals in the presence of high dynamics. Extensive tests are performed using the HiSGR to demonstrate the good performance of some crucial specifications, by employing a real GNSS signal received in an open field and through hardware- in-the-loop simulation. Receiver performance is demonstrated for LEO and GEO scenarios. A ground vehicle running test is performed for demonstration of fast acquisition and reacquisition capabilities under conditions of signal loss. The HiSGR showed good performance and it was stable during the simulations and tests, which proved its capability for future space applications.

A new optimal linear attitude estimator is proposed for single-point attitude estimation using geometric approach, and a recursive optimal linear attitude estimator is developed through filtering noisy measurements. Dot and cross products are taken in order to eliminate the unknown parameters of relationships between measurements and Gibbs vector. The optimality criterion, which does not coincide with Wahba’s constrained criterion, yields linear attitude estimate. A prior rotation is adopted to avoid singularity which occurs when the principal angle is close to π. The recursive algorithm is achieved for the purpose of improving attitude accuracy using all past measurements. For long-term space missions, memory fading concept is introduced into recursive optimal linear attitude estimator. The optimal relative weighting is obtained through minimizing error propagation, and an efficient modification is proposed to significantly reduce the sudden increase of attitude error of recursive optimal linear attitude estimator in special cases. Numerical simulations show that the estimate of optimal linear attitude estimator is almost identical with that of the famous QUaternion ESTimator, and the accuracy provided by recursive optimal linear attitude estimator is over an order magnitude higher than that of optimal linear attitude estimator or QUaternion ESTimator in most cases.