Precise Orbit Determination Research Articles

Geostationary Satellite Orbit Determination by LEO Networks with Small Inclination

In view of the limitation of ground-based Tracking Telemetry and Command (TT&C) system in covering the geostationary satellite in space and time, the method of determining the orbit of the geostationary satellite by the LEO (Low Earth Orbit) multi-satellites network with small orbit inclination was proposed. According to the space environment and optical viewing conditions, the simulation data were screened to simulate the real observation scene. The precise orbit determination (POD) of geostationary satellite was calculated by using the optical angle measurement data and the numerical method. By comparing with the reference orbit, under the condition of platform’s orbit accuracy of 5 m, measurement accuracy of 5-arcsecond, and 12 hours of observation, the POD accuracy of geostationary satellite by two LEO satellites can reach the order of kilometers, while the POD accuracy by four LEO satellites can reach the order of 100 meters. Therefore, the POD accuracy has been greatly improved with the increase of the number of LEO satellites.

Physics‐Based Approach to Thermospheric Density Estimation Using CubeSat GPS Data

AbstractIn Low Earth Orbit (LEO), atmospheric drag is the largest contributor to trajectory prediction error. The current thermospheric density model used in operations, the High Accuracy Satellite Drag Model (HASDM), applies corrections to an empirical density model every 3 hr using observations of 75+ calibration satellites. This work aims to improve global thermospheric density estimation by utilizing a physics‐based space environment model and precise GPS‐based orbit estimates of LEO CubeSats. The data assimilation approach presented here estimates drivers of the Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIE‐GCM) every 1.5 hr using CubeSat GPS information. In this work, Spire Global CubeSat data are used to demonstrate the method using only 10 satellites; the true strength of the method is its potential to exploit data already collected on large LEO constellations (hundreds of CubeSats). Precise Orbit Determination (POD) information from 10 CubeSats over 12 days is used to sense a global density field when Kp historical data show a minor and moderate geomagnetic storm in succession. This paper provides a direct comparison of estimated density, derived by our new method, to HASDM and Swarm mission derived density. A propagation analysis is also executed by comparing the CubeSat POD data to orbits propagated using our estimated density versus HASDM density. The analyses show that the estimated density is within 35% of HASDM during storm‐time conditions, and that the propagation using the estimated density yields an improvement of 26% over NRLMSISE‐00 compared to HASDM, while outperforming HASDM during the second storm peak.

Improved GPS-Based Single-Frequency Orbit Determination for the CYGNSS Spacecraft Using GipsyX

<h3>Summary</h3> This paper presents methods for the precise orbit determination (POD) of a satellite in the CYGNSS constellation based on available single-frequency GPS code and carrier measurements. The contributions include the development and evaluation of procedures for single-frequency POD with GipsyX, improvement of CYGNSS orbit knowledge, and an assessment of its final accuracy. Ionospheric effects are mitigated using the GRAPHIC processing method, and spacecraft multipath effects are calibrated with an azimuth/elevation-dependent antenna calibration map. The method is demonstrated using comparable data from the GRACE mission, from which we infer the expected accuracy of the CYGNSS results. Processing more than 170 days of data from each mission, a 1<i>σ</i> CYGNSS orbit accuracy of 2.8 cm radial, 2.4 cm cross-track, and 6 cm in-track is demonstrated. We expect that achieving this level of performance will expand the set of future scientific investigations that can be undertaken using satellites equipped with single-frequency GNSS.

Precise Orbit Determination of HY-2D using DORIS

Precise Orbit Determination of HY-2D using DORIS

Improving QZSS Precise Orbit Determination using Space-based and Ground-based Observations

Improving QZSS Precise Orbit Determination using Space-based and Ground-based Observations

Reduction of Space Debris Collision Prediction Uncertainty Based on Q-Sat Precise Orbit

Collision probability is employed for evaluating whether there will be a dangerous encounter between 2 space objects. The fidelity of the collision probability mainly depends on the accuracies of orbit prediction and covariance prediction for the space objects. In this paper, the collision probability between the Tsinghua Gravitation and Atmosphere Science Satellite, Q-Sat, and the space debris with a North American Aerospace Defense Command ID of 49863 on 2022 January 18 was calculated. The 2 objects approached each other dangerously close and the event was reported. First, the atmospheric density model is modified by a dynamic approach-based inversion to improve the accuracy of orbit prediction for the Q-Sat. Next, predictions of position error covariance are carried out. Orbits of the next 24 hours are predicted, and the predicted orbits are compared with the actual orbits of the Q-Sat. Backpropagation neural network was trained for predicting the position error covariance. For the space debris, the 2-line element data are employed. Orbit predictions for the space debris are also conducted and compared with the actual orbit. Another backpropagation neural network for predicting the position error covariance for the space debris is trained. Using the covariances from the backpropagation neural network, the error ellipsoids of the 2 objects are established. The error ellipsoids are later projected to the encounter plane to calculate the collision probability. Different from the reports from other institutes, the closest distance between the Q-Sat and the space debris calculated by the current method was 2.71 km. The collision probability was 1.16 × 10 −11 . It was not a dangerous encounter event. The onboard precise orbit determination device enabled improved orbit determination precision and orbit prediction accuracy, which is important for space safety management.

Real-Time LEO Satellite Orbits Based on Batch Least-Squares Orbit Determination with Short-Term Orbit Prediction

The augmentation of the Global Navigation Satellite System (GNSS) by Low Earth Orbit (LEO) satellites is proposed as an effective method to improve the precision and shorten the convergence time of Precise Point Positioning (PPP). Serving as navigation satellites in the future, LEO satellites need to be provided with their high-accuracy orbits in real-time. This would potentially enable the high-accuracy real-time LEO satellite clock determination, and eventually facilitate the high-accuracy ground-based positioning. Studies have been performed to achieve such real-time orbits using a Kalman filter in both the kinematic and reduced-dynamic modes. Batch Least-Squares (BLS) adjustment delivers more stable orbits in near-real-time, as it performs better phase screening. However, it suffers from longer delays compared to the Kalman filter. With the LEO satellite orbit prediction strategies improved over time, this latency can be bridged by short-term orbit prediction. In this study, using real-time GNSS satellite products, the real-time LEO satellite orbits are obtained based on the batch least-squares adjustment and short-term prediction. LEO ephemeris parameters are generated within specific prediction time windows. Using real data from the 500 km GRACE C satellite and 810 km Sentinel-3B satellite, the near-real-time BLS Precise Orbit Determination (POD) results exhibit good accuracy with an Orbital User Range Error (OURE) of 2–4 cm using different real-time GNSS products. A range of delays of the BLS POD processes are assumed, based on tests performed on different processing machines, leading to various prediction windows, from 3–8 min to 12–17 min that correspond to the real-time usage. The orbital prediction errors are shown to be highly correlated with the orbital height and the prediction time. The computational efficiency thus becomes essential to reduce the prediction errors for a certain LEO satellite. For advanced processing units leading to a prediction window shorter or equal to 6–11 min, one can expect a total real-time orbital error budget of 3–5 cm, provided that an appropriate prediction strategy is applied and high-quality GNSS products are used. For a given fitting interval, the ephemeris fitting errors are generally related to the number of ephemeris parameters and the orbital height. Compared with the prediction errors, the ephemeris fitting errors do not play a significant role in the total error budget when using 22 ephemeris parameters.

A Concise Method for Calibrating the Offset of GPS Precise Satellite Orbit

A set of Global Navigation Satellite Systems (GNSS) satellite orbit and clock offset are an essential prerequisite for precise application. However, abrupt changes in accuracy at the boundaries are prevalent in products provided by international GNSS services, resulting in decreased orbit interpolation precision near the daily boundary. In addition, the effect of this phenomenon is reflected in the deterioration of accuracy and the fluctuations in subsequent applications. In this study, time-weighted and equal-weighted calibrated methods were utilized for adjacent Global Positioning System (GPS) satellite orbits and the orbit variations were then corrected for the clock offset to ensure their consistency. The calibration method is evaluated based on the accuracy and smoothness of post-processing kinematic precise point positioning (PPP) and low earth orbit (LEO) precise orbit determination (POD) near the day boundary. In a variety of scientific applications, the results indicate that the proposed calibration method can effectively reduce the excessive differences near the day boundary between adjacent days. Near the boundary, maximum improvements for post-processing kinematic PPP, dynamic LEO precision orbit, kinematic LEO precision orbit are 41.5%, 9.4%, and 20.5%, respectively.

Simulation of the Use of Variance Component Estimation in Relative Weighting of Inter-Satellite Links and GNSS Measurements

Inter-satellite links (ISLs) can improve the performance of the Global Navigation Satellite System (GNSS) in terms of precise orbit determination, communication, and data-exchange capabilities. This research aimed to evaluate a simulation-based processing strategy involving the exploitation of ISLs in orbit determination of Galileo satellites, which are not equipped with operational ISLs. The performance of the estimation process is first tested based on relative weighting coefficients obtained with methods of variance component estimation (VCE) varying in the complexity of the calculations. Inclusion of biases in the ISL measurements allows evaluation of the processing strategy and assessment of the impact of three different sets of ground stations: 44 and 16 stations distributed globally and 16 located in Europe. The results indicate that using different VCE approaches might lower orbit errors by up to 20% with a negligible impact on clock estimation. Depending on the applied ISL connectivity scheme, ISL range bias can be estimated with RMS between 10% to 30% of initial bias values. The accuracy of bias estimation may be associated with weighting approach and the number of ground stations. The results of this study show how introducing VCE with various simulation parameters into the processing chain might increase the accuracy of the orbit estimation.

Estimation of Vertical Phase Center Offset and Phase Center Variations for BDS-3 B1CB2a Signals

The BeiDou Global Satellite Navigation System (BDS-3) broadcast newly developed B1C and B2a signals. To provide a better service for global users, the vertical phase center offset (PCO) and phase center variation (PCV) are estimated for the B1C/B2a ionospheric-free linear combination of the BDS-3 inclined geostationary orbit (IGSO) and medium earth orbit (MEO) satellites in this study. And considering the traditional PCC estimation method needs two Precise orbit determination (POD) processing, based on the correlation between PCO z-offset and PCV, the theoretical analysis and experimental comparison have been made to discuss whether the POD procedure for the PCO estimation can be omitted. The estimated z-offset time series revealed the inadequacy of the solar radiation pressure (SRP) model for the IGSO satellites and the MEO satellites with Pseudo Random Noise code (PRN) C45 and C46. The PCVraws estimated by the traditional method and the PCO estimation omitted method have the same characteristic. The final PCO z-offsets and PCVs calculated by the two schemes agreed very well with differences can be harmlessly ignored, which confirmed that the PCO estimation can be safely omitted to save computation time. The PCC model proposed in this study has been compared with the Test and Assessment Research Center of China Satellite Navigation Office (TARC/CSNO) released model, the qualities of the orbits and BDS-only precise point positioning (PPP) solutions of the new model both show improvements, except for the IGSO orbits. The analysis of the IGSO orbits further verifies the SRP model is not suitable for the IGSO satellites.

Improving the estimation of thermospheric neutral density via two-step assimilation of in situ neutral density into a numerical model

AbstractNeutral thermospheric density is an essential quantity required for precise orbit determination of satellites, collision avoidance of satellites, re-entry prediction of satellites or space debris, and satellite lifetime assessments. Empirical models of the thermosphere fail to provide sufficient estimates of neutral thermospheric density along the orbits of satellites by reason of approximations, assumptions and a limited temporal resolution. At high solar activity these estimates can be off by 70% when comparing to observations at 12-hourly averages. In recent decades, neutral density is regularly observed with satellite accelerometers on board of low Earth orbiting satellites like CHAMP, GOCE, GRACE, GRACE-FO, or Swarm. When assimilating such along-track information into global models of thermosphere–ionosphere dynamics, it has been often observed that only a very local sub-domain of the model grid around the satellite’s position is updated. To extend the impact to the entire model domain we suggest a new two-step approach: we use accelerometer-derived neutral densities from the CHAMP mission in a first step to calibrate an empirical thermosphere density model (NRLMSIS 2.0). In a second step, we assimilate—for the first time—densities predicted for a regular three-dimensional grid into the TIE-GCM (Thermosphere Ionosphere Electrodynamics General Circulation Model). Data assimilation is performed using the Local Error-Subspace Transform Kalman Filter provided by the Parallel Data Assimilation Framework (PDAF). We test the new approach using a 2-week-long period containing the 5 April 2010 Geomagnetic storm. Accelerometer-derived neutral densities from the GRACE mission are used for additional evaluation. We demonstrate that the two-step approach globally improves the simulation of thermospheric density. We could significantly improve the density prediction for CHAMP and GRACE. In fact, the offset between the accelerometer-derived densities and the model prediction is reduced by 45% for CHAMP and 20% for GRACE when applying the two-step approach. The implication is that our approach allows one to much better ’transplant’ the precise CHAMP thermospheric density measurements to satellites flying at a similar altitude. Graphical Abstract

Analysis of Galileo five-frequency precise satellite clock estimation models and its effect on multi-frequency PPP

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) applications. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8–12% for triple-frequency models, and 19–27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi-frequency satellite clock offsets can be improved by 7–18% for dual-frequency PPP, 8–15% for triple-frequency PPP, 4–16% for five-frequency PPP. The positioning accuracy can be further improved by 11–28% for triple-frequency PPP and 7–20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.

Precise orbit determination and baseline consistency assessment for Swarm constellation

Precise orbit determination (POD) and precise baseline determination (PBD) of Swarm satellites with 4 years of data are investigated. Ambiguity resolution (AR) plays a crucial role in achieving the best orbit accuracy. Swarm POD and PBD based on single difference (SD) AR and traditional double difference (DD) AR methods are explored separately. Swarm antenna phase center variation (PCV) corrections are developed to further improve the orbit determination accuracy. The code multipath of C1C, C1W and C2W observations is first evaluated and clear variations in code noise related to different receiver settings are observed. Carrier phase residuals of different time periods and different loop tracking settings of receiver are studied to explore the effect of ionospheric scintillation on POD. The reduction of residuals in the polar and geomagnetic equator regions confirms the positive impact of the updated carrier tracking loops (TLs) on POD performance. The SD AR orbits and orbits with float ambiguity (FA) are compared with the Swarm precise science orbits (PSOs). An average improvement of 27 %, 4 % and 16 % is gained in along-track, cross-track and radial directions by fixing the ambiguity to integer. For Swarm-A/B and Swarm-B/C formations, specific days are selected to perform the DD AR-based POD during which the average distance of the formation satellites is less than 5000 km. Satellite laser ranging (SLR) observations are employed to validate the performance of FA, SD AR and DD AR orbits. The consistency between the SD AR orbits and SLR data is at a level of 10 mm which shows an improvement of 25 % when comparing with the FA results. An SLR residuals reduction of 15 % is also achieved by the DD AR solution for the selected days. Precise relative navigation is also an essential aspect for spacecraft formation flying missions. The closure error method is proposed to evaluate the baseline precision in three dimensions. A baseline precision of 1–3 mm for Swarm-A/C formation and 3–5 mm for Swarm-A/B and Swarm-B/C satellite pairs is verified by both the consistency check and closure error method.

Analysis of Precise Orbit Determination of BDS-3 MEO and IGSO Satellites Based on Several Dual-Frequency Measurement Combinations

The Chinese BeiDou-3 navigation satellite system (BDS-3) is capable of transmitting both old B1I, B3I signals and new B1C, B2a, B2b signals. Current BDS-3 precise orbits are generally calculated using a B1I/B3I combination considering overlap with the BeiDou-2 navigation satellite system (BDS-2). In this contribution, the observation quality of BDS-3 medium earth orbit (MEO) satellites and inclined geosynchronous orbit (IGSO) satellites are analyzed based on three aspects, i.e., carrier to noise ratio (C/N0), pseudo-range noise and pseudo-range multipath (MP). The C/N0 of the MEO satellite is 2~3 dB higher than that of the IGSO satellite at the same elevation angle. Meanwhile, the order of the Root Mean Square (RMS) values of both pseudo-range noise and MP is B1I &lt; B1C &lt; B3I &lt; B2a ≈ B2b. Three kinds of combinations, i.e., B1CB2a, B1CB2b and B1IB3I, are selected for the BDS-3 precise orbit determination (POD) experiment. Orbits are assessed by the orbit-only signal-in-space range error (SISRE) computed between pairs of the three kinds of combinations in this contribution, CODE and GFZ final orbits. Orbit-only SISRE assessment shows that B1CB2a/CODE, B1CB2b/CODE, B1CB2a/GFZ and B1CB2b/GFZ are at the same level with CODE/GFZ, and the orbit-only SISRE is at the level of 5 cm for MEOs and 9 cm for IGSOs, respectively. Meanwhile, B1IB3I/CODE and B1IB3I/GFZ are about 1–2 cm worse. Inter-solution comparison between B1CB2a, B1CB2b and B1IB3I also indicate that B1CB2a and B1CB2b have good consistency, while B1IB3I shows poor performance. Satellite laser ranging (SLR) residuals indicate that the mean RMS is 3–4 cm for the four BDS-3 MEOs for CODE final orbit, GFZ final orbit, B1CB2a and B1CB2b combinations, while the mean RMS value for B1IB3I combination is a few millimeters worse, at approximately 4–5 cm.

Enhanced precise orbit determination of BDS-3 MEO satellites based on ambiguity resolution with B1C/B2a dual-frequency combination

Broadcasting the multi-frequency signals is one of the outstanding advantages of BDS-3 (BeiDou Navigation Satellite System). In addition to the legacy signals B1I and B3I, we are interested in the performance of two new signals B1C and B2a. For the purpose of improving the orbit accuracy of BDS-3 backbone MEOs (Medium Earth Orbits), this study focuses on Precise Orbit Determination (POD) using B1C/B2a dual-frequency measurements. First, the performance of POD will be benefit from an increasing observation quantity and qualities. Observations from the public MGEX (Multi-GNSS Experiment) network are statistically collected, and the number of stations able to track B1C and B2a signals is analyzed. In recent years, the sustainable growth number of stations is up to more than one hundred, which brings the new chance to improve the POD accuracy based on B1C/B2a linear combination. Then, the multipath and post-fit residuals of observations are compared between B1C/B2a and B1I/B3I to investigate the observation qualities. Second, as a key strategy, the ambiguities are successfully fixed during POD processing of BDS-3 MEOs. The ambiguity fixing percentage is as high as 93.1% on average using B1C/B2a combination. Compared with float solutions, the improvements of ambiguity fixed orbits reach 36.2%, 19.9% and 36.6% on the radial, along-track and cross-track components, respectively. For the fixed solutions of B1I/B3I and B1C/B2a, it is noticed that the orbits achieve further benefits from B1C/B2a combination for 8.4%, 6.9% and 8.0% on the radial, along-track and cross-track components, respectively. Finally, the performance of B1C/B2a combination POD is validated by orbital overlapping, the orbit signal-in-space range error (SISRE) analysis, independent technology Satellite Laser Ranging (SLR) and Precise Point Positioning (PPP), respectively. SLR residuals show the radial orbital accuracy has an improvement of 8.0% for C20, C21, C29 and C30 on average when employing B1C/B2a measurements. Compared with B1I/B3I, both static and kinematic PPP based on B1C/B2a orbits indicate the improvement on the vertical component. And a faster and more stable convergence performance is also observed using B1C/B2a combination.

Geosynchronous satellites expanding a future GNSS satellite constellation: A precise orbit determination study

The integration of geosynchronous orbit (GSO) satellites in Global Navigation Satellite Systems (GNSS) is mostly discussed to enable a regional enhancement for tracking. But how do GSO satellites affect the orbit determination of the rest of the constellation? How accurately can these orbits be determined in a future GNSS tracking scenario with optical links? In this simulation study we analyze the benefit of GSO satellites as an expansion of a MEO (Medium Earth Orbit) satellite constellation – we selected the Galileo satellite constellation – for MEO Precise Orbit Determination (POD). We address not only the impact on POD of MEO satellites but also the possibility to precisely determine the GSO satellites – geostationary orbits (GEO) and inclined geosynchronous orbits (IGSO) – in such an expanded MEO constellation. In addition to GNSS microwave observations, we analyze the influence of different optical links between the participating entities: Optical two-way Inter-Satellite Links (OISL) and ground-space oriented Optical Two-Way Links (OTWL). These optical measurements together with the GNSS microwave observations give a remarkable benefit for the POD capability. In the case of GNSS and OTWL, we simulate the measurements with regard to a network of 16 ground stations. We pay great attention to the simulation of systematic effects of all measurement techniques. We discuss the influence on the systematic errors as well as the formal orbit uncertainties. A MEO constellation expanded with GSO satellites as well as the use of optical links together with GNSS observations not only improves the MEO satellite orbits but also the GSOs to a great extent.

Atmospheric Density Response to a Severe Magnetic Storm Detected by the 520 km Altitude Spherical Satellite

The polar-orbiting spherical experimental satellite of China for atmospheric density detection with an altitude of ~520 km was successfully launched on 14 October 2021. Based on the dynamic inversion method for atmospheric density and the precise orbit determination data obtained by its GNSS, we inverted the orbital atmospheric density during the severe geomagnetic storm in early November 2021. In this paper, we compared the atmospheric density data obtained by the spherical satellite with the simulations of the MSISE00 and the DTM, evaluated their error distribution, and analyzed the response of the atmospheric density during the severe geomagnetic storm in the dawn–dusk orbit of 520 km altitude. The properties and the physical processes for the atmospheric density of the time evolutions in different latitudes and the global distributions during the severe geomagnetic storm were obtained. We found that the substantial disturbance enhancement and recovery of the atmospheric density of the dawn–dusk orbit have a close correlation with the geomagnetic indexes Kp and Dst. The elevation extends from the poles to the equator, and the relative variation in two hemispheres demonstrates a bimodal nearly symmetric growth structure. The maximum relative variation of the two hemispheres both occurred in the middle latitude, and, for this case, the enhancement of atmospheric density in the mid-latitude region accounted for a larger proportion. The asymmetry between the northern and southern hemispheres is demonstrated by the fact that the absolute value and absolute change in the southern hemisphere in summer are larger than those in the northern hemisphere, and the bimodal structure of the relative variation is inclined to the northern hemisphere.

On the relation of GNSS phase center offsets and the terrestrial reference frame scale: a semi-analytical analysis

Phase center offsets (PCOs) of global navigation satellites systems (GNSS) transmit antennas along the boresight axis introduce line-of-sight-dependent range changes in the modeling of GNSS observations that are strongly correlated with the estimated station heights. As a consequence, changes in the adopted PCOs impact the scale of GNSS-based realizations of the terrestrial reference frame (TRF). Vice versa, changes in the adopted TRF scale require corrections to the GNSS transmit antenna PCOs for consistent observation modeling. Early studies have determined an approximate value of alpha =-0.050 for the ratio of station height changes and satellite PCO changes in GPS orbit determination and phase center adjustment. However, this is mainly an empirical value and limited information is available on the actual PCO-scale relation and how it is influenced by other factors. In view of the recurring need to adjust the IGS antenna models to new ITRF scales, a semi-analytical model is developed to determine values of alpha for the four current GNSSs from first principles without a need for actual network data processing. Given the close coupling of satellite boresight angle and station zenith angle, satellite PCO changes are essentially compensated by a combination of station height, zenith troposphere delay, and receiver clock offset. As such, the value of alpha depends not only on the orbital altitude of the considered GNSS but also on the elevation-dependent distribution of GNSS observations and their weighting, as well as the elevation mask angle and the tropospheric mapping function. Based on the model, representative values of alpha _text {GPS}=-0.051, alpha _text {GLO}=-0.055, alpha _text {GAL}=-0.041, and alpha _text {BDS-3}=-0.046 are derived for GPS, GLONASS, Galileo, and BeiDou-3 at a 10^circ elevation cutoff angle. These values may vary by varDelta alpha approx 0.003 depending on the specific model assumptions and data processing parameters in a precise orbit determination or precise point positioning. Likewise changes of about pm 0.003 can be observed when varying the cutoff angle between 5^circ and 15^circ .

The preliminary result of orbital atmosphere detector on board spherical satellite

<p indent="0mm">The spherical satellite is Chinese first spherical small satellite, integrating atmospheric composition, atmospheric density detection and precision orbit determination. The payload is the Orbital Atmosphere Detector, which was launched into near circular polar orbit with the orbit altitude of <sc>520 km</sc> and inclination angle of 97.4° on 14 October, 2021. The scientific objectives, operating principle and the ground calibration results of the Orbital Atmosphere Detector are presented in this paper. The preliminary <italic>in-situ</italic> observed results are analyzed and discussed. The observed mass densities are strongly correlated with <italic>F</italic>10.7 and <italic>Kp</italic>. The peak-to-valley ratio of observed mass densities during the quiet period of solar and geomagnetic activity on 3 November 2021 was 3.02; the peak of observed mass density increased from 2.8×10⁻¹³ to 8.0×<sc>10⁻¹³ kg/m³</sc> during the strong geomagnetic storm event on 4 November, 2021, an increase of 2.857 times compared to the MSIS00 model of 1.316 times. The observed data show that the increase in atmospheric density started at the South Pole and spread to the middle and low latitudes, while the MSIS00 model only show a weak symmetrically increase between the northern and southern hemispheres during the storm. The observed results show that the observed data objectively reflect the spatial and temporal distribution of thermosphere density during the quiet period and the geomagnetic storm event, and thermosphere atmospheric model correction can be implemented based on the large amount of observed data.

Design and Analysis of the Cis-Lunar Navigation for the ArgoMoon CubeSat Mission

In the framework of the Artemis-1 mission, 10 CubeSats will be released, including the 6U CubeSat ArgoMoon, built by the Italian company Argotec and coordinated by the Italian Space Agency. The primary goal of ArgoMoon is to capture images of the Interim Cryogenic Propulsion Stage. Then, ArgoMoon will be placed into a highly elliptical orbit around the Earth with several encounters with the Moon. In this phase, the navigation process will require a precise Orbit Determination (OD) and a Flight Path Control (FPC) to satisfy the navigation requirements. The OD will estimate the spacecraft trajectory using ground-based radiometric observables. The FPC is based on an optimal control strategy designed to reduce the dispersion with respect to the reference trajectory and minimize the total ΔV. A linear approach was used to determine the optimal targets and the number and location of the orbital maneuvers. A covariance analysis was performed to assess the expected OD performance and its robustness. The analysis results show that the reference translunar trajectory can be successfully flown and the navigation performance is strongly dependent on the uncertainties of the ArgoMoon’s Propulsion Subsystem and of the orbit injection.