On the practical exploitation of perturbative effects in low Earth orbit for space debris mitigation

This paper presents the results of a numerical evaluation of the natural lifetime reduction in low Earth orbit, due to dynamical perturbations. The study considers two values for the area-to-mass ratio, a nominal ratio which resembles a typical value of spacecraft in orbit today, and an enhanced ratio which covers the surface augmentation. The results were obtained with two orbit propagators, one of a semi-analytical nature and the second one using non-averaged equations of motion. The simulations for both propagators were set up similarly to allow comparison. They both use the solar radiation pressure and the secular terms of the geopotential ($J_2,J_4$ and $J_6$). The atmospheric drag was turned on and off in both propagators to alternatively study the eccentricity build up and the residual lifetime. The non-averaging case also covers a validation with the full 6?×?6 geopotential. The results confirm the findings in previous publications, that is, the possibility for de-orbiting from altitudes above the residual atmosphere if a solar sail is deployed at the end-of-life, due to the combined effect of solar radiation pressure and the oblateness of the Earth. At near polar inclinations, shadowing effects can be exploited to the same end. The results obtained with the full, non-averaging propagator revealed additional de-orbiting corridors associated with solar radiation pressure which were not found by previous work on space debris mitigation. The results of both tools are compared for specific initial conditions. For nominal values of area-to-mass ratio, instead, it is confirmed that this resonance effect is negligible.The paper then puts the findings in the perspective of the current satellite catalogue. It identifies space missions which are currently close to a resonance corridor and shows the orbit evolution within the resonances with a significantly shorter residual orbital lifetime. The paper finishes with a discussion on the exploitation of these effects with regards to the long-term simulation of the space debris environment and a flux and collision probability comparison.     

Multi-instrument observations of large-scale atmospheric gravity waves/traveling ionospheric disturbances associated with enhanced auroral activity over Svalbard

This study reports on observations of large-scale atmospheric gravity waves/traveling ionospheric disturbances (AGWs/TIDs) using Global Positioning System (GPS) total electron content (TEC) and Fabry–Perot Interferometer’s (FPI’s) intensity of oxygen red line emission at 630?nm measurements over Svalbard on the night of 6 January 2014. TEC large-scale TIDs have primary periods ranging between 29 and 65?min and propagate at a mean horizontal velocity of $～$749–761?m/s with azimuth of $～$345–347$°$ (which corresponds to poleward propagation direction). On the other hand, FPI large-scale AGWs have larger periods of $～$42–142?min. These large-scale AGWs/TIDs were linked to enhanced auroral activity identified from co-located all-sky camera and IMAGE magnetometers. Similar periods, speed and poleward propagation were found for the all-sky camera ($～$60–97?min and $～$823?m/s) and the IMAGE magnetometers ($～$32–53?min and $～$708?m/s) observations. Joule heating or/and particle precipitation as a result of auroral energy injection were identified as likely generation mechanisms for these disturbances.     

Effects of space weather on the ionosphere and LEO satellites’ orbital trajectory in equatorial,low and middle latitude

We study the effects of space weather on the ionosphere and low Earth orbit (LEO) satellites’ orbital trajectory in equatorial, low- and mid-latitude (EQL, LLT and MLT) regions during (and around) the notable storms of October/November, 2003. We briefly review space weather effects on the thermosphere and ionosphere to demonstrate that such effects are also latitude-dependent and well established. Following the review we simulate the trend in variation of satellite’s orbital radius (r), mean height (h) and orbit decay rate (ODR) during 15 October–14 November 2003 in EQL, LLT and MLT. Nominal atmospheric drag on LEO satellite is usually enhanced by space weather or solar-induced variations in thermospheric temperature and density profile. To separate nominal orbit decay from solar-induced accelerated orbit decay, we compute $r\text{,}h$ and ODR in three regimes viz. (i) excluding solar indices (or effect), where $r=r_0\text{,}h=h_0$ and $\mathit{ODR}={\mathit{ODR}}_0$ (ii) with mean value of solar indices for the interval, where $r=r_m\text{,}h=h_m$ and $\mathit{ODR}={\mathit{ODR}}_m$ and (iii) with actual daily values of solar indices for the interval ($r\text{,}h$ and ODR). For a typical LEO satellite at h?=?450?km, we show that the total decay in r during the period is about 4.20?km, 3.90?km and 3.20?km in EQL, LLT and MLT respectively; the respective nominal decay ($r_0$) is 0.40?km, 0.34?km and 0.22?km, while solar-induced orbital decay ($r_m$) is about 3.80?km, 3.55?km and 2.95?km. h also varied in like manner. The respective nominal ${\mathit{ODR}}_0$ is about 13.5?m/day, 11.2?m/day and 7.2?m/day, while solar-induced ${\mathit{ODR}}_m$ is about 124.3?m/day, 116.9?m/day and 97.3?m/day. We also show that severe geomagnetic storms can increase ODR by up to 117% (from daily mean value). However, the extent of space weather effects on LEO Satellite’s trajectory significantly depends on the ballistic co-efficient and orbit of the satellite, and phase of solar cycles, intensity and duration of driving (or influencing) solar event.     

First results from the LUCID-Timepix spacecraft payload onboard the TechDemoSat-1 satellite in Low Earth Orbit

The Langton Ultimate Cosmic ray Intensity Detector (LUCID) is a payload onboard the satellite TechDemoSat-1, used to study the radiation environment in Low Earth Orbit ($～$635?km). LUCID operated from 2014 to 2017, collecting over 2.1 million frames of radiation data from its five Timepix detectors on board. LUCID is one of the first uses of the Timepix detector technology in open space, with the data providing useful insight into the performance of this technology in new environments. It provides high-sensitivity imaging measurements of the mixed radiation field, with a wide dynamic range in terms of spectral response, particle type and direction. The data has been analysed using computing resources provided by GridPP, with a new machine learning algorithm that uses the Tensorflow framework. This algorithm provides a new approach to processing Medipix data, using a training set of human labelled tracks, providing greater particle classification accuracy than other algorithms. For managing the LUCID data, we have developed an online platform called Timepix Analysis Platform at School (TAPAS). This provides a swift and simple way for users to analyse data that they collect using Timepix detectors from both LUCID and other experiments. We also present some possible future uses of the LUCID data and Medipix detectors in space.     

Medium Earth Orbit dynamical survey and its use in passive debris removal

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the relatively crowded GNSS neighborhood (graveyard orbits). Recent studies have highlighted the complicated secular dynamics in the MEO region, but also the possibility of exploiting these dynamics, for designing removal strategies. In this paper, we present our numerical exploration of the long-term dynamics in MEO, performed with the purpose of unveiling the set of reentry and graveyard solutions that could be reached with maneuvers of reasonable $\mathrm{\Delta }V$ cost. We simulated the dynamics over 120–200?years for an extended grid of millions of fictitious MEO satellites that covered all inclinations from 0 to 90°, using non-averaged equations of motion and a suitable dynamical model that accounted for the principal geopotential terms, 3rd-body perturbations and solar radiation pressure (SRP). We found a sizeable set of usable solutions with reentry times that exceed $～40$ years, mainly around three specific inclination values: 46°, 56°, and 68°; a result compatible with our understanding of MEO secular dynamics. For $\mathrm{\Delta }V?300$ m/s (i.e., achieved if you start from a typical GNSS orbit and target a disposal orbit with $e<0.3$), reentry times from GNSS altitudes exceed $～70$ years, while low-cost ($\mathrm{\Delta }V?5–35$ m/s) graveyard orbits, stable for at lest 200?years, are found for eccentricities up to $e\approx 0.018$. This investigation was carried out in the framework of the EC-funded “ReDSHIFT” project.     

Study of the radiation fields in LEO with the Space Application of Timepix Radiation Monitor (SATRAM)

We present the analysis of data taken by the Space Application of Timepix Radiation Monitor (SATRAM). It is centred on a Timepix detector (300?$\mathrm{\mu }$m thick silicon sensor, pixel pitch 55?$\mathrm{\mu }$m, 256?×?256 pixels). It was flown on Proba-V, an Earth observing satellite of the European Space Agency (ESA) from an altitude of 820?km on a sun-synchronous orbit, launched on May 7, 2013. A Monte Carlo simulation was conducted to determine the detector response to electrons (0.5–7?MeV) and protons (10–400?MeV) in an omnidirectional field taking into account the shielding of the detector housing and the satellite. With the help of the simulation, a strategy was developed to separate electrons, protons and ions in the data. The measured dose rate and stopping power distribution are presented as well as SATRAM’s capability to measure some of the stronger events in Earth’s magnetosphere. The stopping power, the cluster height and the shape of the particle tracks in the sensor were used to separate electrons, protons and ions. The results are presented as well. Finally, the pitch angles for a short period of time were extracted from the data and corrected with the angular response determined by the simulation.     

Optimal Earth’s reentry disposal of the Galileo constellation

Nowadays there is international consensus that space activities must be managed to minimize debris generation and risk. The paper presents a method for the end-of-life (EoL) disposal of spacecraft in Medium Earth Orbit (MEO). The problem is formulated as a multiobjective optimisation one, which is solved with an evolutionary algorithm. An impulsive manoeuvre is optimised to reenter the spacecraft in Earth’s atmosphere within 100?years. Pareto optimal solutions are obtained using the manoeuvre $\mathrm{\Delta }v$ and the time-to-reentry as objective functions to be minimised. To explore at the best the search space a semi-analytical orbit propagator, which can propagate an orbit for 100?years in few seconds, is adopted. An in-depth analysis of the results is carried out to understand the conditions leading to a fast reentry with minimum propellant. For this aim a new way of representing the disposal solutions is introduced. With a single 2D plot we are able to fully describe the time evolution of all the relevant orbital parameters as well as identify the conditions that enables the eccentricity build-up. The EoL disposal of the Galileo constellation is used as test case.     

Dynamical cartography of Earth satellite orbits

We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term ($～$120?years) integrations of the non-averaged equations of motion. Hence, we characterize the long-term dynamics and the phase-space structure of the Earth-orbiter environment, starting from low altitudes ($～$400?km) and going up to the GEO region and beyond. This investigation was done in the framework of the EC-funded “ReDSHIFT” project, with the purpose of enabling the definition of passive debris removal strategies, based on the use of physical mechanisms inherent in the complex dynamics of the problem (i.e., resonances). Accordingly, the complicated interactions among resonances, generated by different perturbing forces (i.e., lunisolar gravity, solar radiation pressure, tesseral harmonics in the geopotential) are accurately depicted in our results, where we can identify the regions of phase space where the motion is regular and long-term stable and regions for which eccentricity growth and even instability due to chaotic behavior can emerge. The results are presented in an “atlas” of dynamical stability maps for different orbital zones, with a particular focus on the (drag-free) range of semimajor axes, where the perturbing effects of the Earth’s oblateness and lunisolar gravity are of comparable order. In some regions, the overlapping of the predominant lunisolar secular and semi-secular resonances furnish a number of interesting disposal hatches at moderate to low eccentricity orbits. All computations were repeated for an increased area-to-mass ratio, simulating the case of a satellite equipped with an on-board, area-augmenting device. We find that this would generally promote the deorbiting process, particularly at the transition region between LEO and MEO. Although direct reentry from very low eccentricities is very unlikely in most cases of interest, we find that a modest “delta-v” ($\mathrm{\Delta }V$) budget would be enough for satellites to be steered into a relatively short-lived resonance and achieve reentry into the Earth’s atmosphere within reasonable timescales ($～$50?years).     

GRACE accelerometer calibration by high precision non-gravitational force modeling

The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these forces in a low Earth orbit with highly precise accelerometers, for about 15?years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$50?$\text{nm}/{\text{s}}^2$). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$70?$\text{nm}/{\text{s}}^2$ for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.     

Near-infrared study of open clusters Teutsch 10 and Teutsch 25

The astrophysical parameters have been estimated for two unstudied open star clusters Teutsch 10 and Teutsch 25 using the Two Micron All Sky Survey ($2\mathit{MASS}$) database. Radius is estimated as 4.5 arcmin for both clusters using radial density profiles. We have estimated proper motion values in both RA and DEC directions as $2.28\pm 0.3$ and $-0.38\pm 0.11$?mas?yr^?1 for Teutsch 10 and $0.48\pm 0.3$ and $3.35\pm 0.16$?mas?yr^?1 for Teutsch 25 using $\mathit{PPMXL}$¹ catalog. By estimating the stellar membership probabilities, we have identified 30 and 28 most likely members for Teutsch 10 and Teutsch 25 respectively. We have estimated the reddening as $E(B-V)=0.96\pm 0.3$?mag for Teutsch 10 and $0.58\pm 0.2$?mag for Teutsch 25, while the corresponding distances are $2.4\pm 0.2$ and $1.9\pm 0.1$?kpc. Ages of $70\pm 10$?Myr for Teutsch 10 and $900\pm 100$?Myr for Teutsch 25 are estimated using the theoretical isochrones of metallicity Z?=?0.019. The mass function slopes are derived as $1.23\pm 0.30$ and $1.09\pm 0.35$ for Teutsch 10 and Teutsch 25 respectively. Estimated mass function slope for both the clusters are close to the Salpeter value ($x=1.35$) within the errors. Estimated values of dynamical relaxation time are found to be less than cluster’s age for these objects. This concludes that both objects are dynamically relaxed. The possible reason for relaxation may be due to dynamical evolution or imprint of star formation or both.     

Effects of dust polarity and nonextensive electrons on the dust-ion acoustic solitons and double layers in earth atmosphere

Propagation of dustion acoustic solitary waves (DIASWs) and double layers is discussed in earth atmosphere, using the Sagdeev potential method. The best model for distribution function of electrons in earth atmosphere is found by fitting available data on different distribution functions. The nonextensive function with parameter $q=0.58$ provides the best fit on observations. Thus we analyze the propagation of localized waves in an unmagnetized plasma containing nonextensive electrons, inertial ions, and negatively/positively charged stationary dust. It is found that both compressive and rarefactive solitons as well as double layers exist depending on the sign (and the value) of dust polarity. Characters of propagated waves are described using the presented model.     

A robust semi-analytic method to solve the minimum ΔV two-impulse rendezvous problem

A novel semi-analytic approach is developed to determine the minimum $\mathrm{\Delta }V$ for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form $\mathrm{\Delta }V$ estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum $\mathrm{\Delta }V$ transfer between two orbits. These bounds, in conjunction with the bisection method, operate on a nonlinear radical cost function to guarantee linear convergence. This approach has several real world applications including a low earth orbit (LEO) to highly elliptical orbit (HEO), and a HEO to retrograde geosynchronous orbit transfer. The minimum $\mathrm{\Delta }V$ estimates are better than those reported in the existing literature, while run times improved as much as two orders of magnitude over a fixed time Lambert solver. All singularity cases were addressed such that any orbital geometry, including Hohmann and radial elliptic transfers, converged to the global minimum $\mathrm{\Delta }V$. This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.     

Fast solar radiation pressure modelling with ray tracing and multiple reflections

Physics based SRP (Solar Radiation Pressure) models using ray tracing methods are powerful tools when modelling the forces on complex real world space vehicles. Currently high resolution (1?mm) ray tracing with secondary intersections is done on high performance computers at UCL (University College London). This study introduces the BVH (Bounding Volume Hierarchy) into the ray tracing approach for physics based SRP modelling and makes it possible to run high resolution analysis on personal computers. The ray tracer is both general and efficient enough to cope with the complex shape of satellites and multiple reflections (three or more, with no upper limit). In this study, the traditional ray tracing technique is introduced in the first place and then the BVH is integrated into the ray tracing. Four aspects of the ray tracer were tested for investigating the performance including runtime, accuracy, the effects of multiple reflections and the effects of pixel array resolution.Test results in runtime on GPS IIR and Galileo IOV (In Orbit Validation) satellites show that the BVH can make the force model computation 30–50 times faster. The ray tracer has an absolute accuracy of several nanonewtons by comparing the test results for spheres and planes with the analytical computations. The multiple reflection effects are investigated both in the intersection number and acceleration on GPS IIR, Galileo IOV and Sentinel-1 spacecraft. Considering the number of intersections, the 3rd reflection can capture $99.12\%\text{,}99.14\%$, and $91.34\%$ of the total reflections for GPS IIR, Galileo IOV satellite bus and the Sentinel-1 spacecraft respectively. In terms of the multiple reflection effects on the acceleration, the secondary reflection effect for Galileo IOV satellite and Sentinel-1 can reach 0.2?$\text{nm}/{\text{s}}^2$ and 0.4?$\text{nm}/{\text{s}}^2$ respectively. The error percentage in the accelerations magnitude results show that the 3rd reflection should be considered in order to make it less than $0.035\%$. The pixel array resolution tests show that the dimensions of the components have to be considered when choosing the spacing of the pixel in order not to miss some components of the satellite in ray tracing. This paper presents the first systematic and quantitative study of the secondary and higher order intersection effects. It shows conclusively the effect is non-negligible for certain classes of misson.     

Highlights about the performances of storm-time TEC modelling techniques for low/equatorial and mid-latitude locations

A statistical evaluation of storm-time total electron content (TEC) modelling techniques over various latitudes of the African sector and surrounding areas is presented. The source of observational TEC data used in this study is the Global Navigation Satellite Systems (GNSS), specifically the Global Positioning Systems (GPS) receiver networks. For each selected receiver station, three different storm-time models based on empirical orthogonal functions (EOF) analysis, non-linear regression analysis (NLRA) and Artificial neural networks (ANN), were implemented. Storm-time GPS TEC data used for both development and validation of the models was selected based on the storm criterion of $\mathit{Dst}?-50$ nT or $K_p?4$ to take into account both coronal mass ejections (CMEs) and co-rotating interaction regions (CIRs) driven storms, respectively. To make an independent test of the models, storm periods considered for validation were excluded from datasets used during the implementation of the models and results are compared with observations, monthly median values, and International Reference Ionosphere (IRI-2016) predictions. Considering GPS TEC as reference, a statistical analysis performed over six storm periods reserved for validation revealed that ANN model is about 10%, 26%, and 58% more accurate than EOF, NLRA, and IRI models, respectively. It was further found that, EOF model performs 15%, and 44% better than NLRA, and IRI models, respectively, while NLRA is 25% better than IRI. On the other hand, results are also discussed referring to the background ionosphere represented by monthly median TEC (MM TEC) and statistics are provided. Moreover, strengths and weaknesses of each model are highlighted.     

First solar observations with ALMA

The Atacama Large Millimeter-Submillimeter Array (ALMA) has opened a new window for studying the Sun via high-resolution high-sensitivity imaging at millimeter wavelengths. In this contribution I review the capabilities of the instrument for solar observing and describe the extensive effort taken to bring the possibility of solar observing with ALMA to the scientific community. The first solar ALMA observations were carried out during 2014 and 2015 in two ALMA bands, Band 3 ($\lambda =3$?mm) and Band 6 ($\lambda =1.3$?mm), in single-dish and interferometric modes, using single pointing and mosaicing observing techniques, with spatial resolution up to $～$2″ and $～$1″ in the two bands, respectively. I overview several recently published studies which made use of the first solar ALMA observations, describe current status of solar observing with ALMA and briefly discuss the future capabilities of the instrument.     

An analytical model of prominence dynamics

Solar prominences are magnetic structures incarcerating cool and dense gas in an otherwise hot solar corona. Prominences can be categorized as quiescent and active. Their origin and the presence of cool gas ($～{10}^4$?K) within the hot ($～{10}^6\text{K}$) solar corona remains poorly understood. The structure and dynamics of solar prominences was investigated in a large number of observational and theoretical (both analytical and numerical) studies. In this paper, an analytic model of quiescent solar prominence is developed and used to demonstrate that the prominence velocity increases exponentially, which means that some gas falls downward towards the solar surface, and that Alfvén waves are naturally present in the solar prominences. These theoretical predictions are consistent with the current observational data of solar quiescent prominences.     

Real-time spacecraft intercept strategy on J2-perturbed orbits

A real-time intercept strategy for spacecraft under the non-uniform gravitational perturbation of Earth is addressed in this paper. To intercept a target spacecraft on general conic sections, an interceptor considered in this work makes use of a thruster propelling the constant thrust which is comparable to unrealistic impulse-type thrust. The $J_2$ perturbation introduces critical dynamic variations of spacecraft orbiting the Earth, which results in a considerable amount of position error of the interceptor at the final intercept point. In order to release the burden of $J_2$ disturbance and make the miss distance between the target and interceptor small, a real-time intercept technique with an optimal intercept algorithm is suggested. The strategy proposed is to obtain an optimized output iteratively for a given time interval with previously obtained optimal values. These parameters are evaluated by the optimal intercept algorithm suggested. Once the optimal velocity change is obtained to satisfy intercept requirements, although the orbital system is perturbed, it is easy to regenerate a new solution by setting the previous solution as new initial guesses. This strategy is employed iteratively until the interceptor meets the target. Several numerical simulations are performed to highlight the proposed real-time strategy for spacecraft intercept missions.     

Constraining the mass of the black hole GX 339-4 using spectro-temporal analysis of multiple outbursts

We carried out spectro-temporal analysis of the archived data from multiple outbursts spanning over the last two decades from the black hole X-ray binary GX 339-4. In this paper, the mass of the compact object in the X-ray binary system GX 339-4 is constrained based on three indirect methods. The first method uses broadband spectral modelling with a two component flow structure of the accretion around the black hole. The broadband data are obtained from RXTE (Rossi X-ray Timing Explorer) in the range 3.0 to 150.0?keV and from Swift and NuSTAR (Nuclear Spectroscopic Telescope Array) simultaneously in the range 0.5 to 79.0?keV. In the second method, we model the time evolution of Quasi-periodic Oscillation (QPO) frequencies, considering it to be the result of an oscillating shock that radially propagates towards or away from the compact object. The third method is based on scaling a mass dependent parameter from an empirical model of the photon index ($\mathrm{\Gamma }$) – QPO ($\nu$) correlation. We compare the results at 90 percent confidence from the three methods and summarize the mass estimate of the central object to be in the range $8.28–11.89M_{\odot }$.     

Precision analysis of autonomous orbit determination using star sensor for Beidou MEO satellite

This paper focuses on the autonomous orbit determination accuracy of Beidou MEO satellite using the onboard observations of the star sensors and infrared horizon sensor. A polynomial fitting method is proposed to calibrate the periodic error in the observation of the infrared horizon sensor, which will greatly influence the accuracy of autonomous orbit determination. Test results show that the periodic error can be eliminated using the polynomial fitting method. The User Range Error (URE) of Beidou MEO satellite is less than 2?km using the observations of the star sensors and infrared horizon sensor for autonomous orbit determination. The error of the Right Ascension of Ascending Node (RAAN) is less than 60?$\mathrm{\mu }\text{rad}$ and the observations of star sensors can be used as a spatial basis for Beidou MEO navigation constellation.