By simultaneously estimating satellite clock drifts (SCDs) as either constant parameters or piece-wise parameters, we present an improved integrated orbit determination and time synchronization approach for BDS-3 satellites with raw inter-satellite link (ISL) observations. Experiments with L-band data from seven monitoring stations in China and ISL data from eight satellites of the third-generation Beidou Navigation Satellite System (BDS-3) were carried out and the two SCD estimation strategies are validated. It is demonstrated that, with SCDs estimated, the quality of orbits and clock offsets is comparable to those with SCDs corrected using predicted values. The accuracy of the estimated orbits and clocks are up to 0.019 m (radial) and 0.095 ns, respectively, with improvements of 95% and 90%, when compared with the results using the L-band data alone. It is also demonstrated that estimating SCDs time slice by time slice is slightly worse in accuracy but superior in coping with possible frequency jump of satellite clocks.

Optical tracking systems typically trade off between astrometric precision and field of view. In this work, we showcase a networked approach to optical tracking using very wide field-of-view imagers that have relatively low astrometric precision on the scheduled OSIRIS-REx slingshot manoeuvre around Earth on 22 Sep 2017. As part of a trajectory designed to get OSIRIS-REx to NEO 101955 Bennu, this flyby event was viewed from 13 remote sensors spread across Australia and New Zealand to promote triangulatable observations. Each observatory in this portable network was constructed to be as lightweight and portable as possible, with hardware based off the successful design of the Desert Fireball Network. Over a 4-h collection window, we gathered 15 439 images of the night sky in the predicted direction of the OSIRIS-REx spacecraft. Using a specially developed streak detection and orbit determination data pipeline, we detected 2 090 line-of-sight observations. Our fitted orbit was determined to be within about 10 km of orbital telemetry along the observed 109 262 km length of OSIRIS-REx trajectory, and thus demonstrating the impressive capability of a networked approach to Space Surveillance and Tracking.

The European Space Operations Centre currently operates five Copernicus Sentinel satellites in the framework of Europe’s Copernicus Earth observation programme. The routine operations rely on a daily orbit determination, carried out on-ground, consisting in a least-squares fit of a dynamical model to GPS navigation solutions generated on-board. The purpose of this paper is the estimation of realistic uncertainties on this daily determined state vector. By comparison with the orbit derived by Precise Orbit Determination, we estimate the 1-sigma errors at approximately 0.5m and 0.5mm/s. Non-stationary errors in the navigation solution preclude their characterisation with a constant covariance matrix. Error whitening is achieved by decreasing the signal-to-noise ratio in the errors through the use of underestimated weights on the data. The approach keeps the errors on the derived state vector unchanged and allows the covariance on the state vector to become realistic.

This paper is concerned with the preliminary localisation, orbit determination and model-based path forecasting of space debris based on a robust procedure. In this work, an in-orbit observer utilises only relative bearing observations iteratively. To this end, the problem is first formulated in order to calculate the distance vector between the space debris and any orbiting observer. Afterwards, the obtained position vector is corrected through an Extended Kalman Filter (EKF) for shrinking the sensor and process errors and increasing robustness of the computations in the presence of uncertainties. After preliminary positioning, the related classical orbital elements are acquired via the predicted position and velocity vectors using a hybrid technique. Extensive simulations demonstrate the efficacy and robustness of the aforementioned method, and in particular it is verified that the proposed scheme is capable of producing a suitable solution for preliminary localisation and orbit determination of space debris based on the presented space-based observation, which is practical in phasing and chasing manoeuvres of any grabber space robot.

Autonomous navigation has become a key technology for deep space exploration missions. Phobos and Deimos, the two natural moons of Mars, are important optical navigation information sources available for Mars missions. However, during the phase of the probe orbiting close to Mars, the ephemeris bias and the difference between the barycentre and the centre of brightness of a Martian moon will result in low navigation accuracy. On the other hand, Satellite-to-Satellite Tracking (SST) can achieve convenient and high accuracy observation for autonomous navigation. However, this cannot apply for a Mars mission during the Mars orbit phase only by SST data because of a rank defect problem of the Jacobian matrix. To improve the autonomous navigation accuracy of Mars probes, this paper presents a new autonomous navigation method that combines SST radio data provided by two probes and optical measurement by viewing the natural Martian moons. Two sequential orbit determination algorithms, an Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are compared. Simulation results show this method can obtain high autonomous navigation accuracy during the probe's Mars Orbit phase.

We propose a strategy to attack the problems of orbit determination arising from the large number of short arcs. The method uses a solution of the linkage problem depending on the first integrals of the Keplerian motion.

This article proposes a novel method to autonomously determine the relative orbits of a small spacecraft formation flying with a slowly rotating near-Earth asteroid for the asteroid mitigation mission. A combined model of spacecraft-to-asteroid measurements with inter-spacecraft communication is built up. The dynamic model accounting for the perturbations is derived to describe the state variables of the Unscented Kalman Filter (UKF). The Lyapunov function approach is used to design a control law to maintain the orbits of the spacecraft formation. Four navigation scenarios are presented based on the different combinations of multiple measurements: two of them are non-collaborative scenarios which only include the spacecraft-to-asteroid measurements in the measurement models, while the other two are collaborative scenarios with the inter-spacecraft communication added into the measurement models. Simulation results are analysed and compared with each other to show the improvements of the filter performance in the aspects of the convergence speed and the accuracy of the estimator.

This paper presents accurate orbit determination (OD) of the Iran University of Science and Technology Satellite (IUSTSAT) from Global Positioning System (GPS) data. The GPS position data are treated as pseudo-measurements within an onboard orbit determination process that is based on the numerical integration of the equations of motion using an earth gravity model and applying an Extended Kalman Filter for the data processing. In this paper, through accurate tuning of GPS duty cycle and on/off time intervals, a solution is suggested to achieve the desired OD accuracy despite power constraints. Moreover, a new scheme for automatic fault management in the orbit determination system is derived that provides fault detection and accommodation features.

A survey for NEO aiming at 90% completeness for a given size range cannot ignore that a significant fraction of the population is observable essentially only at low solar elongation, in the so called “sweet spots” There are several penalties for such low elongation: poorer observing conditions imply a lower limiting magnitude, shorter available time in each night and a more difficult orbit determination. Our aim is to show that these difficulties can be overcome. We have tested the observation procedures and the mathematical methods of orbit determination on two sweet spot test runs. One was performed at ESO La Silla in Jan–Feb 2005, the other at Mauna Kea in Sept–Dec 2005. The results of the tests are presented in this paper; the observed area was not large enough (especially at Mauna Kea) to discover a significant number of new NEO, the purpose was rather to identify the problems. These tests have allowed us to identify all the key elements to be accounted for in the strategy for a successful sweet spot NEO survey. When very short arc observations from different nights have to be identified, a specific difficulty occurs at the sweet spots: the same set of observations from three nights can be fitted to two incompatible orbits, in most cases including one NEO and one MBA. This can lead to two different failures (false positive, false negative) in deciding whether a NEO has been discovered. The classical theory of preliminary orbits shows that three observations at an elongation less than 116.5° can be compatible with two different orbits. From this theory we have derived an algorithm to find the alternate solution, if it exists, when only one is available. In this way we have generated a set of examples of possible discoveries with two well determined but incompatible solutions. Most of the MBA-NEO alternatives have been solved by finding a known MBA which could be identified; in two cases the MBA solution has been confirmed by a later observation.

The process of cataloguing the minor planet population of the Solar System has experienced a great advance in the last decades with the start-up of several surveys. The large volume of data generated by them has increased with time and given rise to huge databases of asteroids with uneven qualities.

In fact, a significant fraction of these objects have not been enough observed, thus leading to the computation of very poor quality orbits as to carry out useful predictions of the positions of such asteroids. As a result, some objects can get lost, which is particularly embarrassing for those with Earth crossing orbits.

When this situation persists for a long time, the aforementioned databases end up contaminated in the sense that they contain more than one discovery for the same physical object and some kind of action must be taken. The algorithms for asteroid identifications are thought precisely to mitigate this problem and their design will depend upon the quality of the available data for the objects to be identified.

In this paper we will distinguish two cases: when both objects have a nominal orbit and when one of them lacks it. In addition, when the available data poorly constrain the solution, other orbits in the neighbourhood of the nominal one are also compatible with the observations. Using these alternative orbits allows us to find many identifications that otherwise would be missed. Finally, we will show the efficiency of all these algorithms when applied to the datasets distributed by the Minor Planet Center.

This study is based on the definition of the admissible region introduced by Milani et al.(2004); in the search for potential Earth impactors, this theory allows to take into account the partial data of the TSA (Too Short Arcs) from which it is impossible to deduce a full orbit. Only a set of 4 variables (two angles and their instantaneous time derivatives), called an attributable, is known; a few suitable boundary conditions allow to restrict the motions to a specific bounded 2-dimensional region. In this work, a new inner boundary of this region is introduced, based on the geocentric hyperbolic motion of the immediate impactors; the nodal distances (crossings of the virtual asteroidal orbits with the Earth's orbit) are drawn for two different test attributables, associated with a determination of circular and linear orbits. This could reduce the search for impactors (by propagation of the orbits) to a one-dimensional set. A few comments about elongations and complementary curves complete this paper.

The main-belt asteroids are generally considered as the principal source for the near-Earth asteroids (NEAs). The ESA astrometric mission Gaia, due for launch in late 2011, will observe a very large number of asteroids (∼300,000 brighter than V = 20), the majority lying in the main-belt and with an unprecedented positional precision (at the sub-milliarcsecond level). Such high precision astrometry will enable to derive direct measures of the masses of the largest asteroids of which their precise determination will be of utmost significance for the knowledge of physical properties of asteroids. The method for computing the masses is based on the analysis of orbital perturbations during close encounters between massive asteroids (perturbers) and several smaller minor planets (targets). From given criteria of close approaches selection, we give the list of asteroids for which the mass can be determined, and the expected precision of these masses at mission completion.

The Minimum Orbit Intersection Distance (MOID) between two confocal Keplerian orbits is a useful tool to know if two celestial bodies can collide or undergo a very close approach. We describe some results and open problems on the number of local minimum points of the distance between two points on the two orbits and the position of such points with respect to the mutual nodes. The errors affecting the observations of an asteroid result in uncertainty in its orbit determination and, consequently, uncertainty in the MOID. The latter is always positive and is not regular where it vanishes; this prevents us from considering it as a Gaussian random variable, and from computing its covariance by standard tools. In a recent work we have introduced a regularization of the maps giving the local minimum values of the distance between two orbits. It uses a signed value of the distance, with the sign given to the MOID according to a simple orientation property. The uncertainty of the regularized MOID has been computed for a large database of orbits. In this way we have searched for Virtual PHAs, i.e. asteroids which can belong to the category of PHAs (Potentially Hazardous Asteroids) if the errors in the orbit determination are taken into account. Among the Virtual PHAs we have found objects that are not even NEA, according to their nominal orbit.

Some of the problems related to Near Earth Objects (NEOs), like orbit determination and ephemeris computation, are not new, and had to be dealt with since the beginning of NEO astronomy. The latter practically started with the discovery of Comet D/1770 L1 Lexell, that passed very close to the Earth in 1770; studies of the chaotic dynamics of this exceptional object continued well into the XIXth century. At the end of the XXth century there has been a renewal of interest in NEOs, as attested by IAU Symposium 236.

The problem of initial linking of asteroids is of increasing interest for the next generation surveys. During the first week after discovery elliptical elements are very uncertain and other methods are used. A summary is given of 7 initial linking methods. There are two different types: In one, a search area is computed on a second night from the known and undoubtedly linked positions, typically on the first night. The other type assumes candidates which are then checked by the computation of O – C residuals of an orbit. Computations may be classified as belonging to the 3-dimensional space or the 2-dimensional sky-plane. A new basis, with a simpler computational algorithm, is given for the widely used Väisälä method. For a new N-Observation Orbit method a simple, efficient PC-programme is given.

In the next generation surveys, the discovery of moving objects can be successful only if an observation strategy and the identification/orbit determination procedure are appropriate for the diverse apparent motions of the target sub-populations. The observations must accurately measure the displacement over a short interval of time; observations believed to belong to the same object have to be connected into tracklets. Information contained in tracklets is in most cases not sufficient to compute an orbit: two or more of them must be identified to provide an orbit. We have developed a method for recursive identification of tracklets allowing an unbiased orbit determination for all sub-populations and efficient enough to cope with the data flow expected from the next generation surveys. The success of the new algorithms can be easily measured only in a simulation, by consulting a posteriori some “ground truth”.

We present here the results of a simulation of the orbit determination for one month of operations of the future Pan-STARRS survey, based upon a Solar System Model with a downsized population of Main Belt asteroids and a full size populations of Trojans, NEO, Centaurs, Comets and TNO. The results indicate that the method already developed and tested to find identifications of NEO and Main Belt asteroids are directly applicable to Trojans. The more distant objects often require modified algorithms, fitting orbits with only 4 parameters in a coordinate system specially adapted to handle very short arcs of observations. These orbits are mostly used as intermediate results, allowing to find full solutions as more tracklets are identified.

When the number density of detections is as large as expected from the next generation surveys, both joining observations into tracklets and identifying tracklets can produce some false results. The only reliable way to remove them is a procedure of tracklet/identification management. It compares the tracklets and the identifications with a complex logic, allowing to discard almost all the false tracklets and all the false identifications. However, the distant objects still present a challenge for orbit determination: they require three tracklets in separate nights. If this requirement is met we have found no problem in achieving an unbiased orbit determination for all populations. Further work will lead to more advanced simulations, in particular by introducing a realistic model for astrometric and photometric errors.

When a celestial body, e.g., an asteroid, has been observed only over a short time, its orbit is not well determined but may be anywhere in a confidence region where the astrometric residuals are acceptable. This region can be sampled by a swarm of Virtual Asteroids (VA) sharing the reality of the asteroid: one of them is real, but we do not know which one. The problem is how to sample the confidence region with a small number of VA, still being able to solve the main problems of asteroid recovery/identification and impact monitoring.

One class of methods uses random sampling of the confidence region to mimic with the VA population the probabilistic distributions of the orbits. This class includes the Monte Carlo and the Statistical Ranging methods. When it is critical to detect a very small probability (e.g., of a catastrophic impact) by computing a small number of VA orbits, and also when a large catalog of asteroids has to be handled, it is more efficient to sample the confidence region with a geometric object, such as a smooth manifold: it can be sampled uniformly, taking into account its dimension. Our group has developed in the last 6-7 years 1-dimensional sampling methods based upon a differentiable curve, the Line Of Variations (LOV), which can represent, in suitable cases, the spine of the confidence region. The LOV is sampled by uniformly spaced VA, thus interpolation between consecutive VA is possible. This is the basis for the current algorithms of Impact Monitoring, used in Pisa and at JPL. The LOV method is also used for recovery of lost asteroids and for identification of independent discoveries of the same object.

When the asteroid has moved on the sky while being observed by $<1^\circ$, the confidence region is wide in two directions and the LOV may be an inappropriate way of sampling it. We have recently developed 2-dimensional sampling methods based upon the concept of Admissible Region, a 2-dimensional manifold parameterized by a compact subset of the range/range-rate plane. This region is then sampled by triangulation, with each node used as a VA. This allows to define methods for asteroid identification/recovery and for impact monitoring starting from very poor data, such as the ones collected during a single night of observations.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The orbital motion of comets is difficult to characterize accurately due to the rocket-like outgassing of material from the cometary nucleus. The resulting nongravitational accelerations often appear to be fundamentally stochastic in nature and thus pose severe modeling challenges in orbit determination, especially when the comet has been observed for many revolutions. Even so, new techniques have arisen in recent years that give new insight, not only into the motion of the comets, but also into their physical characteristics and spin states. These approaches include modeling of spin axis precession over many decades and the consideration of the seasonal variation in the thrust from discrete jets acting on a rotating nucleus. Such advances have been enabled, in part, by the increasing efforts and capabilities of comet observers worldwide as more and more comets with longer and longer observing arcs become available for study. In this review we specifically consider the application of the Rotating Jet Model to several space mission targets, indicating how this model can often be used to infer the orientation of a comet's spin axis.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We show the utility of the Systematic Ranging technique by analyzing the orbit determination of asteroid 2004 FU$_{162}$, which passed approximately 6400 km from the surface of the Earth on March 31, 2004. The limited observations introduce strong nonlinearities that must be accounted for when estimating the actual encounter distance.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html