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In the domain of Space Situational Awareness (SSA), the challenges related to orbit determination and catalog correlation are notably pronounced, exacerbated by data scarcity. This study introduces an initial orbit determination methodology that relies on data obtained from a single surveillance radar, with the need for fast algorithms within an operational context serving as the main design driver. The result is a linearized least-squares fitting procedure incorporating an analytically formulated approximation of the dynamics under the J 2 perturbation, valid for short-term propagation. This algorithm utilizes all available observables, including range-rate, distinguishing it from other similar methods. A significant contribution of this paper is the enhancement of estimation quality by incorporating information about the object's predicted orbital plane into the methodology, a method denoted as OPOD. The proposed methods are evaluated through a series of simulations against a classical range and angles fitting method (GTDS) to examine the effects of track length and measurement density on the quality of full state estimation, including the impact of using arcs that are too short. The OPOD methodology shows promising results throughout a wide range of scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel method to improve tracking performance based on offset compensation in the identification system after determining the initial orbit of an unknown space object. High-resolution images are necessary to accurately identify the target based on the initial orbit determination information obtained from the search system, which requires highly precise tracking performance at the arcsecond level. We propose a precise tracking technique that enhances the existing simple offset feedback method by incorporating PID gains, enabling the system to meet stringent target identification criteria under more challenging conditions. By applying the PID gain values obtained through extensive Monte Carlo simulations, we achieved a tracking performance within ±15 arcseconds in the worst-case scenario, demonstrating approximately 50 times more precision compared to existing methods. Furthermore, the results showed robust and reliable tracking performance across 11 different trajectories in addition to the worst-case scenario, proving the effectiveness and reliability of our proposed method. [ABSTRACT FROM AUTHOR]

Leveraging space-based optical platforms for space debris and defunct spacecraft detection presents several advantages, including a wide detection range, immunity to cloud cover, and the ability to maintain continuous surveillance on space targets. As a result, it has become an essential approach for accomplishing tasks related to space situational awareness. However, the prediction of the orbits of space objects is crucial for the success of such missions, and current technologies face challenges related to accuracy, reliability, and practical efficiency. These challenges limit the performance of space-based optical space situational awareness systems. To drive progress in this field and establish a more effective and reliable space situational awareness system based on space optical platforms, this paper conducts a retrospective overview of research advancements in this area. It explores the research landscape of orbit determination methods, encompassing orbit association methods, initial orbit determination methods, and precise orbit determination methods, providing insights from international perspectives. The article concludes by highlighting key research areas, challenges, and future trends in current space situational awareness systems and orbit determination methods. [ABSTRACT FROM AUTHOR]

We introduce an initial orbit determination technique that uses only sequential range-rate measurements along fixed lines of sight and time between measurements. Compared to existing velocity-based initial orbit determination methods which impose additional requirements such as concurrent observations, our method may reduce the number of sensors required for a spacecraft to perform autonomous, or onboard, initial orbit determination. The measurements required may be obtained by a single range-rate sensor, such as an X-ray detector observing X-ray pulsars, and an onboard clock. The accuracy of our algorithm is compared with existing techniques for a variety of orbits. Orbit determination errors, in terms of estimated position, are characterized with Monte Carlo simulation techniques. Results indicate that our method achieves better performance compared to an initial orbit determination method utilizing velocity vectors and time of flight. The position error of our technique increases for lower velocities and shorter measurement times, which is consistent with existing velocity-based initial orbit determination methods. [ABSTRACT FROM AUTHOR]

In the Initial Orbit Determination (IOD) context, Admissible Regions are subsets of parameter space of orbital elements that are reckoned as functions of the tracking measurement variables. Physically acceptable orbits, e.g., orbits with negative energies, constitute an Admissible Region. This paper defines sets of orbits that satisfy constraints imposed by the measurement variables. Using a probabilistic representation of constraints on some of the orbital parameters the Admissible Region can be further constrained to give a Probabilistic Admissible Region (PAR). PAR gives a particle cloud representation of the initial probability density function (pdf) of the state of a Resident Space Object (RSO). This paper presents a geometric solution to the Probabilistic Admissible Region (G-PAR). G-PAR is a set of algorithms sharing the same underlying template that geometrically maps postulated statistics on some orbital elements and statistics of the measurement process to the uncertainty in the states. The proposed scheme gives a simple closed-form solution for mapping particles to get the PAR pdf for the first time. This speeds up the PAR initial orbit determination with a single partial state measurement. The effectiveness of the proposed G-PAR is shown on diverse combinations of sensors and prior knowledge. [ABSTRACT FROM AUTHOR]

Optical observation systems for space surveillance are composed of a search system that performs detection and tracking of space objects, and an identification system that acquires the shape information of the target through detailed tracking based on the target's orbital information. In this paper, we analyzed the offset compensation-based tracking performance of the identification system after the initial orbit determination of an unknown space object through simulation. The target is guided to the center of the screen by adjusting the offset value of the target from the center of the captured image using a feedback loop. The tracking performance was evaluated with respect to the design parameters of the identification system, and the system parameters were then finalized for the simulation. The tracking simulation results for a variety of targets showed that the tracking performance met the target performance for most targets with maximum elevation angles of 60 degrees or less. [ABSTRACT FROM AUTHOR]

The Changchun Observatory of the National Astronomical Observatories, Chinese Academy of Sciences, and the Shanghai Astronomical Observatory are used to generate very short arc (VSA) angle observations of objects in low Earth orbit (LEO) and geostationary orbit (GEO) with their ground-based electrical–optical telescope arrays (EA), the Changchun EA and SAO FocusGEO, respectively. These observations are used in this paper. The range-searching (RS) algorithm for initial orbit determination (IOD) is improved through the multiple combinations of observations and the dynamic range-searching step length. Two different computation modes (the normal mode and the refining mode) of the IOD computation process are proposed. The geometrical method for the association is used. The IOD and association methods are extended to the real optical observations for both LEO and GEO objects. The results show that the IOD success rate of arcs from the LEO objects is about 91%, the error of the semimajor axis (SMA) of the initial orbital elements is less than 50 km, and the correlation accuracy rate is about 89%. The IOD success rate of arcs from the GEO objects is higher than 88%, and the correlation accuracy rate is greater than 87%. The recent COSMOS 1408 antisatellite test (ASAT) generated a large amount of debris. The algorithm of this paper and the observations of Changchun EA are used to initially identify new debris, possibly from the ASAT through initial orbit determination and track association. Finally, 64 suspected new pieces of debris can be found. The results show the effectiveness of the IOD and the correlation algorithm, as well as the potential application of the optical–electrical array in studying space events. [ABSTRACT FROM AUTHOR]

Leveraging space-based optical platforms for space debris and defunct spacecraft detection presents several advantages, including a wide detection range, immunity to cloud cover, and the ability to maintain continuous surveillance on space targets. As a result, it has become an essential approach for accomplishing tasks related to space situational awareness. However, the prediction of the orbits of space objects is crucial for the success of such missions, and current technologies face challenges related to accuracy, reliability, and practical efficiency. These challenges limit the performance of space-based optical space situational awareness systems. To drive progress in this field and establish a more effective and reliable space situational awareness system based on space optical platforms, this paper conducts a retrospective overview of research advancements in this area. It explores the research landscape of orbit determination methods, encompassing orbit association methods, initial orbit determination methods, and precise orbit determination methods, providing insights from international perspectives. The article concludes by highlighting key research areas, challenges, and future trends in current space situational awareness systems and orbit determination methods.

Initial orbit determination (IOD), as a basis for initial orbit association and accurate orbit determination (OD), has a crucial role in the process of obtaining space debris orbit information. Among the traditional methods, the Gooding method has better convergence and stability. In this study, the Gooding method is enhanced to solve the issues discovered. A novel initial orbit determination (IOD) method is developed using the proposed improvement measures of the single-parameter initial value determination (SIVD) method, the fitted-curve noise suppression method, the restricted corrective value solution method, the removal of trivial solutions, etc. The experimental results verify the effectiveness of the improved method. The success rate of the initial orbit determination reached 99%, and the accuracy of the solved orbit parameters was significantly improved, especially the semi-major axis (SMA) error of less than 50 km, accounting for 88% of the total. It can be seen that the method meets the demand of space-based space debris cataloging for initial orbit association and can serve in the field of space situational awareness, which has important practical significance and application potential. [ABSTRACT FROM AUTHOR]

In the last decades, the growing in-orbit population of resident space objects has become one of the main concerns for space agencies and institutions worldwide. In this context, fragmentations further contribute to increase the number of space debris and, operationally, it is fundamental to identify the event epoch as soon as possible, even when just a single fragment orbital state, resulting from an Initial Orbit Determination (IOD) process, is available. This work illustrates the Fragmentation Epoch Detector (FRED) algorithm, which deals with the problem through a stochastic approach, starting from a single fragment IOD result (expressed through mean state and covariance) and parent ephemeris (assumed as deterministic). The process populates the fragment ephemeris with a multivariate normal distribution and, for each couple sample-parent, the epochs of parent transit through the Minimum Orbital Intersection Distance (MOID) are first computed on a time window and then clustered in time. For each cluster, both the three-dimensional MOID and the three-dimensional relative distance distributions are derived, and their similarity is statistically assessed. Given that, at the actual fragmentation epoch, MOID and relative distance were equal, the cluster featuring the best matching between the two distributions is considered as the optimal candidate, and the related fragmentation epoch is returned from the time of parent transit through the MOID, in terms of mean and standard deviation. FRED algorithm performance is assessed through a numerical analysis. The algorithm robustness decreases when parent and fragment orbits share a similar geometry, and results get deteriorated if the perturbations and, moreover, the IOD errors are included in the process, but the correct fragmentation epoch is always present among candidates. Overall, FRED algorithm turns out to be a valid choice in operational scenarios, and a sensitivity analysis tests the algorithm out of the nominal conditions. [ABSTRACT FROM AUTHOR]

For the initial orbit determination of uncharted space objects, the operation method for obtaining three or more streak images was proposed and a design parameter analysis of a narrow field of view optical observation system was performed for this purpose. The proposed operational concept consists of repetitive forms of point tracking, streak center point prediction, mount gimbal maneuver, and streak image acquisition for unknown space objects. The central point prediction was performed using Kalman Filter based on a constant acceleration model and analysis was performed in terms of telescope mount gimbal maneuver and stabilization performance by fixing the exposure time for streak shooting. As a result of the simulation for the entire optical observation system, the ratio of the error value defined from the telescope center point to the streak center point is within 2% with respect to FOV. Consecutive streak images can be reliably obtained using the proposed system. [ABSTRACT FROM AUTHOR]

The Changchun Observatory of the National Astronomical Observatories, Chinese Academy of Sciences, and the Shanghai Astronomical Observatory are used to generate very short arc (VSA) angle observations of objects in low Earth orbit (LEO) and geostationary orbit (GEO) with their ground-based electrical–optical telescope arrays (EA), the Changchun EA and SAO FocusGEO, respectively. These observations are used in this paper. The range-searching (RS) algorithm for initial orbit determination (IOD) is improved through the multiple combinations of observations and the dynamic range-searching step length. Two different computation modes (the normal mode and the refining mode) of the IOD computation process are proposed. The geometrical method for the association is used. The IOD and association methods are extended to the real optical observations for both LEO and GEO objects. The results show that the IOD success rate of arcs from the LEO objects is about 91%, the error of the semimajor axis (SMA) of the initial orbital elements is less than 50 km, and the correlation accuracy rate is about 89%. The IOD success rate of arcs from the GEO objects is higher than 88%, and the correlation accuracy rate is greater than 87%. The recent COSMOS 1408 antisatellite test (ASAT) generated a large amount of debris. The algorithm of this paper and the observations of Changchun EA are used to initially identify new debris, possibly from the ASAT through initial orbit determination and track association. Finally, 64 suspected new pieces of debris can be found. The results show the effectiveness of the IOD and the correlation algorithm, as well as the potential application of the optical–electrical array in studying space events.

Initial orbit determination (IOD), as a basis for initial orbit association and accurate orbit determination (OD), has a crucial role in the process of obtaining space debris orbit information. Among the traditional methods, the Gooding method has better convergence and stability. In this study, the Gooding method is enhanced to solve the issues discovered. A novel initial orbit determination (IOD) method is developed using the proposed improvement measures of the single-parameter initial value determination (SIVD) method, the fitted-curve noise suppression method, the restricted corrective value solution method, the removal of trivial solutions, etc. The experimental results verify the effectiveness of the improved method. The success rate of the initial orbit determination reached 99%, and the accuracy of the solved orbit parameters was significantly improved, especially the semi-major axis (SMA) error of less than 50 km, accounting for 88% of the total. It can be seen that the method meets the demand of space-based space debris cataloging for initial orbit association and can serve in the field of space situational awareness, which has important practical significance and application potential.

The problem of initial orbit determination (IOD) for Low Earth Orbit (LEO) objects using bistatic radar too-short arc (TSA) observations is addressed. For TSA observations, the traditional IOD methods suffer low accuracy. For LEO objects with stable attitude, the high order kinematic parameters can be obtained from the time derivatives of the radar echo phase. In this paper, an analytical IOD method is presented using bistatic radar TSA observations, which contain the position measurements (bistatic range, azimuth angle, and elevation angle) and the high order kinematic measurements (bistatic velocity, acceleration, and jerk). As the undetermined target state variables constitute a complex system of equations that can only be solved iteratively, an auxiliary coordinate system based on the bistatic geometry is defined to help reduce the equations to one unary quartic equation. Further, the closed-form expressions of the orbital state are derived. The performance of the proposed method is evaluated using linearization approximations. Numerical simulations are carried out for several typical LEO observation scenarios to demonstrate the performance of the proposed method.

Under the too short arc scenario, the evolutionary-based algorithm has more potential than traditional methods in initial orbit determination. However, the underlying multimodal phenomenon in initial orbit determination is ignored by current works. In this paper, we propose a new enhanced differential evolution (DE) algorithm with multimodal property to study the angle-only IOD problem. Specifically, a coarse-to-fine convergence detector is implemented, based on the Boltzmann Entropy, to determine the evolutionary phase of the population, which lays the basis of the balance between the exploration and exploitation ability. A two-layer niching technique clusters the individuals to form promising niches after each convergence detected. The candidate optima from resulting niches are saved as supporting individuals into an external archive for diversifying the population, and a local search within the archive is performed to refine the solutions. In terms of performance validation, the proposed multimodal differential evolution algorithm is evaluated on the CEC2013 multimodal benchmark problems, and it achieved competitive results compared to 11 state-of-the-art algorithms, which present its capability of multimodal optimization. Moreover, several IOD experiments and analyses are carried out on three simulated scenarios of space-based observation. The findings show that, compared to traditional IOD approaches and EA-based IOD algorithms, the proposed algorithm is more successful at finding plausible solutions while improving IOD accuracy. [ABSTRACT FROM AUTHOR]

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The large amount of low earth orbit (LEO) space debris has a serious impact on the safe operation of orbital spacecraft. Space-based optical observation is the mainstream development direction for space debris observation. For centimeter sized space debris in LEO, the observable duration obtained by the LEO space-based telescope is relatively short. It is difficult to determine the initial orbit from the single arc of observation, and the error of the initial orbit is difficult to evaluate. Based on the admissible region method, this paper establishes the initial orbit determination and error estimation algorithm. Aiming at the problem that the initial orbit of space-based short-arc optical observation is not easy to be determined, this paper proposes a circular orbit auxiliary admissible region method. The LEO space debris observation experiment on commercial remote sensing satellites is carried out to verify the proposed calculation method, and to lay a foundation for the future research on observation-to-observation association using initial orbits. [ABSTRACT FROM AUTHOR]

Space-based optical sensors are attracting increasing research attention as they can measure the angle of space targets over large areas, facilitating low-cost, wide-area space target surveillance. Studying the effect of observation geometry on short-arc angles-only initial orbit determination is important for analysing the surveillance capability of systems that use optics as the main means for surveilling different areas of space. In this paper, the initial orbit is calculated based on the unit vector method (UVM); the geometric dilution of precision (GDOP)—derived under the condition that the approximate Lagrangian coefficient and distance are constant—is used as the parameter for the uncertainty distribution of the target orbit solution. A suitable coordinate system transformation is conducted and all possible observation geometry relationships between the target and the sensor are expressed in terms of the angle between orbital planes and the right ascension of the target and sensor in the transformed coordinate system. Simulation experiments show that the GDOP is approximately equal to that obtained statistically through Monte Carlo simulation experiments. The accuracy of the initial orbit solution is poor when the target and optical sensor are at the same right ascension and declination, or in the same orbital plane. [ABSTRACT FROM AUTHOR]

Satellite orbit information is crucial for ensuring that global navigation satellite systems (GNSSs) provide appropriate positioning, navigation and timing services. Typically, users can obtain access to orbit information of a specific accuracy level from navigation messages or precise ephemeris products. Without this information, a system will not be able to provide normal service. In response to this problem, initial orbit information of a certain level of precision must be obtained to support subsequent applications, such as broadcasting or precise ephemeris calculations, thereby ensuring the successful subsequent operation of the navigation system. One of two ways to calculate the initial orbit of a GNSS satellite is to utilize ground tracking stations to observe satellite vector information in the geocentric inertial system; the second way is to utilize GNSS range observations and known orbit information from other satellites. For the second approach, some researchers use the Bancroft algorithm combined with receiver clock offset to determine the initial orbit of GNSS satellites. Because this method requires an additional known receiver clock offset, we study the dependence of the Bancroft algorithm on clock offset in GNSS orbit determination. By assessing the impact of errors of different magnitude on the accuracy of the orbit results, we obtain experimental conclusions. After comprehensively analyzing various errors, we determine the accuracy level that the Bancroft algorithm can achieve for orbit determination without considering receiver clock correction. Dual-frequency and single-frequency pseudorange data from International GNSS Service stations are used in orbit determination experiments. When a small receiver clock offset is considered and no correction is made, the deviations in the calculated satellite positions in three dimensions are approximately 979.3 and 1118.1 m (dual and single frequency); with a satellite clock offset, these values are approximately 928.8 and 1062.7 m (dual and single frequency). [ABSTRACT FROM AUTHOR]

A sustainable use of the outer space becomes imperative for preserving current operational missions and enabling the placement of new space-based technology in the outer space safely. The uncontrolled growing number of resident space objects (RSO) increases the likelihood of close conjunctions and therefore collisions that will populate the space environment even more. To prevent such situations, orbit catalogues of RSO are built and maintained, which are used to assess the collision risk between RSO. In order to keep the catalogues up-to-date, a worldwide ground-based infrastructure is used to collect observations coming from different observation techniques. The current study focuses on the so-called stare and chase observation strategy using an active and passive-optical system. The final aim is to correct the pointing of the telescope so that the target will be within the field of view of the laser beam, thus enabling the acquisition of laser ranges. By doing so, objects with poor ephemerides, available e.g. from Two Line Elements (TLE), will not pose a problem anymore for the rather small field of view of the laser beam. The system gathers both angular and range measurements, which can be used for an immediate orbit determination, or improvement, that will enhance the accuracy of the predictions helping other stations to acquire the target faster and permitting the station to repeat the procedure once more. The development of the observation strategy is particularized for the Zimmerwald Laser and Astrometry Telescope (ZIMLAT), located at the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald (SwissOGS), Switzerland. Likewise, all the implemented algorithms were tested using real measurements from ZIMLAT and the tracking camera. • Validation of the measurements acquired by the tracking camera mounted on ZIMLAT. • Comparison and implementation of three object recognition algorithms for the staring phase. • Comparison and implementation of two possibilities for the chasing phase. • Optimization of the selected algorithms for their implementation in a real-time system. • Increase the set of observables to azimuth, elevation, range and apparent brightness. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for Initial Orbit Determination (IOD) based on a modification of the Laplace’s geocentric method. The orbital elements for Near-Earth asteroids (1864) Daedalus, 2003 GW, 2019 JA8, a Hungaria-type asteroid (4690) Strasbourg, and the asteroids of the Main Belt (1738) Oosterhoff, (2717) Tellervo, (1568) Aisleen and (2235) Vittore were calculated. Input data observations from the Minor Planet Center MPC database and Astronomical Observatory of the Technological University of Pereira (OAUTP; MPC code W63) were used. These observations cover observation arcs of less than 22 days. The orbital errors, in terms of shape and orientation for the estimated orbits of the asteroids, were calculated. The shape error was less than 53 × 10–3 AU, except for the asteroid 2019 JA8. On the other hand, errors in orientation were less than 0.1 rad, except for (4690) Strasbourg. Additionally, we estimated ephemerides for all bodies for up to two months. When compared with actual ephemerides, the errors found allowed us to conclude that these bodies can be recovered in a field of vision of 95’ × 72’ (OAUTP field). This shows that Laplace’s method, though simple, may still be useful in the IOD study, especially for observatories that initiate programs of minor bodies observation.

The solution of the short-arc angles-only orbit determination problem has large uncertainty because the topocentric range is not observable. For a certain angular observation tracklet with measurement noise, there exist numerous potential orbits, all of which are compatible with the observations. However, the solution of a deterministic initial orbit determination algorithm is usually far different from the true orbit, especially for the semimajor axis and the eccentricity. A new sampling method is proposed to describe the probability distribution of the orbit determination solutions. Firstly, a series of orbits are sampled in the semimajor axis - eccentricity plane. A chi-square test method is proposed to select candidate orbits from the sample orbits. The weights of the candidate orbits are calculated to measure their probability being the true orbit. Finally, the kernel density estimation algorithm is used to estimate the probability density function of the true orbits. With some a priori assumptions, the candidate orbits can be further screened, and their weight can be modified. The a priori knowledge can significantly improve the accuracy of the orbit determination solution.

• A novel initial orbit determination method for optical track association is presented. • The role of the orbit determination in the track-to-track association is discussed. • Proposed methods for optical and radar tracks are compared against classical alternatives. The detection and identification of Resident Space Objects (RSOs) from survey tracks requires robust and efficient orbit determination methods for the association of observations of the same RSO. Both Initial Orbit Determination (IOD) and Orbit Determination (OD) methods perform the orbital estimation in which the association of tracks relies. The choice of proper IOD and OD methods is essential for the whole data association, since they are in charge of providing the estimation required to evaluate the figure of merit of the association. In this paper, we review the state of the art and propose a novel method that does not require initialisation, accounts for measurement noise and provides a full estimation (i.e., state vector and covariance) from an arbitrary number of optical observations. To do so, a boundary value problem is formulated to find a pair of ranges leading to a minimum residuals of the observations. The proposed methods are compared against classical alternatives simulated in scenarios representative of the current space debris environment. [ABSTRACT FROM AUTHOR]

Multi-fidelity approaches to orbit-state probability density prediction reduce computation time, but introduce a systematic error in the single-point prediction of a spacecraft state. An estimate of the systematic error may be quantified using cross-validation. Credibilistic filters based on Outer Probability Measures (OPMs) enable a principled and unified representation of random and systematic errors in object tracking. The quantified error of the multi-fidelity approach defines an OPM-based transition kernel, which is used in a credibilistic filter to account for the systematic error in the orbit determination process. An approach based on automatic domain splitting is proposed to reduce the error beyond what is normally achievable with multi-fidelity methods. A proof-of-concept for the approach is demonstrated for a simulated scenario tracking a newly-detected space object in low-Earth orbit via two ground stations generating radar measurements. An OPM-based definition of the admissible region combined with the multi-fidelity credibilistic filter establishes custody of the object. [ABSTRACT FROM AUTHOR]

Under the too short arc scenario, the evolutionary-based algorithm has more potential than traditional methods in initial orbit determination. However, the underlying multimodal phenomenon in initial orbit determination is ignored by current works. In this paper, we propose a new enhanced differential evolution (DE) algorithm with multimodal property to study the angle-only IOD problem. Specifically, a coarse-to-fine convergence detector is implemented, based on the Boltzmann Entropy, to determine the evolutionary phase of the population, which lays the basis of the balance between the exploration and exploitation ability. A two-layer niching technique clusters the individuals to form promising niches after each convergence detected. The candidate optima from resulting niches are saved as supporting individuals into an external archive for diversifying the population, and a local search within the archive is performed to refine the solutions. In terms of performance validation, the proposed multimodal differential evolution algorithm is evaluated on the CEC2013 multimodal benchmark problems, and it achieved competitive results compared to 11 state-of-the-art algorithms, which present its capability of multimodal optimization. Moreover, several IOD experiments and analyses are carried out on three simulated scenarios of space-based observation. The findings show that, compared to traditional IOD approaches and EA-based IOD algorithms, the proposed algorithm is more successful at finding plausible solutions while improving IOD accuracy.

The Optical Wide-field patroL-Network (OWL-Net) is a Korean optical space surveillance system used to track and monitor objects in space. In this study, the characteristics of four Initial Orbit Determination (IOD) methods were analyzed using artificial observational data from Low Earth Orbit satellites, and an appropriate IOD method was selected for use as the initial value of Precise Orbit Determination using OWL-Net data. Various simulations were performed according to the properties of observational data, such as noise level and observational time interval, to confirm the characteristics of the IOD methods. The IOD results produced via the OWL-Net observational data were then compared with Two Line Elements data to verify the accuracy of each IOD method. This paper, thus, suggests the best method for IOD, according to the properties of angles-only data, for use even when the ephemeris of a satellite is unknown.

Space-based optical sensors are attracting increasing research attention as they can measure the angle of space targets over large areas, facilitating low-cost, wide-area space target surveillance. Studying the effect of observation geometry on short-arc angles-only initial orbit determination is important for analysing the surveillance capability of systems that use optics as the main means for surveilling different areas of space. In this paper, the initial orbit is calculated based on the unit vector method (UVM); the geometric dilution of precision (GDOP)—derived under the condition that the approximate Lagrangian coefficient and distance are constant—is used as the parameter for the uncertainty distribution of the target orbit solution. A suitable coordinate system transformation is conducted and all possible observation geometry relationships between the target and the sensor are expressed in terms of the angle between orbital planes and the right ascension of the target and sensor in the transformed coordinate system. Simulation experiments show that the GDOP is approximately equal to that obtained statistically through Monte Carlo simulation experiments. The accuracy of the initial orbit solution is poor when the target and optical sensor are at the same right ascension and declination, or in the same orbital plane.

This paper focuses on the track-to-object association problem based on the two-line elements (TLE) set. The TLE's short-term propagation error characteristics are analyzed to capture its uncertainty. Further, a four-step track-to-object association algorithm is designed for the optical observation data. First, for too-short arc tracklets, a circular orbit determination algorithm is proposed to calculate the inclination and the right ascension of the ascending node. Second, the TLEs are filtered based on these results. Nearly 96% of the TLEs can be filtered, which significantly improves the association efficiency. The last two steps consist of two association processes. A first-order association process is implemented first to get candidate objects, with the angles root mean square error as the metric. Then a precise association process checks the candidate objects and gives the final association result. The proposed approach is tested with simulated and observed data, respectively. With simulated data, the true positive rate is 98.7%. With the observed data, the association results were validated using the precise orbit ephemerides. [ABSTRACT FROM AUTHOR]

The admissible region method provides a reliable orbit initialization framework for space objects with extremely limited observations. In general, the uncertainty of the admissible region is either ignored or treated as a probability distribution. However, the probabilistic characterization requires that one possess exact knowledge of the distribution of all random errors, e.g., the observation process, the constraint parameters, and the observer related information, which may not be available in realistic scenarios. In this paper, we explore the use of Outer Probability Measure (OPM) theory to achieve a more truthful characterization of the uncertainty of the admissible region, dubbed the Possibilistic Admissible Region (PAR+). Considering that the uncertainty of the constraints is epistemic and modeled by possibility functions, a rigorous possibilistic uncertainty representation is achieved without the need of known random statistics of the system. To wit, the method presented herein can be appropriately interpreted as initializing our inference of a dynamical system with a so-called uninformative prior. The developed PAR+ models the uncertainty of the admissible region as an OPM represented by a collection of particles. It provides a method for space object tracking in the presence of assumed ignorance and unknown randomness (i.e. uninformative prior). The PAR+ for the commonly used angles-only and radar measurements are developed and illustrated using simulated scenarios. • A more credible admissible region framework: PAR+ is developed. • The epistemic uncertainty results from ignorance is properly modeled by OPMs. • PAR+ for the commonly used optical and radar measurements are proposed. • Particle and GMM+ implementations are developed to initiate possibility filters. [ABSTRACT FROM AUTHOR]

A single electro-optical (EO) sensor used in space debris observation provides angle-only information. However, space debris position can be derived using simultaneous optical measurements obtained from two EO sensors located at two separate observation sites, and this is commonly known as triangulation. In this paper, we propose a new triangulation algorithm to determine space debris position, and its analytical expression of Root-Mean-Square (RMS) position error is presented. The simulation of two-site observation is conducted to compare the RMS positioning error of the proposed triangulation algorithm with traditional triangulation algorithms. The results show that the maximum RMS position error of the proposed triangulation algorithm is not more than 200 m, the proposed triangulation algorithm has higher positioning accuracy than traditional triangulation algorithms, and the RMS position error obtained in the simulation is nearly consistent with the analytical expression of RMS position error. In addition, initial orbit determination (IOD) is carried out by using the triangulation positioning data, and the results show that the IOD accuracy of two-site observation is significantly higher than that of the single-site observation.

In this work we present a conceptual analysis of the use of the novel Italian multibeam radar sensor BIRALES for space surveillance. The dedicated orbit determination algorithm is described in detail. The algorithm is tailored to the peculiar configuration of the receiver gain pattern and is devoted to both reconstructing the track of the object transiting in the receiver field of view and estimating its state vector. The performance of the sensor is assessed with numerical simulations, offering an analysis on both pointing strategies and orbit determination accuracy for different survey configurations. • An innovative initial orbit determination algorithm for radar sensors is presented. • The method is applied to the Italian multibeam radar sensor BIRALES. • The sensor observation capabilities and orbit determination accuracy are investigated. [ABSTRACT FROM AUTHOR]

This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits—namely the orbit set—that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus allowing for a compact analytical description of the orbit set. The automatic domain splitting tool controls the truncation error of the polynomial approximation by patching the uncertainty domain with different polynomial expansions, effectively creating a mesh. The algorithm is tested for different observing strategies to understand the working boundaries, thus defining the region for which the admissible region is necessary to extract meaningful information from observations and highlight where the new method can achieve a smaller uncertainty region, effectively showing that for some observing strategies it is possible to extract more information from a tracklet than the attributable. Consequently, the method enables comparison of orbit sets avoiding sampling when looking for correlation of different observations. Linear regression is also implemented to improve the uncertainty estimation and study the influence of the confidence level on the orbit set size. This is shown both for simulated and real observations obtained from the TFRM observatory. [ABSTRACT FROM AUTHOR]

When building a space catalogue, it is necessary to acquire multiple observations of the same object for the estimated state to be considered meaningful. A first concern is then to establish whether different sets of observations belong to the same object, which is the association problem. Due to illumination constraints and adopted observation strategies, small objects may be detected on short arcs, which contain little information about the curvature of the orbit. Thus, a single detection is usually of little value in determining the orbital state due to the very large associated uncertainty. In this work, we propose a method that both recognizes associated observations and sequentially reduces the solution uncertainty when two or more sets of observations are associated. The six-dimensional (6D) association problem is addressed as a cascade of 2D and 4D optimization problems. The performance of the algorithm is assessed using objects in geostationary Earth orbit, with observations spread over short arcs. [ABSTRACT FROM AUTHOR]

In this paper, the observation performance of the electro-optical telescope system which surveils the unknown space objects, is analyzed by the Modeling & Simulation(M&S). The operation concept for the observation of the unknown space objects using two telescope systems is considered and the M&S models are constructed. Based on the operation concept for observing the unknown space objects, the estimated orbit is generated by Initial Orbit Determination(IOD) and the observation performance is analyzed according to the offset compensation cycle for the estimated orbit. The result of the M&S based analysis in this paper shows that the observation performance increases with the shorter offset compensation cycle, and decreases with the longer offset compensation cycle. Therefore, to improve the performance of the telescope system which surveils the unknown space objects, the observation system with accurate initial orbit determination or shorter offset compensation cycle should be designed and constructed. [ABSTRACT FROM AUTHOR]

• Numerical approach to solve the problem of angles-only relative orbit determination. • Focus given to low Earth near-circular orbits with intersatellite distance of a few dozen km. • Performance of the method assessed using real flight data. A practical and effective numerical method is presented, aiming at solving the problem of initial relative orbit determination using solely line-of-sight measurements. The proposed approach exploits the small discrepancies which can be observed between a linear and a more advanced relative motion model. The method consists in systematically performing a series of least-squares adjustments at varying intersatellite distances in the vicinity of a family of collinear solutions coming from the linear theory. The solution presenting the smallest fitting residuals is then selected. The investigations specifically focus on the rendezvous in low Earth near-circular orbit with a noncooperative target. The objective is to determine the relative state of the formation using only bearing observations when the spacecraft are separated by a few dozen kilometers without any a priori additional information. The method is validated with flight data coming from the ARGON (2012) and AVANTI (2016) experiments. Both cases demonstrate that an observation time span of a few maneuver-free orbits is enough to compute a solution which can compete with Two-Line Elements in terms of accuracy. [ABSTRACT FROM AUTHOR]

Abstract With the combination of two evolutionary algorithms EDA and DE, a new method of initial orbit determination for satellites based on ground-based too-short-arc is established. Compared with other algorithms, the proposed method focuses on the most densely populated region in the solution space rather than the individual with best fitness value. Both the global information and local information are well fused in the search of optimum. In the method (a , e , M) are treated as variables of the optimization, and the optimization procedure is carried out as a two-stage hierarchical optimization problem which has three variables for each stage. Kernel density estimation is applied to build the probability distribution model without any assumptions of the specified distribution, accompanied by handling semi-major axis and eccentricity as a pair of dependent variables in the construction of the probability for the correlation between them in the practice. Numerical experiments with real ground-based observations show that the proposed method is applicable to too-short-arc with even 3 s, and the result of bias in several kilometers can be achieved with 5 ″ error added to angular measurements. [ABSTRACT FROM AUTHOR]

Both Global Navigation Satellite Systems and X-ray pulsar-based navigation system use relative position information to provide accurate spacecraft navigation. To supplement that navigation information, an absolute reference position from other types of measurements should be provided; however, that may increase the complexity or decrease the autonomy of the navigation system. To overcome those drawbacks, this paper proposes an initial orbit determination method using only relative position increment measurements and their corresponding epoch. The proposed method can be summarised as three steps: first, determining the orbital plane from a set of relative position vectors; next, determining the shape of the orbit by solving an ellipse fitting problem in two dimensions; finally, estimating the absolute position and all six orbital elements according to Kepler's equation and geometric relations. Monte Carlo simulations were done to analyse the feasibility and features of the proposed method. The results show that the algorithm we used does not need an initial guess and is robust. It can obtain an acceptable result from a 20% portion of an orbit when the signal-to-noise ratio is set at 15 dB with determining the inclination and right ascension of the ascending node quickly and accurately. [ABSTRACT FROM AUTHOR]

An optical tracking system has advantages for observing geostationary earth orbit (GEO) satellites relatively over other types of observation system. Regular surveying for unidentified space objects with the optical tracking system can be an early warning tool for the safety of five Korean active GEO satellites. Two strategies of positioning on the observed image of Communication, Ocean and Meteorological Satellite 1 are tested and compared. Photometric method has a half root mean square error against streak method. Also null eccentricity method for initial orbit determination (IOD) is tested with simulation data and real observation data. Under 10 minutes observation time interval, null eccentricity method shows relatively better IOD results than the other time interval. For follow-up observation of unidentified space objects, at least two consecutive observations are needed in 5 minutes to determine orbit for geosynchronous orbit space objects.

Optical observation system provides angle-only measurement for orbit determination of space object. Range measurement can be directly acquired using laser ranging or tone ranging system. Initial orbit determination (IOD) by using angle- only data set shows discrepancy according to the measurement time interval. To solve this problem, range measurement data should be added for IOD. In this study, two-site optical observation was used to derive the range information. We have observed nine geostationary earth orbit satellites by using two-site optical observation system. The determination result of the range shows the accuracy over 99.5% compared to the results from the satellite tool kit simulation. And we confirmed that the orbit determination by the Herrick-Gibbs method with the range information obtained from the two-site observation is more accurate than the orbit determination by Gauss method with the one-site observation. For more accurate two-site optical observation, a baseline should satisfy an optimal condition of length and more precise observation system needed.

Gauss and Laplace methods for initial orbit determination (IOD) are classical orbit determination tools and have been used very efficiently in optical satellite surveillance system. Several studies related to these two methods have been released until now. In this study, we found that the trends of IOD accuracy for different time interval between three pairs of measurement datas show unexpected results. Therefore, we checked the possible cause of these differences. In order to check various orbit types, we used most of satellite data which is able to obtain. To check the characteristics of methodology-only, we used simulated observation data. And we used real observation data for specific satellites to check the characteristics appeared when we applyed these methods to optical satellite surveillance system. As a result, we found that trends of IOD accuracy for time interval could be different because of satellite position observed.

We used an optical observation system with a 0.6m wide-field telescope and 5 computers system in KASI (Korean Astronomy and Space Science Institute) for satellite optical observation. Optical data have errors that are caused by targeting, expose start time and end-point determination. Gauss method for initial orbit determination was tested using angle-only data simulated by KODAS. And suitable time span is confirmed for result which has minimum errors. Initial orbit determination results are proved that optical observation system in KASI is possible satellite tracking for a short period. And also through differential correction, initial orbit determination results are improved.

Commonly, a non-cooperative space target is tracked using angle-only data. An approach utilised in many tracking problems is to perform an initial orbit determination (IOD) step and then transition to sequential estimation. In this paper, a space-based passive tracking strategy is proposed that combines IOD and sequential estimation. For the space-based IOD problem, a modified Laplace’s method is derived, in which the non-spherical effect of Earth is considered and more than three pairs of angle measurements are fused. For the sequential estimation, a robust filtering algorithm, termed the robust square-root cubature Kalman filter, is developed. An adaptive factor is introduced in the developed algorithm, to ensure robustness to measurement malfunctions. Simulation results demonstrate that the proposed strategy can be used in actual engineering applications. [ABSTRACT FROM AUTHOR]

The possibility of the future deployment of tethered satellites has created a need for a preliminary orbit determination method capable of determining whether or not a satellite is tethered to another satellite. Classical preliminary orbit determination methods, which are used for untethered satellites, typically require two or more position vectors along with their respective observation times in order to determine a preliminary orbital element set. However, these conventional methods can't distinguish between an untethered satellite and a tethered one, whose motion is modified due to the presence of a tether force. The use of conventional methods on a satellite which is part of a tethered satellite system will result in the calculation of inaccurate orbital elements. Modifications have been made to the p-iteration preliminary orbit determination method in order to allow for the identification of these tethered satellites. The modifications allow for the calculation of a modified gravitational parameter, which can be used to distinguish between a tethered satellite and an untethered one. This paper applies this modified p-iteration method to the problem of the quick identification of a tethered satellite. The performance of this method is evaluated through scenarios of differing tether lengths, levels of observation error, and orbital eccentricities. Due to the need for the preliminary orbit determination to be achieved quickly, only short time intervals between observations were considered. The manner in which this preliminary orbit information can be used to obtain tether parameters for the subsequent differential correction process is also described. [ABSTRACT FROM AUTHOR]

Intermediate perturbed orbits, which were proposed earlier by the first author and are calculated based on three position vectors and three measurements of angular coordinates of a small celestial body, are examined. Provided that the reference time interval encompassing the measurements is short, these orbits are close in the accuracy of approximation of actual motion to an orbit with fourth-order tangency. The shorter the reference time interval is, the better is the approximation. The laws of variation of the errors of methods for constructing such intermediate orbits with the length of the reference time interval are formulated. According to these laws, the rate of convergence of the methods to an exact solution in the process of shortening of the reference time interval is, in general, three orders of magnitude higher than that of conventional methods relying on an unperturbed Keplerian orbit. The considered orbits are among the most accurate of their class that is defined by the order of tangency. The obtained theoretical results are verified by numerical experiments on determining the orbit of 99942 Apophis. [ABSTRACT FROM AUTHOR]

Gauss method for the initial orbit determination was tested using angle-only data obtained by orbit propagation using TLE and SGP4/SDP4 orbit propagation model. As the analysis of this simulation, a feasible time span between observation time of satellite resulting the minimum error to the true orbit was found. Initial orbit determination is performed using observational data of GPS 26 and Koreasat 2 from 0.6m telescope of KAO(Korea Astronomy Observatory) and precise orbit determination is also performed using simulated data. The result of precise orbit determination shows that the accuracy of resulting orbit is related to the accuracy of the observations and the number of data.