Initial Orbit Determination Research Articles

Initial Orbit Determination Solution Distribution with Gooding Algorithm and Performance Enhancement

Initial Orbit Determination Solution Distribution with Gooding Algorithm and Performance Enhancement

Too-Short-Arc Association and Clustering Method for Space-Based Optical Observations

Space-based optical observation is assuming an increasingly significant role in space surveillance and tracking. However, it often yields tracks that are too short, which are known as too short arcs (TSAs). A single TSA lacks sufficient information for reliable initial orbit determination of a resident space object. Therefore, it is typically necessary to perform tracklet association during catalog building and maintenance. This study presents a novel tracklet association method that improves upon existing techniques by combining admissible regions and nonlinear orbital uncertainty propagation. Proceeding by constructing TSA association matrices and TSA clustering matrices, the bond energy algorithm, traditionally employed in the design of distributed database systems, is applied to cluster TSAs based on the association results between two arbitrary TSAs. Furthermore, the proposed splitting algorithm reduces the computational load associated with clustering multiple tracklets and effectively handles erroneous association results. To assess the effectiveness of this approach, it was tested in a space-based optical-survey scenario, accounting for practical observation uncertainties. The simulation results demonstrate that the method achieves a high level of accuracy in both TSA association and clustering.

Single track orbit determination analysis for low Earth orbit with approximated J2 dynamics

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 J2 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.

Neural Network–Assisted Initial Orbit Determination Method for Libration Point Orbits

Neural Network–Assisted Initial Orbit Determination Method for Libration Point Orbits

Initial orbit determination of some cislunar orbits based on short-arc optical observations

Initial orbit determination of some cislunar orbits based on short-arc optical observations

Initial orbit determination via artificial intelligence for too-short arcs

In the framework of Space Traffic Management (STM) the growing number of space debris and the consequent increased risk of collisions have become a topic of great interest. Moreover, the difficulty of detecting and characterizing a Resident Space Object (RSO) in terms of orbital parameters makes this research field very challenging. In most cases the available observations have a very short duration and an accurate estimation of the orbit is very difficult. This paper introduces the Initial Orbit Determination via Artificial intelligence (IODA) algorithm, a reliable and accurate orbit estimator combining metaheuristic and artificial intelligence frameworks to perform precise orbit determination from Very Short Arcs (VSAs). Starting from an initial orbit estimate derived through an Artificial Bee Colony (ABC) algorithm, a Physics Informed Extreme Learning Machine is employed to increase the accuracy of the predicted orbit. Results on simulated data have shown the robustness of the algorithm to random parameters initialization and a percentage of success of 89% of retrieving the reference orbit with an error under 1 km and 0.01 km/s on the initial target’s state.

Simulated annealing-particle swarm optimization initial orbit determination method for too-short-arcs

The initial orbit determination (IOD) of a non-cooperative satellite through space-based optical angle-only measurement data is a fundamental task. However, due to the lack of relative distance information of the targets, traditional methods have problems with poor accuracy and robustness in orbit determination results. The application of particle swarm optimization algorithm for IOD under optical too-short-arcs (TSA) measurement data has achieved good results. However, there is still a problem of convergence to local extremum. This article proposes a simulated annealing-particle swarm optimization (SA-PSO) hierarchical algorithm, which combines the efficient searchability of particle swarm optimization with the fine searchability of simulated annealing algorithm to achieve robust and precise optimization of non-cooperative targets orbit elements. The experimental results show the SA-PSO algorithm significantly improves the accuracy of orbit elements prediction compared to the particle swarm optimization algorithm and proves its effectiveness.

Positioning Error Estimation Method for Short-Arc Angles-Only Initial Orbit Determination

The development of space surveillance capabilities has received increased emphasis with time. Suitable evaluation parameters are investigated to analyze the effects of multiple factors on short-arc angles-only initial orbit determination. This investigation is crucial for designing surveillance system parameters. In this paper, the orbit determination equations where the target state is linear were derived by assuming that Lagrangian coefficients are constant and taking the minimum residual sum as the optimization objective. From this paper’s analysis, it was demonstrated that because the position uncertainty distribution primarily lies in the line-of-sight vector, the upper limit of relative positioning error (RPE) can be used as the evaluation parameter of the determination accuracy in scenarios where a high-orbit target is observed by a low-orbit sensor observes. An empirical relationship was also found, indicating that the upper limit of RPE is proportional to the observation error, −2.5 power of the observation arc length, and the 0.5 power of the observation interval.

Non-Cooperative LEO Satellite Orbit Determination Using Single Station for Space-Based Opportunistic Positioning

Space-based opportunistic positioning is a crucial component of resilient positioning, navigation, and timing (PNT) systems, and it requires the acquisition of orbit information for non-cooperative low Earth orbit (LEO) satellites. Traditional methods for orbit determination (OD) of non-cooperative LEO satellites have difficulty in achieving a balance between reliability, hardware costs, and availability duration. To address these challenges, this study proposes a framework for single-station orbit determination of non-cooperative LEO satellites. By utilizing signals of opportunity (SOPs) captured by a single ground station, the system performs initial orbit determination (IOD), precise orbit determination (POD), and orbit prediction (OP), enabling the long-term determination of satellite positions and velocities. Under the proposed framework, the reliability and real-time performance are dependent on the initial orbit determination and the orbit calculation based on the dynamical model. To achieve initial orbit determination, a three-step algorithm is designed. (1) An improved search method is employed to estimate a coarse orbit using single-pass Doppler measurements. (2) Data association is conducted to obtain multi-pass Doppler observations. (3) The least squares (LS) is implemented to determine the initial orbit using the associated multi-pass Doppler measurements and the coarse orbit. Additionally, to enhance computational efficiency, two fast orbit calculation algorithms are devised. These algorithms leverage the numerical stability of the Runge–Kutta integrator to reduce computations and exploit the strong correlation among nearby time intervals of orbits with small eccentricities to minimize redundant calculations, thereby achieving orbit calculation efficiently. Finally, through positioning experiments, the determined orbits are demonstrated to have accuracy comparable to that of two-line elements (TLE) updated by the North American Aerospace Defense Command (NORAD).

Initial orbit determination in range search based on dynamic thresholds

Initial orbit determination in range search based on dynamic thresholds

Initial Orbit Determination of Periodic Orbits in the Earth-Moon System with Ground-based Optical Observations

Initial Orbit Determination of Periodic Orbits in the Earth-Moon System with Ground-based Optical Observations

An Improved Range-Searching Initial Orbit-Determination Method and Correlation of Optical Observations for Space Debris

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.

Improved Initial Orbit Determination Based on the Gooding Method of Low Earth Orbit Space Debris Using Space-Based Observations

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.

A multifidelity approach to robust orbit determination

This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem and detect possible outliers in the processed measurements. The uncertainty on the initial estimate is propagated forward in time and progressively reduced by exploiting sensor data available in said propagation window. Differential algebra techniques and a novel automatic domain splitting algorithm for second-order Taylor expansions are used to efficiently propagate uncertainties over time. A multifidelity approach is employed to minimize the computational effort while retaining the accuracy of the propagated estimate. At each observation epoch, a polynomial map is obtained by projecting the propagated states onto the observable space. Domains that do no overlap with the actual measurement are pruned thus reducing the uncertainty to be further propagated. Measurement outliers are also detected in this step. The refined estimate and retained observations are then used to improve the robustness of batch orbit determination tools. The effectiveness of the algorithm is demonstrated for a geostationary transfer orbit object using synthetic and real observation data from the TAROT network.

New Space Object Cataloguing through Very-Short-Arc Data Mining

The space surveillance network collects significant quantities of space object monitoring data on a daily basis, which varies in duration and contain observation errors. Cataloguing space objects based on these data may result in a large number of very short arcs (VSAs) being wasted due to cataloguing flaws, poor data quality, data precessing, and so on. To address this problem, an effective data mining method based on tracklet-to-object matching is proposed to improve the data utilization in new object cataloguing. The method can enhance orbital constraints based on useful track information in mined tracklets, improve the accuracy of catalogued orbits, and achieve the transformation of omitted observations into “treasures”. The performance of VSAs is evaluated in tracklet-to-object matching, which is less sensitive to tracklet duration and separation time than initial orbit determination (IOD) and track association. Further, the data mining method is applied to new space object cataloguing based on radar tracklets and achieved significant improvements. The 5-day data utilization increased by 9.5%, and the orbit determination and prediction accuracy increased by 11.1% and 23.6%, respectively, validating the effectiveness of our method in improving the accuracy of space object orbit cataloguing. The method shows promising potential for the space object cataloguing and relevant applications.

Initial Orbit Determination Based on Intelligent Optimization Algorithm

Classical methods for initial orbit determination (IOD) include Laplace method, Gauss method, and their variations. In addition to this, based on the characteristic of optical observation data nowadays, experts propose some other IOD methods, like Double-r method and admissible region method. One of the ways to determinate the orbit through double-r method is to guess distances of the target from the observer at two epochs—usually at the first and the last one. By doing so, we can solve the Lambert problem, and use its solution as the initial guess of the orbit. Furthermore, we can improve the initial guess by iterations to reduce the root mean square (RMS) of the observations. The admissible method is based on the concept of attributable (longitude, latitude, and their rates). With some conceptions, the admissible region described by the range and range rate from the observer is characterized. Using triangulation we can find the nodal point that makes the RMS minimal. In our work, we apply one intelligent optimization method—the particle swarm optimization method to the two methods, based on simulated and real data, and compare the results with that of modified Laplace method. At last, we briefly discuss the possibility of applying the double-r method to the orbit link problem.

A stochastic approach to detect fragmentation epoch from a single fragment orbit determination

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.

Fast angles-only relative navigation using polynomial dynamics

A fast and efficient method for initial relative orbit determination from bearing-angle measurements is introduced. The range ambiguity problem for angles-only relative navigation is addressed by modeling nonlinear effects with a novel second-order mapping from relative orbit elements (ROE) to relative position coordinates. This model is used to form a system of polynomial constraint equations linking the line-of-sight measurements to the ROE. An efficient method for solving this system is developed around the insight that the ROE scale with the ratio of the inter-spacecraft separation to the orbit radius and are therefore small for most applications of interest. The method uses a truncated expansion of the quadratic formula to recursively eliminate unknowns, reduce the dimension of the system, and ultimately acquire an approximate solution. Strategies for improving robustness, efficiency, and accuracy are developed and the method is applied to general second-order systems as well as to a broad range of intial relative orbit determination scenarios. Modifications to the constraint equations and a solution algorithm are introduced to address the challenge of bias in the bearing-angle measurements.

Continuous Streak Image Acquisition Optical Observation System Design for Initial Orbit Determination of Uncharted Space Objects

Continuous Streak Image Acquisition Optical Observation System Design for Initial Orbit Determination of Uncharted Space Objects

Initial Orbit Determination from Only Heading Measurements

This work introduces the problem of initial orbit determination (IOD) from only heading measurements. Such a problem occurs in practice when estimating the orbit of a spacecraft using visual odometry measurements from an optical camera. After reviewing the problem geometry, a simple solution is developed in the form of an iterative scheme on the parameters describing the orbital hodograph. Numerical results are presented for an example spacecraft in low lunar orbit. The principal intent of this brief study is to communicate the existence of a new class of IOD problem to the community and to encourage the broader study of hodographs and heading-only IOD.