Initial Orbit Determination Method Research Articles

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

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

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.

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.

An orbit determination approach to associating optical tracklets of space objects

The advances in the optical space surveillance technology and the possibly more deployments of space-based optical sensors enable more and more space objects detectable and make the catalog expansion more realistic. The cataloging of an optically detected new object requires finding three or more tracklets over a few days from the object. In this process, the tracklet-to-tracklet association is a critical step, but associating short-arc optical tracklets remains a difficult task. This paper develops a novel orbit determination approach to the optical tracklet association. The main idea is to determine accurate orbit elements from two tracklets of the same object by exclusively using the Gooding angles-only initial orbit determination (IOD) method. Before applying the Gooding IOD method to two tracklets apart by a few days, the dominant secular effects on the angular observations have to be considered. The significant short-periodic effects may also need consideration if tracklet-to-tracklet IOD is to achieve high accuracy. In this paper, the secular effects from the J2 and lunisolar gravitational perturbations, as well as the short-periodic effects due to J2 and J2,2, are accounted for in the tracklet-to-tracklet IOD. Extensive tests using tracklets from low Earth orbit (LEO), high elliptical orbit (HEO), medium Earth orbit (MEO), geosynchronous Earth orbit (GEO), and Molniya orbit are performed to assess the performance of the developed method. It is shown that the true positive (TP) rate for associating two tracklets from the same object within 48 h is 98.3% for LEO objects and higher than 89.8% for HEO and Molniya objects. The TP rate is remarkably high at around 99.0% for MEO and GEO objects. The analytic approach is also computationally very efficient. The results demonstrate the strong applicability of the developed method to associate optical tracklets of uncatalogued objects of all orbit types.

An analytical initial orbit determination method using two observations from a bistatic radar

An analytical initial orbit determination (IOD) method using two observations from a bistatic radar is proposed. Each observation contains bistatic range and the doppler frequency shift, azimuth angle and elevation angle. This problem arises from the challenging catalogue process for small space debris, which features sparse radar observations. By incorporating doppler measurements into the original Lambert’s IOD problem which uses two position vectors and can only be solved iteratively, we show that an analytical solution can be obtained. The specific angular momentum conservation equation and the specific mechanical energy equation are used as kinematic constraints. An ad hoc coordinate system is proposed to derive the solution. The geometric dilution of precision (GDOP) metric is analysed to express the IOD accuracy using a linearization method. Simulations are carried out to demonstrate the performance of the proposed method.

Initial Orbit Determination Method for Low Earth Orbit Objects Using Too-Short Arc Based on Bistatic Radar

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, we propose an analytical IOD method 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, we define an auxiliary coordinate system based on the bistatic geometry to help reduce the equations to one unary quartic equation. Further, we derive closed-form expressions of the orbital state. 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.

Generalization of a method by Mossotti for initial orbit determination

Here, we revisit an initial orbit determination method introduced by O. F. Mossotti employing four geocentric sky-plane observations and a linear equation to compute the angular momentum of the observed body. We then extend the method to topocentric observations, yielding a quadratic equation for the angular momentum. The performance of the two versions is compared through numerical tests with synthetic asteroid data using different time intervals between consecutive observations and different astrometric errors. We also show a comparison test with Gauss’s method using simulated observations with the expected cadence of the VRO–LSST telescope.

Unit Sphere-Constrained and Higher Order Interpolations in Laplace’s Method of Initial Orbit Determination

This paper explores an alternative interpolation approach for the line-of-sight measurements in Laplace’s method for angles-only initial orbit determination (IOD). The classical implementation of the method uses Lagrange polynomials to interpolate three or more unit line-of-sight (LOS) vectors from a ground-based or orbiting site to an orbiting target. However, such an approach does not guarantee unit magnitude of the interpolated line-of-sight path except at the measurement points. The violation of this constraint leads to unphysical behavior in the derivatives of the interpolated line-of-sight history, which can lead to poor initial orbit determination (IOD) performance. By adapting a spherical interpolation method used in the field of computer graphics, we can obtain an interpolated line-of-sight history that is always unit norm. This new spherical interpolation method often leads to significant performance improvements in Laplace’s IOD method, with comparable robustness to measurement noise as the traditional interpolation methods. This paper also demonstrates the benefit of interpolating through more than three data points, which is easily enabled up to an arbitrary number of measurements by recursive definitions of the interpolations.

Angles-Only Initial Orbit Determination of Low Earth Orbit (LEO) Satellites Using Real Observational Data

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.

Robust Initial Satellite Orbit Determination method using a Modified Kalman Filter

The control segment in satellite navigation systems is responsible for estimating satellite orbit and clock bias which is required for a reliable Position, Navigation and Timing (PNT) user service. Initial orbit determination is a crucial step which accounts for all unknowns/anomalous parameters such as satellite orbit manoeuvres, on board and receiver clock frequency variations and environmental effects. It is vital that the estimates of the orbits and clock are insensitive to these factors. In this paper, an initial orbit determination method is presented using existing robust methodology for estimation of initial satellite position and its propagation using a variant of the Kalman Filter (KF) which allows the initial position determination process to be independent of satellite and receiver anomalies. The derivation of this KF variant is presented. Preliminary results obtained from simulated data are shown. The said method is checked for robustness by comparing results obtained for a given satellite position data set with that from the conventional Kalman Filter. The conventional KF exhibits divergence due to anomalies which are eliminated by the use of the method presented in this paper.

A combination method using evolutionary algorithms in initial orbit determination for too short arc

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.

Initial Orbit Determination Using Very Short Arc Data Based on Double-Station Observation

A method of initial orbit determination (IOD) of a space object, which uses very short arc (VSA) data of double-station observations, is presented. Closed-form solutions of the initial orbit are derived, and these solutions utilize radial measurements (the range, velocity, and acceleration) from two radar stations. The performance of the method based on the geometric dilution of precision (GDOP) metric is analyzed in detail. The analytical approximation expressions of the GDOP metric are also derived, and these expressions can serve as guidance for choosing an observation arc in order to obtain better IOD performance. Comparison of the analytical results with Monte Carlo simulations shows good consistency. Theoretical analysis and simulation results show that several seconds of VSA data can produce an IOD accuracy of several kilometers in position and several meters per second in velocity, provided that highly accurate measurements of phase-derived velocity and acceleration are available.

Direct Uncertainty Estimates from Angles-Only Initial Orbit Determination

Initial orbit determination methods yield only a point solution, with no information about the quality of or confidence in the solution. However, probabilistic information may be inferred directly from the initial orbit determination process, given measurement uncertainty characteristics. A state uncertainty estimate is derived directly from Gauss’s angles-only initial orbit determination method using a novel technique based on sigma points. This method is tested across a range of simulated orbit types and observation geometries. Comparisons with a standard least-squares-based approach are made, and the direct uncertainty estimates are shown to be more realistic than the least-squares estimates. The state and uncertainty estimates from this method are also shown to be suitable to initialize an unscented Kalman filter for processing further measurements.

An initial orbit determination method from relative position increment measurements

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 informat...

An Improved Double r-iteration IOD Method for GEO UCTs Based on SBSS System

The purpose of initial orbit determination, especially in the case of angles-only data for observation, is to obtain an initial estimate that is close enough to the true orbit to enable subsequent precision orbit determination processing to be successful. However, the classical angles-only initial orbit determination methods cannot deal with the observation data whose Earth-central angle is larger than 360°. In this paper, an improved double r-iteration initial orbit determination method to deal with the above case is presented to monitor geosynchronous Earth orbit objects for a spacebased surveillance system. Simulation results indicate that the improved double r-iteration method is feasible, and the accuracy of the obtained initial orbit meets the requirements of re-acquiring the object.

Orbit determination by genetic algorithm and application to GEO observation

This paper demonstrates an initial orbit determination method that solves the problem by a genetic algorithm using two well-known solutions for the Lambert’s problem: universal variable method and Battin method. This paper also suggests an intuitive error evaluation method in terms of rotational angle and orbit shape by separating orbit elements into two groups. As reference orbit, mean orbit elements (original two-lines elements) and osculating orbit elements considering the J2 effect are adopted and compared. Our proposed orbit determination method has been tested with actual optical observations of a geosynchronous spacecraft. It should be noted that this demonstration of the orbit determination is limited to one test case. This observation was conducted during approximately 70min on 2013/05/15UT. Our method was compared with the orbit elements propagated by SGP4 using the TLE of the spacecraft. The result indicates that our proposed method had a slightly better performance on estimating orbit shape than Gauss’s methods and Escobal’s method by 120km. In addition, the result of the rotational angle is closer to the osculating orbit elements than the mean orbit elements by 0.02°, which supports that the estimated orbit is valid.

A method of initial orbit determination for long arc data

According to the principles of the unit vector method (UVM), a method of initial orbit determination for long arcs is presented. This method is applicable not only to long arc data but also to short arc data and is suitable for earth satellites with arbitrary orbital eccentricity and inclination. This method has a good accuracy of initial orbit determination and good convergence. It offers a basis for extending the application of the UVM method from initial orbit determination to orbit improvement.

A new method of initial orbit determination

We present a new method of initial orbit determination for angles-only data. The technique is applicable with only three data sets but the formalism can incorporate arbitrarily large amounts of data. The algorithm rests on the fact that the orbital plane is usually very well determined, as a consequence of the central nature of the gravitational force, and a theorem of W. R. Hamilton's from 1846. His result states that the velocity vector describes a circle in the orbital plane in a particular manner. Tests on a variety of deep-space artificial satellites show that the method has promise. Unfortunately it does not work very well on the stressing cases of current practical application-high eccentricity orbits. As no other method does either, the opportunities still exist for a significant advance in this area of celestial mechanics.

Initial orbit determination - The pragmatist's point of view

view Abstract Citations (26) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Initial orbit determination - The pragmatist's point of view Marsden, B. G. Abstract The practicality of the standard Gauss method and the Väisälä-Cunningham variant is discussed from the point of view of modern computational technology. The methods are considered both in their general form and when they are adapted to handle the partial knowledge that might exist in a given situation. A demonstration is given of the direct linkage of two observations of a minor planet at one opposition with one at a neighboring opposition and thus how three-observation orbit determinations can sometimes be of value in identfication work on minor planets. Taff's criticism of Gauss' method of initial orbit determination of the grounds of the small radius of convergence of the f and g series is shown to be completely unwarranted. Publication: The Astronomical Journal Pub Date: August 1985 DOI: 10.1086/113867 Bibcode: 1985AJ.....90.1541M Keywords: Asteroids; Celestial Mechanics; Gauss Equation; Orbit Calculation; Solar Orbits; Amor Asteroid; Boundary Value Problems; Iterative Solution; Series Expansion; Astronomy full text sources ADS |