Doppler-Only Initial Orbit Determination for an Orbiting Transmitter

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 solution of the initial relative orbit determination problem using angles-only measurements is important for orbital proximity operations, satellite inspection and servicing, and the identification of unknown space objects in similar orbits. In this paper, a preliminary relative orbit determination performance analysis is conducted utilizing the linearized relative orbital equations of motion in cylindrical coordinates. The relative orbital equations of motion in cylindrical coordinates are rigorously derived in several forms included the exact nonlinear two-body differential equations of motion, the linear-time-varying differential equations of motion for an elliptical orbit chief, and the linear-time-invariant differential equations of motion for a circular orbit chief. Using the nonlinear angles-only measurement equation in cylindrical coordinates, evidence of full-relative-state observability is found, contrary to the range observability problem exhibited in Cartesian coordinates. Based on these results, a geometric approach to assess initial relative orbit determination performance is formulated. To facilitate a better understanding of the problem, the focus is on the 2-dimensional initial orbit determination problem. The results clearly show the dependence of the relative orbit determination performance on the geometry of the relative motion and on the time-interval between observations. Analysis is conducted for leader-follower orbits and flyby orbits where the deputy passes directly above or below the chief.

In this paper, optical target monitoring orbit determination using the Gooding algorithm based on the 400 km altitude space platform was researched. The measurement error was set to 3″ and 6″ respectively for 800 km, 1500 km altitude low Earth orbits and 36 000 km altitude geosynchronous orbit to determine the initial orbit and precise orbit. Simulation results show that the initial orbit determination accuracy of the 4~15 min arc is about 10 km, and the 1~2 min arc is about 100 km when the measurement data error is between 3″ and 6″. The error of 15 min initial determination arc is 100 m. As the arc is less than 10 min, the improved error accuracy of the orbit is in the order of km scale. As the measurement data error is 3″, the initial orbit determination accuracy of the 15~20 min arc is about tens of kilometers, and that of the 8~10 min arc is 100 km. The improved orbit has an error of km. When the measurement data error is 6″, the accuracy of the initial orbit determination of the 20 min arc is at the magnitude of 10 km, the accuracy of the initial orbit determination of the 8~15 min arc is at the magnitude of 100 km, and the error accuracy of the improved orbit is at the magnitude of 10 km.

The following thesis regards the use of small aperture telescopes for space domain awareness efforts. The rapidly populating space domain was motivation for the development of a new operation scheme to conduct space domain awareness feasibility studies using small telescopes. Two 14-inch Schmidt-Cassegrain Telescopes at the California Polytechnic State University and the Air Force Research Lab in Kirtland AFB, NM, in conjunction with a dedicated CCD camera and a commercial DSLR camera, were utilized to conduct optical observations on satellites in Earth orbit. Satellites were imaged during August 2019, and from January 2020 to March 2020, resulting in the collection of 77 valid images of 16 unique satellites. These images were used to obtain celestial spherical coordinates, which were used in Gauss and Double-R angles-only initial orbit determination methods. Initial orbit determination methods successfully produced valid results, reaffirming the feasibility of using small aperture telescopes for such methods. These orbit determinations were used to propagate orbit states forward in time to determine the feasibility of future imaging of the targets with the same apparatus. Propagation results demonstrated that initial orbit determinations rapidly decayed in accuracy over distant times and are most accurate for immediate satellite passes. In addition, an attempt to combine multiple initial orbit determinations using Lambert’s problem solutions was made. Combination of these multiple initial orbit determinations resulted in either no orbit state accuracy improvement compared to individual initial orbit determinations, or a decrease in accuracy compared to these methods. Ultimately, efforts demonstrated that small telescope usage is feasible for orbit determination operations, however there may be a need for hardware and operational revisions to improve the ability of the apparatus.

I have constructed and demonstrated a new fast-running algorithm to perform refined orbit determination for any spacecraft in GEO (geosynchronous Earth orbit), without user requirement for an a priori orbit estimate. We now have a refined method for GEO initial orbit determination (IOD). This is enabled by the use of equinoctial orbit elements, by a one-dimensional search in the equinoctial orbit element mean argument of orbit longitude, by the use of sensor locations to reduce the one-dimensional search, and by convergence boundaries of the nonlinear least squares (LS) algorithm. I shall refer herein to the new algorithm as LS_GEO_IOD. Algorithm LS_GEO_IOD uses any desired perturbative acceleration model for numerical trajectory integration, and its success appears to be independent of input measurement type.

In recent years, the number of space objects has been increasing rapidly. It has become crucial to utilize multi-source information fusion techniques for the orbit measurement and cataloguing of numerous objects. This report elaborates on the utilization of ground-based radar, optical, and space-based optical measurements in joint precision orbit determination. Regarding the real-time surveillance of a vast amount of space debris, investigations have been conducted concerning the initial orbit determination upon the first detection of targets, data association, orbit refinement, and the generation of catalogued orbital elements.Space-based technologies assume a particularly crucial role owing to their remarkable advantages in temporal and spatial coverage. To fulfill the data processing requisites for orbit determination of space-based measurement platforms, the onboard GNSS precision orbit determination software, SODA, has been developed, attaining centimeter-level accuracy in orbit determination. In the scenario of long-arc tracking via ground single-station astronomical optical cameras, an orbit determination accuracy within the range of several tens of meters can be accomplished. In the situation where multiple satellites are equipped with optical cameras, a substantial enhancement in the monitoring performance of space debris can be achieved both temporally and spatially.

TLE로부터 SGP4/SDP4 모델을 이용하여 인공위성의 가상의 위치 정보를 얻은 후 Gauss 방법을 사용하여 인공위성의 예비궤도를 결정해보았다. 예비궤도 결정에 필요한 임의의 세 점 사이의 시간간격을 변화시켜 얻은 결과를 위성의 위치 참값과 비교하여 최소의 차이를 가지는 관측 시간 간격을 찾아보았으며, Gauss 예비궤도 결정법의 성능을 비교, 분석하였다. 실제 인공위성 관측 결과와의 비교를 위해서 한국천문연구원의 광시야 망원경을 사용하여 GPS위성(PRN 26)과 무궁화 2호의 광학관측 데이터를 얻은 후 같은 방법으로 예비궤도를 결정해 보았다. 인공위성의 정밀궤도결정을 위하여 시뮬레이션에서 얻어진 가상의 광학관측 데이터를 가지고 정밀케도결정을 수행하였으며, 관측 데이터의 오차와 관측 시간 간격에 따라 정밀궤도결정을 수행하여 원하는 정밀도를 얻기 위한 관측 시스템의 조건에 대해서 알아보았다. Gauss method for the initial orbit determination was tested using angle-only data obtained by orbit propagation using TLB 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.

Initial orbit determination is highly enabling for operational awareness and safety in space. Reliable orbit determination in non-Keplerian systems, such as multi-body orbital mechanics, is challenging due to chaotic and unpredictable motion of these systems over long time scales. Typical approaches to non-Keplerian orbit determination use explicit integration with numerical shooting methods to propagate candidate trajectories. These methods often break down for measurement gaps on the order of days or even hours. This work presents a novel algorithm for non-Keplerian orbit determination using sparse grid collocation methods. The approach provides many benefits, including a large region of convergence without a close initial guess, as well as increased stability and performance over long observing time scales. A further advancement is made for estimating periodic orbits, in which a repeating orbit and its natural period are determined simultaneously from angles-only measurements. Orbit determination using collocation may significantly reduce sensor tasking requirements and enhance capabilities in complex orbital environments such as cislunar space.

An investigation has been initiated to examine the concept of determining an initial orbit using angles-only observations over a short arc from a single space based sensor. The methods of Laplace and Gauss for angles-only initial orbit determination were the methods of choice for this study. To apply these methods, one has to solve a system of non-linear equations which have multiple solutions. Typical solution schemes recommend using an iterative solution technique with a first guess to start. However, since only one solution will be found using such a technique, the success of this approach will depend entirely upon how good (or bad) the first guess is. We have found that this technique is not satisfactory for performing initial orbit determination over short arcs of data. In this paper we will discuss past methods used in solving these non-linear equations and then we will present our approach which involves finding all the necessary solutions and determining which solution is correct.

This paper is predicated on determining the effectiveness of angles-only initial orbit determination (IOD) methods when limited observational data is available for low-Earth orbit (LEO) rocket body debris. The analysis will be conducted with data obtained from Lockheed Martin Space’s Space Object Tracking (SpOT) facility, focusing on their observational data from 2018 that contains tracking of rocket body debris for less than one minute per overhead pass. After the IOD accuracies are better understood, a feasibility study will follow that investigates the possibility of cataloguing LEO orbital debris from a single optical observation facility with similar observational capabilities as that of the SpOT facility. The IOD accuracy analysis will investigate nine different rocket bodies, with a total of 50 orbital passes of data included in the research. Three main IOD approaches will be tested for each data set to determine the best method in achieving high levels of IOD accuracy: a traditional three-point method, an iterative method, and an assumed-circular orbit method. Application of the iterative approach results in increased accuracy for the resultant initial orbit determination as compared to the three-point IOD method, and an assumed-circular orbit assumption allows for a further increase in accuracy, especially for observed objects in near-circular orbits. The feasibility of cataloguing debris from a singular optical facility shows promise, as subsequent target acquisition after an object’s initial observation is determined to be achievable under the correct circumstances. By choosing a correct telescope pointing angle based on the IOD results from one pass of data, an observed rocket body debris object would pass through the field of view of SpOT’s spotter scope (0.7-degrees) during its next overhead pass for two different test cases. An increase field of view would increase both the likelihood of acquiring the target object and the amount of time the object is visible by the telescope.

Space-based orbit determination problem using line-of-sight measurements appears in two equivalent cases: 1) to estimate the observer’s orbit when observing a known planetary body (navigation problem) and 2) to determine the orbit of an unknown observed body when the observer’s orbit is known (surveillance problem). These two problems are mathematically equivalent. Star trackers provide attitude autonomy to interplanetary missions while the estimation of position still relies on communications to Earth’s ground stations. This paper shows that, in interplanetary missions, autonomy for position estimation can be obtained just by observing visible planets using star trackers. In any space mission and, in particular interplanetary missions, autonomy plays a critical role for the success of the mission, especially if temporary or permanent failure occurs in the communication system. This study first solves the position and velocity (state) estimation problem as a single-point problem using the Pn space-based Initial Orbit Determination (IOD) algorithm 8 and then uses this estimation to initiate a filtered estimation of the state using Extended Kalman Filter (EKF). Space observations of line-of-sight directions constitute the measurements of two distinct problems: when estimating the orbit of an unknown observed body (space-based orbit determination problem) and when estimating the observer’s orbit when the observed body is known (navigation problem). There is a perfect duality between these two problems as they share the same mathematics meaning that any method capable of solving one problem can be used to solve the other. However, when the distances between observer and observed become large, as in interplanetary missions, the problem becomes more complicated. In fact, ∗Texas A&M University Affiliate. E-mail: reza.aero@gmail.com †Professor, 746C H.R. Bright Bldg, Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, AAS Fellow, AIAA Associate Fellow. IEEE Senior member. E-mail: mortari@tamu.edu

We consider initial determination of asteroid orbits in the case of small numbers of observations and short observational arcs. For asteroids having long arcs, we can assess the orbital uncertainties with the help of the covariance matrix that, in the phase space of the orbital elements, defines a set of probability ellipsoids. In initial orbit determination, because of the nonlinear characteristics and multiple solutions of the inversion problem, we cannot readily use the covariance matrix to estimate the orbital uncertainties. However, by computing the eigenvalues and eigenvectors of the formal correlation matrix (that is, by deriving the eigenorbits), we can discern the most indeterminate orbital elements. Here we solve the eigenproblem for 17 single-apparition asteroids.

Space-based initial orbit determination (IOD) is crucial for space situational awareness. However, classical algorithms often fail to converge or become trapped in trivial solutions when applied to very short arc scenarios with angles-only measurements. To overcome this challenge, this paper proposes a simple and fast algorithm based on the online sequential extreme learning machine (OSELM). First, the dynamic model and angles-only measurement model of the space target were constructed. Then, an OSELM-based orbit determination algorithm is designed, including the generation of the training dataset, data preprocessing, and network structure design, which focuses on establishing a nonlinear mapping model from angles-only measurements to the orbital state of space targets using the OSELM. Finally, numerical simulations for low Earth orbit (LEO) scenarios demonstrate the algorithm's high accuracy in estimating the target initial state, along with strong noise resistance and generalization capability.

This paper presents a novel approach to identify, localize, and associate resident space objects (i.e. Earth-orbiting satellites) across a series of unresolved optical images, to serve as an input to the process of initial and/or precise orbit determination. The images will contain stars and (potentially) satellites, which generally will blend together. The approach involves a sequence of steps including image processing, centroiding, registration, star elimination, and object association. The goal is to develop algorithms that are compact and lend themselves to onboard operation, so that local space domain awareness can be performed by any spacecraft with a taskable camera. Results are presented using imagery obtained from a ground sensor, with satellites in various types of orbits being imaged.

Real-time orbit determination of Low Earth orbit satellite based on RINEX/DORIS 3.0 phase data and spaceborne GPS data