Content uploaded by David A Vallado
Author content
All content in this area was uploaded by David A Vallado
Content may be subject to copyright.
A preview of the PDF is not available
Orbit determination using ODTK version 6
Abstract and Figures
The Orbit Determination Tool Kit (ODTK) is a com-mercial software product from Analytical Graphics, Inc., that performs orbit determination and analysis. Its key features include a tracking-data simulator, an ex-tended (Kalman-like) sequential filter, a fixed-interval smoother and a variable lag smoother. There are a vari-ety of custom tools to aid the researcher and analyst, including estimation of multiple satellite parameters and time-varying measurement biases, autonomous meas-urement editing, and data reporting and graphing. ODTK Version 6 builds upon previous successful ver-sions and introduces significant new capabilities.
Figures - uploaded by David A Vallado
Author content
All figure content in this area was uploaded by David A Vallado
Content may be subject to copyright.
... In the context of this application, these aiding observations are available to the filtering-based estimator from a pre-mission designed spacecraft orbit. This trajectory, which includes the spacecraft kinematic state for the entire mission span, can be obtained via a high-precision, physics-based orbit propagator embedding models of gravitational effects from celestial bodies, atmospheric drag, solar radiation pressure and possibly models of thrusting maneuvers [34]. Nevertheless, ground-dependent subsystems (e.g., ground-based networks for radiometric measurements) must also be regarded among the means aiding observations are most commonly retrieved from. ...
... It is worth stressing that appropriate modeling of the aiding variance-covariance statistics throughR k is mandatory to adopt this strategy in a Kalman estimator. In principle, these variances should be finely tuned according to the thoroughness of the source delivering aiding observations (e.g., how sophisticated the physics-based propagator in the software suite for orbit design and maneuver planning is [34]). However, absence of this information can be assumed. ...
Ground-based assets traditionally aid space vehicle navigation, but the need for autonomy is steadily growing to meet the demands of future deep-space exploration. This paper proposes a customized Trajectory-Aware Extended Kalman Filter (TA-EKF) architecture, which conforms to the kinematic approach for OD based on GNSS. Challenges at high altitudes, such as reduced GNSS signal availability and poor geometry, necessitate advanced filtering architectures leveraging external aiding data. When the receiver is not expected to interface with on-board guidance and control subsystems, aiding observations—in the form of a pre-mission planned spacecraft trajectory—allow to pursue precise and accurate OD only relying on GNSS measurements. Two alternative OAEKF designs are formulated, which foresee observation-domain and state-domain integration of aiding observations, respectively. While the former design acts directly on the filter posterior, the latter aims to overcome deficiencies in the state prediction owing to misspecified process dynamics. The feasibility of using terrestrial GNSS signals in MTO is thus demonstrated against aiding observation errors and mismodeling. The developed OAEKF models are thoroughly assessed via extensive MC analyses, comparing their OD performance against a standalone EKF solution in a dedicated constellation simulator and mission planner.
... Satellite observation can be classified as optical observations, radio observations, and radı̇o interferometry [2,19]. Keplerian (classical) six independent elements describe a satellite's motion in space entirely. ...
... The transmitter and the receiver may be satellite onboard or ground station equipment. Table 1 shows the most common ground-based observation and tracking methods and their measured values [19]. Table 2 shows the most common space-based object (satellite) observation and tracking methods and their measured values. ...
Satellite operators utilize a two-stations turn around ranging (TAR) system to reduce the ground station measurement system's complexity and cost while having the same or better orbit determination accuracy for communication satellites orbit determination recently. This study investigates two stations' performance, four-way ranging on communication satellite orbit determination, operational conformance, and cost. The observation data sets are collected using traditional single station tracking (SST) and the new method TAR. The computed results using the Monte Carlo method encourage the satellite operators to use a four-way ranging system to observe and measure required data sets. TAR performance is evaluated, taking SST as a reference. The six classical orbital elements (a, e, i, RAAN, AoP, and TA) are compared for large numbers of observation data. The SST and TAR results are very close to each other. The worst-case calculated Euclidian distance between SST and TAR is 1.893 km at the epoch below the 6 km success criteria. The TAR observation method is appropriate to collect data sets for precise orbit determination. This work result indicates that satellite operators should consider deploying TAR stations to collect two-station range data sets and compute the orbit for nominal north-south station-keeping maneuvers (NSSK) and east-west station-keeping (EWSK) maneuver operations. The TAR method is superior to SST in terms of accuracy, operational conformance, and costs.
... OD processes related to measurement generation and processing are performed using the Ansys Orbit Determination Tool Kit (ODTK). 9 Used in tandem, these tools allow for complete simulation of the proposed mission. The specifics of the proposed mission configuration, including details relating to the tracking system, are presented below, followed by the details related to planning and estimating the target's orbit. ...
This paper presents the simulation of a cislunar rendezvous and proximity operations (RPO) mission where a chaser satellite uses a progressive set of maneuvers to approach a non-cooperatively tracked target satellite occupying an Earth-Moon L1 libration point orbit. The approach maneuvers are informed by the eigendecomposition of the monodromy matrix along the target's orbit and the relative orbit determination (OD) conducted by the chaser satellite. Analysis shows that a well configured tracking network is quite capable of guiding a chaser satellite to within at least 1000 km of the target and that the OD is sufficiently accurate perform dynamical systems analyses using the target's estimate.
... This paper outlines the sensor models used in AGI's Orbit Determination Tool Kit (ODTK) and the methodology we use for configuring them. Background information on ODTK itself is available in [1]. The focus is on "metric" observations such as azimuth, elevation, range, Doppler, right ascension, declination, etc. used in orbit determination. ...
Best practices for calibrating orbit determination sensors in general and space situational awareness (SSA) sensors in particular are presented. These practices were developed over the last ten years within AGI and most recently applied to over 70 sensors in AGI's Commercial Space Operations Center (ComSpOC) and the US Air Force Space Command Space Surveillance Network (SSN) to evaluate and configure new sensors and perform ongoing system calibration. They are generally applicable to any SSA sensor and leverage some unique capabilities of an SSA estimation approach using an optimal sequential filter and smoother. Real world results are presented and analyzed.
... The B C value can be estimated during the OD process. This requires an initial B C value if the individual terms of Equation (1) are unknown or changeable over time [21]. The 2-day arc tracking data from two sites given in this paper are considered to provide a sufficient amount of tracking data for the OD process. ...
The global electro-optical (EO) and laser tracking sensor network was considered to investigate improvements to orbit prediction (OP) accuracy of space debris by combining angle and laser ranging data. However, it is worth noting that weather, schedule and visibility constraints can frequently limit the operations of such sensors, which may not result in sufficient tracking data for accurate OP. In this study, several 1-day OP results for low Earth orbit (LEO) space debris targets were demonstrated under a limited observation environment to verify the OP accuracy through the combination of angle and laser ranging data from two sites. For orbit determination (OD) processes, it was considered to analyze the OP accuracy by one site providing both 2–day arc angle data and 1-day arc laser ranging data, while the other was limited to 1-day arc angle data. In addition, the initial ballistic coefficient ( B C ) application method was proposed and implemented for the improvement of OD/OP accuracy, which introduces the modified correction factor depending on the drag coefficient. In the cases of combining the angle and laser ranging data, the OP results show the 3D position difference values are below 100 m root mean square (RMS) with small position uncertainty. This value satisfies the target OP accuracy for conjunction assessments and blind laser ranging (about 50–100 m at 1000 km altitude). The initial B C application method also shows better OP accuracy than the method without the correction factor.
... During the mission design phase prior to launch, ODTK is used for simulating the groundbased and inter-satellite tracking, and for the determination of expected orbit accuracy based on the processing of simulated measurements 6 . The HelioSwarm simulation approach was adapted from the successful application of ODTK for navigation simulation, analyses, and operations with missions in similar orbit regimes such as NASA's IBEX (3:1 lunar resonant orbit), LADEE (cislunar phasing loops), and TESS (2:1 lunar resonant orbit) missions 7,8 . ...
The HelioSwarm mission concept consists of a cluster design with 1 Hub and 8 Nodes co-orbiting the Earth in a 2:1 Lunar resonant orbit. A variety of navigation constraints, assumptions, and schedules were considered during design of the navigation strategy to minimize the need for ground-based tracking and communication. Each Node will only be capable of communicating with the Hub, with no direct connections to other nodes or the ground. The Hub will be tracked from the ground and perform two-way inter-satellite ranging with each Node. Simulated ground and space-based tracking measurements are used to determine the expected orbit accuracy.
Accurate ballistic coefficients play an important role in orbit determination and target recognition of space targets. In order to quickly and effectively calculate the target’s ballistic coefficient, AGI's ODTK (Orbit Determination Tool Kit) software is introduced, detailed operation steps and parameter settings are designed, and simulation is build to verify the effectiveness of executing the task of ballistic coefficient estimation by the ODTK software. The results of this paper have reference value for researchers engaged in space target surveillance.
In many Space Surveillance and Tracking (SST) operations, from the cataloguing of trackable space objects to orbit determination and correlation, ground-based measurements play a central role. In this frame, the monitoring and, if necessary, the update of the sensors' calibration parameters is of utmost importance to correctly evaluate the positions of tracked objects. In this work, a method for the metrological characterization of ground-based sensors for SST applications is implemented, and the performance of the developed sensor calibration tool is assessed. Starting from the acquisition of information about the sensor and data from Tracking Data Messages and Orbit Ephemeris Messages, and assuming a Gaussian distribution for all the observed parameters, the tool computes the residuals and outputs the main statistics for all the parameters of interest. The distributions of the residuals are analyzed to evaluate the statistical significance of the results and the robustness of the hypothesis of Gaussian distribution.
The population of space debris in near-Earth space is continuously growing and it represents a serious problem for active satellites and spacecraft. A performant ground-based and space-based network of sensors is necessary for space surveillance and consequently to prevent new collisions and monitoring atmospheric reentry of these objects. This paper illustrates the possible role of the Italian ground-based novel bi-static radar sensor, named BIRALET, for space monitoring and resident space objects tracking. The main characteristics of the receiver system, the Sardinia Radio Telescope with its P-band mono-beam receiver, are described in detail. Then, a preliminary analysis of the performance of the sensor is presented, and the results of numerical simulations are shown, providing a general overview on both observation capabilities and orbit determination accuracy achievable with the Sardinia Radio Telescope.
An alternative to the typical means of maneuver reconstruction
and calibration is presented which uses the orbit determination
process to directly provide an estimate of short duration orbital
maneuvers. The proposed method uses a sequential filter and
fixed interval smoother to estimate the satellite state forward and
backward across the time of the maneuver. The resulting
maneuver estimate, which is derived directly from the output of
the smoother, is supplemented by the existence of an associated
covariance. Examples of this process using both real and
simulated tracking data are presented in conjunction with a
comparison to standard reconstruction and calibration methods
using least squares.
Our new forward running Varible Lag Smoother (VLS) solves nonlinear multidimensional es-timation problems, provides results in near-real-time, combines …lter and smoothing calculations with one user speci…ed operation, and does not require calculation of a state-sized covariance matrix inverse. Our use of a variable smoothing lag enables optimal solutions of existing orbit determination problems.
This book presents fundmentals of orbit determination--from weighted least squares approaches (Gauss) to todays high-speed computer algorithms that provide accuracy within a few centimeters. Numerous examples and problems are provided to enhance readers understanding of the material. * Covers such topics as coordinate and time systems, square root filters, process noise techniques, and the use of fictitious parameters for absorbing un-modeled and incorrectly modeled forces acting on a satellite. * Examples and exercises serve to illustrate the principles throughout each chapter. * Detailed solutions to end-of-chapter exercises available to instructors.
Gerlach investigated the rotatorial Brownian motion of a small mirror suspended on a fine wire. It follows from the theorem of equipartition that the average square deviation of the mirror will depend on the temperature alone of the surrounding gas. Gerlach verified this for a large range of pressures (1 to 10-6 atm). The analogy which we found that exists between this problem and the well-known treatment of the shot effect by Schottky enables us to give a more detailed theory of this phenomenon. If the displacement, registered during a time, long compared with the characteristic period of the mirror, is developed into a Fourier series, we find the square of the amplitude of each Fourier component to be a function of the pressure and molecular weight of the surrounding gas as well as of its temperature, (formula 18). The sum of the squares, however, is a function of the temperature alone (proved in section 4). This explains why the curves registered by Gerlach at different pressures, though all giving the same mean square deviation, are quite different in appearance. To get the fluctuating torque on the mirror, the expression: deltap2---=16pi.1n.1c¯DeltatDeltao is obtained for the fluctuation in time of the pressure of a gas on the wall (section 5). In this n represents the number of molecules per cc, c¯ is the mean velocity and Deltao is the surface of the wall.
The Global Positioning System (GPS) is a constellation of 24 navigation satellites developed and deployed by the U.S. Department of Defense to provide worldwide real-time positioning capability to its military and civilian users. Generally, GPS absolute positioning solutions are computed by using an iterative procedure that requires an initial approximate value for the receiver's position. This paper evaluates a direct, noniterative algorithm for computation of the position and clock error of a single GPS receiver. An exact solution is obtained with four GPS satellites in view. The algorithm automatically combines all available GPS pseudorange measurements when more than four satellites are observed. Experimental results show that reliable absolute positioning is achieved by using the algorithm, and that the computational efficiency is improved by a factor of 2.3 over the traditional iterative method.
A sequential orbit determination algorithm is given which models
auto-correlated gravity errors for near circular orbits. Using results
from geodesy theory (Kaula, 1959; Heiskanen, 1967), it is demonstrated
that gravity modeling error auto-correlation cannot be approximated with
the Kalman white process noise model. The resulting auto-correlated
orbit error process is transformed from the status of non-Markov to
Markov at the expense of an assumption which imposes symmetries on
certain covariance functions. It is emphasized that the character of the
trajectory estimation problem is significantly changed by recognizing
and using the auto-correlation property associated with gravity modeling
errors.