Orbit determination using GPS including perturbations due to geopotential coefficients of high degree and order and solar radiation pressure

The main target here is to determine the orbit of an artificial satellite, using signals of the GPS constellation and least squares algorithms implemented through sequential Givens rotations as a method of estimation, with the aim of improving the performance of the orbit estimation process and, at the same time, minimizing the computational procedure cost. Geopotential perturbations up to high order and direct solar radiation pressure were taken into account. It was also considered the position of the GPS antenna on the satellite body that, lately, consists of the influence of the satellite attitude motion in the orbit determination process. An application has been done, using real data from the Topex/Poseidon satellite, whose ephemeris is available at Internet. The best accuracy obtained in position was smaller than 5 meters for short period (2 hours) and smaller than 28 meters for long period (24 hours) orbit determination. In both cases, the perturbations mentioned before were taken into consideration and the analysis occurred without selective availability on the signals measurements.

A Discussion Related to Orbit Determination Using Nonlinear Sigma Point Kalman Filter

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Simple orbit determination using GPS based on a least-squares algorithm employing sequential givens rotations

A low-cost computer procedure to determine the orbit of an artificial satellite by using short arc data from an onboard GPS receiver is proposed. Pseudoranges are used as measurements to estimate the orbit via recursive least squares method. The algorithm applies orthogonal Givens rotations for solving recursive and sequential orbit determination problems. To assess the procedure, it was applied to the TOPEX/POSEIDON satellite for data batches of one orbital period (approximately two hours), and force modelling, due to the full JGM-2 gravity field model, was considered. When compared with the reference Precision Orbit Ephemeris (POE) of JPL/NASA, the results have indicated that precision better than 9 m is easily obtained, even when short batches of data are used. Copyright (c) 2007.

Application of the GPS system for preliminary satellite orbit determination

In this paper, we discuss a method of preliminary orbit determination for an artificial satellite based on the navigation message of the GPS constellation. Orbital elements are considered as state variables and a simple dynamic model, based on the classic two-body problem, is used. The observations are formed by range and range and range-rate with respect to four visible GPS. A discrete Kalman filter with simulated data is used as filtering technique. The data are obtained through numerical propagation (Cowell's method), which considers special perturbations for the GPS satellite constellation and a user satellite. © 1997 COSPAR. Published by Elsevier Science Ltd.

Real time orbit determination using GPS navigation solution

This work analyses a real time orbit estimator using the raw navigation solution provided by GPS receivers. The estimation algorithm considers a Kalman filter with a rather simple orbit dynamic model and random walk modeling of the receiver clock bias and drift. Using the Topex/Poseidon satellite as test bed, characteristics of model truncation, sampling rates and degradation of the GPS receiver (Selective Availability) were analysed. Copyright © 2007 by ABCM.

Onboard and real-time artificial satellite orbit determination using GPS

An algorithm for real-time and onboard orbit determination applying the Extended Kalman Filter (EKF) method is developed. Aiming at a very simple and still fairly accurate orbit determination, an analysis is performed to ascertain an adequacy of modeling complexity versus accuracy. The minimum set of to-be-estimated states to reach the level of accuracy of tens of meters is found to have at least the position, velocity, and user clock offset components. The dynamical model is assessed through several tests, covering force model, numerical integration scheme and step size, and simplified variational equations. The measurement model includes only relevant effects to the order of meters. The EKF method is chosen to be the simplest real-time estimation algorithm with adequate tuning of its parameters. In the developed procedure, the obtained position and velocity errors along a day vary from 15 to 20 m and from 0.014 to 0.018 m/s, respectively, with standard deviation from 6 to 10 m and from 0.006 to 0.008 m/s, respectively, with the SA either on or off. The results, as well as analysis of the final adopted models used, are presented in this work. © 2013 Ana Paula Marins Chiaradia et al.

Comparison between Two Methods to Calculate the Transition Matrix of Orbit Motion

Two methods to evaluate the state transition matrix are implemented and analyzed to verify the computational cost and the accuracy of both methods. This evaluation represents one of the highest computational costs on the artificial satellite orbit determination task. The first method is an approximation of the Keplerian motion, providing an analytical solution which is then calculated numerically by solving Kepler's equation. The second one is a local numerical approximation that includes the effect of J(2). The analysis is performed comparing these two methods with a reference generated by a numerical integrator. For small intervals of time (1 to 10s) and when one needs more accuracy, it is recommended to use the second method, since the CPU time does not excessively overload the computer during the orbit determination procedure. For larger intervals of time and when one expects more stability on the calculation, it is recommended to use the first method.

Determination of onboard coplanar orbital maneuvers with orbits determined using GPS

In the present paper a study is made in order to find an algorithm that can calculate coplanar orbital maneuvers for an artificial satellite. The idea is to find a method that is fast enough to be combined with onboard orbit determination using GPS data collected from a receiver that is located in the satellite. After a search in the literature, three algorithms are selected to be tested. Preliminary studies show that one of them (the so called Minimum Delta-V Lambert Problem) has several advantages over the two others, both in terms of accuracy and time required for processing. So, this algorithm is implemented and tested numerically combined with the orbit determination procedure. Some adjustments are performed in this algorithm in the present paper to allow its use in real-time onboard applications. Considering the whole maneuver, first of all a simplified and compact algorithm is used to estimate in real-time and onboard the artificial satellite orbit using the GPS measurements. By using the estimated orbit as the initial one and the information of the final desired orbit (from the specification of the mission) as the final one, a coplanar bi-impulsive maneuver is calculated. This maneuver searches for the minimum fuel consumption. Two kinds of maneuvers are performed, one varying only the semi major axis and the other varying the semi major axis and the eccentricity of the orbit, simultaneously. The possibilities of restrictions in the locations to apply the impulses are included, as well as the possibility to control the relation between the processing time and the solution accuracy. Those are the two main reasons to recommend this method for use in the proposed application.

Comparação de modelos para o cálculo de pertubações orbitais devidas à maré terrestre

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Pertubações orbitais devidas a maré terrestre

Pós-graduação em Física - FEG

Determinação de órbitas com o GPS através de mínimos quadrados recursivo com rotações de Givens

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spin-orbit coupling in the superconducting phase and DDW states of high-T-c cuprates

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Tm-afm nonlinear motion control with robustness analysis to parametric errors in the control signal determination

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Pareto Frontier for the time-energy cost vector to an Earth-Moon transfer orbit using the patched-conic approximation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)