Application of numerical integration techniques for orbit determination of state-of-the-art LEO satellites

Somodi, B.; Földváry, Lóránt

doi:10.3311/pp.ci.2011-2.02

Cited by 14 publications

(7 citation statements)

References 8 publications

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“…The solution of the equations system is achieved through numerical integration methods suitable for ordinary differential equations [32,33]. The performance of the numerical integration methods is critical and depends on the integration step and the method's order.…”

Section: Dynamic Orbit Determinationmentioning

confidence: 99%

“…wherer denotes the acceleration vector, m the satellite's mass and F the sum of all forces acting on the satellite, which in general includes both gravitational and non-gravitational contributions. The solution of the equations system is achieved through numerical integration methods suitable for ordinary differential equations [32,33]. The performance of the numerical integration methods is critical and depends on the integration step and the method's order.…”

Section: Dynamic Orbit Determinationmentioning

confidence: 99%

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Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis

Papanikolaou

Tsoulis

2018

Geosciences

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An analysis of current static and time-variable gravity field models is presented focusing on the medium to high frequencies of the geopotential as expressed by the spherical harmonic coefficients. A validation scheme of the gravity field models is implemented based on dynamic orbit determination that is applied in a degree-wise cumulative sense of the individual spherical harmonics. The approach is applied to real data of the Gravity Field and Steady-State Ocean Circulation (GOCE) and Gravity Recovery and Climate Experiment (GRACE) satellite missions, as well as to GRACE inter-satellite K-band ranging (KBR) data. Since the proposed scheme aims at capturing gravitational discrepancies, we consider a few deterministic empirical parameters in order to avoid absorbing part of the gravity signal that may be included in the monitored orbit residuals. The present contribution aims at a band-limited analysis for identifying characteristic degree ranges and thresholds of the various GRACE- and GOCE-based gravity field models. The degree range 100–180 is investigated based on the degree-wise cumulative approach. The identified degree thresholds have values of 130 and 160 based on the GRACE KBR data and the GOCE orbit analysis, respectively.

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Section: Dynamic Orbit Determinationmentioning

confidence: 99%

Section: Dynamic Orbit Determinationmentioning

confidence: 99%

Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis

Papanikolaou

Tsoulis

2018

Geosciences

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“…Due to their computational efficiency and prominent use in orbit determination [20], multistep algorithms, such as the one described by Lundberg [21], and hereafter referred to as the KroghShampine-Gordon method, are used in this analysis. Finally, although numerous other studies have examined the accuracy of select integration methods with respect to each other in an effort to illuminate truncation errors [3,21,22], the two remaining error sources are examined here: roundoff errors and errors due to mismodeled forces.…”

Section: Introductionmentioning

confidence: 99%

Accuracy of Numerical Algorithms for Satellite Orbit Propagation and Gravity Field Determination

McCullough

Bettadpur

McDonald

2015

Journal of Spacecraft and Rockets

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The orbit determination process, such as that used for the Gravity Recovery and Climate Experiment, known as GRACE, is highly dependent upon the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant errors in the computed state corrupt this comparison and induce errors in the least-squares estimate of the satellites' states, as well as the gravity field. Due to the high accuracy of the intersatellite ranging measurements from GRACE, numerical computations must mitigate errors to maintain a similar level of accuracy. One error source is the presence of roundoff errors in the computed intersatellite range-rate when integrating continuous, smoothly varying accelerations with double-precision arithmetic. These errors occur at approximately 8 pm∕s root mean square and limit the accuracy of numerically integrating background gravity field models to degrees/orders 260 and 410 for satellite pairs flying at altitudes of 500 and 300 km respectively. In addition, the integration of filtered, transient accelerations, which occur on timescales much smaller than the integration step size, induce errors at an approximately 10 nm∕s in range-rate, becoming a limitation as more advanced intersatellite measurement techniques approach this level of accuracy. Nomenclature At= linearized dynamical equationŝ e ρ = unit vector along the line of sight between two coorbiting spacecraft FX; t = differential equations describing the dynamics of the state X GX i ; t i = function describing the observation Y at time t i as a function of the state X i at time t i H = m × n-dimensional mapping matrix H = linearized equations relating the observation deviations to the state deviations n = degree P n = Legendre polynomial of degree n R e = mean radius of the Earth, m r = satellite's mean orbital radius, m r 1;2 = vector of satellite positions, m v 1;2 = vector of satellite velocities, m∕s X = n × 1-dimensional "true" state vector (where n is the number of parameters to estimate) X = n × 1-dimensional nominal state vector (where n is the number of parameters to estimate) x = n × 1-dimensional state deviation vector (where n is the number of parameters to estimate) Y = m × 1-dimensional vector of observations (where m is the number of observations) y = m × 1-dimensional observation deviation vector (where m is the number of observations) δT = gravity field potential error δ_ ρ = range-rate error, m∕s ϵ = m × 1-dimensional vector of estimation errors θ = satellite separation angle, deg _ ρ = intersatellite range-rate, m∕s σ n = degree error variance

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“…Thus, quality control of the numerical methods is required for each individual orbit analysis (Montenbruck and Gill 2000) prior to the operational use in the procedure of orbit determination products. A variety of tests for the comparison of numerical integrators through orbit analysis can be found in Hull et al (1972), Fox (1984), Montenbruck (1992), Somodi and Földvary (2011). One commonly used test in the corresponding literature is the numerical analysis of Keplerian orbits.…”

Section: Introductionmentioning

confidence: 99%

Assessment of numerical integration methods in the context of low Earth orbits and inter-satellite observation analysis

Papanikolaou

Tsoulis

2016

Acta Geod Geophys

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The integration of differential equations is a fundamental tool in the problem of orbit determination. In the present study, we focus on the accuracy assessment of numerical integrators in what refers to the categories of single-step and multistep methods. The investigation is performed in the frame of current satellite gravity missions i.e. Gravity Recovery and Climate Experiment (GRACE) and Gravity Field and steady-state Ocean Circulation Explorer (GOCE). Precise orbit determination is required at the level of a few cm in order to satisfy the primary missions' scope which is the rigorous modelling of the Earth's gravity field. Therefore, the orbit integration errors are critical for these low earth orbiters. As the result of different schemes of numerical integration is strongly affected by the forces acting on the satellites, various validation tests are performed for their accuracy assessment. The performance of the numerical methods is tested in the analysis of Keplerian orbits as well as in real dynamic orbit determination of GRACE and GOCE satellites by taking into account their sophisticated observation techniques and orbit design. Numerical investigation is performed in a wide range of the fundamental integrators' parameters i.e. the integration step and the order of the multistep methods.

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Application of numerical integration techniques for orbit determination of state-of-the-art LEO satellites

Cited by 14 publications

References 8 publications

Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis

Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis

Accuracy of Numerical Algorithms for Satellite Orbit Propagation and Gravity Field Determination

Assessment of numerical integration methods in the context of low Earth orbits and inter-satellite observation analysis

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