Dealing with uncertainties in angles-only initial orbit determination

Armellín, Roberto; Lizia, P. Di; Zanetti, Renato

doi:10.1007/s10569-016-9694-z

Cited by 16 publications

(11 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In the computation of this preliminary solution, a high-order algorithm that solves two Lambert's problems between the central epoch and the two ends of the observed arc is used. For more details, the reader can refer to Armellin et al (2016). It is finally worth noting that Kepler's dynamics are considered throughout this section, even though the proposed approach does not rely on any Keplerian assumption.…”

Section: Dals Convergence Propertiesmentioning

confidence: 99%

Nonlinear representation of the confidence region of orbits determined on short arcs

Principe

Armellín

Lizia

2019

Celest Mech Dyn Astr

Self Cite

View full text Add to dashboard Cite

The total number of active satellites, rocket bodies, and debris larger than 10 cm is currently about 20,000. If all resident space objects larger than 1 cm are considered, this number increases to an estimate of 700,000 objects. The next generation of sensors will be able to detect small-size objects, producing millions of observations per day. However, due to observability constraints, long gaps between observations will be likely to occur, especially for small objects. As a consequence, when acquiring observations on a single arc, an accurate determination of the space object orbit and the associated uncertainty is required. This work aims to revisit the classical least squares method by studying the effect of nonlinearities in the mapping between observations and state. For this purpose, high-order Taylor expansions enabled by differential algebra are exploited. In particular, an arbitrary-order least squares solver is implemented using the high-order expansion of the residuals with respect to the state. Typical approximations of differential correction methods are then avoided. Finally, the confidence region of the solution is accurately characterized with a nonlinear approach, taking advantage of these expansions. The properties and performance of the proposed methods are assessed using optical observations of objects in LEO, HEO, and GEO.

show abstract

Section: Dals Convergence Propertiesmentioning

confidence: 99%

Nonlinear representation of the confidence region of orbits determined on short arcs

Principe

Armellín

Lizia

2019

Celest Mech Dyn Astr

Self Cite

View full text Add to dashboard Cite

show abstract

“…Generally, the solving process for EKF is divided into two parts including predicting and updating times. During the estimation step, the measurement error covariance is first considered as follows (Wu et al, 2013;Kaufman et al, 2016;Armellin et al, 2016):…”

Section: No 4 P O S I T I O N I N G a N D T R A J E C T O Ry P R E Dmentioning

confidence: 99%

“…The first stage of this is to precisely detect the orbits of debris (Flury, 1995). Orbit determination (Armellin et al, 2016; Curtis, 2013) is germane to one of the branches of astronomy, which observes, calculates and predicts space objects' orbits. One common application of orbit determination is supporting Global Positioning System (GPS) satellites (Montenbruck et al, 2005) Andres Johan Lexell and Friedrich Gauss initiated modern orbit determination (Sten and Aspaas, 2013).…”

Section: Introductionmentioning

confidence: 99%

“…Gruntman (2014) researched some methods that use optical methods for detecting sub millimetre and millimetre size debris in low earth orbits. In addition, some further research on extensions of these methods has also been conducted in Armellin et al (2016) and Kaufman et al (2016) for further analysis of the uncertainties. Figure 1 exhibits the proposed plan of robust in-orbit localisation and orbit prediction of the space debris.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Positioning, Preliminary Orbit Determination, and Trajectory Prediction of Space Debris using In-Space Iterative-Bearing-Only Observations

2017

View full text Add to dashboard Cite

This paper is concerned with the preliminary localisation, orbit determination and model-based path forecasting of space debris based on a robust procedure. In this work, an in-orbit observer utilises only relative bearing observations iteratively. To this end, the problem is first formulated in order to calculate the distance vector between the space debris and any orbiting observer. Afterwards, the obtained position vector is corrected through an Extended Kalman Filter (EKF) for shrinking the sensor and process errors and increasing robustness of the computations in the presence of uncertainties. After preliminary positioning, the related classical orbital elements are acquired via the predicted position and velocity vectors using a hybrid technique. Extensive simulations demonstrate the efficacy and robustness of the aforementioned method, and in particular it is verified that the proposed scheme is capable of producing a suitable solution for preliminary localisation and orbit determination of space debris based on the presented space-based observation, which is practical in phasing and chasing manoeuvres of any grabber space robot. K E Y

show abstract

“…The TOV technique allows for the exact mapping of the PDF from the observation domain into the orbit domain. Armellin et al [18], [19] realized the observationsto-solution (O2S) mapping using the Differential Algebra (DA) tools. The unscented transformation (UT) technique is also used in the uncertainty analysis for the IOD problem [20].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Analysis of the Short-Arc Initial Orbit Determination

Tao

Gong

et al. 2020

IEEE Access

View full text Add to dashboard Cite

The solution of the short-arc angles-only orbit determination problem has large uncertainty because the topocentric range is not observable. For a certain angular observation tracklet with measurement noise, there exist numerous potential orbits, all of which are compatible with the observations. However, the solution of a deterministic initial orbit determination algorithm is usually far different from the true orbit, especially for the semimajor axis and the eccentricity. A new sampling method is proposed to describe the probability distribution of the orbit determination solutions. Firstly, a series of orbits are sampled in the semimajor axis-eccentricity plane. A chi-square test method is proposed to select candidate orbits from the sample orbits. The weights of the candidate orbits are calculated to measure their probability being the true orbit. Finally, the kernel density estimation algorithm is used to estimate the probability density function of the true orbits. With some a priori assumptions, the candidate orbits can be further screened, and their weight can be modified. The a priori knowledge can significantly improve the accuracy of the orbit determination solution. INDEX TERMS Error analysis, initial orbit determination, Kernel density estimation, orbit sampling, short-arc optical observations.

show abstract

Dealing with uncertainties in angles-only initial orbit determination

Cited by 16 publications

References 19 publications

Nonlinear representation of the confidence region of orbits determined on short arcs

Nonlinear representation of the confidence region of orbits determined on short arcs

Robust Positioning, Preliminary Orbit Determination, and Trajectory Prediction of Space Debris using In-Space Iterative-Bearing-Only Observations

Uncertainty Analysis of the Short-Arc Initial Orbit Determination

Contact Info

Product

Resources

About