Nonlinear Observability for Relative Orbit Determination with Angles-Only Measurements

Kaufman, Evan; Lovell, T. Alan; Lee, Taeyoung

doi:10.1007/s40295-015-0082-9

Cited by 41 publications

(12 citation statements)

References 11 publications

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“…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%

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

2017

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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

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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%

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

2017

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“…As discussed in the Introduction, Reference [7] applied the Lie derivative method on the full nonlinear dynamic model, resulting in observability conditions for LOS measurements. This paper extends this work to three other dynamic models and discusses observability conditions for each one of them.…”

Section: Observability Analysis For Relative Motion With Los Mea-surementioning

confidence: 99%

“…However, the process of deriving the full rank condition for N 3 is complicated and therefore not shown here. Readers may refer to Reference [7] to have a better understanding. Instead, we extend the observability conditions to relative motion models with different orders of nonlinearities.…”

Section: Observability Analysis For Relative Motion With Los Mea-surementioning

confidence: 99%

“…Taking LOS measurement only, Woffiden and Geller [3,4] discussed relative orbit estimation based on the Hill-Clohessey-Wiltshire dynamic model [5,6] and concluded this scenario is unobservable. Using the Lie derivative method, Kaufman, et al [7] showed that with LOS measurement only, the nonlinear relative orbital dynamics are observable under certain geometric conditions. Psiaki [8] considered relative orbit estimation from the view of orbital element differences and widely discussed the improvement of observability by adding J2 perturbation or altering orbital element differences.…”

Section: Introductionmentioning

confidence: 99%

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Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes

Butcher¹

2016

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Using Government drawings, specifications, or other data included in this document for any purpose other than Government procurement does not in any way obligate the U.S. Government. The fact that the Government formulated or supplied the drawings, specifications, or other data does not license the holder or any other person or corporation; or convey any rights or permission to manufacture, use, or sell any patented invention that may relate to them. This report is the result of contracted fundamental research deemed exempt from public affairs security and policy review in accordance with SAF/AQR memorandum dated 10 Dec 08 and AFRL/CA policy clarification memorandum dated 16 Jan 09. This report is available to the general public, including foreign nationals. Copies may be obtained from the Defense Technical Information Center (DTIC) (http://www.dtic.mil).

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“…rendezvous and docking) [13]. In [14] and in [15] the authors have shown that considering the full nonlinear dynamics of the spacecraft will results in improved state estimation in otherwise weakly observable or unobservable linear models. Hence, we consider linearized spacecraft relative motion equations and apply our hybrid Kalman filter to estimate the state from aperiodic position measurements.…”

Section: Introductionmentioning

confidence: 99%

Robust Hybrid Kalman Filter for a Class of Nonlinear Systems

Malladi

Sanfelice

Butcher

2018

2018 Annual American Control Conference (ACC)

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Motivated by real-world applications with intermittent sensor data, an extended Kalman filter is formulated as a hybrid system and constructive conditions on its parameters guaranteeing an asymptotic stability property are provided. The dynamical properties of the estimation error are first characterized infinitesimally so to yield bounds on the rate of convergence and overshoot that depend on the parameters. By recasting the problem as the stabilization of a compact set, robustness properties of the proposed algorithm in the presence of disturbances in the system dynamics as well as measurement noise in the output are established. The proposed strategy is applied to spacecraft relative motion control with position-only measurements.

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Nonlinear Observability for Relative Orbit Determination with Angles-Only Measurements

Cited by 41 publications

References 11 publications

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

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

Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes

Robust Hybrid Kalman Filter for a Class of Nonlinear Systems

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