Incorporating Uncertainty in Admissible Regions for Uncorrelated Detections

Worthy, Johnny L.; Holzinger, Marcus J.

doi:10.2514/1.g000890

Cited by 18 publications

(4 citation statements)

References 18 publications

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“…It is assumed that no information can be reliably used to determine these states from measurements. The following notation was developed by Worthy et al [32]. Using equations (9) and (11) and the fact that the measurement cannot be dependent on xu, the following measurement function can be written.…”

Section: Appendix: VImentioning

confidence: 99%

Space Object Detection in Images Using Matched Filter Bank and Bayesian Update

Murphy

Holzinger

Flewelling

2017

Journal of Guidance, Control, and Dynamics

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Electro-optical sensors, when used to track space objects, are often used to produce detections for some orbit determination scheme. Instead, this paper proposes a series of methods to use electro-optical images directly in orbit determination. This work uses the SNR optimal image filter, called a matched filter, to search for partially known space objects. By defining a metric for measuring matched filter template similarity, a bank of matched filters is efficiently defined by partitioning the prior knowledge set. Once partitioned sets are known, the matched filter bank can be localized to regions of the sky. A method for hypothesis testing the result of a matched filter for a space object is developed. Finally, a framework for orbit determination based on the matched filter result is developed. Simulation shows that the analytic results enable a better framework for implementing matched filters for low SNR object detection.

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Section: Appendix: VImentioning

confidence: 99%

Space Object Detection in Images Using Matched Filter Bank and Bayesian Update

Murphy

Holzinger

Flewelling

2017

Journal of Guidance, Control, and Dynamics

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“…Double-R iteration and Gooding's method allow for longer time periods between observations, but require a guess to initialize the iteration. These classical angles-only IOD algorithms are sensitive to noise and to certain observertarget geometryas shown in both our own previous work [3][4][5] and also various other IOD studies [6][7][8][9][10][11]. All angles-only IOD algorithms mentioned utilize the observer-target geometry and assumptions defined from the Kepler problem to define a point solution, thus lacking any uncertainty information.…”

Section: Introductionmentioning

confidence: 99%

Angles-Only Initial Orbit Determination via Multivariate Gaussian Process Regression

2022

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Vital for Space Situational Awareness, initial orbit determination (IOD) may be used to initialize object tracking and associate observations with a tracked satellite. Classical IOD algorithms provide only a point solution and are sensitive to noisy measurements and to certain target-observer geometry. This work examines the ability of a Multivariate GPR (MV-GPR) to accurately perform IOD and quantify the associated uncertainty. Given perfect test inputs, MV-GPR performs comparably to a simpler multitask learning GPR algorithm and the classical Gauss–Gibbs IOD in terms of prediction accuracy. It significantly outperforms the multitask learning GPR algorithm in uncertainty quantification due to the direct handling of output dimension correlations. A moment-matching algorithm provides an analytic solution to the input noise problem under certain assumptions. The algorithm is adapted to the MV-GPR formulation and shown to be an effective tool to accurately quantify the added input uncertainty. This work shows that the MV-GPR can provide a viable solution with quantified uncertainty which is robust to observation noise and traditionally challenging orbit-observer geometries.

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“…In the last years a probabilistic approach is becoming more popular: here the AR is described as a bivariate uniform probability density function (PDF), where, thus, each point of the constrained plane has the same probability to represent the real observation. Although more complete because it easily allows for the inclusion of uncertainties in observations, measurements and timing-as described by Worthy III and Holzinger (2015a)-this approach also poses some new difficulties. Indeed, Worthy III and Holzinger (2015b) describe the constraints for the variables transformations and conclude that in general it is very difficult to transform a PDF if the transformation function is not linear or the PDF is not Gaussian (Park and Scheeres 2006), and both assumptions usually do not hold for the IOD case.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic data association: the orbit set

Pirovano

Santeramo

Armellín

et al. 2020

Celest Mech Dyn Astr

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This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits-namely the orbit set-that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus allowing for a compact analytical description of the orbit set. The automatic domain splitting tool controls the truncation error of the polynomial approximation by patching the uncertainty domain with different polynomial expansions, effectively creating a mesh. The algorithm is tested for different observing strategies to understand the working boundaries, thus defining the region for which the admissible region is necessary to extract meaningful information from observations and highlight where the new method can achieve a smaller uncertainty region, effectively showing that for some observing strategies it is possible to extract more information from a tracklet than the attributable. Consequently, the method enables comparison of orbit sets avoiding sampling when looking for correlation of different observations. Linear regression is also implemented to improve the uncertainty estimation and study the influence of the confidence level on the orbit set size. This is shown both for simulated and real observations obtained from the TFRM observatory.

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Incorporating Uncertainty in Admissible Regions for Uncorrelated Detections

Cited by 18 publications

References 18 publications

Space Object Detection in Images Using Matched Filter Bank and Bayesian Update

Space Object Detection in Images Using Matched Filter Bank and Bayesian Update

Angles-Only Initial Orbit Determination via Multivariate Gaussian Process Regression

Probabilistic data association: the orbit set

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