Satellite Shape Recovery from Light Curves with Noise

2019

The shape and attitude of resident space objects directly affect the orbit propagation via drag and solar radiation pressure. Obtaining information beyond an object state also is integral to identifying an object, aid in tracing its origin and its capabilities. For objects that have a significant distance to the observer, only non-resolved imaging is available, which does not reveal any details of the object. So-called non-resolved light curve measurements, i.e., brightness measurements over time, can be used to determine the shape of convex space objects using an inversion scheme. The inversion process starts by first determining the Extended Gaussian Image (EGI) and then solving the Minkowski problem to obtain the closed shape result. However, the light curve inversion problem is, by its nature, an under-determined problem. Hence, it is very sensitive to the sequencing of the observations collected. In this paper, the observability assessment for the light curve shape inversion pr...

Aerospace

In recent years, the increase in space activities has brought the space debris issue to the top of the list of all space agencies. The fact of there being uncontrolled objects is a problem both for the operational satellites in orbit (avoiding collisions) and for the safety of people on the ground (re-entry objects). Optical systems provide valuable assistance in identifying and monitoring such objects. The Sapienza Space System and Space Surveillance (S5Lab) has been working in this field for years, being able to take advantage of a network of telescopes spread over different continents. This article is focused on the re-entry phase of the object; indeed, the knowledge of the state of the object, in terms of position, velocity, and attitude during the descent, is crucial in order to predict as accurately as possible the impact point on the ground. A procedure to retrieve the light curves of orbiting objects by means of optical data will be shown and a method to obtain the attitude ...

Journal of Guidance, Control, and Dynamics, 2014

This paper presents a new method, based on a multiple-model adaptive estimation approach, to determine the most probable shape of a resident space object among a number of candidate shape models while simultaneously recovering the observed resident space object's inertial orientation and trajectory. Multiple-model adaptive estimation uses a parallel bank of filters, each operating under a different hypothesis to determine an estimate of the physical system under consideration. In this work, the shape model of the resident space object constitutes the hypothesis. Estimates of the likelihood of each hypothesis given the available measurements are provided from the multiple-model adaptive estimation approach. The multiplemodel adaptive estimation state estimates are determined using a weighted average of the individual filter estimates, whereas the shape estimate is selected as the shape model with the highest likelihood. Each filter employs the Unscented estimation approach, reducing passively-collected electrooptical data to infer the unknown state vector comprised of the resident * Graduate Student, space object's inertial-to-body orientation, position and respective temporal rates. Each hypothesized shape model results in a different observed optical cross-sectional area. The effects of solar radiation pressure may be recovered from accurate angles-data alone, if the collected measurements span a sufficiently long period of time, so as to make the non-conservative mismodeling effects noticeable. However, for relatively short arcs of data, this effect is weak and thus the temporal brightness of the resident space object can be used in conjunction with the angles data to exploit the fused sensitivity to both resident space object shape model and associated trajectory. Initial simulation results show that the resident space object model and states can be recovered accurately with the proposed approach.

2012

This paper presents a method to determine the shape of a space obje t in orbit while simultaneously recovering the observed space object ’s inertial orientation and trajectory. This work studies a shape estimation approa ch b sed on octant triangulation applied to light curve and angles data fusion . The filter employs the Unscented estimation approach, reducing passively-co llected electro-optical data to infer the unknown state vector comprised of the space object inertial-tobody orientation, position and their respective temporal r ates. Recovering these characteristics and trajectories with sufficient accuracy is shown in this paper. The performance of this strategy is demonstrated via simulated sc narios.

2016

The spatial distribution of the polarized component of the power reflected by a macroscopically smooth but microscopically roughened curved surface under highly directional illumination, as characterized by an appropriate bi-directional reflectance distribution function (BRDF), carries information about the three-dimensional (3D) shape of the surface. This information can be exploited to recover the surface shape locally under rather general conditions whenever power reflectance data for at least two different illumination or observation directions can be obtained. We present here two different parametric approaches for surface reconstruction, amounting to the recovery of the surface parameters that are either the global parameters of the family to which the surface is known a priori to belong or the coefficients of a low-order polynomial that can be employed to characterize a smoothly varying surface locally over the observed patch.

This paper presents an efficient geometric method to find the mathematical model for the normal orbit of a moving satellite observed from a given station on the earth. The method relies on getting a sufficient number of observations oriented from the earth station to the satellite which moves on its predictable orbit on the celestial space. The concurrence of the revolution of the earth and the motion of the satellite is utilized to orient the calculated normal orbit in its fixed plane. Rather than deriving the geometric model for the case of a known orbital plane, we reformulate the method of solution to study the case of an unknown orbital plane. Since the earth station rotates with the earth and the satellite moves, the lines of observation are generatrices of a ruled surface with the elliptic orbit as one directrix . In this paper we assume that the satellite obeys the Keplerian laws and that the true anomaly of the orbit is the only time-dependent Kepler element.

IEEE Transactions on Geoscience and Remote Sensing, 2021

This paper describes an investigation of the source of geospatial error in digital surface models (DSMs) constructed from multiple satellite images. In this study the uncertainty in surface geometry is separated into two spatial components; global error that affects the absolute position of the surface, and local error that varies from surface point to surface point. The global error component is caused by inaccuracy in the satellite imaging process, mainly due to uncertainty in the satellite position and orientation (pose) during image collection. The key sources of local error are; lack of surface appearance texture, shadows and occlusion. These conditions prevent successful matches between corresponding points in the images of a stereo pair. A key result of the investigation is a new algorithm for determining the absolute geoposition of the DSM that takes into account the pose covariance of each satellite during image collection. This covariance information is used to weigh the evidence from each image in the computation of the global position of the DSM. The use of covariance information significantly decreases the overall uncertainty in global position and also results in a 3-d covariance matrix for the global accuracy of the DSM. This covariance matrix defines a confidence ellipsoid within which the actual error must reside. Moreover, the absolute geoposition of each image is refined to the reduced uncertainty derived from the weighted evidence from the entire image set. The paper also describes an approach to the prediction of local error in the DSM surface. The observed variance in surface position within a single stereo surface reconstruction defines the local horizontal error. The variance in the fused set of elevations from multiple stereo pairs at a single DSM location defines the local vertical error. These accuracy predictions are compared to ground truth provided by LiDAR scans of the same geographic region of interest. The prediction of global and local error is compared to the actual errors for a number of geographic locations and mixes of satellite type. The predicted error bounds contain the observed errors according to the allowed percentage of outliers.

2015

The population of space debris increased drastically during the last years. Collisions involving massive objects may produce large number of fragments leading to significantly growth of the space debris population. An effective remediation measure in order to stabilize the population in LEO, is therefore the removal of large, massive space debris. To remove these objects, not only precise orbits, but also more detailed information about their attitude states will be required. One important property of an object targeted for removal is its spin period and spin axis orientation. If we observe a rotating object, the observer sees different surface areas of the object which leads to changes in the measured intensity. Rotating objects will produce periodic brightness vari ations with frequencies which are related to the spin periods. Photometric monitoring is the real tool for remote diagnostics of the satellite rotation around its center of mass. This information is also useful, for exa...

AIAA Guidance, Navigation, and Control (GNC) Conference, 2013

The observability of space object attitude from light curve data is analyzed. Light curves, which are the time-varying apparent brightness of sunlight reflected off a space object and measured by an observer, depend on the object position, attitude, surface material, shape, and other parameters. Previous work employing light curve data for shape estimation requires the availability of good attitude estimates. This paper explores the possibility of obtaining attitude information from the brightness measurements themselves. Some types of attitude estimate errors are detectable from individual brightness measurements, but other attitude errors lie in the nullspace of the Fisher information matrix and are not observable in the static case. Analytical expressions for the nullspace vectors are derived. The observability of the light curve model parameters is also briefly addressed.

Applied Optics, 1987

The inversion of satellite photometry data to produce a 2-D distribution of volume emission rate of optical emissions in the upper atmosphere does not provide a unique solution, but this problem may be alleviated by the application of the minimum cross-entropy (MCE) principle. This principle provides a rational criterion of choice for the selection of that distribution of volume emission rate which is maximally noninformative a subject to the constraints imposed by the data (namely, the integrated column brightness measurements). A practical and effective iterative algorithm is developed to compute the MCE reconstruction of volume emission rates. This algorithm is then applied to both synthetic and real satellite photometer data to demonstrate the effectiveness of the proposed inversion scheme. I(p,0) = J J(p cosOs sinp, p sino + s cosqb)ds.