Non-gaussian error propagation in orbital mechanics pdf

Nonlinear propagation of uncertainty using simplified dynamical model of nonkeplerian motion inkwan park1 and daniel j. The central idea is to replace evolution of initial conditions for a dynamical sys. The university of texas at austin cockrell school of. Uncertainty quantification is a valuable methodology in the field of astrodynamics, but approaches are often computationally expensive or rely on assumptions that do not account for non gaussian posteriors or the nonlinear evolution of the a priori uncertainty. Worked with orbital phase guidance and control leaders to produce an integrated gnc system.

Nonlinear uncertainty propagation in orbital elements christopher t. Correct characterization of nongaussian probability density functions arising from nonlinear transformations such as nonlinear dynamics and coordinate transformations. The orbit perturbation dynamics model and orbital error are briefly. In statistics, propagation of uncertainty or propagation of error is the effect of variables uncertainties or errors, more specifically random errors on the uncertainty of a function based on them. Lecture 4 propagation of errors department of physics. Numerical examples indicate that the procedure is very efficient and generated sample fields satisfy the target spectral.

Security classification of this page unclassified 19. Nongaussian error propagation in orbital mechanics 1996. Apr 29, 2019 uncertainty quantification is a valuable methodology in the field of astrodynamics, but approaches are often computationally expensive or rely on assumptions that do not account for non gaussian posteriors or the nonlinear evolution of the a priori uncertainty. Nonlinear propagation of orbit uncertainty using non. Accurate collision probability calculation using gaussian mixture in. Akella december 2016 other professional highlights. Since for some decades i mainly made a living by studying a variety of non gaussian statistical variables in physics, you probably dont want to get me started telling their many diverse stories. Orbital prediction error propagation of space objects. Mechanics and control of flight award, american institute of aeronautics and astronautics aiaa, january 2014 myron l. Cambridge core communications and signal processing introduction to optical quantum information processing by pieter kok skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. Uncertainty quantification is a valuable methodology in the field of astrodynamics, but approaches are often computationally expensive or rely on assumptions that do not account for nongaussian posteriors or the nonlinear evolution of the a priori uncertainty.

Pdf an approach for nonlinear uncertainty propagation. Directional distributions in tracking of space debris. Thanks for contributing an answer to physics stack exchange. Uncertainty quantification for space situational awareness.

The investigation starts with the feasibility of nongasdynamic orbital deployment of twin tethers without any involvement of expensive rocket propulsion means. The analysis of working status of robust filters shows that the. Based on the polynomial chaos theory, both the state yt and the stochastic parameter a can be represented as polynomial chaos expansion pce models as 2 y t. Kelso ts 2007 validation of sgp4 and isgps200d against gps precision ephemerides. Publications professor sir michael victor berry, frs. Pdf an approach for nonlinear propagation of orbit uncertainties is.

Analytical nonlinear propagation of uncertainty in the twobody problem k fujimoto, dj scheeres, kt alfriend journal of guidance, control, and dynamics 35 2, 497509, 2012. The electric field associated with the gaussian beam inside the dielectric medium consists of the paraxial result and higherorder nongaussian correction terms. Gmms have been successfully used in orbital mechanics for uncertainty propagation 27,28, orbit determination 29,30, and conjunction assessment 33. On february 10, 2009, the satellite communications company iridium lost contact with one of its spacecraft, iridium 33. Directional distributions in tracking of space debris john t kent department of statistics university of leeds leeds ls2 9jt, uk email.

Oxis then a ut gaussian approximation of the unknown true nongaussian pdf denoted byfox. Analysis of the representation of orbital errors and improvement of their modelling 381 abstract in space situational awareness ssa, it is crucial to assess the uncertainty related to the state vector of resident space objects rso. An approach to active target satellite tracking is presented. Nonconservative forces in orbital mechanics very quickly lead to the evolution of non. The kinematic models based on differential orbital elements and unbiased converted measurements are adopted to approximate the dynamic orbital relative tracking system, and then followed by the proposed redundant adaptive robust extended kalman filter rarekf. Uncertainty quantification in orbital mechanics adams. This paper demonstrates the use of polynomial chaos expansions for the nonlinear, non gaussian propagation of orbit state uncertainty. Nonlinear propagation of orbit uncertainty using nonintrusive polynomial chaos brandon a. This uncertainty plays a fundamental role in, for example, collision risk assessment and reentry predictions. Such beams have a wide range of applications in many fields including. Propagation of errors 3 u if x and y are correlated, define sxy as. Efficient, accurate, and nongaussian error propagation. Akella, with 92 highly influential citations and 100 scientific research papers. The hybrid filtering scheme is designed to provide accurate and consistent estimates when measurements are sparse without incurring a large computational cost.

The twobody problem model with nonconservative atmospheric drag forces. Born3 university of colorado, boulder, co, 80309, usa this paper demonstrates the use of polynomial chaos expansions pces for the nonlinear, nongaussian propagation of orbit state uncertainty. An unscented kalmanparticle hybrid filter for space. The time evolution of a pdf is described by the fokkerplanck equation fpe 60. Subject terms space situational awareness, orbital mechanics, non linear covariance propagation 15. This work proposes and analyzes a smolyaktype sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms input data of the model. Analysis of the representation of orbital errors and. A reallife laser beam is not truly gaussian, as shown in fig. However, the intrusive polynomial chaos method ipcm requires tedious modification of the governing equations, which might introduce errors and can be impractical. Since for some decades i mainly made a living by studying a variety of nongaussian statistical variables in physics, you probably dont want to get me started telling their many diverse stories. Soc 86, 2424 note on the invariance of the phase difference between two waves. Junkins risk assessment judicial evidential reasoning for decision support applied to orbit insertion failure andris d.

Asking for help, clarification, or responding to other answers. An approach for nonlinear propagation of orbit uncertainties is discussed while making use. Abstract pdf 555 kb 2017 assessment of fetal exposure to 4g lte tablet in realistic scenarios using stochastic dosimetry. Christopher mattson for supporting me in this research. In later work, in 1997, he introduced the dependency on the orbital elements and associated probability distribution functions. After propagation for some time, the state uncertainty may become non gaussian. Hollow gaussian beams hgb are a special class of doughnut shaped beams that do not carry orbital angular momentum oam. However, the dynamics governing the orbital mechanics e.

When the variables are the values of experimental measurements they have uncertainties due to measurement limitations e. Various covariance realism tests and metrics have been used to assess realism with a primary focus on determining the length of gaussian validity, i. There are also some other special cases that have gaussian distributions. Nonlinear uncertainty propagation of orbital mechanics. Since solving the fpe for high dimensional dynamic system is very difficult, orbital uncertainty propagations are. The ones marked may be different from the article in the profile. Gmms have been successfully used in orbital mechanics for uncertainty propagation,18,19 orbit determination,20 21 and conjunction assessment. The method first generates gaussian sample fields and then maps them into non.

Gaussian homogeneous stochastic field can be generated is developed. The classic polynomial chaos method pcm, characterized as an intrusive methodology, has been applied to uncertainty propagation up in many dynamic systems. When compared to monte carlo methods, nonintrusive, i. Security classification of abstract unclassified 20. Nonlinear analytical uncertainty propagation for relative mo tion. Nazarenko in 1992 proposed to study the evolution of the density of particles assuming a continuous distribution. Nonlinear propagation of orbit uncertainty using non intrusive polynomial chaos brandon a. Monte carlo simulations mcs, state transition tensors, polynomial chaos expansion, etc. Subject terms space situational awareness, orbital mechanics, nonlinear covariance propagation 15. Adaptive gaussian mixture method for uncertainty propagation in space surveillance. This thesis presents a proof that nonlinear systems do not produce gaussian output distributions, even when inputs are gaussian. A new permanent leo debris removal system marshall h. Berry001 2 berry, m v, 1965, the diffraction of light by ultrasound, ph.

One could borrow from statistical mechanics using for example boltzmann equation. Nonlinear propagation of uncertainty using simplified dynamical model of non keplerian motion inkwan park1 and daniel j. Born3 university of colorado, boulder, co, 80309, usa this paper demonstrates the use of polynomial chaos expansions pces for the non linear, non gaussian propagation of orbit state uncertainty. In this paper, we present an unscented kalmanparticle hybrid filtering framework for recursive bayesian estimation of space objects. Scheeres2 1university of colorado at boulder, 429 ucb, boulder, co, 80309, u. This allows the system designer to obtain a fullydescribed non gaussian output distribution. To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite. Siam journal on scientific computing siam society for. A secondorder taylor series is then used to propagate both skewness and kurtosis through a system model. The measurement statistics are assumed to be gaussian with. When does the uncertainty become nongaussian kyle t. Pce 34 quanti es nongaussian uncertainty by using a linear combination of orthogonal polynomials op as a surrogate model for the underlying nonlinear function. The propagation of a gaussian beam in a homogeneous, isotropic, local, linear, and nonmagnetic dielectric medium is studied using the angular spectrum representation for the electric field.

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying fokkerplanck equation fpe is defined on a relatively high dimensional 6d statespace and is driven by the nonlinear perturbed keplerian dynamics. The investigation here presented is focused on the nonkeplerian behavior of such large tether systems, considered in a first approximation as rigid or very stiff and massless. Gmms have been successfully used in orbital mechanics for uncertainty propagation 27, 28, orbit determination 29, 30, and. The weighted sum of the gaussian elements after propagation approximates the resulting nongaussian pdf. While providing a thorough background in orbital mechanics is beyond the scope of this paper, an excellent reference is pc12, which discusses orbital elements and propagation in detail. Correct characterization of errors in the model dynamics e. Gaussian mixture method to propagate orbital uncertainty. Using linear expansions in tensor products of univariate orthogonal polynomial bases, polynomial chaos expansions approximate the stochastic solution of the ordinary differential equation describing the propagated orbit, and include information on covariance. Satellite collision probability estimation using polynomial chaos. In astrodynamics, uncertainty mapping using the state transition matrix stm. Non gaussian beams also exhibit this effect, but a gaussian beam is a special case where the product of width and divergence is the smallest possible. Uncertainty propagation in orbital mechanics via tensor. Hollow gaussian beam generation through nonlinear interaction.

Orion multipurpose crew vehicle mpcv orbital navigation lead 92014 to 92015 coled the development of the absolute navigation design during orbital. The mean and covariance of different components of the gaussian mixture model. Orbit uncertainty propagation and sensitivity analysis with. Gaussian translation processes journal of engineering mechanics april 1984 nongaussian simulation. A method by which sample fields of a multidimensional non. Merged citations this cited by count includes citations to the following articles in scholar. This cited by count includes citations to the following articles in scholar. Introduction to optical quantum information processing by. Siam journal on scientific computing society for industrial. Using linear expansions in tensor products of univariate ortho. This allows the system designer to obtain a fullydescribed nongaussian output distribution. Nongaussian beams also exhibit this effect, but a gaussian beam is a special case where the product of width and divergence is the smallest possible. This paper demonstrates the use of polynomial chaos expansions for the nonlinear, nongaussian propagation of orbit state uncertainty. Cumulative distribution function mapbased spectral correction.

An unscented kalmanparticle hybrid filter for space object. Spacecraft uncertainty propagation using gaussian mixture. Gaussian sample fields with the aid of an iterative procedure. After propagation for some time, the state uncertainty may become nongaussian. Siam journal on numerical analysis siam society for. To properly characterize non gaussian density functions arising in the problem of longterm propagation of state uncertainties, a gaussian sum filter adapted to the twobody problem in space. Dynamic system uncertainty propagation using polynomial chaos. Multielement separated representations for orbit uncertainty.