A new method for the statistical simulation of the virtual values of parameters in inverse orbital dynamics problems

Avdyushev, V. A.

doi:10.1134/s0038094609060094

Cited by 9 publications

(13 citation statements)

References 7 publications

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“…Note that some points of this paper have been presented before in Avdyushev (2009). Nevertheless, the material expounded here is distinguished by much more systematic viewpoint and also new results of no small account.…”

Section: Introductionmentioning

confidence: 84%

“…If the estimation subspace is not flat then the substitution of p O forp can lead to appreciably other results, especially whenσ is large enough (Avdyushev 2009). It goes without saying that the choice must be forp.…”

Section: Nonlinear Methodsmentioning

confidence: 97%

“…To compensate somehow the lack of information on the distribution ofσ 2 , we propose to simulate virtual parameter values by two stages (Avdyushev 2009). At the first stage one uses scheme (17) with some generated sample of the random disturbances δp =σ ν N , where as a result of solving the LS-problem one gets an estimateσ 2 * of the varianceσ 2 .…”

Section: Nonlinear Methodsmentioning

confidence: 99%

“…For this introducing a modulating random factor (17) and (18) is enough: δp = rσ ν N . Consequently, the simplified analog (19) is rewritten as (Avdyushev 2009) …”

Section: Linear Methodsmentioning

confidence: 99%

“…With the advent of quick-operating and multiprocessor computers, recently one tends to employ statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations (Chernitsov et al 1998;Virtanen et al 2001;Bordovitsyna et al 2001;Williams et al 2005;Muinonen et al 2006;Avdyushev and Banschikova 2007;Desmars et al 2009;Avdyushev 2009;Emel'yanov 2010), which is generally required when V. A. Avdyushev (B) Celestial Mechanics and Astrometry Department, Applied Mathematics and Mechanics Institute, 634050 Tomsk, Russia e-mail: sch@niipmm.tsu.ru planning future observations and identifying celestial bodies, and also in the problems of asteroid hazard.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear methods of statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations

Avdyushev

2011

Celest Mech Dyn Astr

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Determination of orbital parameters from observations is formally a nonlinear inverse problem for solving which evidently nonlinear methods are required. Meanwhile, an accompanying stage in solving the inverse problem is the evaluation of parametric accuracy to which, however, linear methods are conventionally applied. This is quite justified if parametric errors caused by observation errors are rather small, otherwise this is not at all since the nonlinearity of the inverse problem can be considerable to influence on the evaluations of parametric accuracy especially when the observations are very few. With the advent of quick-operating and multiprocessor computers, recently one tends to employ statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations. In the paper are just discussed the methods designed specially for nonlinear statistic simulation of virtual parameter values. Their efficiency is investigated in application to estimating uncertainties in the orbit of Jovian satellite S/2003 J04 whose orbital parameters are ill-determined owing to scanty available observations. Indices of nonlinearity are introduced for making decision in the choice between linear and nonlinear methods.

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Section: Introductionmentioning

confidence: 84%

Section: Nonlinear Methodsmentioning

confidence: 97%

Section: Nonlinear Methodsmentioning

confidence: 99%

“…For this introducing a modulating random factor (17) and (18) is enough: δp = rσ ν N . Consequently, the simplified analog (19) is rewritten as (Avdyushev 2009) …”

Section: Linear Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear methods of statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations

Avdyushev

2011

Celest Mech Dyn Astr

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Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

Avdyushev¹

2017

Celest Mech Dyn Astr

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Construction of confidence regions in problem on probabilistic study into motion of minor bodies of the solar system

2012

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Different approaches to constructing regions of possible motions of minor bodies are examined. An economical approach to the minimization of the number of points of the initial region by means of defin ing this region with its boundary surface is offered, and the estimations of its efficiency are given. The methods for estimating the admissibility of the linear approach are considered. For this purpose, simple methods for calculating the nonlinear factors are offered, which makes it possible to classify a problem to be solved as either strongly or weakly nonlinear. Recommendations are given on the possibility of reducing the concrete estimation problem to a weakly nonlinear one, where the more economical linear approach can be used. The combined method of mapping the initial region in time is also offered which unites the linear and nonlinear approaches. By example of two asteroids, the area of applicability of linear mappings is estimated.

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A new method for the statistical simulation of the virtual values of parameters in inverse orbital dynamics problems

Cited by 9 publications

References 7 publications

Nonlinear methods of statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations

Nonlinear methods of statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

Construction of confidence regions in problem on probabilistic study into motion of minor bodies of the solar system

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