Inversion-conforming data sets processing
First Claim
1. A method for accessing, processing, and representing information whereby a data representation is generated in correspondence with a plurality of data-point projections,each of said data-point projections extending from respective data-point coordinates to intersect an approximating relationship, intersections of said data-point projections with said approximating relationship substantially establishing respective inversion-conforming data sets which comprise projected coordinates for points that conform to a corresponding data inversion at respective said intersections, each of said sets of projected coordinates comprising a respective subset of corresponding said data-point coordinates and at least one parametrically determined variable measure, each said parametrically determined variable measure being determined in correspondence with said approximating relationship and at least one data-point coordinate of said respective subset, said approximating relationship establishing respective correspondence between said at least one data-point coordinate and said at least one parametrically determined variable measure, said approximating relationship being determined in correspondence with a parametric approximative form and at least one parameter estimate, and said data representation being rendered in correspondence with said parametric approximative form and at least one inversion parameter estimate;
- said method comprising;
activating means for said accessing, processing, and representing information whereby at least one form of inversion-conforming data sets processing is effectuated, accessing provided data, establishing said parametric approximative form, establishing at least one respective inversion parameter estimate, determining said approximating relationship as related to said parametric approximative form and said at least one respective inversion parameter estimate, and effectuating said at least one form of inversion-conforming data sets processing;
said means for accessing, processing, and representing information comprising;
a control system, and said control system being configured for providing said activating, said effectuating, and said representing information;
said effectuating including implementing and effecting at least one form of parameter estimating in correspondence with said provided data whereby said at least one inversion parameter estimate is generated.
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Abstract
In lieu of the common practice of attempting to maximize the likelihood of sample deviations from unknown true values, representations of data inversions are generated by implementing optimizing techniques which are based upon a concept of maximizing the likelihood of deviations of successively determined inversion-conforming data sets from previously acquired (hence invarient) data- point samples. Inversion-conforming data sets are considered to be sets of coordinate points which correspond to the projection of respective data points along corresponding coordinates onto a fitting approximation or onto the locus of any respectively rendered approximating relationship which corresponds to a data inversion or a considered estimate of the same.
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Citations
23 Claims
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1. A method for accessing, processing, and representing information whereby a data representation is generated in correspondence with a plurality of data-point projections,
each of said data-point projections extending from respective data-point coordinates to intersect an approximating relationship, intersections of said data-point projections with said approximating relationship substantially establishing respective inversion-conforming data sets which comprise projected coordinates for points that conform to a corresponding data inversion at respective said intersections, each of said sets of projected coordinates comprising a respective subset of corresponding said data-point coordinates and at least one parametrically determined variable measure, each said parametrically determined variable measure being determined in correspondence with said approximating relationship and at least one data-point coordinate of said respective subset, said approximating relationship establishing respective correspondence between said at least one data-point coordinate and said at least one parametrically determined variable measure, said approximating relationship being determined in correspondence with a parametric approximative form and at least one parameter estimate, and said data representation being rendered in correspondence with said parametric approximative form and at least one inversion parameter estimate; -
said method comprising;
activating means for said accessing, processing, and representing information whereby at least one form of inversion-conforming data sets processing is effectuated, accessing provided data, establishing said parametric approximative form, establishing at least one respective inversion parameter estimate, determining said approximating relationship as related to said parametric approximative form and said at least one respective inversion parameter estimate, and effectuating said at least one form of inversion-conforming data sets processing;
said means for accessing, processing, and representing information comprising;
a control system, and said control system being configured for providing said activating, said effectuating, and said representing information;
said effectuating including implementing and effecting at least one form of parameter estimating in correspondence with said provided data whereby said at least one inversion parameter estimate is generated. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. A data processing system comprising:
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a control system;
means for accessing, processing, and representing information;
said control system being configured for providing said accessing, processing, and representing information; and
said control system being configured for generating at least one data inversion in correspondence with a parametric approximative form;
said processing including;
accessing information, effectuating at least one form of inversion-conforming data sets processing, and rendering at least one data representation in correspondence with said at least one data inversion;
said effectuating including;
accessing provided data, establishing said parametric approximative form, establishing at least one determined form for an approximating relationship as related to said parametric approximative form and at least one respective parameter estimate, and implementing and effecting at least one form of parameter estimating in correspondence with said provided data whereby said at least one data inversion is generated, said data inversion being generated in correspondence with a plurality of data-point projections, each of said data-point projections extending from respective data-point coordinates to intersect said approximating relationship, intersections of said data-point projections with said approximating relationship substantially establishing respective inversion-conforming data sets which comprise projected coordinates for points that conform to said data inversion at respective said intersections, each of said sets of projected coordinates comprising a respective subset of said data-point coordinates and at least one correspondingly determined variable measure, each said determined variable measure being determined in correspondence with said approximating relationship and at least one data-point coordinate of said respective subset, and said approximating relationship establishing respective correspondence between said at least one data-point coordinate and said at least one correspondingly determined variable measure. - View Dependent Claims (11, 12, 13, 14)
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15. A weighting coefficient generator comprising means for generating a representation of at least one weighting coefficient,
said weighting coefficient being rendered as substantially related to inverse proportion of the estimated variability of a parametrically determined variable measure, said parametrically determined variable measure being restricted to the confines of an approximating relationship, said approximating relationship being established in correspondence with a parametric approximative form and at least one parameter estimate, said at least one parameter estimate being generated in correspondence with a plurality of approximation-conforming data sets, each of said approximation-conforming data sets comprising a corresponding subset of respective data-point coordinates and at least one respectively determined variable measure, each said respectively determined variable measure being determined in correspondence with said approximating relationship and at least one data-point coordinate of the corresponding said subset, each said subset excluding a sample for the coordinate which corresponds to the respective said parametrically determined variable measure, said estimated variability riot being represented by the variance of a respectively considered data-point-sample acquisition for said variable, said estimated variability not being represented as an effective variance of a respectively considered data-point-sample acquisition for said variable, said estimated variability being represented in correspondence with possible variations in said parametrically determined variable measure, said possible variations being associated with uncertainty in at least one respective lateral component, said at least one respective lateral component being implemented to establish said parametrically determined variable measure as restricted to said confines, variability of said lateral component being related to considered variations in possible outcomes in the sampling acquisition of respective elements of corresponding subsets of data-point coordinates, said estimated variability substantially representing possible dispersions in said parametrically determined variable measure as related to represented uncertainty in the respectively considered sampling of at least one element of the corresponding said subset, said at least one element respectively corresponding to said lateral component, said dispersions being considered in correspondence with restraints imposed by said approximating relationship, and representation of said uncertainty being related to considered variations in possible outcomes of orthogonal component acquisition sampling of a form corresponding to the sampling used in acquiring the respective coordinate sample for said at least one element; -
said means for generating including;
a control system, means for accessing, processing, and representing information, and said control system being configured for providing said accessing, processing, and representing information;
said processing including;
accessing provided data, representing said estimated variability in correspondence with said approximating relationship, and rendering said weighting coefficient in correspondence with the inverse of said estimated variability. - View Dependent Claims (16, 17)
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18. An output product comprising a data representation generated by a data processing system, and
said data representation being rendered in correspondence with at least one data inversion; -
said data representation comprising;
processed information, andsaid processed information establishing a descriptive correspondence of a determined parametric approximative form;
said output product being generated by;
activating means for accessing, processing, and representing information whereby at least one form of inversion-conforming data sets processing is effectuated, accessing provided data, effectuating said at least one form of inversion-conforming data sets processing, and rendering said data representation in correspondence with said effectuating;
said effectuating including;
implementing and effecting at least one form of parameter estimating in correspondence with said provided data whereby at least one inversion parameter estimate is generated, said at least one inversion parameter estimate being generated in correspondence with a plurality of data-point projections and said parametric approximative form, each of said data-point projections extending from respective data-point coordinates to intersect an approximating relationship, said approximating relationship being determined in correspondence with said parametric approximative form and at least one parameter estimate, intersections of said data-point projections with said approximating relationship substantially establishing respective inversion-conforming data sets which comprise projected coordinates for points that conform to a respective data inversion at said intersections, each of said sets of projected coordinates comprising a subset of said respective data-point coordinates and at least one correspondingly determined variable measure, each said determined variable measure being determined in correspondence with said approximating relationship and at least one data-point coordinate of said respective subset, and said approximating relationship establishing respective correspondence between said at least one data-point coordinate and said at least one correspondingly determined variable measure;
said data processing system comprising;
said means for accessing, processing, and representing information, and means for specifying and providing said effectuating;
said means for accessing, processing, and representing information comprising;
a control system, and said control system being configured for providing said activating, said effectuating, and said representing information. - View Dependent Claims (19, 20, 21, 22)
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23. A method for rendering a data representation of at least one correction to a considered data inversion of a determined parametric approximative form,
said correction being rendered in correspondence with said considered data inversion and successive simulations of data, said correction being generated by: -
representing an initial estimate of said correction in correspondence with a respectively considered approximating relationship of corresponding parametric approximative form, rendering said simulations by combining successive estimates of said correction with a characteristic representation of error deviations, rendering inversions of said successive simulations by implementing similar processing techniques for successively processing said simulations that were used in the processing of data to generate said considered data inversion, rendering said successive estimates of said correction by combining prior said estimates with said considered data inversion and with respective inversions of said successive simulations, and implementing and effecting at least some form of successive estimate approximating and thereby rendering inversions of said successive simulations to more closely replicate said considered data inversion;
said method comprising;
activating means for accessing, processing, and representing information whereby said data representation is rendered, accessing provided data, effectuating at least one form of parameter estimating in correspondence with said provided data whereby said correction is generated, and including said correction in the rendering of said data representation;
said means for accessing, processing, and representing information comprising;
a control system, said control system being configured for providing said activating, said effectuating, and said representing information; and
said method excluding rendering characteristic form iterations by a data processing system configured for implementing at least one form of inverse deviation variation weighting for representing the weight of respective function related deviations.
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Specification