Abstract: Representations of data inversions are generated by alternate forms of maximum likelihood estimating which are rendered in correspondence with dependent coordinate mappings of path-oriented displacements. The dependent coordinate mappings are alternately considered to represent either path coincident deviations, path-oriented data-point projections. Normal displacements are rendered in normalized coordinates as a shortest distance between respective data samples and successive fitting function approximations. Deficiencies in representing likelihood as related to nonlinearities and heterogeneous precision are compensated by essential weighting of respectively mapped path-oriented displacements.

Abstract: Reduction deviations are rendered as dependent coordinate mappings of two-dimensional displacements which characterize restraints associated with deviations of observation sampling measurements from a fitting function. The mappings are considered to be represented by both projections and path coincident deviations. Data inversions are generated as loci and discriminated by criteria corresponding to deviations associated with alternate forms for representing essential weighting. Deficiencies related to nonlinearities and heterogeneous precision are compensated by essential weight factors.

Abstract: Representations of data inversions are generated by alternate forms of maximum likelihood estimating which are rendered in correspondence with dependent coordinate mappings of path-oriented displacements. The dependent coordinate mappings are alternately considered to represent either path coincident deviations, path-oriented data-point projections. Normal displacements are rendered in normalized coordinates as a shortest distance between respective data samples and successive fitting function approximations. Deficiencies in representing likelihood as related to nonlinearities and heterogeneous precision are compensated by essential weighting of respectively mapped path-oriented displacements.

Abstract: Representations of data inversions are generated by alternate forms of maximum likelihood estimating and associated least-squares and regression analysis which are rendered in correspondence with either single component residual deviations or projections between data samples and inversion-conforming data sets. Deficiencies in representing likelihood as related to errors-in-variables data and heterogeneous precision are compensated by composite weighting of likelihood elements. Composite weight factors employ both normalization to establish non-skewed homogeneous likelihood elements and fundamental weighting to compensate for associated non-linearly and establish common units for combining orthogonal coordinate-oriented data-point projections. Respective weight factors are related to alternately considered fundamental variables.

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.

Abstract: Representations of data inversions are generated by the processing of least-squares and maximum likelihood estimates which are rendered in correspondence with inversion-conforming data sets being related to considered sets of sampled data-point coordinates and respective parametric approximative form. Inversion-conforming data sets are considered to be sets of coordinates for points which correspond to the projection of respective data points along corresponding coordinates onto a fitting approximation or onto the locus of an alternate approximating relationship which respectively corresponds to a data inversion or a considered estimate of the same. Slope-handling and alternate projection normalizing coefficients may be implemented to provide common units for combining orthogonal coordinate-oriented data-point projections for rendering respective inversions.

Abstract: The invention is directed to a fiber-optic sensor for measuring acoustic signals originating from a single point remote from the sensor.

Abstract: Discriminate reduction data processing is disclosed as means of providing ltivariate linear and nonlinear data reduction for the evaluation of statistically representative approximating parameters which effectively minimize parametric expressions representing sums of normalized datum variances. Weight factors are provided as products of datum error deviation coordinate normalizing proportions to account for nonlinearities, nonuniform error distributions, variable precision uncertainties. Selective data sampling is provided so as not to require certain transformation weight factor coordinate normalizing proportions. Conformal analysis is provided as an optional replacement for regression analysis to account for errors in more than a single variable parameter. Nested parameter evaluation is provided to evaluate parameters that are embedded within term functions.

Abstract: Discriminate reduction data processing is disclosed as means of providing multivariate linear and nonlinear data reduction for the evaluation of statistically representative approximating parameters which effectively minimize parametric expressions representing sums of normalized datum variances. Weight factors are provided as products of datum error deviation coordinate normalizing proportions to account for nonlinearities, nonuniform error distributions, variable precision uncertainties. Selective data sampling is provided so as not to require certain transformation weight factor coordinate normalizing proportions. Conformal analysis is provided as an optional replacement for regression analysis to account for errors in more than a single variable parameter. Nested parameter evaluation is provided to evaluate parameters that are embedded within term functions.

Abstract: Data processing systems are disclosed which use arithmetic processors with final stage discriminate rectifiers and discriminate data sampling to evaluate parameters which effectively minimize parametric expressions representing sums of normalized datum variances to provide corresponding data representations which account for such items as nonlinearities, nonuniform error distributions, and variable precision uncertainties. Conformal analysis is provided as an optional replacement for regression analysis to account for significant errors in more than a single variable parameter. The applications include general forms of curve fitting, transformations, function approximations and corresponding forms of real time data processing. The systems provide for both linear and nonlinear forms of data reduction.