A coefficient generator, data processing system and method of data reduction in correspondence with multiple-term parametric relationships, and particularly provides for data reduction in correspondence with approximative descriptions which include multiple dependent-variable terms whose higher order derivatives do not vanish. Forms of inverse of deviation variations are implemented to provide weighting which will correct for nonlinear function variations. The forms of inverse deviation weighting are implemented for representing forms of residual weighting and forms of implied squared residual weighting. Represented phases of function similation establish adept equations and implement forms of data processing and representing. Adept data processors correspondingly provide for characterizing approximating relationships in correspondence with provided data.

A signal detection and classification technique that provides robust decision criteria for a wide range of parameters and signals in the presence of noise and interfering signals. The technique uses dynamical models for deriving filters and classifiers optimized for a particular category of signals of interest. The dynamical filters and classifiers can be implemented based on nonlinear dynamical principles. The invention is able to efficiently reveal deterministic properties of observed data signals in a numerically fast and efficient manner.

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. Variance or alternate representation, as related to statistically independent sampling, is utilized as assumed applicable or replaced by composite variability representing single coordinate variations as affected by orthogonal coordinate sampling dispersions. Statistical rendition is generated as a replacement for unquantifiable dependent variable representation.

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.

The present invention relates to a non-linear characteristic reproducing apparatus wherein a non-linear transformation processing is applied to a state quantity to be outputted. A non-linear behavior of products and parts is reproduced through modeling.[Solving means] there are provided a non-linear characteristic reproducing unit for receiving an estimated observation quantity at the subsequent sampling time of an input state quantity and determining a normalized estimated value in which an estimated value is normalized by an estimated observation quantity at the subsequent sampling time, and a state quantity transformation unit for transforming the input state quantity at the subsequent sampling time to the output state quantity at the subsequent sampling time in accordance with a non-linear operation based on the a normalized estimated value determined in the non-linear characteristic reproducing unit.