Implementation of Non-Linear Estimators using Monospline.

Abstract

This paper presents a method for the realization of non-linear estimators based on spline interpolation. The difference of a monomial and its interpolating spline forms a monospline and then a quadrature formula is induced. When the knots of the monospline at which the conditional density is discretized are allowed to vary, a class of optimal quadrature formulas is obtained. To find the monospline with optimal knots a set of non-linear algebraic equations must be solved. If the symmetry property of the monospline is applied, the order of the non-linear equations can be reduced by about one-half. An interation scheme of Newton type is introduced to solve the monospline. The quadrature formula associated with this monospline has the so-called positivity property which is essential in the practical implementation of non-linear recursive estimators. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1976
Accession Number
ADA039582

Entities

People

  • A. H. Wang
  • R. L. Klein

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Bayes Theorem
  • Curve Fitting
  • Electrical Engineering
  • Engineering
  • Equations
  • Estimators
  • Interpolation
  • Iterations
  • Linear Algebraic Equations
  • Nonlinear Algebraic Equations
  • Scientific Research
  • Simultaneous Equations
  • Symmetry

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis