Least Squares and Linear Unbiased Minimum Variance Estimation in Euclidean Space and Hilbert Space.

Abstract

The estimation of an unknown vector-valued parameter in a linear model with additive noise is treated. The least-squares theory is given for the case both parameter and observation are elements of Hilbert space, and the solution is put in recursive form. A Gauss-Markov type theorem for linear unbiased minimum variance estimation is proved, again for the case both parameter and observation are elements of Hilbert space, and the solution is put in recursive form for the finite-dimensional case only. A modification of the linear unbiased minimum variance estimate which accounts for some prior information is given. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1974
Accession Number
AD0780105

Entities

People

  • Philip H. Fiske
  • William L. Root

Organizations

  • University of Michigan

Tags

DTIC Thesaurus Topics

  • Acquisition
  • Additives (Chemicals)
  • Banach Space
  • Data Acquisition
  • Functional Analysis
  • Hilbert Space
  • Observation

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space
  • Space - Space Objects