Internal Variables in the Lattice for Cholesky Factorization. Kalman Filtering, and Model Identification.

Abstract

The Levinson recursions provide an efficient algorithm for factoring the inverse of a Toeplitz correlation matrix R into its upper and lower triangular Cholesky factors. These factors produce a Gram-Schmidt orthogonalization of the underlying time series. The recursions are routinely used to compute reflection coefficients for implementing whitening and predicting filters in lattice form. These are also used to go back and forth between reflection coefficients, order-increasing whiteners, and correlations. One of this document's main purposes is to show how the Levinson recursion for going back and forth between correlations, reflection coefficients, and order-increasing whiteners may be replaced with a dual set of recursions for going back and forth between correlations, reflection coefficients, and order increasing synthesizers.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1984
Accession Number
ADA149431

Entities

People

  • C. Demeure
  • Louis L. Scharf

Organizations

  • University of Rhode Island

Tags

Communities of Interest

  • Advanced Electronics
  • C4I
  • Ground and Sea Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Electrical Engineering
  • Engineering
  • Equations
  • Kalman Filtering
  • Logistics Management
  • Mathematics
  • Military Research
  • Probability
  • Random Variables
  • Reflection
  • Rhode Island
  • Security
  • Sequences
  • Statistics
  • Test And Evaluation

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra
  • Wave Propagation and Nonlinear Chaotic Dynamics.