Proofs and Techniques Useful for Deriving the Kalman Filter

Abstract

This note is a tutorial in matrix manipulation and the normal distribution of statistics, concepts that are important for deriving and analysing the Kalman Filter, a basic tool of signal processing. We focus on the proof of the well-known fact that the sum of two n-dimensional normal probability density functions is also normal. While this theorem is usually taken for granted in the signal processing field, proving it provides an insightful excursion into techniques such as Gaussian integrals and the Matrix Inversion Lemma.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2008
Accession Number
ADA485785

Entities

People

  • Don Koks

Organizations

  • Defence Science and Technology Group

Tags

Communities of Interest

  • Electronic Warfare

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Australia
  • Convolution Integrals
  • Covariance
  • Electronic Warfare
  • Filters
  • Integrals
  • Kalman Filters
  • Language
  • Normal Density Functions
  • Probability
  • Probability Density Functions
  • Random Variables
  • Signal Processing
  • Theses
  • Warfare

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.
  • Systems Analysis and Design