Brief Tutorial on the Kalman Filter

Abstract

A derivation of the Kalman filter equations is presented which should provide a concise introduction to Kalman filter theory for scientists, engineers, and mathematicians alike. An elementary derivation of the basic Kalman filter, the 1-step Kalman predictor, is given first in 1-dimension and then in n-dimension. The well known prediction-correction formulation of the Kalman filter equations are derived for the filtered estimate, or current state estimate. Then, the state prediction is obtained from the filtered estimate. It is assumed that the reader has a background in probability theory and some exposure to stochastic processes.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1994
Accession Number
ADA286571

Entities

People

  • John Podesta

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Data Science
  • Equations
  • Equations Of State
  • Filtration
  • Information Science
  • Kalman Filtering
  • Kalman Filters
  • Linear Systems
  • Mathematical Filters
  • Probability
  • Probability Density Functions
  • Random Variables
  • Standards
  • Stationary Processes
  • Statistical Algorithms
  • Stochastic Processes

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Theoretical Analysis.