Analysis of Bias, Variance and Mean Square Estimation Error in Reduced Order Filters

Abstract

The Kalman filter gives the optimal minimum variance, unbiased estimate of the system state. It is shown in this paper that for a ROF one cannot in general obtain an unbiased estimator. The conditional mean of the estimation error is non-zero and, therefore, the true covariance of the estimation error is not equal to the second moment of the estimation error as implied in some previous work. This problem of bias is recognized in the work of several references; however, the reduced order problem was not addressed. It is shown that a reduced order filter in general will be biased. The equations for the second moment, true covariance, and bias are presented for the continuous dynamics, continuous measurement and continuous dynamics, discrete measurement ROF problem. The results include the subcases of continuous and impulsive control.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1974
Accession Number
AD0785197

Entities

People

  • Jesse C. Ryles
  • Robert B. Asher

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Covariance
  • Dynamics
  • Equations
  • Error Analysis
  • Errors
  • Estimators
  • Filters
  • Filtration
  • Kalman Filtering
  • Kalman Filters
  • Linear Filtering
  • Measurement
  • New York
  • Sensitivity
  • Stochastic Processes
  • Tactical Aircraft

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Regression Analysis.