THE APPLICATION OF STATISTICAL FILTER DESIGN TO A PARTICULAR PROBLEM

Abstract

A particular solution of the optimum filter design is presented for the class of problems where the noise is normally distributed and the data are described by a normal distribution. This is an application of the general results obtained in previous memos. This particular problem lends itself to an analytic solution and in fact turns out to yield a linear filter. This linear filter has long been used in tracking problems but it is believed that this is the first rigorous derivation. Three examples are given which represent the complete range of characteristics of the filter and one is able from them to make statements about the necessary 'memory' of the filter. One is also able to draw conclusions about how often one should sample a function based upon the irregularity of the function and on the noise that contaminates the measurements.

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Document Details

Document Type
Technical Report
Publication Date
Jul 21, 1953
Accession Number
AD0020805

Entities

People

  • W. I. Wells

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Convolution
  • Convolution Integrals
  • Detection
  • Detectors
  • Digital Computers
  • Distribution Curves
  • Distribution Functions
  • Equations
  • Filters
  • Government Procurement
  • Governments
  • Intervals
  • Measurement
  • Normal Distribution
  • Probability
  • Probability Distribution Functions
  • Probability Distributions

Readers

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