Parameter Estimation in Linear Filtering

Abstract

Suppose on a probability space (omega, F, P) a partially observable random process (x sub l, Y sub 1, t > or = 0; is given where only the second component (y sub 1) is observed. Furthermore assume that (x sub 1, y sub 1) satisfy a certain system of stochastic differential equations driven by independent Wiener processes (W sub 1 (t)) and (W 2 (sub 2)). We obtain a large deviation inequality for the maximum likelihood estimator (m.l.e.) of the unknown parameter theta = (alpha, beta). This inequality enables us to prove the strong consistency, asymptotic normality and covergence of the moments of the m. l.e. The method of proof can be extended to obtain similar results when multi- dimensional instead of one dimensional processes are considered and theta is a k-dimensional vector.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1989
Accession Number
ADA218566

Entities

People

  • G. Kallianpur
  • R. S. Selukar

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Data Science
  • Differential Equations
  • Equations
  • Estimators
  • Functional Analysis
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • Linear Filtering
  • Mathematical Filters
  • North Carolina
  • Plastic Explosives
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Analytical Mechanics
  • Statistical inference.

Technology Areas

  • Space