Likelihood Ratio Test for the Equivalence of Two Autoregressive Moving-Average Time Series

Abstract

To passively detect quiet sources, future sonar systems will require more sensors, which may contribute to operator overload. The methods described in this report have the potential to automatically determine if two sonar tracks, for example, correspond to the same source, thereby improving operator performance. Specifically, a likelihood ratio test for the equivalence of two autoregressive moving average (ARMA) time series is derived. This test investigates the structural characteristics of the two time series through the ARMA parameters. Four cases of this test are presented for examining the ARMA parameters, series means, and/or innovations variances. The autoregressive (AR) time series is treated separately, not only because AR parameters are easier to estimate, but also because many time series can be characterized by an AR process. Monte Carlo analysis has shown that the likelihood ratio test has a good fit to the chi square distribution, with degrees of freedom equal to the number of parameters being tested.

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Document Details

Document Type
Technical Report
Publication Date
Sep 15, 1999
Accession Number
ADA370599

Entities

People

  • Gerald W. Swope

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Direction Finding
  • Equations
  • Equations Of State
  • False Alarms
  • Information Operations
  • Measurement
  • Military Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Rhode Island
  • Signal Processing
  • Simulations
  • Sonar Signals
  • Undersea Warfare

Readers

  • Approximation Theory.
  • Regression Analysis.
  • Sensor Fusion and Tracking Systems.