Considerations of the Error Variances of Time-Averaged Estimators for Correlated Processes
Abstract
This report considers the sample and error variances of both time- averaged correlation function and parameter estimators for stationary discrete complex processes. Analytic expressions for the variance of the biased, time- averaged auto and cross-channel correlation function estimators of stationary discrete complex processes are developed. These expressions relate the variance of these estimators not only to the size of the observation windows used to obtain the estimates, but also to the correlation of the processes as well. They provide a performance measure which can be used to specify the window size of the observation interval required to achieve a specific value of this variance. A unique aspect of this development is the determination of the functional dependence of these expressions in terms of the process temporal and cross- channel correlation. Validation of the analytic expressions is obtained using Monte-Carlo simulation. Furthermore, computed results are presented for the error variances of several parameter estimators for which analytical expressions are lacking. Their performance is compared to that of the exact Cramer-Rao bound as a function of process correlation and data window size. Both Gaussian and non-Gaussian processes are considered as well as both single and multichannel processes.... Autoregressive Processes, Parameter Estimation, Random Processes, Cramer-RAO Bound, Error Variance, Ergodicity.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1992
- Accession Number
- ADA261796
Entities
People
- James H. Michels
Organizations
- Rome Laboratory