# Accession Number:

## ADA083559

# Title:

## Least-Squares Polynomial Fits to Gaussian Random Walk Segments,

# Descriptive Note:

# Corporate Author:

## NAVAL SURFACE WEAPONS CENTER DAHLGREN VA

# Personal Author(s):

# Report Date:

## 1980-01-01

# Pagination or Media Count:

## 39.0

# Abstract:

This report addresses the least-squares l.s. polynomial approximation of gaussian random walk r.w. segments. The r.w.s treated are assumed to be generated by the summation of zero mean, stationary, gaussian random sequences of real numbers. Expressions are developed that relate the statistics of these stationary underlying sequences to the statistics of the associated coefficients and residuals of fit of the approximating l.s. polynomials. When more than one segment of a given r.w. has been approximated, the statistical relationship between the residuals of the fits to the different segments is explicitly defined. Finally, an example using the main results is presented. It involves calculating the statistics of the fit residuals when the given r.w. is generated by the fractional frequency errors of an atomic clock. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability