A single-record estimator for correlation functions of nonstationary random processes

The need for estimation of auto- and cross-correlation functions of nonstationary random processes arises in many problems of communication, signal processing, system identification and control. The practical evaluation of such correlation functions is hindered by the fact that ensemble averages are extremely burdensome to obtain. This paper proposes a time-average estimator that yields unbiased and consistent estimates of those correlation functions by use of a single record of the processes involved. It is expected that this estimator will be applicable in most cases of practical interest since the conditions for its validity are fairly weak.