A New Weighted Average

The minimum variance unbiased estimator, (m.v.u.e.), of the current process value is ohtained in the situation where the process changes between measurement times by random jumps and the measurement of the process is itself subject to measurement variation. Segments of a continued fraction provide an easy algorithm for the solution of the m.v.u.e. for successive values of the process value. These segments provide an easy method of expressing the variance of the m.v.u.e. as well. The m.v.u.e. is used to study the efficiencies of various estimators of the current process value such as the most recent measurement and the arithmetic moving average.