Propagation of error analysis in least-squares procedures with second-order autoregressive measurement errors

Accuracy evaluation is an integral part of parameter estimation by least
squares. We present an analysis of error propagation when the measurement
error is a second-order autoregressive process. When measurement
correlation is neglected, least squares underestimate the uncertainty. In
order to scale up uncertainty, we investigated autoregressive measurement
errors, calculated their correlation, and assessed the estimate
uncertainty in terms of the sampling frequency. Our results, which are
amenable to approximations and numerical computation, show clearly the way
correlation influences error propagation and are useful in devising
strategies for optimal measurement design.