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.