Compensating distortion effects in repeated measurements under non-stationary conditions

Abstract

In this paper a compensation technique is presented for applications using repeated measurements under moderate non-stationary measurement conditions. The assumption is that the measurement conditions are stationary during a single repeated measurement but non-stationary over the entire measurement time. The objective with repeated measurements is often to retrieve an estimate of the (noise reduced) signal and its uncertainties. In order to obtain accurate estimates of these two quantities, stationary measurement conditions must be guaranteed under the measurement time. A condition that in many situations is difficult to achieve, e.g., during long measurement times or in a rapidly changing environment. The proposed method compensates for linear dynamic changes during the measurement time, where the dynamical changes, the underlying signal waveform and the noise covariance are considered unknown. The theoretical effect of moderate non-stationary conditions on repeated measurements is analyzed and experimentally validated. Estimation results using the proposed technique are presented for repeated ultrasonic measurements under non-stationary temperature conditions. The results show accurate signal estimation and noise characterization with uncorrelated normally distributed residuals, in contrast to standard synchronization techniques.