Phase estimation of recurring patterns in nonstationary signals

Abstract

A phase estimation algorithm is presented to estimate the phase of a recurring pattern in a nonstationary signal. The signal is modelled by a template signal that represents one revolution of the recurring pattern, and that the frequency of this pattern can change at any time with no assumptions about local stationarity. The algorithm uses a constraint maximum likelihood estimator (MLE) to estimate the phase of the recurring pattern in the time series. Using the dynamic programming techniques from the dynamic time warping (DTW) algorithm, the solution is found in an efficient manner. The algorithm is applied to the digitization of meter readings from analog consumption meters.

As of today, analog consumption meters are still widely used to measure the consumption of gas, electricity and water. Often, smart home appliance use a simple reflective photosensor located on a rotating part of the meter to obtain information about the state of the consumption meter. The algorithm presented in this thesis accurately estimates the phase of the repeating pattern that occurs in the sensor observation when the meter rotates. Using this estimate, the signal of the photosensor can be converted to an estimate of the total resource consumption and consumption rate.

The algorithm improves in accuracy over conventional methods based on peak detection, and is shown to work in cases where the peak detection methods fails. Examples of this are signals where there is no distinctive peak in the signal or a signal where the recurring pattern is reversed. Furthermore, a template compression scheme is proposed that is used to decrease the computational complexity of the algorithm. Different time series compression methods are applied to the algorithm and evaluated on their performance.