Model-based Estimation and Inference Procedures for Clock Synchronization
Accurate clock synchronization is essential in the operation of networks. In applications in which it can be performed frequently, the process generally relies upon the estimation of the relative offset of two different clocks. However, due to limited power resources in Wireless Sensor Networks, it cannot be performed often. Thus in order to obtain a longer lasting synchronization, the relative frequency of two clocks is also estimated.
In the literature, there are estimators for relative offset and frequency based on a variety of techniques including graphical methods, maximum likelihood estimation, and least squares estimation. However, there has been no extensive study to compare the performance of these estimators. In this dissertation, the existing estimators are examined in detail and several alternative least squares-based estimators are developed and compared with the existing estimators in an exhaustive study.
Although there is a large literature on estimating relative offset and frequency, there is little to no research regarding inference. This topic is of potentially great importance because it may possibly lead to limiting unneeded synchronization, resulting in better conservation of network power resources. Recent work has focused on the construction of confidence intervals for relative offset and while it does not address relative frequency, it is an important first step towards developing procedures that do. In this work, it has been assumed that the network delays that occur during the synchronization process are independent, but this may not be appropriate in all applications. The network delays are often modeled as independent exponential random variables. Thus to improve upon the existing confidence interval methodology, in this dissertation the use of bivariate exponential distributions is introduced to capture the anticipated correlation between the network delays. Moreover, an alternative confidence interval procedure for offset is developed and is then used to illustrate how the assumption of independent network delays can potentially lead to improper inference about relative offset.