Displacement Estimation for Homodyne Michelson Interferometers Based on Particle Filtering

Abstract: The current method for displacement estimation for homodyne Michelson interferometer is biased and gives little information about the statistical properties of the estimate. This thesis suggests an alternative estimation method, which has the potential to address these shortcomings. The method is based on a bootstrap Particle smoother, and gives similar displacement estimate quality compared to the least squares based method that is commonly used today. It is however significantly more computationally intensive, and hence the estimation quality has to be improved, while reducing the execution time, to obtain an algorithm that improves on the current one. In total, four estimation methods, based on particle filters or particle smoothers, are implemented in Matlab and evaluated. The recommended method is the most accurate one and is simple to implement in other programming languages. Most of the evaluation is done based on simulated data, but the three methods that work are tested on measured data as well. They all give reasonable displacement estimates for the measured data, but as the true displacement is unknown, the quality of the estimates cannot be assessed based on the measured data. Apart from the evaluation of the estimation methods, an introduction to both particle filtering and interferometry is given in the report, as well as a summary of the current, least squares based, estimator.