Michal Staniaszek

Time Delay Estimation in Gravitationally Lensed Photon Stream Pairs

This was my final year dissertation project, supervised by Peter Tiňo. I developed a system in C to estimate the time delays between streams of gravitationally lensed photons. I created a photon stream simulator, using Poisson processes to model the arrival times of photons. I used a least squares method to build a baseline estimator which was then used to perform piecewise linear estimates of functions. Time delay estimation was done using this baseline estimator combined with either a numerical or probabilistic method to determine the goodness of fit between models. I compared the baseline method with a simple kernel density estimator on sinusoidal functions of varying frequencies and randomly generated functions. In most cases the kernel density estimator provided a better estimate, but the results were not statistically significant. The project was awarded the “Best Research Project” prize by the Computer Science department at the University of Birmingham, receiving a mark of 94%, and was submitted to the 2013 SET awards.

You can find the project on GitHub. There is also a lengthy report which details all aspects of the project. Alternatively, you can read a shorter summary submitted for the SET awards.