Tutorial on running median subtraction filter with its application on new physics searches

What is it about?

This work provides numerical demonstrations with formal proofs of the effectiveness of a well known statistical filter namely Running Median Subtraction Filter (RMSF) in the data analysis process directed to the search for transient signals. Transient means anything which lasts for a short duration. The research work done in our group involves the search for transient exotic low-mass field (ELF) signals which are hypothesized to be generated from the merger of black holes and neutron stars. We use the data from the Global Positioning System (GPS) satellites, which house very precise atomic clocks. If ELFs exist then such a field can interact with the fundamental particles like electrons and quarks (fermions) of the atomic clocks and lead to a transient change in the fine structure constant and the fermion masses. One can look for new field interactions and hence new physics by analyzing the GPS data. This RMSF filter is very useful for such data analysis processes. This filtering technique involves subtracting off the median from the data points in a particular window and then sliding this window throughout the data set. The resulting processed data is cleaned from the unnecessary background clutter or baseline curvatures, which very often is present in a particular data set. Usually such baselines are needed to be removed from the data by adopting a filtering process. However, a filtering process may also affect the sought after signal in the data. RMSF, with an appropriate choice of its window size, is quite effective in removing the undesired baselines from a data set without having any significant impact on the signal of interest. We rigorously show the statistical operation of RMSF filter on a typical data set and also on specific components of the data set based on results from numerical simulations and also provide formal mathematical proofs.

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Photo by Chris Liverani on Unsplash

Photo by Chris Liverani on Unsplash

Why is it important?

This paper will help one to understand and decide upon the use of RMSF with a specific window size in various data analysis purposes.