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Take the Eh? train: Distributed Acoustic Sensing (DAS) of commuter trains in a Canadian City

[Fotech Solutions] attach a Distributed Acoustic Sensing (DAS) system to an existing telecom fiber that follows the Red Line of the City of Calgary Light Rail Transit (LRT). The City does not have a Global Positioning Satellite (GPS) system to track the position of trains on the Red Line, and very few trains in the fleet are even GPS equipped. Therefore, we propose DAS tracking as an alternative to the retrofit and development of a GPS-based system or as a companion to a future system. Trains on the Red Line register as intensity peaks in the DAS soundfield, and we deduce the DAS distance between the City Hall LRT station (the origin) and the Tuscany station (the terminus) for all trains on the system by tracking intensity peaks. To estimate DAS position from DAS distance, we use the speedometer logs and GPS-position logs from one of the few GPS-equipped trains on the Red Line. We track this train with DAS during three trips from City Hall station to Tuscany station and then obtain the logs for those trips. Analysis of the logs shows that more than 98% of the GPS positions are either null-valued or are repeats of previous values. This paucity of actual positions suggests that the effective GPS positions lie on a very coarse grid. We convert the coarse GPS-positions into GPS distances and interpolate them onto the dense speedometer-grid using a Kalman filter. The heading along the Redline changes more slowly than its distance so we approximate a unit heading-vector on the dense grid. We show that the product of the Kalman GPS-distance and the unit heading-vector gives an optimal GPS heading-vector on the dense grid. Latitude and longitude at points along the dense grid correspond to the north-south and east-west components of the GPS heading-vector, respectively. We Kalman filter the DAS distances onto the dense-grid and we find also that this minimizes a number of DAS noise sources. With the Kalman DAS-distances and Kalman GPS-positions on the same dense-grid, we now have an optimal relationship that is time independent. For as long as the fiber and the Red Line themselves remain stationary, all DAS distances obtained from tracking future trains defines unique latitude and longitude positions in real time. 
Take the Eh? train: Distributed Acoustic Sensing (DAS) of commuter trains in a Canadian City
Journal of Applied Geophysics 183 (2020) 104201
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