Sure. I've been working on this problem for about 5 years now, starting with the collection of barometric pressure from Android devices. I'm currently working on this with iPhones at Sunshine [1], where we collect pressure data (along with other metrics), but pressure is the most valuable.

There are researchers who use this data - we have collected about 4 billion atmospheric pressure measurements that we have distributed for academic and government research. The primary researchers are Cliff Mass and his lab at the University of Washington. There are also groups in Canada and the US that are using the data. IBM is now also collecting and using smartphone pressure data through their mobile apps. [2]

Generally speaking, the current trend is to take the live data stream, run it through a quality-control algorithm and then use kalman filters in the WRF data assimilation package.

There are some papers published, but it is still early. I will find some links to papers if you'd like to read them. [3]

[1] https://thesunshine.co/

[2] http://www.nytimes.com/2015/10/29/technology/ibm-to-acquire-...

[3] Utility of Dense Pressure Observations for Improving Mesoscale Analyses and Forecasts: http://www.atmos.washington.edu/~hakim/papers/madaus_hakim_m...