My son uses his iPhone GPS for car navigation with Tom Tom. I think it has the sirf3 GPS chip. If it does you should be able to get an NMEA file to save and download to your computer. That file should have the Doppler data in it as well.
You may need to download and install some sort of logging app. to make it log the data.
It would be a shame if you got the iPhone wet though....

Make sure you use a very good waterproof bag and even put it inside a zip lock bag inside that as well.