Yes. You are looking for the Geolocation API, here's a simple demo. Here is sample code from Dive Into HTML5 and HTML Rocks. Works great from web pages hosted on iOS and Android phones, it's a simple API to use. Strictly speaking it's not GPS; it's a generic location API. On mobile devices like iPhones location is often provided by WiFi or cell tower fixes and not the GPS radio.
When a Wifi button is on the wifi connexion works fine I can see longitude and latitude changing (GPS and Data buttons are off).
When GPS and DATA buttons are on (and wifi button off) geolocation coordinates longitude and latitude are frozzen (no updates)... no change...
one possible anwser can be here found on this answered Jun 6 '13 at 6:51 by Eduardo: https://stackoverflow.com/a/16955512
I tested it, and it worked for me...
I now used "https://github.com/domoritz/leaflet-locatecontrol"...
(And I don't know why the answer body must be at least 30 characters.)