The camera does not need GPS capabilities itself, but if you want to connect a digital elevation model to the real world you need control points on the ground with known real-world coordinates.
Old-school photogrammetry was about triangulating points in different photos to figure out relative positions (stereophotogrammetry). It could be done painstakingly by hand, or more recently automated by computer program. A more complicated set of algorithms can be used to determine multiple camera positions and perspectives (and common features detected in multiple images) in software now referred to as "structure from motion." With it you can easily find thousands of points in space to define a 3D model. All you need is a bunch of photos. Photoscan is a commercial software to do this. Open source here: http://ccwu.me/vsfm/ And more expensive software with more capabilities is available through Leica or other GIS software makers.