Originally posted by bertwert was under the impression that GPS worked on triangulation - solving the distance to three known points (satellites) to determine the location in a 3D plane. As the distance is determined based on a time difference, a fourth satellite is required for this.
You basically have four unknowns (x, y, z, t) and therefore need four "equations" so to speak to solve. More satellites provide more accuracy, with increased certainty.
You got it! For a complete position and time solution, you have 4 variables --> need 4 independent measurements (the time-delays wrt the satellites; in GPS-speak: "pseudo-ranges") to solve for the 4 variables !!
If you think your clock is good (enough), you can get (X, Y, Z) (or, equivalently, Lat, Lon, Altitude - the overall GPS system includes some assumptions about the shape of the Earth: the geoid and sea level). Conversely, if you fix/quess your altitude, you can get time/lat/lon.