What is a location.

use the W3 spec for location http://dev.w3.org/geo/api/spec-source.html

Latitude
Longtitude
Altitude
Accuracy
AltitudeAccuracy
Heading
Velocity
Timestamp

What does it mean for an object to be at a location?

Given the frequency of updates, and the accuracy of the reading, an object exists in a probability polygon. A lat/long may put the person in the vicinity of their home. An error estimate of at least 20 feet means the person could be anywhere in the home. There are lat/longs that are impossible for people to be in, inside of walls for instance. So probability changes. Without the benefit of house plans, the first time traveling over a path defines that path as a >0 probability (openstreetmaps does this).