How can I determine vehicle positions in the coordinate systems 'WGS 1984' or 'Sphere Mercator'/'Mercator (sphere)' or use background images meeting some well-defined coordinate system?
PTV Vissim does not use any map projection and does not consider any map projection of background files. Instead, PTV Vissim uses an own local, metric coordinate system defining a flat surface.
PTV Vissim does not provide any coordinate transformations, but since PTV Vissim 10, an example using formulas in User-Defined Attributes (UDAs) to determine coordinates in Sphere Mercator/Mercator (sphere) is provided here: c:\Users\Public\Documents\PTV Vision\PTV Vissim 10\Examples Training\Evaluation\WGS Coordinates.UDA
Any background files created in CAD or GIS systems should adopt this local coordinate system. Match the coordinate values of some central point in the network, for example a node or the Reference point: Base Data > Network Settings > Display > Background maps > Reference point in network
Regarding the use of background images, refer to the following section in the manual or the online PTV Vissim Help: 'Creating and editing a network' > 'Inserting a background image' > 'Using background images' > 'Loading image file as background image'.
To change the coordinate system in AutoCAD Map 3D refer to: http://docs.autodesk.com/MAP/2010/ENU/AutoCAD%20Map%203D%202010%20User%20Documentation/HTML%20Help/index.html?url=WSDB47C494325B6C408BC35393B34A2175-procedure.htm,topicNumber=d0e6120