Need to get current location(road) is public or private

You will first have to match the GPX trace of the truck to the OSM street network. This is often called "map matching", and both well-known OSM routing engines Graphhopper and OSRM support it. You will want to install one of them on your system and load the relevant OSM data into it. Performing the map matching yields a sequence of graph edges (most likely) traversed by the vehicle, and you can then look at the properties of these edges to find out whether they are public or private roads.

NB not all routing engines/routing profiles will even route over private roads - a road marked private without explicit access for motor vehicles will often be ignored for routing. Also, before you even start, perhaps you should ensure that private roads are actually marked as such in OSM in the area you are interested in; otherwise you might as well not bother.

Last not least, remember that in executing this map matching, the resulting list of edges and the public/private information is a database derived from OpenStreetMap and hence subject to the ODbL share alike license, which depending on your exact use case may mean that you have to make the data available under the ODbL license, and make users aware that data comes from OSM.