Radar-Like GPS-Tracked-Objects Visualization

[ChrisW67]

The top half looks lot like a custom widget job.
Perhaps you might get a little inspiration from the Analog Clock Example. Give your widget a way to store a list of points, add, remove etc. Inthe paintEvent() you could draw the concentric circles, crosshairs and any points your widget has been told about.

I would not worry about the (assumed) classic radar sweeping animation until you can get to grips with the basics.

[StrikeByte]

I would use the QGraphics system for it
make graphics items for all the gps devices and place them in a QGraphicsItemGroup

[Radek]

Check QwtPolar. I have no experience with it but it seems to be your library. You will need Qwt - it is in the repository, and then compile QwtPolar most likely. QwtPolar is not in the repository so far but, perhaps, there are some compiled packages around.
When searching QwtPolar, search with Google.

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Edit: You will need to compile Qwt, too. The Debian repository contains Qwt 6.0 and QwtPolar depends on Qwt 6.1 ...