Creating a compass on a non-directionally aware device

Creating a compass on a non-directionally aware device

I need to develop a compass for a device we are using. This device is
directionally unaware (no gyroscope), but has a GPS module. How can I make
a compass, with a needle, that leads from a start coordinate (likely their
current position) to an end coordinate?
My current thoughts are:
Poll coordinates on the GPS sensor as quickly as appropriate.
Record coordinates where the PDOP is within a respectable range (maybe
less than 2.0).
Determine the direction they are facing based on the coordinate changes of
them walking.
I have a few issues with this though:
Firstly, the unit has to be moved around to get a sense of where they are.
Doesn't seem like it would be the most accurate, i.e. how many past points
do you use to determine direction change?
I'm not really sure if this is a feasible solution. Is there some
implementation theory I can read on this?
Is there a better way to solve my problem? The scope of the project
involves going from a 'current location' to some geo-tagged item in an oil
field.
Using a Windows Mobile 6.5 device - C# on VS2008.