>
>      Is there any way you can think of to shorten the sample period to let's
>say 1 second without adding too much expensive hardware (gyroscopes,
>accelerometers and such) ? Perhaps some kind of linear regression algorithm
>or a PID loop?

Magnetic compass. $50
At the GPS read, grab the heading info, and the compass bearing. Now, the
compass can read you realtime, your deviation from the GPS heading, until
the next sample.

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