On Mon, 31 Oct 2011 12:43:48 -0700 (PDT), Dale Gillespie
wrote:

I had a Raymarine Sportpilot on my old C-Dory. It came with its own
compass and took input from the compass and the GPS. This S1000 has no
compass and apparently the input from the GPS isn't updated fast
enough or something. We need an iPilot!

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I think you've hit the nail on the head: GPS does not update quickly
enough to maintain directional stability at slow speed. The only
thing that GPS knows is position. It computes direction from
adjacent points. If the points are too close together (slow speed
error jitter), then direction will be inaccurate.