01z Jun 8—Why Jacob's Anchored positions are more uncertain than underway

Update, the next morning:  He did not anchor, as speculated here, but indeed went straight through to land in Trinity Beach (Yorkeys Knob Marina), north part of Cairns.

We can see on the Google Earth presentation of Jacob's track that the reported GPS positions are more scattered over a larger range than when he is anchored than when he is underway. You can see this in the Google Earth presentation online. Zoom into the track before he anchored at Flynn Reef. Below is a sketch of the situation.

I apologize for all of these rough sketches in this note. This is a passing thought (and timely) that does not justify, and i hope not require, finer artwork.

The yellow range shows the position reports from an anchored position. They spread over about 4.5 miles range. GPS has an inherent accuracy of about 100m or better.  The pink positions are his reports from the same system once underway.  In both cases, our presentation of each hourly position report is a sliding average over the past 3 hr.

Here is a plausibility argument of why the position scatter might be larger when anchored.... and indeed an argument that he might be anchored once again (03z Jun 8).

The position accuracies are poor because the GPS antenna is below decks with a limited view of the horizon. With limited view, it sees only a few satellites, and the intersection angles are narrow, which introduces large fix uncertainties.

Here schematically we see LOP1 intersecting with LOP2, and then consider a small error in LOP2 called 2'. We see the resulting error in intersection is large, whereas with a steeper intersection (ie nearer 90º intersection) the same small error in one of them has less effect on the fix.  And on top of that, a 2-d GPS fix  (ie elevation at sea level is known)  actually requires 3 LOPS. The third one is key to how GPS works; it is used to remove the time uncertainty in the signals—the "LOPs" are actually range rings measured by how long it takes the signal to get to the GPS antenna from the satellite.

Here is a schematic of the restricted view of the sky from within the vessel...

The outer circle is the sky; the areas on the sky are what is seen through two port light windows on either side of the vessel—I do not know the real geometry of this on Jacob's boat.  When the boat rolls, one side sees higher, the other looks into the water. When the boat yawls, one window looks more forward; the other more aft, and so on.

When anchored the boat does move around at the end of the anchor line, but if the wind is strong, it is likely to be held more or less in line, and if it does sail back and forth some in the wind, it will be a relatively slow change.

It seems the view of the sky will change with time when anchored, but that it will be much slower and less dramatic than when sailing (rowing).

When underway, this theory is that the two portlight views sample much more of the sky during a fix than they do at anchor, which gives the GPS access to more satellites and hence better fixes than when anchored with limited view.

This may or may not be true. There may be other factors at play.  I am standing by to hear your thoughts on this.  Post a comment if you have another interpretation of any support for this idea.

For now, and for the moment, I will use this argument in a video below that he has anchored again, near Cairns anchorage CA1 or CA4.  I say that because his track progressed normally from the last anchorage to this location and then just stopped and scattered.

The alternative is he is fighting against the wind and not making progress, which is effectively like anchoring, when it comes to sampling the sky through limited access.

I have not heard from his since he left Flynn Reef, so i do not know the answer.

Here is a video discussion of the points above and others related to his current position: