Re: Things we remember...

In article <hduq74$uev$3@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
mstemper@xxxxxxxxxxxxxxxxxxxx (Michael Stemper) wrote:

In article <mike-A7D23C.12595617112009@xxxxxxxxxxxxxxxxxxxxxxxxxx>, Mike Ash
<mike@xxxxxxxxxxx> writes:
In article <4b0e4cf1.541876359@xxxxxxxxxxxxxxxxxx>, fairwater@xxxxxxxxx
(Derek Lyons) wrote:

Having more channels still means shorter lock up time and greater
accuracy (especially on the move), but even so a modern three channel
unit considerably outperforms it's predecessors.

Wouldn't four channels be the minimum? Since you're working off time
*differences*, three satellites isn't enough to localize the four
dimensions (three spatial and one time) that you need in order to know
where you are, unless you can apply some other constraint in addition.

Three channels is enough to give you latitude and longitude. When my
unit can only reliably see three satellites, it explicitly goes into
"2-D Navigation" mode.

Three channels is enough to give you a fix with a single dimension of
uncertainty. I believe the actual shape is a hyperbola, or something
similar to that. This does *not* give you latitude/longitude unless you
can add an additional external constraint, like "I am on the surface of
the earth". (And your GPS receiver actually knows the shape of the
Earth.)

Actually, close to ground level, elevation readings from (at least my)
GPS are pretty crummy. If you look at the geometry of the situation,
all of the birds are above (or close to above) you. In my car, I've
seen the elevation reading increase during a long descent into a valley.

All of the satellites being above the horizon doesn't hurt altitude
readings at all. What does hurt altitude readings is the fact that, most
of the time, most of the satellites are off to the side, and usually
there isn't one close to directly overhead. Because of the angles
involved, this means that your error in time differences results in a
larger error for altitude than for horizontal positioning. Basically,
each satellite gives you a dimension along the line between you and the
satellite. If they're all off to the side, then you have a lot of data
for "side" but not much for "up"

On the other hand, the times that I've used it in a passenger jet,
the readings seemed to make sense -- varying within a few feet during
calm level flight. Different geometry, because now there's the
possibility of some birds looking up at you.

The angle down to the horizon from a passenger jet's cruising altitude
is pretty small, roughly 3 degrees. The chances of having a satellite's
angle at any given time be less than 0 but greater than -3 degrees are
miniscule. "Looking up" makes no difference to the GPS geometry.

I've used GPSes quite a bit in aircraft and they all work fine on the
ground and in the air. You just have to understand that you get a double
whammy in altitude, because you care much more about precise altitude
than you do about precise lat/lon, and because GPS provides less precise
altitude than lat/lon. This is why aircraft use pressure-based
altimeters even when GPS is available.

--
Mike Ash
Radio Free Earth
Broadcasting from our climate-controlled studios deep inside the Moon
.

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