[time-nuts] Thunderbolt & Lady Heather 48 hour precision survey

[Magnus Danielson]

On 11/27/2010 11:33 AM, Rob Kimberley wrote:
> Comes down to the simple fact that it needs to know its position accurately
> in order to give you good timing. I found this one out the hard way many
> (many) years ago with an old single channel Trimble unit, where we had to
> manually enter a known position in order to speed up acquisition. We were in
> London at BBC Broadcasting House, and I inadvertently put the longitude of
> the site East instead of West of Greenwich, and wondered why my 1PPS was
> ramping off!
>
> :-)

This is quite easily understood when confronted with the basic 
pseudo-range equations:

p1 = sqrt((x1-x)^2 + (y1-y)^2 + (z1-z)^2) - b
p2 = sqrt((x2-x)^2 + (y2-y)^2 + (z2-z)^2) - b
p3 = sqrt((x3-x)^2 + (y3-y)^2 + (z3-z)^2) - b
p4 = sqrt((x4-x)^2 + (y4-y)^2 + (z4-z)^2) - b

p1 is the pseudo-range to sat 1 which has position (x1, y1, z1) for the 
time of observation. Similarly for sat 2, 3 and 4.
The receiver position is at (x, y, z) and the time-offset is hidden in 
the pseudo-range scaled bias term b.

The better we know the receiver position (x, y, z) we can reduce the 
error in estimating the b term.

Since the above equations have 4 unknowns, you need 4 birds to solve it.

While these equations are non-linear, there is a linear solution to the 
above problem lurking in there. A nice little exercise with paper and pen.

Cheers,
Magnus