Hi Lawrence:

Your #1 is not Differential GPS, but what's commonly called "Poor Man's
DGPS".  To get DGPS what's done is to use a base receiver at a known
location and it determines the range and range rate errors to each
satellite.  This information is transmitted by the Low Frequency beacons
and by the WAAS satellites.  The rover GPS receiver applies the
corrections for range error to each of those satellites it's tracking
and also makes a correction because of the time delay in the correction
based on the range rate.  This gets you into the area of 1 meter.

There's a neat simplification of DGPS patented by CSI.  Now, with
Selective Availability turned off, the errors to each satellite is
stable with time and so you don't need to constantly be measuring it.
Instead you can take a single receiver to a known location and let the
receiver determine range and range rate corrections for all the sats
that are visible (a 12 channel receivers is very desirable for this) and
then the receiver sends these corrections to it's self and as the single
receiver moves about it is a true DGPS receiver with an accuracy that
slowly degrades with time and once all the satellites have set will be
back to a plain GPS receiver so this method is only good for a
relatively short period of time.

Your #2 is called a pseudolite system.  It was used when the GPS system
spec was published and before there were any satellites in orbit to test
receivers.  It's also used on missile ranges and other places to improve
the geometry by adding pseudo satellites on towers, hilltops, etc.  Note
that the Dilution Of Position gets lower as the geometry of the sats
gets better and/or denser.  the DOP is bad if all the satellites you are
tracking are in the same general direction.  Ideally, in the northern
hemisphere,  there would be a satellite to the West, South, East and
directly overhead.  There will never be one at the North horizon because
of the orbit inclination.

Your #3 is using what's called carrier phase is applied to the GPS
system since you are looking at the phase of a cycle of the received
signal.  If you envelope detected the ultrasonic signal and just looked
at the rising edge then it word be analogous to what's called code phase
GPS reception.  The difference in the GPS detection methods is huge.
Code phase is used for civilian receivers and gets you in the 10 meter
area, and with DGPS into the 1 meter area.  Surveyors developed the
carrier phase method and they get down into the mili meter area.  The
Real Time Kinematic system achieve mm accuracy while the receiver is moving.

Note that the GPS system depends on absolute time.  Think of a boat out
in S.F. Bay that's all fogged in.  If a fog horn #1 starts exactly on
the hour and the boat hears the horn exactly 10 seconds past the hour
then the boat is on a circle with a radius of about 10,000 feet from the
for horn.  If fog horn #2 starts exactly 1 minute past the hour and the
boat hears that horn at 1:05 past  the hour then the boat is about 5,000
feet from horn #2.  But if the captains watch is off then there is an
error in the boats position.  One way around the clock error is to add
another fog horn.  After noting the times from all 3 fog horns it's
possible to calculate the error in the boat's clock and so a timex watch
can be used instead of an Rolex.  For a 3 dimensional fix 4 sources are
needed.

GPS in fact works in a very similar way.  The prior Transit system
required the Nuke subs to have atomic clocks, expensive even for the
military.

Note that in the fog horn analogy no information was gained by the phase
of the sound.  Now suppose that the clock error has been calculated and
the boat has a precise 1 pulse per second sampling signal to trigger an
A/D connected to a microphone tuned to pickup the foghorn frequency.
Now you will have a phase angle for each fog horn, say 37 degrees for
horn #1, 273 degrees for horn #2 and 50 degrees for horn #3.  But you
don't know the number of full wavelength to each ot the horns.  In GPS
this is called the integer ambiguity.  There are a large number of
possible positions where the solution to the integer ambiguity is
valid.  One way around this with the GPS system is to wait a moment to
let the satellites move a long way and then take another data point.
After some number of minutes with a new fix once every second there is
only one solution to where the fixed point is on the ground and this
position is known very precisely.

So an RTK survey system can give you mm accuracy on a moving GPS
receiver, but at considerable cost.

There are a number of what you call Local Positioning Systems.  Usually
they are radio based.  One is the aircraft Distance Measuring Equipment
(DME) and there are a number of patented variants on this theme. An
early 911 location system for cell phones used the difference of the
time of arrival from one cell phone to multiple cell towers to locate
the phone in the triangular cell.  A good place for a lot of ideas is
the USPTO search site. But to get started you need to find some class
numbers that are for what you are looking for, so go here first:
http://www.uspto.gov/go/classification/uspcindex/indexa.htm


Note that of all the things that can be measured such as distance,
volume ,mass, etc. the one that is heads and shoulders the most precise
is measuring time intervals, so you want a system that measures a time
interval rather than some other quantity.

Have Fun,

Brooke Clarke, N6GCE
http://www.RPC68.com

>Date:    Tue, 11 Nov 2003 15:35:10 -0600
>From:    llile@SALTONUSA.COM
>Subject: Re: [EE:] GPS vs LPS
>
>OK, we all know that GPS is good at locating positions down to some
>accuracy that is good enough to tell if you are on Mount Everest or not,
>but generally not accurately enough for many tasks.  For instance, a
>surveyor needs to know where he is within 2 cm, a robot lawnmower needs to
>know where it is within 6 inches maybe.  An automated farming machine, say
>a robot 4 bottom plow or a robot planter needs to know where it is
>withinhalf a meter maybe.  Any of these would benefit from a Local
>Positioning System, something that would cover just a few thousand square
>feet with immensely better relative accuracy.
>
>This might allow a robot lawnmower to employ efficient mowing algorithms,
>instead of random (efficient in terms of processor power) blundering
>about.
>
>How would one go about cooking this up?  I have scratched my head about it
>a little.
>
>1.  Have a central GPS reciever at a stable position, say on a pole or one
>the roof of a house.  Read it's location once.  Then forever after, read
>it's location again, and rebroadcast the *error* from the most recent
>reading versus the very first reading to your robot cotton picker on a
>different frequency.  Your robot cotton-picker recieves GPS, also recieves
>this error correcting signal, and with a little math gets a little more
>preceise indication of where it happens to be.  Doesn't seem like this
>scheme could get you down to an inch though
>
>2. Duplicate GPS on a small scale.  Have 3 or more transmitters near the
>corners of your property/farm field/Yard at stable positions.  Continually
>broadcast signals from the three and your robot needs to figure out how to
>decode them into GPS-like distance signals.  Unfortunately, the GPS
>transmitters are synched in a very accurate way linked to the atomic
>clock, something that would be hard to manage in a small, cheap, homemade
>system.
>
>3. Duplicate GPS with ultrasonic waves.  The way I figure it 40KHZ sound
>has a wavelength on the order of .7 cm (this could be way off I did it
>from memory)  and if one could use three or more ultrasonic transmitters
>to determine distance from known points, one might be able to calculate a
>local position within centimeter accuracy.  One scheme that comes to mind
>is this:  Each transmitter sends a radio pulse, considered to be
>instantaneous at these scales, and it's address by radio at the beginning
>of an ultrasonic pulse.  The delay between the leading edge of the radio
>pulse and the leading edge of the sonic pulse would translate directly
>into distance.  The three transmitters could do this in sequence, thereby
>avoiding "packet collision" problems.  Each one would have to be addressed
>so the reciever would know which one it was looking for. Sionce the
>transmitters poll, they can share the same transmit frequency and each
>ahave a reciever so they know when to fire.   The recieved signal delay
>would tell you how far in space you were from each unit, and if I do my
>geometry correctly 3 transmitters would result in two possible positions
>for your hapless robot, one of them being several feet in the air. However
>the 2D coordinates (generally what matters anyway) would only have one
>possible position.    Sounds like a lot of math for a poor PIC.  However,
>might be accurate enough to keep your robot mower out of the flower bed!
>
>
>
>any other ideas?  None of these are simple enough.
>
>
>-- Lawrence Lile
>Senior Project Engineer
>Toastmaster, Inc.
>Division of Salton, Inc.
>573-446-5661 voice
>573-446-5676 fax
>
>
>
>
>

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