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From: Henry Spencer <>
Subject: Re: GPS in orbit
Date: Thu, 11 Apr 1996 15:01:14 GMT

In article <> (Jim McCoy) writes:
>I am a little curious as to how GPS works in for determining position
>while in orbit.  I can't remember the altitude of the sats used for 
>making a fix and so I guess my question is really two parts...

The GPS birds are in 12-hour orbits, far above LEO (but below GEO).

>        - Does generic commercial GPS gear work in orbit?

Yes and no.  GPS signal coverage in LEO is comparable to that on the ground,
but the GPS receivers do need some special design because of the relatively
high velocities involved.  (Also, generic commercial GPS gear is required to
blank its outputs if speed or altitude is above certain limits, to prevent
its use in missile guidance.)

>        - What happens if you take a GPS fix from an altitude _above_
>          the GPS sats?

It doesn't work too well.  The transmissions are beamed toward Earth; the
beams are broad enough to spill over somewhat, but once you get well away
from Earth -- even somewhat below the GPS birds' altitude -- your receiver
can hear only the spillover from satellites that are almost on the other
side of Earth.  It may still be workable, but special techniques will be
needed and precision will be poor.
Americans proved to be more bureaucratic           |       Henry Spencer
than I ever thought.  --Valery Ryumin, RKK Energia |

From: Henry Spencer <>
Subject: Re: How does GLOBAL POSITIONING SYSTEM (GPS) work???
Date: Tue, 23 Jul 1996 22:35:25 GMT

In article <> (cs-student) writes:
>I know that the GPS reciever looks for at least 4 GSP satellites, and is
>then able to compute a 3D fix on it's position (ie: Lat, Long and Alt). My
>question is, how does the system work, and what kind of data do the
>satellites transmit?

The satellites basically transmit very accurate time signals, along with
supplementary information like exact orbital elements.

Assume for the moment that you have a clock synchronized with theirs. 
Listening to one satellite puts you on the surface of a sphere, whose
radius is determined by the difference between your clock and the signal
you hear.  Two satellites put you on the intersection of two spheres, i.e.
a circle.  Three satellites cuts it down to two points, one of which can
typically be rejected as implausible because it is far out in space. 

Of course, in practice you don't start out with a synchronized clock.
So instead of a point, three satellites give you a curve, with your
position on the curve determined by the (unknown) offset between your
clock and the satellite clocks.  Adding a fourth satellite gets you
back to a point, because there will normally be only one point on the
curve which has a time offset consistent with the fourth satellite's
signal.  This also, incidentally, tells you the time very accurately.

Having five or more satellites in view is a considerable advantage,
because with only four, sometimes two of them will be quite close to
each other in the sky and this hurts accuracy.
 ...the truly fundamental discoveries seldom       |       Henry Spencer
occur where we have decided to look.  --B. Forman  |

Date: 7 Dec 87 03:36:09 GMT
From:  (Phil R. Karn)
Subject: Re: NAVSTAR (was Re: space news from Oct 5 AW&ST)

Actually, there may well be a less sinister reason for giving civilians
a different mode than the military reserves for itself.

It is pretty much a fact of life in communications that any signal you
can receive, you can jam. This goes for spread spectrum just as for
conventional narrowband modes. The fact that the C/A (clear access) code
on GPS is a simple length 1023 linear polynomial that is public
knowledge also makes it possible to jam the system.  The military
channel of GPS is spread with a different code that is the product of
two very long, relatively prime PN sequences. One has length 15,345,000
and the other 15,345,037. At 10.23 million chips/sec, this code would
take 38 weeks to repeat, but it is instead restarted every week at 0000
UTC Sunday. By keeping this sequence secret, it becomes much harder to
jam the signal.

Of course, because the sequence repeats each week, it is at least
theoretically possible to record the entire spread signal for later use
-- if you have a receiver with enough extra performance to make up for
the lack of coding gain, and if you have a place to put all those bits.


Date: 23 Nov 88 06:12:20 GMT
From:!  (Phil Karn)
Subject: Re: Relativity acceleration question

More info on the relativistic aspects of GPS from the satellite navigation
chapter of Handbook of Modern Electronics and Electrical Engineering:

The GPS demonstration satellites carry rubidium and cesium frequency
standards with long-term stabilities on the order of 1e-12 to 1e-13.  This
is several orders of magnitude smaller than the relativistic frequency
offset of 4.45e-10. The onboard clocks are slowed down by this amount to
make them appear "on frequency" to observers on the ground.


Date: 26 Nov 88 20:38:39 GMT
From:!  (Phil Karn)
Subject: Re: Relativity acceleration question

A very complete description of GPS is contained in the book I mentioned
before, Handbook of Modern Electronics and Electrical Engineering.
It's published by Wiley-Interscience; ISBN 0-471-09754-3.

To summarize, each GPS satellite transmits on two frequencies, L1 and L2.
L1 is 1575.420 MHz and L2 is 1227.600 MHz (we radio amateurs lost the
1215-1240 MHz section of our 23cm band several years ago for this reason).
The two carriers are generated coherently by multiplication of the internal
atomic clock reference of 10.23 MHz (lowered as described earlier to
compensate for relativistic effects).

The two frequencies are provided to allow for correction of ionospheric
propagation delay. 

Both signals are binary phase modulated in quadrature by pseudo-random
sequences; this means that the signals are actually direct sequence
spread-spectrum (i.e., you won't hear them on your R-7000).  One spreading
sequence is 1023 chips long; this is called the C/A (clear access) code, and
is public. The chip rate for this code is 1.023 megachip/s, so it repeats
every millisecond.

The other is the P (precision) code, and is classified. However, the P code
is known to be the product of two different PN codes, one of length
15,345,000 and the other of length 15,345,037. Transmitted at a chip rate of
10.23 megachip/s (10x the C/A rate), it takes 38 weeks to repeat. In
operation, however, each satellite uses a different section of the P code
sequence, and each satellite restarts its sequence every week at 00:00:00
UTC Sunday.

Total transmitter power is 20 watts, split 4:2:1 between the C/A channel of
L1, the P channel of L1, and L2. Antenna gain is 13.7 dB.

In addition to the spreading sequences, each signal contains a 50 bps
data stream containing an orbital ephemeris.


Date: 15 Jul 91 18:45:26 GMT
From: ssc-vax!bcsaic!hsvaic!  (Dani Eder)
Subject: Re: GPS position improvement

In article <492@aplcomm.JHUAPL.EDU> (Edwards Thomas G S1A x8297 ) writes:
>In article <1991Jul4.164819.4475@esseye.UUCP> jongsma@esseye.UUCP (Ken Jongsma) writes:
>>All SA means is that a "noise" factor is superimposed on the position
>>data provided by the satellites. 
>I have heard that it might be possible to increase the civillian resolution
>of GPS under SA by examining the "noise" and making resonable guesses about
>it.  I assume that such degrading is probably done by digital computers
>running random number generators, which often have certain predictabilities
>about them.

More correctly, the basic GPS signal is intentionallly in error by some
distance and direction from the true signal, and the encrypted portion
that the military has access to tells you how much the intentional
error is.  Thus, the accuracy of the civilian signal can be changed
in software by simply changing the error you tell it to broadcast.

This error feature can be defeated by having a receiver or two located
at fixed and accurately known positions (like right at a geodetic
survey marker).  The measured error in the received signal
(where GPS tells you you are minus where you really are known from
ground truth) can then be used to correct position measurements
of other receivers whose real positions are not known in advance.
Dani Eder/Boeing/Advanced Civil Space/(205)464-2697(w)/461-7801(h)/#905, 1075
Dockside Dr.,Huntsville,AL35824/Member: Space Studies Institute
Physical Location: 34deg 37' N 86deg 43' W +100m alt.

Date: Tue, 24 Nov 1992 21:21:54 GMT
From: Henry Spencer <>
Subject: Computer synchronisation by GPS

In article <> (Dave Hopkins) writes:
>As I understand it GPS has a number of accurate (atomic) clocks which are
>fundamental to determining ones position. One of the quoted applications
>for GPS is for synchronising computer systems across the world using this
>time information.
>How would such a system work and what advantages would this offer over
>conventional handshaking techniques?

GPS position-finding works by determining how far you are from several of
the satellites, and then finding the intersection of the spheres defined
by those distances.  The distances, in turn, are found by measuring
speed-of-light lag of the signals from the satellites.

The satellites just basically broadcast extremely accurate time signals
("the time is now 12:45:23.6465346533") plus current orbital positions.
Of course, what you can observe is not absolute lag, but relative lag --
how long the signal from one satellite took relative to another -- but
with an extra satellite or two, and accurate knowledge of the orbits,
you can solve for the satellites' idea of the time and for your position.

Since this scheme demands very accurate clocks on the satellites, and
getting a position involves figuring out what absolute time they think
it is, a GPS receiver quite incidentally knows the time down to a
fraction of a microsecond.  (In the spiffy military models, a fraction
of a nanosecond.)

The usual sorts of synchronization protocols go to great lengths to deal
with the problem of *not* having a common absolute time reference.  With
GPS, you *have* a common absolute time reference.  All GPS receivers,
anywhere in the world, agree on the exact instant when the GPS system
clock reads 1:45:67.8727634 (with several more decimal places if the
receiver is a spiffy one).  If your computer has a GPS receiver, and you
tell it to start processing at 11:17:05.8368461 sharp, it will start
processing in exact synchronization with any other similarly-equipped
computer that got the same instructions.
MS-DOS is the OS/360 of the 1980s.      | Henry Spencer @ U of Toronto Zoology
              -Hal W. Hardenbergh (1985)|  utzoo!henry

From: (Jordin Kare)
Subject: Re: Inertial Navigation Systems: how cheap?
Date: Sun, 28 May 2000 17:24:27 GMT

In article <8gbe5l$s3l$>, "Geoffrey A. Landis"
<> wrote:

> In article <>
> Jordin Kare, writes:
> >time-difference-of-arrival with 3 stations will give a 2-D position
> Hmmm-- should give 3-D position, no?  (Assuming that you can resolve one
> ambiguity, which will typically be "is this object above ground or
> underground?")

No, you're thinking you get distance from each of the 3 stations, which
gives you 2 points which are the intersections of three spheres -- three
independent measurements.  TDOA gives you the *difference* in distance
from two stations; two stations alone define a hyperboloid on which the
receiver must lie, and three stations define two hyperboloids with the
receiver lying on the curve of intersection -- you only get n-1
independent measurements from n beacons.  To get a position, you need one
more constraint, which is typically an assumption that the receiver is on
the surface of the Earth (and you need a geospatial model to tell you the
altitude at each point, although for modest accuracy and beacons near the
surface the model can be "the Earth is a perfect sphere" or even "the
Earth is flat").   Or, of course, four beacons (with some constraints on
their relative locations, e.g., they can't be coplanar or you get a large
error bound normal to the plane if you're near the plane).

> >with good accuracy using only a passive receiver.
> I'm trying to think how to do this with a passive receiver.  You must be
> assuming a good on-board clock

One way to look at TDOA is that you use one beacon as the clock, and get
measurements from the other N-1.  It's not a particularly *good* way to
look at it, since the error model for a real on-board clock is very
different from the error model for TDOA, but in principle it's correct.

Jordin Kare

From: (Henry Spencer)
Subject: Re: GPS and space positioning
Date: Wed, 1 Nov 2000 23:59:25 GMT

In article <do2ot8.d3u.ln@tomcat.edgehp.invalid>,
Dale Pontius <dale@casper.edgehp.invalid> wrote:
>How implicit is the assumption that the receiver is *inside*
>the sphere of the satellites' orbits?

That assumption is not strongly present.  However, there is a major
practical problem:  the satellites do not radiate in all directions.
Their antennas put out fairly narrow beams, pointed at Earth.  Once you're
even near the satellite altitude, you can hear only satellites in a small
ring of the sky (Earth blocks the middle of the ring).  That usually
doesn't even give you a full set of satellites, and even when it does,
the geometry is lousy and the resulting fixes quite imprecise.

There has been discussion of ways to fix this, notably the possibility of
adding a rear-side antenna to the GPS satellites to radiate low-power
signals for highly sensitive receivers in high-altitude satellites.
Nothing specific has been done about it yet.

>But what about outside the satellites' orbit? I'm sure GPS
>could be used, but would the garden variety algorithms my
>friend's $120 model uses get confused?

Unquestionably.  In fact, it probably wouldn't work even in LEO, because
it is not designed to cope with various consequences of an 8km/s orbital
velocity, e.g. Doppler shifts.  (There are GPS receivers for use in LEO
satellites, but they are expensive specialty products.)  At high altitude,
it would never see enough satellites.
Microsoft shouldn't be broken up.       |  Henry Spencer
It should be shut down.  -- Phil Agre   |      (aka

From: (Henry Spencer)
Subject: Re: GPS and space positioning
Date: Sat, 11 Nov 2000 17:15:18 GMT

In article <>,
Ian Stirling  <> wrote:
>Doppler shift is already an issue, IIRC, +-2Km/s is what it is, with
>a stationary reciever...

Not quite.  Doppler shift due to Earth's rotation is only about +-500m/s.
The satellites themselves are moving at about 4km/s, but only about 1km/s
of that, worst case, is along the line of sight.  Moreover, the two
vectors are not lined up and the sum is less than the sum of their

>...with a moving one, it goes to +-11Km/s.

Only with special receivers.  GPS receivers for use on satellites are
*not* just normal commercial receivers with the limits taken off.
When failure is not an option, success  |  Henry Spencer
can get expensive.   -- Peter Stibrany  |      (aka

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