The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Configuring a GPS-like Network
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Yimin Rong

Posts: 29
Registered: 12/13/04
Configuring a GPS-like Network
Posted: Mar 27, 2006 11:53 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Consider a network of four receivers, two transmitters and one

* the four receivers are set up such that they are not co-planar
* the four receivers are fixed in position
* the clocks in the receivers are not initially synchronized, but it
can be assumed that they do not drift significantly
* one transmitter is fixed in position; it can be assumed to be visible
to all receivers can at all times
* the second transmitter is mobile; it can be assumed to be visible to
at least one receiver at all times
* the transmitters are not synchronized with anything
* the transmitters send a unique ID at regular intervals; the signal
propagates at the speed of light (30 cm/ns) and is read by the
receivers; there is no time information encoded in the signal, only the
* the transmitters are "read-only"
* the receivers send the transmitter ID and the receiver timestamp to
the processor

If the initial configuration of the network is not known, what is the
minimum setup required to determine a common time reference and the
positions of the receivers?

Allowable operations:

* the processor may query a receiver to determine its current time
* the processor may use the results from the fixed transmitter for any
* the mobile transmitter may be moved anywhere; it may or may not be
visible to all the receivers
* the mobile transmitter may be moved to be << 30 cm from any receiver;
that is, no significant propagation delay between the transmitter and
the receiver
* the mobile transmitter may be moved directly underneath each
receiver; it will always be visible to that receiver
* one receiver may be defined as the origin
* two receivers may be defined as an x-axis or a y-axis
* as an absolute last resort, the positions of one or more receivers
can be measured directly!

Setting up a common time reference seems easy enough, for example the
Simple Network Time Protocol describes how to accurately synchronize
remote clocks.

I think I can get an estimate of the z-coordinate and an orientation
for each receiver by moving the transmitter next to each and then
underneath. I'm stuck at determining the x-y coordinates. The
restriction that the mobile transmitter is not always visible to all
receivers really complicates the matter.

I'm thinking the only option is to measure the positions of all the
receivers directly, that is, the "last resort" operation above.

Anyway, any assistance or references on-line or otherwise would be
greatly appreciated.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.