Hi Saka;<br><br>AFAIK any transmitter that can be modelled as a point source in 3D should be inverse square, it's just electromagnetic radiation after all :-)<br><br>If you have enough points in your grid of known (x, y, p1, p2, p3) then you can do a least squares fit on all of the parameters. Of course if your transmitters move around, you are stuck. Again, a poor r-squared / big residuals would indicate errors. Also, if your transmitters are relatively far away from the grid but close to each other, I would think you would start to get an ill-conditioned system.<br>
<br>I don't mind continuing the discussion by e-mail if you like. Certainly our colleagues on this list are probably not so interested in the problem.<br><br>chris dot hermansen at tecogroup dot ca<br><br><div class="gmail_quote">
On Wed, Jun 22, 2011 at 10:26 PM, Saka Royban <span dir="ltr"><<a href="mailto:sakaroyban@yahoo.com">sakaroyban@yahoo.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div><div style="font-family:times new roman,new york,times,serif;font-size:12pt"><div>Thanks a lot Chris.<br>some points:<br>1. Are u sure that all transmitters of this type use inverse square law?<br>2. If we don't know position of transmitters, can we still solve the problem in least square? maybe using dD=Di-Dj paramater or so.<br>
3. I think we can suppose all transmitters to be from the same mark, so the fixed constant in formula.<br><br>(this subject sounds a bit off topic, regarding postgis. Do u know any better place (i.e mailing list or so) for this kind of discussions?)<br>
<br>Best Regards<br>Saka<br><br></div><div style="font-family:times new roman,new york,times,serif;font-size:12pt"><br><div style="font-family:times new roman,new york,times,serif;font-size:12pt"><font face="Tahoma" size="2"><div class="im">
<hr size="1"><b><span style="font-weight:bold">From:</span></b>
Chris Hermansen <<a href="mailto:chris.hermansen@tecogroup.ca" target="_blank">chris.hermansen@tecogroup.ca</a>><br><b><span style="font-weight:bold">To:</span></b> PostGIS Users Discussion <<a href="mailto:postgis-users@postgis.refractions.net" target="_blank">postgis-users@postgis.refractions.net</a>><br>
</div><b><span style="font-weight:bold">Sent:</span></b> Wed, June 22, 2011 9:39:36 AM<div><div></div><div class="h5"><br><b><span style="font-weight:bold">Subject:</span></b> Re: [postgis-users] Interpolation problem<br>
</div></div></font><div><div></div><div class="h5"><br>
<p>Oh wait. Maybe each transmitter occupies a separate xy location so you are then able to calculate distance from each transmitter using an inverse square law and finally solve for the unknown xy location?</p>
<p>If so you should be able to first determine your constants Ki i = 1,2,3 for each transmitter in</p>
<p>Si = Ki / (Di * Di)</p>
<p>by doing a least squares fit on the known signal strengths vs known distances (calculated from known xy).</p>
<p>If the fit doesn't provide small residuals / high correlation then you will probably have a hard time with your subsequent computations...</p>
<div class="gmail_quote">On 2011-06-21 9:57 PM, "Chris Hermansen" <<a rel="nofollow" href="mailto:chris.hermansen@tecogroup.ca" target="_blank">chris.hermansen@tecogroup.ca</a>> wrote:<br>> Would not there be isolines of the same signal strength? In that case there<br>
> is no unique x,y for a given signal strength...<br>> On 2011-06-21 9:54 PM, "Saka Royban" <<a rel="nofollow" href="mailto:sakaroyban@yahoo.com" target="_blank">sakaroyban@yahoo.com</a>> wrote:<br>
>> yes, of course.there is a unique x,y for each triple measurements.<br>
>> This measurements are, in fact, Received Signal Strength so it means more<br>>> distance less RSS value.<br>>><br>>><br>>><br>>><br>>><br>>> ________________________________<br>
>> From: Chris Hermansen <<a rel="nofollow" href="mailto:chris.hermansen@tecogroup.ca" target="_blank">chris.hermansen@tecogroup.ca</a>><br>>> To: PostGIS Users Discussion <<a rel="nofollow" href="mailto:postgis-users@postgis.refractions.net" target="_blank">postgis-users@postgis.refractions.net</a>><br>
>> Sent: Wed, June 22, 2011 8:35:05 AM<br>>> Subject: Re: [postgis-users] Interpolation problem<br>>><br>>><br>>> What are the three measurements? Is it reasonable to assume that knowing<br>
> three<br>
>> measurement values tells you the location ie is there a unique x,y for<br>> each<br>>> triple of measurements?<br>>> On 2011-06-21 8:54 PM, "Saka Royban" <<a rel="nofollow" href="mailto:sakaroyban@yahoo.com" target="_blank">sakaroyban@yahoo.com</a>> wrote:<br>
>>> Hi all<br>>>> I'm not sure whether this can be done completely via PostGIS or it needs<br>> some<br>>>> programming. Anyway, at this step no problem with programming if Knowing<br>> the<br>
>>>way<br>>>><br>>>><br>>>> and algorithm.<br>>>> I have point shapefile (arranged like a grid) and for each point there is<br>> 3<br>>>> similar measurements (obtained via 3 transmitters) and, of course, x and<br>
> y<br>>>> coordinates. The problem is that when i have a new point with these 3<br>> measures,<br>>>><br>>>> How can i interpolate its coordinates and specify its location?<br>>>> Maybe helpful to say, this type of measurement is distance dependent but<br>
>>> unfortunately i don't know the exact formula.<br>>>><br>>>> Any help would be appreciated.<br>>>> Best Regards<br></div>
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