# [postgis-users] Interpolation problem

Chris Hermansen chris.hermansen at tecogroup.ca
Wed Jun 22 22:40:29 PDT 2011

```Hi Saka;

AFAIK any transmitter that can be modelled as a point source in 3D should be
inverse square, it's just electromagnetic radiation after all :-)

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.

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.

chris dot hermansen at tecogroup dot ca

On Wed, Jun 22, 2011 at 10:26 PM, Saka Royban <sakaroyban at yahoo.com> wrote:

> Thanks a lot Chris.
> some points:
> 1. Are u sure that all transmitters of this type use inverse square law?
> 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.
> 3. I think we can suppose all transmitters to be from the same mark, so the
> fixed constant in formula.
>
> (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?)
>
> Best Regards
> Saka
>
>
> ------------------------------
> *From:* Chris Hermansen <chris.hermansen at tecogroup.ca>
> *To:* PostGIS Users Discussion <postgis-users at postgis.refractions.net>
> *Sent:* Wed, June 22, 2011 9:39:36 AM
>
> *Subject:* Re: [postgis-users] Interpolation problem
>
> 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?
>
> If so you should be able to first determine your constants  Ki i = 1,2,3
> for each transmitter in
>
> Si = Ki / (Di * Di)
>
> by doing a least squares fit on the known signal strengths vs known
> distances (calculated from known xy).
>
> If the fit doesn't provide small residuals / high correlation then you will
> probably have a hard time with your subsequent computations...
> On 2011-06-21 9:57 PM, "Chris Hermansen" <chris.hermansen at tecogroup.ca>
> wrote:
> > Would not there be isolines of the same signal strength? In that case
> there
> > is no unique x,y for a given signal strength...
> > On 2011-06-21 9:54 PM, "Saka Royban" <sakaroyban at yahoo.com> wrote:
> >> yes, of course.there is a unique x,y for each triple measurements.
> >> This measurements are, in fact, Received Signal Strength so it means
> more
> >> distance less RSS value.
> >>
> >>
> >>
> >>
> >>
> >> ________________________________
> >> From: Chris Hermansen <chris.hermansen at tecogroup.ca>
> >> To: PostGIS Users Discussion <postgis-users at postgis.refractions.net>
> >> Sent: Wed, June 22, 2011 8:35:05 AM
> >> Subject: Re: [postgis-users] Interpolation problem
> >>
> >>
> >> What are the three measurements? Is it reasonable to assume that knowing
> > three
> >> measurement values tells you the location ie is there a unique x,y for
> > each
> >> triple of measurements?
> >> On 2011-06-21 8:54 PM, "Saka Royban" <sakaroyban at yahoo.com> wrote:
> >>> Hi all
> >>> I'm not sure whether this can be done completely via PostGIS or it
> needs
> > some
> >>> programming. Anyway, at this step no problem with programming if
> Knowing
> > the
> >>>way
> >>>
> >>>
> >>> and algorithm.
> >>> I have point shapefile (arranged like a grid) and for each point there
> is
> > 3
> >>> similar measurements (obtained via 3 transmitters) and, of course, x
> and
> > y
> >>> coordinates. The problem is that when i have a new point with these 3
> > measures,
> >>>
> >>> How can i interpolate its coordinates and specify its location?
> >>> Maybe helpful to say, this type of measurement is distance dependent
> but
> >>> unfortunately i don't know the exact formula.
> >>>
> >>> Any help would be appreciated.
> >>> Best Regards
>
> _______________________________________________
> postgis-users mailing list
> postgis-users at postgis.refractions.net
> http://postgis.refractions.net/mailman/listinfo/postgis-users
>
>

--
Chris Hermansen
*Vice President*

TECO Natural Resource Group Limited
301 · 958 West 8th Avenue
Vancouver BC CANADA · V5Z 1E5
Tel +1.604.714.2878 · Cel +1.778.840.4625
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