On Sat, 20 Dec 2008 17:04:16 -0500, Philip Martel <pomartel@comcast.net> wrote:> > "Frnak McKenney" <frnak@far.from.the.madding.crowd.com> wrote in message > news:856dnZH-b6KZjNDUnZ2dnUVZ_vSdnZ2d@earthlink.com... >> On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com> >> wrote: >>> Hi.. I needed a few tips on 2-D localisation of a sound source using 2 >>> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a >>> single frequency source and in-accessible with the only known >>> characteristics being the ones measured from an oscilloscope. >>> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO >>> DSP >>> so please be kind enough to elaborate those "few tips"...Thanks :-) >> >> Ford, >> >> Just to make sure we're working with the same impression, I'm >> interpreting your phrase "COLLINEAR WITH THE SOURCE" this way: >> >> S: source >> M1,M2: microphones >> >> A-----M1---------M2---------S-----B >> >> As Fred has pointed out, as stated this is a 1-D localization >> problem, not a 2-D problem. >> >> And I'm assuming this is a "mathematical" problem (Oscilloscope has >> infinite bandwidth and values can be read from it with infinite >> precision, microphones are omnidirectional and infinitely small and >> can be placed with infinite accuracy, instantaneous measurements, >> etc.) >> >> S is a "single-frequency source" -- a simple sine wave with >> frequency "F". You can measure F with the 'scope, which, with the >> speed of sound in air will yield wavelength -- the length of one >> full compression-rarefaction cycle from S. >> >> But... unless you have some way of causing a recognizable "hiccup" >> from S -- starting and stopping it, for example -- I think I have to >> go along with Fred: it's insoluble, at least as stated. You need >> more information, such as "the position of S is known within a >> one-wavelength distance", or "S starts and stops", or something >> else. >> > Well, the intensity of a sound falls off as 1/(distance^2). Assuming that > both microphones are on the same side of the sound source, let the amplitude > of the sound as measured at the mics be A1 and A2 and the distance between > the source and the mics be d1 and d2. Let the distance between the mics be > d, and to simplify the math let A1 >A2 (and therefore d1 < d2). Call the > amplitude of the sound at unit distance A. > A1 = A/(d1^2) > A2 = A/(d2^2) = (A/((d1+d)^2) > so A1/A2 = (d1+d)^2/d1^2) > (d1+d)/d1 = sqrt(A1/A2) = R > d1+d = R* d1 > d = (R-1)* d1 > d1 = d/(R-1) = d(sqrt(A1/A2)-1)Philip, Well color me purple and call me an eggplant! I was really enjoying these nice trees... where did this _forest_ suddenly appear from? <grin?> There's still a bit of ambiguity in that, given S is a point source, and it's also presumably invisible and in another room so you can't "see" it or "listen" to it, you could be dealing with: A----M2-------------M1-------S--------B or A----M2----------------------S--------M1-------B but you do know that S is to the "right" of the microphone with the weaker signal. Taking a third reading off to the "left" of _that_ microphone guarantees that you can combine its amplitude and the amplitude measured at the microphone with the weaker signal, using your forumlation, and trust the result. This could explain why collinearity was introduced, although the "amplitude" approach could equally handle a 2-D or 3-D location problem. You'd just need to take more measurements. I think I'll go fix another cup of tea (hopefully the results will be slightly less embarassing <grin!>). Anyone see a way to solve this with only two measurements? Thanks, Philip. Frank -- "Science is not a linear march to truth but a tortuous road with blind alleys and a rubbernecking delay every mile or two. Our road map is not objective reality but the patterns of human thoughts and theories." -- Stephen Jay Gould, "Eight Little Piggies" -- Frank McKenney, McKenney Associates Richmond, Virginia / (804) 320-4887 Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)
Sound Source Localisation...HELP!!!!
Started by ●December 18, 2008
Reply by ●December 21, 20082008-12-21
Reply by ●December 21, 20082008-12-21
On Sun, 21 Dec 2008 07:39:42 -0600, Frnak McKenney <frnak@far.from.the.madding.crowd.com> wrote:>On Sat, 20 Dec 2008 17:04:16 -0500, Philip Martel <pomartel@comcast.net> wrote: >> >> "Frnak McKenney" <frnak@far.from.the.madding.crowd.com> wrote in message >> news:856dnZH-b6KZjNDUnZ2dnUVZ_vSdnZ2d@earthlink.com... >>> On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com> >>> wrote: >>>> Hi.. I needed a few tips on 2-D localisation of a sound source using 2 >>>> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a >>>> single frequency source and in-accessible with the only known >>>> characteristics being the ones measured from an oscilloscope. >>>> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO >>>> DSP >>>> so please be kind enough to elaborate those "few tips"...Thanks :-) >>> >>> Ford, >>> >>> Just to make sure we're working with the same impression, I'm >>> interpreting your phrase "COLLINEAR WITH THE SOURCE" this way: >>> >>> S: source >>> M1,M2: microphones >>> >>> A-----M1---------M2---------S-----B >>> >>> As Fred has pointed out, as stated this is a 1-D localization >>> problem, not a 2-D problem. >>> >>> And I'm assuming this is a "mathematical" problem (Oscilloscope has >>> infinite bandwidth and values can be read from it with infinite >>> precision, microphones are omnidirectional and infinitely small and >>> can be placed with infinite accuracy, instantaneous measurements, >>> etc.) >>> >>> S is a "single-frequency source" -- a simple sine wave with >>> frequency "F". You can measure F with the 'scope, which, with the >>> speed of sound in air will yield wavelength -- the length of one >>> full compression-rarefaction cycle from S. >>> >>> But... unless you have some way of causing a recognizable "hiccup" >>> from S -- starting and stopping it, for example -- I think I have to >>> go along with Fred: it's insoluble, at least as stated. You need >>> more information, such as "the position of S is known within a >>> one-wavelength distance", or "S starts and stops", or something >>> else. >>> >> Well, the intensity of a sound falls off as 1/(distance^2). Assuming that >> both microphones are on the same side of the sound source, let the amplitude >> of the sound as measured at the mics be A1 and A2 and the distance between >> the source and the mics be d1 and d2. Let the distance between the mics be >> d, and to simplify the math let A1 >A2 (and therefore d1 < d2). Call the >> amplitude of the sound at unit distance A. >> A1 = A/(d1^2) >> A2 = A/(d2^2) = (A/((d1+d)^2) >> so A1/A2 = (d1+d)^2/d1^2) >> (d1+d)/d1 = sqrt(A1/A2) = R >> d1+d = R* d1 >> d = (R-1)* d1 >> d1 = d/(R-1) = d(sqrt(A1/A2)-1) > >Philip, > >Well color me purple and call me an eggplant! > >I was really enjoying these nice trees... where did this _forest_ >suddenly appear from? <grin?> > >There's still a bit of ambiguity in that, given S is a point source, >and it's also presumably invisible and in another room so you can't >"see" it or "listen" to it, you could be dealing with: > > > A----M2-------------M1-------S--------B > >or > > A----M2----------------------S--------M1-------B > >but you do know that S is to the "right" of the microphone with the >weaker signal. Taking a third reading off to the "left" of _that_ >microphone guarantees that you can combine its amplitude and the >amplitude measured at the microphone with the weaker signal, using >your forumlation, and trust the result. > >This could explain why collinearity was introduced, although the >"amplitude" approach could equally handle a 2-D or 3-D location >problem. You'd just need to take more measurements. > >I think I'll go fix another cup of tea (hopefully the results will >be slightly less embarassing <grin!>). Anyone see a way to solve >this with only two measurements? > >Thanks, Philip. > > >Frank >-- > "Science is not a linear march to truth but a tortuous road with > blind alleys and a rubbernecking delay every mile or two. Our > road map is not objective reality but the patterns of human > thoughts and theories." > -- Stephen Jay Gould, "Eight Little Piggies"Using the power decay works great when there are no reflections, but often works very poorly for the cases like you described where the sensors and emitter may be in a room or different rooms (or when there's interference). If the signal really is just a tone, it's going to be a tough nut to crack without some significant limiting assumptions. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by ●December 22, 20082008-12-22
Hi, Eric. Thanks for joining in. Our story so far (trimmed... in keeping with the holidays <grin!>)): On Sun, 21 Dec 2008 09:09:16 -0700, Eric Jacobsen <eric.jacobsen@ieee.org> wrote:> On Sun, 21 Dec 2008 07:39:42 -0600, Frnak McKenney ><frnak@far.from.the.madding.crowd.com> wrote: > >>On Sat, 20 Dec 2008 17:04:16 -0500, Philip Martel <pomartel@comcast.net> wrote: >>> >>> "Frnak McKenney" <frnak@far.from.the.madding.crowd.com> wrote in message >>> news:856dnZH-b6KZjNDUnZ2dnUVZ_vSdnZ2d@earthlink.com... >>>> On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com> >>>> wrote: >>>>> Hi.. I needed a few tips on 2-D localisation of a sound source using 2 >>>>> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a >>>>> single frequency source and in-accessible with the only known >>>>> characteristics being the ones measured from an oscilloscope.--snip-->>>> Just to make sure we're working with the same impression, I'm >>>> interpreting your phrase "COLLINEAR WITH THE SOURCE" this way: >>>> >>>> S: source >>>> M1,M2: microphones >>>> >>>> A-----M1---------M2---------S-----B--snip-->>>> And I'm assuming this is a "mathematical" problem (Oscilloscope has >>>> infinite bandwidth and values can be read from it with infinite >>>> precision, microphones are omnidirectional and infinitely small and >>>> can be placed with infinite accuracy, instantaneous measurements, >>>> etc.) >>>> >>>> S is a "single-frequency source" -- a simple sine wave with >>>> frequency "F". You can measure F with the 'scope, which, with the >>>> speed of sound in air will yield wavelength -- the length of one >>>> full compression-rarefaction cycle from S.--snip-- And I now wish I hadn't said:>>>> ...it's insoluble, at least as stated. You need >>>> more information, such as "the position of S is known within a >>>> one-wavelength distance", or "S starts and stops", or something >>>> else.--snip-- And Philip contributed the Something Else:>>> Well, the intensity of a sound falls off as 1/(distance^2).-- embarassingly obvious math snipped <grin!> -- I tried to cover my assets with:>>There's still a bit of ambiguity in that, given S is a point source, >>and it's also presumably invisible and in another room so you can't >>"see" it or "listen" to it, you could be dealing with: >> >> A----M2-------------M1-------S--------B >> >>or >> >> A----M2----------------------S--------M1-------B--snip--> Using the power decay works great when there are no reflections, but > often works very poorly for the cases like you described where the > sensors and emitter may be in a room or different rooms (or when > there's interference).I'm not sure I stated all my assumptions, but the mental image I was working with had S, M1, and M2 in a separate location, one isoalted from O, the unnamed-in-this-context Observer with his trusty Oscilloscope. S's position within that location was unknown, but I did assume that the positions of M1 and M2 were known to any required degree of accuracy and could be repositioned anywhere with equal accuracy (waldoes? elves?). And since the original problem statement didn't mention the possibility of interference, I ignored it as well (not something I'd feel safe doing in the RealWorld(tm) <grin!>).> If the signal really is just a tone, it's going to be a tough nut to > crack without some significant limiting assumptions.When you're working with a textbook problem (or something equally realistic, say as an astral projection <grin!>) one can get away with a lot of assumptions that wouldn't be reasonable to make when one is working on a customer's problem. If nothing else, the consequences of errors are generally much less severe: a couple of exam points vs. the possible loss of a contract. <grin!> Meanwhile, the OP appears to have folded his tent and stolen off into the night, leaving behind only speculation. Sigh. Frank -- There is something fascinating about science. One gets such wholesome returns of conjectures out of such trifing investment of fact. -- Mark Twain -- Frank McKenney, McKenney Associates Richmond, Virginia / (804) 320-4887 Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)
