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Time Delay Localization-----------------------This directory has files for doing time-delay localization. Intime-delay localization, a source emits a sound (or some other type ofsignal), which is received at a number of microphones (or other sensors). The sound arrives at the microphones at slightly different times. Forany two microphones, the delay between the arrival times at themicrophones determines a curve -- a hyperbola -- on which the soundsource must lie. With three or more microphones, the intersectinghyperbolas determine the sound source location.Since there is error in the measurement of the time delays, there willbe error in the measured location. Multiple time-delay measurementsallow the position of the sound source to be pinpointed with higheraccuracy.To make this localization method work, you need to know - the locations of the microphones (the array), - the speed of sound (assumed to be uniform over the whole area), and - either (1) the time delays between pairs of microphones, or (2) the arrival times of the sound signal at the different microphones (from which the time delays are computed) The M-files of interest areenterDelays.m lets you enter the time delays between microphonesfileDelays.m reads the time delays from a file instead of from the keyboardlocateDelays.m given the time delays, computes and plots best-fitting locationenterTimes.m lets you enter the times the signal arrived at each microphonefileTimes.m reads arrival times from a file instead of from the keyboardlocateTimes.m given arrival times, computes and plots best-fitting locationtest.m example run of the code (uses testarray4 and testpos12)locAccuracy.m plots the relative accuracy of locations for a given arrayAuxiliary functions aretimesToDelays.m auxiliary function for enterTimes; calculates delayscheckScale.m controls entering times in seconds or millisecondsbestFit.m actually computes the best-fit locationCalcDeltaTimes.m auxiliary fn to bestFit; calculates arrival timesCalcDeltaJacobian.m axuiliary fn to bestFit; computes guess-location errordist.m Euclidean distance functionshowResults.m plots microphones, hyperbolae, and best-fit locationplotPhones.m auxiliary function to showResults; plotsPlotHyperbola.m plots a hyperbolaPlotHyperbolas.m plots several hyperbolaeSpiesberger.m closed-form solution for 3-phone case
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