Localisation of impacts on solid objects using wavelet transform and likelihood estimation

D. T. Pham
Z. Ji
O. Peyroutet
M. Yang
Z. Wang
M. Al-kutubi

The Time Difference Of Arrival (TDOA) method, often used for sound source localisation, is not suitable
for locating the source of dispersive waves. It is difficult to establish the actual time of arrival of a dispersive wave because of the dependency of its velocity on its frequency. To overcome this timing uncertainty, two novel approaches for the localisation of an impulsive acoustic source in a solid object are proposed in this paper. The Wavelet Transform is utilised to extract different frequency components from the recorded acoustic signals for estimation of the group velocities of the various frequencies. Maximum Likelihood Estimation (MLE) is introduced to improve the accuracy and reliability of the localisation. In the paper, three localisation methods based on these techniques are introduced and compared.

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Submitted by Ze Ji on Sun, 02/07/2006 - 4:21pm.
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It's a very interesting

Submitted by Vlado on Thu, 06/07/2006 - 10:38am.

It's a very interesting study. Have you considered restating the projection-slice theorem for use with wavelets and applying it for solving the localisation problem instead of maximum likelihood estimation?

At first glance applying multiresolution analysis methods on the full depth of the problem will possibly bring a more detailed view of the problem domain. I might be wrong though.

Thanks

Submitted by Ze Ji on Thu, 06/07/2006 - 1:31pm.

Thanks for your attention.

The advantage of the virtual conference is that I have more time to think about the answer. :-)

1. I have not considered the projection-slice theorem with wavelets. However, I would like to have a look at it, and probably discuss it with you before the end of IPROMS.

2. For the second question, I will try to answer it as I understand. Yes, you are right. There should be a criterion to judge where could be problematic. As mentioned in the paper, the performance is sensitive to the selected frequencies for the calculation.

Please do not hesitate to ask more questions and correct me.

Thanks

Well, it is one question

Submitted by Vlado on Thu, 06/07/2006 - 1:58pm.

Well, it is one question really.

What I mean is that probably there is merit in looking at the problem in N (3,4) dimentional space, where the dimentions ar the number of microphones used. The study of its wavelet basis should show how the position and surface material properties influence the coeffients in the wavelet basis, in the time/frequency range you care to study. My guess is that there will be distinctive spikes due to the phase difference of the signals picked up by the microphones.

Sorry for the confusion. :-)

Submitted by Ze Ji on Thu, 06/07/2006 - 3:41pm.

Sorry for the confusion. :-) I hope now I can answer your question partially.

The impulsive signals are transient. It is expected that there should be at least one distinctive spike in the wavelet domain, which can represent the arrival times. However, the global maximums or local peaks are not reliable to be used as the arrival times. This is because the dispersion is still there, even in the very narrow bandwidths after wavelet transform. The dispersion and attenuation affect the location of the global peak or spike. This is why MLE was used to calculate the probability, instead of a determinant value.

Localisation of impacts on solid objects using wavelet transform and likelihood estimation

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