Concerns & Next Steps
Potential Sources of Error
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A prominent issue for us during the project was the rate at which we were sampling the microphones. We are limited to 4 microphones at 48khz, when ideally we’d prefer 96khz or 192khz to obtain more samples per cycle.
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We had issues with a limited sampling rate. The sampling rate is one of the most impactful parameters in our project that could easily affect our errors dramatically. At 48kHz, with 18cm separation between the hydrophones and the speed of water at approximately 1500m/s, we have approximately 11 possible angles within 180 degrees that we can identify. On the other hand, at 96kHz, we can have approximately 23 possible angles within 180 degrees that we can identify. Hence we can see that as we increase the sampling rate, the number of possible angles increases.
The reason for the limited sampling rate is due to the ADC’s interleaving for higher sample rates. In our case, we have 4 ADC's capable of sampling at 48 kHz, and when we’re sampling higher, we’re actually just using them in parallel with an offset between each. (1*192 kHz = 48 *4 = 96 *2). This explained the peculiar issue where everytime we doubled our sampling rate, we reduced the number of microphones we could simultaneously record by to half.
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Another issue is that the software abstracts one audio interface from 4 independent sound cards. As a result, due to the clocking on my computer, we can be offset as high as 4 samples. This means my initial calibration calculation offset can be offset up to 12.5cm.
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Moreover, the audio sound cards had a hardware filter built into them. The beacon can actually emit frequencies in the range of 20khz to 40khz. These hardware filters acted as low-pass filters, limiting our frequencies to only those within human range (20khz). As a result, we couldn’t test higher frequencies (E.g. 40Khz)
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tau = Possible angles per 90°
d=distance between hydrophones (m)
Fs=Sampling rate
S = speed of sound in water (m/s)
Next Steps
DSP PCB
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While the project has served as a good proof on concept using existing hardware, the complete problem has not been solved. As mentioned in our progress reports, the accuracy of our system is contingent on three core factors: sampling rate, the distance between hydrophones and the speed of sound in water. As a result, the only factor we have control over is the sampling rate. While with our current array of 4 USB audio interfaces functioning at 48Khz each can only get an accuracy of 15.625 degrees, our next step would be to create a custom PCB with a 4 channel Digital Signal Processing Chip. Some of these chips would enable us to sample as high as 25 Mega samples per second or, an accuracy as high as 0.03 degrees, a 520 time improvement!
Decreasing Runtime
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Ultimately, our project will need to run in real time. However, currently our system is very computationally intensive and could not be run in real time. In addition, if we were to in fact make a custom Printed Circuit Board with a mounted DSP chip, we would be working with more data, more often, and would not an even lighter weight model than what we are currently using.
Build Multiple Arrays
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While most research has been down with a linear array, certain array orientations have greater error rates. Multiple linear arrays on different access could enable greater versatility.
References:
Gray, Nicholas C. Interleaving ADCs for Higher Sample Rates. Texas Instruments, www.ti.com/lit/wp/snaa111/snaa111.pdf.
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