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ee:hydrophones:start [2018/01/28 11:11] Ryan Summers |
ee:hydrophones:start [2018/01/28 15:18] Ryan Summers |
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| ===== Introduction ===== | ===== Introduction ===== | ||
| - | //Note: The purpose of this page is to describe how the arrival times are acquired on a number of hydrophone channels. This documentation does //not// describe how that information is turned into bearings or how it is used in localization.// | + | //Note: The purpose of this page is to describe how the arrival times are acquired on a number of hydrophone channels. Documentation describing how that information is turned into a pinger bearing is found [[cs:hydrophones:pinger_bearing:start|here]].// |
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| Further simplifications can be applied to the problem as well. By ensuring that the hydrophones are close enough, it can be guaranteed that the arrival time difference will never exceed one half wavelength (the signals are sinusoidal with a maximum frequency of 40KHz). The cross correlation now only needs to be completed within +/- half a wavelength (which increases accuracy and decreases required processing). This means that the arrival time difference can never exceed approximately 12.5 microseconds. Because the speed of sound in water is 1498 m/s, the hydrophones must be spaced within 1.8cm of each other. | Further simplifications can be applied to the problem as well. By ensuring that the hydrophones are close enough, it can be guaranteed that the arrival time difference will never exceed one half wavelength (the signals are sinusoidal with a maximum frequency of 40KHz). The cross correlation now only needs to be completed within +/- half a wavelength (which increases accuracy and decreases required processing). This means that the arrival time difference can never exceed approximately 12.5 microseconds. Because the speed of sound in water is 1498 m/s, the hydrophones must be spaced within 1.8cm of each other. | ||
| + | To calculate a cross correlation, set time delays of [-12.5, 12.5] microseconds on the signal and calculate the overlapping area for each time delay. Calculating overlap is done by multiplying the value of the origin hydrophone at a time step by the value of the shifted hydrophone function at the same time step and summing up all multiplied values. When both are positive or negative, a point constructively adds to the correlation. When the signs don't match on the points, the correlation decreases. When both signals are identical, the correlation is maximal. | ||
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| + | ==== Summary ==== | ||
| Now that the theoretical aspects are out of the way, the foundation of the problem starts to take shape. | Now that the theoretical aspects are out of the way, the foundation of the problem starts to take shape. | ||
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| - Cross-correlate the X, Y, and Z axis signals against the reference to calculate time of flight delay. | - Cross-correlate the X, Y, and Z axis signals against the reference to calculate time of flight delay. | ||
| - | The cross correlation step is simple mathematics. Note that cross-correlation boils down to multiplying individual points of two signals together and accumulating, so if the signals are big it can take quite a bit of time. We will discuss how to handle this later. | + | The main difficulty exists in sampling the signals. It is important that samples are taken simultaneously on each of the hydrophones and that the signals are sampled fast enough to ensure that the precision is accurate enough (for example, at a sampling frequency of 1MHz, the time of arrival can never be more precise than a single microsecond). Therefore, the system must be capable of simultaneously sampling four channels at a minimum rate of 1MHz. |
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| - | The main difficulty exists in sampling the signals. It is important that samples are taken simultaneously on each of the hydrophones and that the signals are sampled fast enough to ensure that the precision in time of flight is accurate enough (for example, at a sampling frequency of 1MHz, the time of arrival can never be more precise than a signal microsecond). Therefore, the system must be capable of simultaneously sampling four channels at a minimum rate of 1MHz. | + | |
