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cs:hydrophones:multilateration:start [2017/09/14 00:18] Brian Moore [Full Solution] |
cs:hydrophones:multilateration:start [2017/09/14 00:23] Brian Moore [Depth Sensor Substitution] |
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- | Which requires only 4 hydrophones, $h_0,h_1,h_2,$ and $h_3$ plus the depth sensor measuring $z_{sub}$ to compared against the known depth of the pinger $z_pinger$. | + | Which requires only 4 hydrophones, $h_0,h_1,h_2,$ and $h_3$ plus the depth sensor measuring $z_{sub}$ to compared against the known depth of the pinger $z_{pinger}$. |
However, the depth sensor will always measure the absolute depth of the submarine regardless of the submarine's orientation $R(\psi,\phi,\theta)$. Thus the difference measured will always be $z_{pinger}-z_{sub} = Z_{global}$. | However, the depth sensor will always measure the absolute depth of the submarine regardless of the submarine's orientation $R(\psi,\phi,\theta)$. Thus the difference measured will always be $z_{pinger}-z_{sub} = Z_{global}$. | ||
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- | Azimuth = arctan(\frac{Y}{X}), \qquad | + | Azimuth = arctan\left(\frac{Y}{X}\right), \qquad |
- | Inclination = arctan(\frac{Z}{\sqrt{X^2+Y^2}}), \qquad | + | Inclination = arctan\left(\frac{Z}{\sqrt{X^2+Y^2}}\right), \qquad |
Range = \sqrt{X^2 + Y^2 + Z^2} \\ | Range = \sqrt{X^2 + Y^2 + Z^2} \\ | ||