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Unformatted text preview: 34 DEAD-RECKONING ERROR 124 34 Dead-Reckoning Error An unmanned, untethered underwater vehicle operating near large metallic marine structures has to navigate without a magnetic compass, and in some cases without any acoustic ranging available. In these cases, a viable approach is dead-reckoning based on the yaw gyro and on the body-referenced velocity over ground, from a Doppler acoustic sensor. Specifically, if is yaw angle, U is forward speed, and [ x, y ] is the position in a global frame of reference, dead-reckoning entails propagating x = U cos y = U sin . Let us consider a yaw rate gyro with a noise variance of . 0025 rad 2 /s 2 ; it is Gaussian noise. The speed sensor is also subject to Gaussian noise, but this has variance . 0001 m 2 /s 2 . The yaw rate sensor is measuring r = and the speed sensor is measuring U . The platform on which these sensors is mounted goes through a known circular trajectory, with U = 1 . 5 m/s and r = / 150 rad/s , and the sensors are sampled five times per second. Question: Assuming that at time zero, there is no error in x, y, , what are the mean and standard deviation of the x , y , and range ( x 2 + y 2 ) errors at the end of one complete circle?...
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- Spring '05