Gyro Drift modeled as random walk and exponentially

Gyro Drift modeled as random walk and exponentially correlated processes AE 645 Integrated INS/GPS Navigation April 2, 2009

Gyro drift – an example of random walk

Gyro Drift modeled as first-order exponentially correlated process

AE 457 – 641: Navigation and Guidance: Quiz 1 (February 13, 2012, Monday) Time: 1 hr should be enough, but no more than 2 hrs. Que. 1 Air Traffic Controller, Sunanda, granted Captain Rahul permission to take off from Mumbai Airport. So, before taking off, Rahul initialized the airplane’s navigation platform by using the earth’s gravity and the spin vector. Suppose the platform has both north and east tilt, and some azimuth error. [The answers below are expected to be analytical, not numerical. ] • What are the ideal measurements of the 3 -axis accelerometer and gyros in the geographic frame while the plane is still on the ground? • What would be the measurement of the three-axis accelerometer in the platform frame? • What would be the measurement of the east gyro on the platform? • What are the tilt angles that the platform should be tilted by in order to align the platform vertical with the geographic vertical? • What is the azimuth angle by which the platform should be rotated so as to align the platform north and east with the geographic north and east?

Que. 2 Some platform misalignment with the geographic frame remained after the above process, however. • Suppose the remaining north tilt is 3 millirad. How much would be the east velocity error (in ft/s) in 3 minutes after takeoff? • Suppose Rahul gets a Doppler radar measurement of this east velocity then, and the measurement is accurate to 2 ft/s. Could he use this measurement to reduce the tilt error? How much would be the revised tilt error? • If the angle of the Doppler measurement were 45 degrees from the east, what would be the revised tilt error of the platform? • Now suppose the tilt error is taken care of by the Doppler measurements, but there was an initial azimuth tilt error of 0. 5 degree, and the flight is southbound to Goa, with a speed of 600 ft/s. How much would be the east velocity error (in ft/s) in 20 minutes from takeoff just due to the azimuth tilt error? Ignore the earlier north tilt. • With a 2 ft/s accurate Doppler measurement again, in the direction of flight, how much this azimuth error would be reduced to?