哈工大导航原理大作业

《导航原理》作业(惯性导航部分)

一、题目要求

A fighter equipped with SINS is initially at the position of ︒35 NL and

︒122 EL,stationary on a motionless carrier. Three

gyros X G ,Y G ,Z G ,and three accelerometers, X A ,Y A ,Z A are installed along the axes b X ,b Y ,b Z of the body frame respectively. Case 1:stationary onboard test

The body frame of the fighter initially coincides with the geographical frame, as shown in the figure, with its pitching axis b X pointing to the east,rolling axis b Y to the north, and azimuth axis b Z upward. Then the body of the fighter is made to rotate step by step relative to the geographical frame.

(1) ︒10around b X (2) ︒30around b Y (3) ︒50-around b Z

After that, the body of the fighter stops rotating. You are required to compute the final output of the three accelerometers on the fighter, using both DCM and quaternion respectively,and ignoring the device errors. It is known that the magnitude of gravity acceleration is 2/8.9g s m =. Case 2:flight navigation

Initially, the fighter is stationary on the motionless carrier with its board 25m above the sea level. Its pitching and rolling axes are both in the local horizon, and its rolling axis is ︒45on the north by east, parallel with the runway onboard. Then the fighter accelerate along the

runway and take off from the carrier.

The output of the gyros and accelerometers are both pulse numbers,Each gyro pulse is an angular increment of sec arc 1.0-,and each accelerometer pulse is g 6e 1-,with 2/8.9g s m =.The gyro output frequency is 10 Hz,and the accelerometer ’s is 1Hz. The output of gyros and accelerometers within 5400s are stored in MATLAB data files named and , containing matrices gm of 35400⨯ and am of 35400⨯ respectively. The format of data as shown in the tables, with 10 rows of each matrix selected. Each row represents the out of the type of sensors at each sample time.

The Earth can be seen as an ideal sphere, with radius and spinning rate

rad/s 10292.75-⨯, The

errors of sensors are ignored, so is the

effect of height on the magnitude of gravity. The output of the gyros are to integrated every . The rotation of geographical frame is to be updated every 1s, so are the velocities and position of the figure. You are required to:

(1)Compute the final attitude quaternion, longitude, latitude, height, and east, north, vertical velocities of the fighter.

(2)Compute the total horizontal distance traveled by the fighter. (3)Draw the latitude-versus-longitude trajectory of the fighter, with horizontal longitude axis.

(4)Draw the curve of the height of fighter, with horizontal time axis.