导航原理大作业 哈工大

导航原理作业（惯性导航部分）

Task description

A fighter equipped with SINS is initially at the position of 35o NL and 122o EL, stationary on a motionless carrier. Three gyros, G X, G Y, G Z, and three accelerometers, A X, A Y, A Z, are installed along the axes X b, Y b, Z b of its 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 X b pointing to the east, rolling axis Y b to the north, and azimuth axis Z b upward. Then the body of the fighter is made to rotate step by step relative to the geographical frame:

(1) 10o around X b

(2) 30o around Y b

(3) –50o around Z b

After that, the body of the fighter stops rotating. You are required to compute the final outputs of the three accelerometers on the fighter, using both direction cosine matrix and quaternion respectively, and ignoring the device errors. It is known that the magnitude of gravity acceleration is g = 9.8m/s2.

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 45o north by east(北偏东), parallel with the runway onboard. Then the fighter accelerates along the runway and takes off from the carrier. The outputs of the gyros and accelerometers are both pulse numbers. Each gyro pulse is an angular increment of 0.1 arc-sec, and each accelerometer pulse is 1e-6g, with g = 9.8m/s2. The gyro output frequency is 10Hz, and the accelerometer’s is 1Hz. The outputs of the gyros and accelerometers within 5400s are stored in MATLAB data files named gout.mat and aout.mat, containing matrices gm of 54000×3 and am of 5400×3 respectively. The format of the data is as shown in the tables, with 10 rows of each matrix selected. Each row represents the outputs of the type of sensors at each sampling time.

The Earth can be seen as an ideal sphere, with radius 6368.00km and spinning rate 7.292×10-5 rad/s, The errors of the sensors are ignored, so is the effect of height on the magnitude of gravity. The outputs of the gyros are to be integrated every 0.1s. The rotation of the geographical frame is to be updated every 1s, so are the velocities and positions of the fighter. 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 the fighter, with horizontal time axis.

A X A Y