The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008
846
Tail rotor
Figure 6. Block scheme of the simulation environment.
Fuselage
Parameters
Value (m 2 )
Description
Sx 0.10 Equivalent area along x axis
Sy 0.22 Equivalent area along x axis
position output by the dynamic model block, then a uniformly
distributed noise is added to such measurement to simulate a
real operation. The noise amplitude was set to 10 cm. Again a
Zero Order Hold block was implemented to simulate an update
rate of 4 Hz. For the magnetometer we added a 2 deg uniformly
distributed noise to the orientation measurement returned by the
dynamic model. The magnetometer output was then timely
discretized with a Zero Order Hold block with an update rate of
120 Hz. Technical specifications for the GPS receiver and the
earth-field magnetic sensor are reported in table 4 and 5
respectively.
GPS
Receiver Type:
GPS Update Rate:
Pos/Vel Update Rate:
Accuracy Position EPS:
SBAS:
Start-up Time Cold start:
Tracking Sensitivity:
Timing Accuracy:
Operational Limits
Altitude:
Velocity:
16 channels
L1 frequency. C/A code
4 Hz
tOO Hz
2.5mdP
2.0mCEP’
34s
-158 dBm
50 ns RMS
18 km
515 m/s {1854 km/h)
Sz
0.15 Equivalent area along x axis
Table 4. Technical specifications for the GPS receiver.
Table 3. Parameters used for the fuselage modeling.
3.3 The EKF simulation block
3.2 Simulation of measurement sensors
According with the servos, the four outputs returned by
helicopter dynamic model, according with the input servos,
were used to simulate the operation of three measurement
sensors embedded in the MTi-G unit: the IMU platform, the
GPS receiver and the 3-axis magnetometer.
In order to properly combine together the data obtained by the
positioning and orientation sensors integrated in the Mti-G unit,
an Extended Kalman filter (EKF) had to be employed. The filter
takes as input the following parameters:
- Translational acceleration, derived in the body frame from
IMU accelerometers;
As regards the first sensor, input parameters are represented by
the translational acceleration and the angular velocity in the
body frame as derived from the solution of the first two
equations shown in (5).To better simulate the behaviour of a
real attitude sensor we added a uniformly distributed noise,
whose amplitude has been calculated as product between the
noise density and the square root of the sensor bandwith.
Corresponding values were obtained by the IMU specifications
reported in table 4. Moreover, the update rates were simulated
by using Zero Order Hold blocks, i.e. Simulink components
able to hold the signal for a certain amount of time. In this case
the update rate was set to 200 Hz.
IMU sensor performance
Dimensions:
Full Scale (standard):
Linearity:
Bias stability 5 (1<r):
Scale Factor stability 5 (1a):
Noise:
Alignment error:
Bandwidth {standard):
Max update rate:
rate of turn
3 axes
* 300 deg/s
0.1% of FS
5 deg/s
0.1 deg/s/n'Hz
0.1 deg
40 Hz
512 Hz
acceleration
3 axes
± 50 m/s 2
0.2% of FS
0.02 m/s 2
0.05%
0.002 m/sVVHz
0.1 deg
30 Hz
512 Hz
Magnetic sensor performance
Dimensions:
Full Scale (standard):
Linearity:
Bias stability 5 {1 a):
Scale Factor stability 5 (1o):
Noise:
Alignment error:
Bandwidth (standard):
Max update rate:
3 axes
± 750 mGauss
0.2% of FS
0.5 mGauss
0.5%
0.5 mGauss (1o)
0.1 deg
10 Hz
512 Hz
Table 5. Specifications for the magnetic sensor.
- Angular velocity as measured in the body frame by the IMU
gyros;
- Inertial position provided by the GPS receiver;
- Attitude measurements provided by the magnetometer.
Obviously all these data are considered noisy as mentioned in
the previous subsection.
In our filter implementation the state equation is described as
follows:
** =/(■**-!, i,W w ) (6)
Table 3. Specifications for the IMU accelerometers and gyros.
A similar approach was adopted even for the GPS receiver and
the magnetometer. The GPS sub-block takes as input the inertial
while the measurement equation is:
Z, = Ms,. V,)
(7)
