Laboratory of Aircraft Instrumentation Systems Navigation group

Laboratory of Aircraft Instrumentation Systems Navigation group
Department of Measurement
Czech Technical University in Prague
Faculty of Electrical Engineering
Project “Enhanced Navigation Algorithms in Joint Research
and Education” outcomes and best practice exchange
Supported by Norway grants under the No. NF-CZ07-ICP-3-2082015 and
the program CZ07 - Scholarship Programme and Bilateral Scholarship Programme
1/23
Project carrier
NavLIS group
Czech Technical University in Prague, Faculty of Electrical Engineering, Dept. of Measurement
http://www.cvut.cz/
Project partner
Centre of Autonomous Marine Operations and Systems - AMOS group
NTNU - Norwegian University of Science and Technology, http://www.ntnu.edu/
Project aim
 merging applied research of two research groups with one common aim to improve the performance of navigation
systems.
 “know-how” exchange by comparing of used methodologies and approaches (accurate navigation systems are crucial
in applications where precise positioning of manned or unmanned vehicles are required).
 exchange the best practice in the field of education and R&D enhancing the level of current state-of-the-art in
navigation systems and education practices which are closely connected with R&D activities performed at both
institutions.
2/23
Intro of CTU in Prague – FEE, Dept. of Measurement
The Czech Technical University in Prague (CTU in Prague), founded in 1707, is one of the oldest technical universities and
currently the leading technical university in the Czech Republic with approx. 23 000 students enrolled in engineering
courses. It offers 78 Master degree and 55 PhD. programs. CTU in Prague with over 1700 members of academic staff is also
one of the largest research institutions in the Czech Republic.
The project team is formed by the Navigation Group of the Laboratory of Aircraft
Instrumentation, which is a part of the Department of Measurement, Faculty of
Electrical Engineering (FEE) at CTU in Prague. All study programmes at FEE are
closely linked to faculty’s research activities. FEE alone ranks among the top 5
research institutions in the Czech Republic. The Department of Measurement
carries out research in measurement and instrumentation, including avionics,
diagnostics and non-destructive testing. In its field of interest, the department
cooperates actively on joint projects with teams from several universities (e.g.
Shizuoka University, National University of Ireland, Instituto Superior TecnicoLisboa; PTB Berlin and Braunschweig, etc.). On the basis of numerous research
achievements, the department cooperates in R&D with national and international
companies specialized in various industries such as transportation, medicine and
telecommunications, in addition to governmental institutes in military and space
programs.
3/23
Project teams
Assoc. Prof. Jan Roháč, PhD. – project coordinator
a coordinator of activities carried on within the NavLIS
group aimed at research and development of navigation
systems and their measuring units.
Prof. Thor I. Fossen – managing person at the partner inst.
a codirector at the AMOS group with research fields including
mathematical modeling/simulation of aircraft, marine craft,
unmanned vehicles, guidance, navigation and control
systems.
Martin Šipoš, PhD. - Assistant professor
deals with the calibration of inertial sensors, signal and
data processing, and development of navigation systems
and their measuring units.
Prof. Tor Arne Johansen – Professor at NTNU
deals with unmanned aerial vehicles, maritime and offshore
control applications, autonomous systems and networked
control, nonlinear state estimation and system identification.
Musfiqul Alam - PhD. student
focused on application of adaptive data processing
approaches in control systems, and applied optimal control
theory in complex aerospace systems.
Jakob Mahler Hansen – PhD. student
deals with nonlinear observers for tight integration of IMU
and GNSS pseudo-range and carrier-phase-ambiguity
resolution.
Pavel Brož - Master degree student
deals with development of navigation systems and their
measuring units, experimental verification, PCB design.
Kristoffer Gryte – PhD. student
deals with fixed-wing UAV applications and operation from
autonomous floating docking station.
4/23
Project secondary focus – goals
Short-term mobility
There will be planned 1 week and/or 2 week stays at CTU and NTNU to perform experiments and consult the solutions,
initialize the project in the form of a kick-off, exchange know-how in the field of education. In addition, dedicated lectures
will be held based on specialized topics.
Development of the project web pages
The project dissemination/communication will be ensured by the project web pages. The pages will be further
maintained even after 06/2016 to archive and update project outcomes and provide the project sustainability.
Joint publications
Data and know-how exchange will enable to compare different approaches to navigation solution and thus bring up with
new ideas suitable for publishing.
Development of new study materials
Based on obtained practice and knowledge transfer there will be created educational material for students how to
approach different applications from the navigation and applied methodology point of view.
Public events
At each institution there will be organized a public workshop informing about progress in navigation technology.
Short courses
There are planned 2 courses (1 week/each) on a voluntary basis for the students which will be held at each partner
institution – lecturing will be granted by both institutions.
5/23
Field testing – different vehicles
 fixed-wing UAV
 fast boat
 aircraft Slingsby T67C (GA)
6/23
Czech Technical University in Prague
Faculty of Electrical Engineering
Department of Measurement
Robust navigation solution using EKF
given by Jan Rohac
Supported by Norway grants under the No. NF-CZ07-ICP-3-2082015 and
the program CZ07 - Scholarship Programme and Bilateral Scholarship Programme
7/23
Mini-navigation system
is a 10 DoF navigation system consisting of 3x gyros, 3x
accelerometers, 3x magnetometers, and absolute pressure sensor.
The system consists of MPU9150 inertial measurement unit, MS5611
pressure sensor, and GPS uBlox MAX M8W receiver. All data are fused
via Kalman filtering to provide a navigation solution in form of
position, velocity, and attitude. Output data are provided via RS232
and/or CAN with CANaerospace. protocol implemented.
Parameters
1x MS5611
Measurement range:
(10-1200) mbar
Resolution:
0.065 down to 0.012 mbar
Accuracy (25°C, 750mbar): ±1.5 mbar  10 cm
Response time:
(0.5-8.22) ms
MPU9150 unit
Gyros, accelerometers:
Measurement range:
programmable
Resolution:
down to 0.008 deg/s, 0.06 mg
Initial bias offset:
± 20 deg/s, ± 80(150) mg
Noise density (at 10Hz): 0.005 deg/s/√Hz, 0.4 mg/√Hz
Magnetometer:
Measurement range:
± 1200 µT
Sensitivity:
0.3 µT/LSB
8/23
Navigation system for harsh environment applications
uses tactical-grade gyros CRG20 and a multi-axial framework IMU unit
DMU10, both from Silicon Sensing manufacturer. The system is aided by
GPS receiver whose data are fused with the inertial ones via Kalman
filtering. The system provides at its output data about position, velocity,
attitude. Output data are provided via RS422, RS232, and/or CAN with
CANaerospace protocol implemented.
Parameters
1x CRG20 gyro
Measurement range:
Resolution:
In-Run bias stability:
Angular random walk:
g-sensitivity:
DMU10 unit
Measurement range:
In-Run bias stability:
A/V random walk:
Noise in BW=100 Hz:
g-sensitivity:
±300 deg/s
0.031 deg/s
≤ 10 deg/h
≤ 1 deg/h
0.1 deg/s/g
±300 deg/s, ±10g
≤ 15 deg/h, 0.05mg
≤ 0.4 deg/h, 0.05 m/s/h
0.1 deg/s, 1 mg
0.003 deg/s rms /g
9/23
Tactical grade Inertial navigation system
consists of only inertial sensors, such as fiber optic gyroscopes DSP-3100
(KVH) and quartz accelerometers INN-204 (Innalabs). The systems is
controlled by STM32F7xxx microcontroller that synchronizes the
readings, pools data, solves the navigation equations as well as fuses
data via Extended Kalman Filtering. Accelerometers have an analog
output in form of current and thus it is converted via an AD converter
ADS1282 board belonging to each accelerometer. All data are provided
with a sampling rate 1 kHz. Estimates of position, velocity, and attitude
are then at 100 Hz.
Parameters
Gyros:
3x 1-axis DSP 3100
Measurement range:
Bias offset:
In-Run bias stability:
Angular random walk:
Bandwidth:
Accelerometers:
3x 1-axis INN-204
Measurement range:
Bias:
Bias stability (2 hours):
Scale factor:
Resolution:
Bandwidth:
Input voltage:
± 375 deg/s
± 20 deg/h
 1 deg/h
0.0667 deg/h
440 Hz
±30 g
 10 mg
 60 µg
(1.23 up to 1.52) mA/g
 5 µg
800 Hz
± (12 up to 18) V
10/23
AVAR analysis - Allan deviation plots
11/23
IMU/GNSS loosely-coupled int. scheme – 12-state model
GYR bias
LP filtering
w
(w – b)
-
3x GYR
Control
vector u
3x ACC
LP filtering
Centripetal
force
Gravity
SF
SF
GYR bias
GPS
measurements
GPS data
validation
Position
Meas
vector y
Velocity in BF
EKF
Body
into
NED
Position in NED
Attitude
Note: SF is a Specific Force, LP is a Low-Pass, BF – Body frame, NED is a North-East-Down frame
GYR – Gyro, ACC – Accelerometer, EKF – Extended Kalman Filter
𝑓 𝒙, 𝒖 =
𝑪𝑛𝑏 𝒗𝑏
𝒂𝑏 + 𝒗𝑏 × 𝝎𝑏 − 𝒃𝜔 − 𝑪𝑏𝑛 𝒈𝑛
1 sin 𝜙 tan 𝜃 cos 𝜙 tan 𝜃
0
cos 𝜙
− sin 𝜙
𝝎𝑏 − 𝒃𝜔
0 sin 𝜙 sec 𝜃 cos 𝜙 sec 𝜃
𝒃𝜔
ℎ 𝒙 = 𝒑𝑛
12/23
Enhanced IMU/GNSS/pressure sensor
13/23
Enhanced IMU/GNSS/pressure sensor
Position
Altitude profile
Altitude (m)
Position North (m)
GPS off
Direction
Altitude estimation with GPS off
Airport
Profile
Max. error in vertical channel
Without barometer
19.6 m
With barometer
2.7
RMSE
Without barometer
8.9 m
With barometer
1.0 m
Time (s)
Parameters of
the rectangle: 8 x 4 km
Flown distance: 22 km
Average speed: 165 km/hr
When GPS off (30 sec.):
Flown distance: 1.4 km
Error in hor. plane: 96 m
Altitude (m)
Position East (m)
Ref. altitude
Without barometer
With barometer
Time (s)
14/23
Enhanced IMU/GNSS loosely-coupled int. scheme
cascaded 2 stage EKF
Euler’s angle
Pre-processing
preserving the
dynamics
3x GYR
Attitude estimation
EKF 1
SF*
Adaptive preprocessing with
vibration suppression
3x ACC
-
Dynamic
Detection
Azimuth
Azimuth
estimation
from GPS
velocity
GYR bias
ACC bias
Centripetal force
Velocity in Body frame
Position and
velocity estimation
EKF 2
Position & Velocity
in NED
Position & velocity from GPS
GPS
measurements
GPS data
validation
Velocity from GPS
Note: SF* is a specific force when no dynamics is detected and is used to aid the attitude estimation
GYR – Gyro, ACC - Accelerometer
15/23
Enhanced IMU/GNSS loosely-coupled int. scheme – EKF1
Input: ARS
Output: Euler angles, ARS bias
Measurements: Accelerometer (ACC), Azimuth/heading (𝜓𝐺𝑃𝑆 ) from GPS velocity
 And the ARS bias is fed back to the ARS input.
 One of the crucial part in the EKF1 is the dynamic detection. The ACC data is only used as measurement whenever
there is not dynamics in the vehicles motion is detected.
Azimuth from the GPS velocity 𝜓𝐺𝑃𝑆 = 𝑎𝑡𝑎𝑛2 𝑉𝐺𝑃𝑆 𝐸𝑎𝑠𝑡 , 𝑉𝐺𝑃𝑆 𝑁𝑜𝑟𝑡ℎ .
Azimuth aiding from the GPS velocity is only used when 𝑛𝑜𝑟𝑚𝑉𝑒𝑙𝐺𝑃𝑆 =
𝑉𝐺𝑃𝑆 2𝑁𝑜𝑟𝑡ℎ + 𝑉𝐺𝑃𝑆 2𝐸𝑎𝑠𝑡 + 𝑉𝐺𝑃𝑆 2𝐷𝑜𝑤𝑛 > 5 𝑚/𝑠
For the dynamic detection 3 needed parameters are:
The norm of the ACC data compensated from gravity 𝐴𝐶𝐶𝑛𝑜𝑟𝑚 =
The norm of the ARS data 𝐴𝑅𝑆𝑛𝑜𝑟𝑚 =
𝐴𝑐𝑐𝑥2 + 𝐴𝑐𝑐𝑦2 + 𝐴𝑐𝑐𝑧2 .
(𝐴𝑅𝑆𝑥 − 𝐴𝑅𝑆𝑏𝑖𝑎𝑠𝑥 )2 +(𝐴𝑅𝑆𝑦 − 𝐴𝑅𝑆𝑏𝑖𝑎𝑠𝑦 )2 +(𝐴𝑅𝑆𝑧 − 𝐴𝑅𝑆𝑏𝑖𝑎𝑠𝑧 )2 .
The rate of change of azimuth/heading 𝜓 =
𝐴𝑅𝑆𝑦 −𝐴𝑅𝑆𝑏𝑖𝑎𝑠𝑦 sin 𝜙
cos 𝜃
+
𝐴𝑅𝑆𝑧 −𝐴𝑅𝑆𝑏𝑖𝑎𝑠𝑧 cos 𝜙
cos 𝜃
.
16/23
Enhanced IMU/GNSS loosely-coupled int. scheme – EKF2
Inputs: Euler angles in the form of Direction cosine matrix, ACC data compensated for centripetal acceleration
Output: Position in NED frame, Velocity in body frame, ACC bias
Measurements: Position from GPS in NED, Velocity_down from GPS
 The ACC bias estimated from EKF2 is fed back to EKF1 in the case where ACC data is used as measurement.
GPS based position validation
A GPS position is predicted based on the 2 second data history of GPS positions using quadratic polynomial fitting via
root mean square error (RMSE) minimization.
Error is calculated between the latest GPS position and the predicted GPS position
𝑒𝑟𝑟𝑜𝑟𝑔𝑝𝑠
= 𝑙𝑎𝑠𝑡𝑒𝑠𝑡𝐺𝑃𝑆𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 − 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑𝐺𝑃𝑆𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
If the magnitude of the error is greater than the threshold value, then the GPS data is discarded.
𝑒𝑟𝑟𝑜𝑟𝑔𝑝𝑠
𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
> 𝑡ℎ𝑒𝑟𝑠ℎ𝑜𝑙𝑑𝑔𝑝𝑠𝑒𝑟𝑟𝑜𝑟 ; 𝑑𝑠𝑐𝑟𝑎𝑑 𝐺𝑃𝑆 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛.
17/23
Enhanced IMU/GNSS loosely-coupled int. scheme
𝑝
- 21 state model
𝑝
𝑁
𝐸
𝑝𝐷
𝑣𝑁
𝑣𝐸
𝑣𝐷
𝑎𝑥
𝑎𝑦
𝑎𝑧
𝜑
𝜃
𝑥= 𝜓
𝜔𝑥
𝜔𝑦
𝜔𝑧
𝑏𝑎𝑥
𝑏𝑎𝑦
𝑏𝑎𝑧
𝑏𝑔𝑥
𝑏𝑔𝑦
𝑏𝑔𝑧
𝑝𝐺𝑃𝑆 𝑁
𝑝𝐺𝑃𝑆 𝐸
𝑝𝐺𝑃𝑆 𝐷
𝑣𝐺𝑃𝑆 𝑁
𝑣𝐺𝑃𝑆 𝐸
𝑣𝐺𝑃𝑆 𝐷
𝑦 = 𝑠𝑓
𝑥
𝑠𝑓𝑦
𝑠𝑓𝑧
𝜔𝑥
𝜔𝑦
𝜔𝑧
𝑥𝑘+1
𝑇 × 𝑣𝑁𝐸𝐷 + 12𝑇 2 × 𝐶𝑏2𝑛 × 𝑎𝑏
𝑇 × 𝐶𝑏2𝑛 × 𝑎𝑏
− 𝑇 𝜏𝑎𝑎𝑐 × 𝑎𝑏
1 𝑠𝑖𝑛𝜑 × 𝑐𝑜𝑠𝜃 𝑐𝑜𝑠𝜑 × 𝑐𝑜𝑠𝜃
= 𝑥𝑘 + 𝑇 × 0
𝑐𝑜𝑠𝜑
−𝑠𝑖𝑛𝜑
× 𝜔𝑏
0 𝑠𝑖𝑛𝜑 𝑐𝑜𝑠𝜃
𝑐𝑜𝑠𝜑 𝑐𝑜𝑠𝜃
− 𝑇 𝜏𝑔𝑦𝑟 × 𝜔𝑏
0
0
𝑝𝑁𝐸𝐷
𝑣𝑁𝐸𝐷
𝑧𝑘 = 𝑎 + 𝑏 + 𝐶𝑛2𝑏 × 0 0
𝑏
𝑎
𝜔𝑏 + 𝑏𝑔
1
𝑇
18/23
Enhanced IMU/GNSS loosely-coupled int. scheme - 21 state model
Position
4
2
x 10
N-est
GPS
0
-2
0
100
200
300
400
500
600
700
800
900
1000
4
2
x 10
E-est
GPS
0
-2
0
100
200
300
400
500
600
700
800
900
1000 -1200
200
D-est
GPS
0
-200
0
100
200
300
400
500
600
700
800
900
N-est
GPS
-1400
-1600
-1800
180
185
190
195
200
1000
Time (s)
E-est
GPS
-1000
-1200
178
180
182
184
186
188
190
192
194
196
198
4
2
D-est
GPS
0
175
180
185
190
195
200
205
19/23
Enhanced IMU/GNSS loosely-coupled int. scheme - 21 state model
Velocity
20
EKF velN
vN gps
0
-20
-40
0
200
400
600
800
-16
-18
-20
-22
1000
EKF velN
vN gps
185
190
195
200
205
210
20
EKF velE
vE gps
0
-20
-40
0
-16
EKF velE
vE gps
-18
-20
200
400
600
800
1000
2
EKF velD
vD gps
0
175
180
185
190
195
200
205
0
EKF velD
vD gps
-2
200
400
Time (s)
600
800
1000
210
1
-1
-2
-4
0
-14
175
180
185
190
195
200
20/23
Enhanced IMU/GNSS loosely-coupled int. scheme - 21 state model
ACC bias
0.05
BiasACCx
0
-0.05
0
100
200
300
400
500
600
700
800
900
1000
0.05
BiasACCy
0
-0.05
0
100
200
300
400
500
600
700
800
900
1000
-3
4
x 10
BiasACCz
2
0
0
100
200
300
400
500
600
700
800
900
1000
Time (s)
21/23
Enhanced IMU/GNSS loosely-coupled int. scheme - 21 state model
GYRO bias
0.05
BiasARSx
0
-0.05
0
100
200
300
400
500
600
700
800
900
1000
-0.1
BiasARSy
-0.15
0
100
200
300
400
500
600
700
800
900
1000
0.03
0.02
BiasARSz
0.01
0
100
200
300
400
500
Time (s)
600
700
800
900
1000
22/23
Conclusion




the most valuable estimates are biases of the inertial sensors
incorporation of the magnetometer is problematic due to hard and soft-iron distortion
in-flight calibration of IMU alignment and hard and soft-iron effect are recommended
without GPS available still it is hard to keep accuracy of the navigation solution in reasonable bounds
Thank you for your attention!
Jan Roháč
CTU in Prague, Faculty of Electrical Engineering
Department of Measurement
email: jan.rohac@fel.cvut.cz
23/23
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