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KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association
Institute of Systems Optimimization
Integrated Navigation Systems - Fusing GNSS with Inertial Sensors -
Prof. Dr.-Ing. habil. Gert F. Trommer
2 Institute of Systems Optimization 2013
Overview
• Basics of Global Navigation Satellite Systems (GNSS)
• Basics of Inertial Navigation Systems (INS)
• GNSS/INS Data Fusion
• Loosely Coupled GNSS/INS Integration
• Tightly Coupled GNSS/INS Integration
• Tightly Coupled GNSS/INS Smoother
• Deeply Coupled GNSS/INS Integration
• Platform Model Aided Navigation System
• Inertial Aided GNSS Compass
3 Institute of Systems Optimization 2013
Basics of Global Navigation Satellite Systems (GNSS)
2 2 2 ( ) ( ) ( ) S S U S U S U Uc T X X Y Y Z Z c t
( , , )S S SX Y Z
( , , )U U UX Y Z
S Uc T c t
Measured Time Delay
Satellite/Receiver-Coordinates Receiver-Clock Error
Properties of single GNSS receiver:
• Position coordinates
• Velocity vector
• No attitude Information
• Dependant of at visibility of least
4 GNSS satellites
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Ringlaser Gyro (RLG)
Fiber Optic Gyro (FOG)
Capacitive Acceleromer
Vibrating Beam
Accelerometer
Basics of Inertial Navigation Systems (INS)
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nn en
dn
n-frame
i-frame
xb
yb zb
b-frame
Coordinate Systems
• Inertial Frame: reference to accelerometer and rotation rate measusements
• Body Frame: reference to mounting of accelerometers and gyroscopes
• Navigation Frame: north, east, down relative to earth surface
6 Institute of Systems Optimization 2013
Inertial Measurement Unit (IMU)
• 3 orthogonal rotation sensors
• 3 orthogonal accelerometers
+
Strapdown Algorithm (SDA)
• Tranformation of accelerometer data
from body frame into navigation frame
by gyroscope measurement data
• Integration of accelerometer data
=
Inertial Navigation System (INS)
• position coordinates
• velocity vector
• attitude angles
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t t '
ges
0 0
0
0
s = a (t'') dt'' dt' time = 6 minutes
= s (initial position error)
+ ( v ) t (initial velocity error) 0
2
3
v = 1 km / h s 100 m
1 + ( a) t (bias accelerometer) a = 1 mg s 650 m
2
1 + g ( ) t (bias gyroscope)
6
2
= 1°/h s 380 m
1 + g ( ) t (initial alignment errror) = 1 mrad s 650 m
2
For a straight flight and for short time periods
the accumulated position error is given by:
INS Error Estimation
Positio
n E
rror
8 Institute of Systems Optimization 2013
Inertial Navigation
• Measuremt of rotation rate
and accelearation
• Calculation of position,
velocity vector and attitude
• Inherently autonomous
• Updaterate typically 1 ms
• Short term stability
GNSS
• Measurement of pseudoranges
and range rates to satellites
• Calculation of position and
velocity vector
• Dependant from satellite signals
• Updaterate 0.1 -1 s
• Long term stability
Integration with Fusion
Filter
• Position, velocity and attitude
• Long term stability
• High update rate
GNSS/INS Data Fusion
9 Institute of Systems Optimization 2013
estimated
position
true
position
GNSS position measurement
x
Correction of position, velocity and accelerometer bias, aided by GNSS position
measurement:
• corrected position = weighted mean between estimation and measurement
• increase of estimated velocity
• increase of measured accelerometer data by adjustment of estimated
accelerometer bias
corrected
position estimation
Example: correction of strapdown result by position aiding
m
2
0 0
1-dim measurement of acceleration a a a SDA estimated position s + s
1Cause of position error : s = s + ( v ) t + ( a) t
2
ma
10 Institute of Systems Optimization 2013
-1- T - T
k k k k k k
+ - -
k k k k k k
+ -
k k k k
K = P H H P H + R
x = x - K H x - y
P = I - K H P
Principle of Data Fusion by Kalman Filter
Prädiktion:
Estimation:
- +
k 1 k k k k
- + T
k 1 k k k k
x = x + B u
P = P + Q
11 Institute of Systems Optimization 2013
Position Velocity Attitude
GNSS
IMU Strapdown Algorithm
(SDA)
Kalman
Filter
SDA
Corrections (position, velocity
Bias)
Loosely - Coupled GPS/INS Integration
estimated position
and velocity vector
measured position
and velocity vector
12 Institute of Systems Optimization 2013
Simulation: INS Position Error
Growth of Position Errors at GPS Loss
Time / s
Po
siti
on
serr
or
/ m
Tactical Grade IMU
Gyro: 1 °/h
Accelerometer: 1 mg
13 Institute of Systems Optimization 2013
Position Velocity Attitude
GNSS
IMU Strapdown Algorithm
(SDA)
Kalman
Filter
Pseudorange Prädiction
SDA
Corrections (position, velocity
Bias)
Tightly - Coupled GPS/INS Integration
präd k= h (x )
mess
Difference of position
estimation und calculated
satellite position
Satellite
Ephemerides
14 Institute of Systems Optimization 2013
Simulation Loosely vs. Tightly Coupled GNSS/INS
Position Error (m)
Time (s)
3 Sat. 2 Sat. 1 Sat.
10
20
30
40
50
60
70
80
200 400 600 800 1000 1200 0
Tightly
Loosely
90
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Position Error (m)
Time (s)
200
400
600
800
1000
200 400 600 800 1000 1200 0
1 Sat. Tightly
Loosely
1200
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Test Drives
• Real sensor data provided by:
–
–
• Access to onboard sensors (BMW only)
• Independent GPS/INS high accuracy
reference component (RT3000, ITE gin2)
• Location of drives:
– Karlsruhe
– Munich
Navigation-
Filter
Analysis
C++
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Tightly
Loosely
49.008
49.012
49.016
49.020
49.024
Breite (°)
8.395 8.400 8.405 8.410 8.415 8.420
Länge (°)
Zeit (s)
Satelliten
B
A
B
A
Experimental Results: Loosely vs. Tightly
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-500 0 500 1000
-1000
-500
0
500
1000
East [m]
No
rth
[m
]
Bridging of von GPS Loss
by means of Fixed Interval Smoother
• Smoother processes measurement data
forward and backward in time
optimal bridging of GPS Loss
• Tightly coupled processing of DGPS-
pseudoranges and carrierphases
• Resolving of carrier phase ambiguities
Real Time Solution
Smoother Solution
Karte
: © L
andesverm
essungsam
t Ba
-Wü ©
Magic
Maps G
mbH
Tightly Coupled GNSS/INS Smoother
Uncertainty
Time Known Position
at t1
Know Positon at
t2
19 Institute of Systems Optimization 2013
Tightly Coupled Smoother
position, velocity, attitude, biases, scale factors
KF /
smoother ambiguities
state vars.,
covariance
matrices,
IMU data
common
mode errors
rot. rate,
acc.
pseudoranges,
carrier phases,
doppler
IMU GNSS base GNSS
smoother fwd./rev.
-
• Data can be
processed forward
and reverse
• Resolved
ambiguities are
logged an re-used
• At least two runs are
required to resolve
most of the
ambiguities
• After each KF run a
smoother run can
be involved
20 Institute of Systems Optimization 2013
Field Test
Start
Karlsruhe
Equipment
Ashtech Z-FX (rover)
Trimble 4000 SSi (base)
Litef uFors 6, Litef B290
Field test
Lasts 1h 18min
Urban areas, highways, hills, forests
Max base line separation: approx. 12km
Equipment Overview
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Results: Bridging Outages I
3 min GPS outage
due to trees
Source: GoogleEarth
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Results: Bridging Outages II
Bird’s eye view: 3 min GPS outage
Source: Landesvermessungsamt Baden-Württemberg
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Deeply Coupled GNSS/INS Integration
- Simultaneous Navigation and Tracking -
Research Topic
GNSS Receiver Design with Integrated
Inertialsensors
Optimization of GNSS Signal
Tracking
Objectives
Robust navigation and robust signal
tracking at high dynamics and low
C/N0, eg. during jamming
Consideration of characteristic
properties of carrier frequency
measurement
Reduction of computation load by low
measurement update rates
Deep Integration Navigation Filter
and Correlator Control
GNSS
RF-Frontend/
Correlatorchip
IMU-Data
Quelle: http://www.dancewithshadows.com/aviation/wp-content/
uploads/2009/05/boeing-x-45-uav.jpg
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Deeply Coupled GNSS/INS - Overview
GNSS IMU
Datafusion
• GNSS/INS Integration
Complete Navigation Solution
GNSS receiver is sensitive to signal
losses, signal interferences (jamming)
and trajectory dynamics
Navigation Solution
Increased Robustness
Aiding of GNSS-Reception by IMU
25 Institute of Systems Optimization 2013
Deeply Coupled GNSS/INS Integration
SDA
Kalman
New: Aiding by IMU
• Receiver tracks satellite signals
using navigation solution
• Stabilization concerning:
Jamming, Acceleration, Signal
loss
Standard approach:
• Reciever tracks each satellite
individually
• No further tracking if satellite
signal is blocked
IMU
GPS
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Kanal
NCOs
IMU SDA
Navigation-
filter
Channel
NCOs
DLL-Discr.
FLL-Discr.
Code-
Control
Satellite
Orbits Advantages
Aiding at low C/N by IMU
Aiding at high trajectory dynamics
No re-acquisition after loss of GNSS signal necessary
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Hardware Test with Space Segment Simulator
• Realtime System Test
• Scenario-Simulation
– GPS Signal at Antenna
Input
– Rotationrate & Acceleration
• Variation
– Trajectory Dynamics
– Signal Strenght
– Antenna Pattern
• Reproducibility
– GPS Receiving Conditions
– IMU Errors
GPS Space
Segment
Simulator
Simulated Trajectory
Navigation System
- GPS Hardware
- Realtime OS
- GPS Software
- GPS/INS Integration
IMU-
Simulation
(Data)
Position Result Log-Data
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Stabilizes signal reception
during jamming
Jamming
Jamming-Resistance
Good Recpetion
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Stabilizes satellite reception
during acceleration
Stability during dynamic flight
1) 1)
2)
2)
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Deeply Coupled GPS/INS Integration for Pedestrian Navigation
• Functionality
– Aiding of GPS signal tracking by means of
coupling with torso step detection system
Deeply Coupled System with SDR-GPS-Receiver
HF Front-End: SiGe4120L
31 Institute of Systems Optimization 2013
• Step length and direction provided by torso subsystem
• GPS Integration by Stochastic Cloning Kalmanfilter
• Seamless navigation even when crossing through buildings
Integration of “step-coupling” into signal tracking
Prediction
GPS
Step estimation
Starting
point
32 Institute of Systems Optimization 2013
Platform Model Aided Navigation
Institute of Flight System Dynamics
(Technical University München)
Institute of Systems Optimization
(Karlsruhe Institute of Technology)
Institute of Aerospace Systems
(Technical University Braunschweig)
Sponsored by
Development of innovative non-linear
data fusion filters
Aiding navigation by means of dynamic
vehicle models
Vehicle model based prefiltering of
sensor data
Goals
Improvement of estimation accuracy
for position and attitude in GPS flights
Limited growth of estimation errors
during GPS outages
Application to fixed wing aircrafts and
rotorcrafts
Methods
33 Institute of Systems Optimization 2013
Mutual aiding of INS/VDM
Accelerometer bias
estimation error
Growth of velocity
estimation error
Growth of airspeed
estimation error
Growth of
VDM aerodynamic
forces error
Comparison of
IMU + VDM
output
Correction
of velocity!
Correction
of bias!
• Model aided navigation can
bound velocity errors
• Estimation of IMU biases and
model parameters/wind
Model aided navigation could
reduce error growth
significantly
34 Institute of Systems Optimization 2013
Navigation filter structure
?
INS
Kalman filter
(error state)
Aiding sensors
IMU
δpINS, δvINS, δφINS, δba, δbw
a, ω
pINS, vINS, φINS
Vehicle
Dynamics Model
(VDM)
Control inputs u
pVDM, vVDM, φVDM
Aims
Mutual aiding of INS and VDM
Support of aiding sensors for VDM
35 Institute of Systems Optimization 2013
INS
Kalman filter
(error state)
Aiding sensors
IMU
δpINS, δvINS, δφINS, δba, δbw
a, ω
pINS, vINS, φINS
Vehicle
Dynamics Model
(VDM)
Control inputs u
pVDM, vVDM, φVDM
+
- Pseudo
measurement
δpVDM, δvVDM, δφVDM, δcVDM
The mechanical dynamic model of the vehicle estimates the movements of the
body according to the control inputs for the fins or the motors. These estimated
body motions are fused with the estimated motions of the INS within a central
Kalman filter
36 Institute of Systems Optimization 2013
Simulation Result for a Quadrocopter with MEMS Inertial
Sensors
GNSS denied after 60 s
37 Institute of Systems Optimization 2013
Inertial Attitude Determination
continuous availability of attitude
solution
poorly observable yaw angles for
low dynamics
Attitude Determination System
• accurate heading and elevation
information
• permanent availability
• high integrity
Inertial aided GNSS Compass
GNSS Attitude Determination
attitude solution without offset
GNSS dropouts
time consuming ambiguity
resolution
Fusion of both systems to create a multi-sensor attitude
determination system
38 Institute of Systems Optimization 2013
• processing of carrier phase
measurement
• ambiguity resolution uses double
differenced GNSS signals:
extraction of attitude angles from
estimated base vector:
AB,east
AB,north
arctanr
r
AB,down
AB
arcsin( )r
r
ij,AB ij,
T T
i AB AB
1je e r N
Principle
position
accuracy
angle
error
A
B
i
j
ie
je
39 Institute of Systems Optimization 2013
• Kalman Filter aiding:
• accelerometer measurements
for roll and pitch angles
• magnetometer measurements
for yaw angles
• estimation of angle errors and
gyroscope biases in an error state
Kalman Filter
Inertial Attitude Filter
• propagation of attitude angles in
a strapdown algorithm
IMU
GYRO
ACC
Strapdown
Algorithm
b
MAG bm
ba
Error State
Kalman
Filter
ˆ
ˆb
ˆ ˆ ˆ, ,
40 Institute of Systems Optimization 2013
Multi-sensor attitude determination system
double
differenced
carrier phase
Attitude-Filter Error-State
Kalman Filter
attitude
error sensor
biases
magnetic
field
Pre-
processing
Extended
LAMBDA
GPS
Rec1
GPS
Rec2
carrier
phase BaseVec-
Filter Extended KF
arctan()
acceleration,
angular rate
IMU Strapdown
base
vector
integer
ambiguities
yaw and pitch
angle
yaw and
pitch angle
floating
ambiguities,
covariances
MAG
Inertial attitude System GNSS attitude system
baseline length
41 Institute of Systems Optimization 2013
Test Equipment
• GNSS System:
– single-frequency Magellan AC12 GNSS
receivers
– single-frequency u-blox ANN-MS-1-00
patch antennas
– baseline length: 20 cm
• Inertial Attitude System
– ADIS 16255 gyroscopes
– SCA 3000 D01 accelerometers
– HMC 5843 3-axes magnetic field sensor
42 Institute of Systems Optimization 2013
Con-
straints
Mean
TTFF
#
Fixes
# wrong
fixes
- 229 s 700 432
39.6%
1.4 s 900 0
48.1 s 900 3
0.3%
1.02 s 900 0
Time to First Fix
0 100 200 300 400 500 600 700 800 900 10000
500
1000
start time [s]
TT
FF
[s]
no constraints
0 100 200 300 400 500 600 700 800 900 10000
200
400
start time [s]
TT
FF
[s]
base length constraints
0 100 200 300 400 500 600 700 800 900 10000
5
10
start time [s]
TT
FF
[s]
base length and pitch constraints
0 100 200 300 400 500 600 700 800 9000
5
start time [s]
TT
FF
[s]
base length, pitch and yaw constraints
5cml
15
30
5cml
15
5cml
43 Institute of Systems Optimization 2013
Performance
0 100 200 300 400 500 600 700 800 9004
6
8
10
ya
w [
°]
time [s]
0 100 200 300 400 500 600 700 800 900-10
0
10
20
pitch
[°]
time [s]
0 100 200 300 400 500 600 700 800 9000.18
0.19
0.2
0.21
ba
se
line
le
ng
th [
m]
time [s]
Highly accurate
yaw angle estimation
GNSS
Solution Mean
Standard
deviation
Yaw 6.5° 1.02°
Pitch -0.05 3.6°
Baseline
length 19.46 cm 1.55 cm
44 Institute of Systems Optimization 2013
Thank you for
your attention!