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SCPNT 2015 Stanford, CA
Student Presentation 11 November 2015
Jinsil Lee* and Jiyun Lee*
KAIST*
Sam Pullen
Stanford University
Vertical Position Error Bounding for
Integrated Sensors to Support
Unmanned Aerial Vehicles (UAVs)
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UAV Applications
2
Source: CBS News, Dec. 2013 Source: New York Times, Aug. 2014
Amazon’s Delivery Drone Project Wing by Google
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UAV Operational environment
3
• Navigation sensor error
• Flight technical error (FTE)
• Path planning error
• etc
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Goal: Vertical navigation
error bound for UAV
4
• Navigation sensor error
• Flight technical error (FTE)
• Path planning error
• etc
Provide vertical navigation error bound for UAV
based on their navigation sensors and algorithm
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Outline
5
Local-Area Differential (LAD) GNSS for UAV Network Operations
• KAIST LAD-GNSS Test-bed Hardware Configuration
• UAV flight test to simulate vertical navigation error bounding
with LAD-GNSS
UAV vertical position error bounding for integrated sensors
• UAV navigation sensors and algorithms
• Error models for integrated sensors
• Simulation results using derived error models for each
sensor scenarios
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Outline
6
Local-Area Differential (LAD) GNSS for UAV Network Operations
• KAIST LAD-GNSS Test-bed Hardware Configuration
• UAV flight test to simulate vertical navigation error bounding
with LAD-GNSS
UAV vertical position error bounding for integrated sensors
• UAV navigation sensors and algorithms
• Error models for integrated sensors
• Simulation results using derived error models for each
sensor scenarios
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7
Local-Area Differential (LAD) GNSS for
UAV Network Operations
LAD-GNSS
Ground
Subsystem
Ctrl
GNSS
UAVs
Differential
Correction
• Prior work proposed LADGNSS architectures to provide
increased accuracy, safety, and reliable navigation to UAVs
[S. Pullen, et al, ION ITM 2013].
Data
Positioning accuracies
of one meter or less
within 5 to 100 km of
the controller station
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KAIST LAD-GNSS
Test-bed Hardware Configuration
8
KAIST LAD-GNSS IMT Antenna & Receivers
(Existing)
(Expanded)
73m
83m
44m 16m
70m
79m
Pseudo-User
46m
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Session B4, Paper #8 9
KAIST LAD-GNSS
Test-bed Hardware Configuration
LAD-GNSS
Ground
Subsystem
Ctrl
GNSS
Differential
Correction
Data
950 m
APM2.6 Controller
Novatel
Receiver
(ProPak-V3)
Modem
(Receive Differential
Correction)
Novatel
Antenna
Will be replaced
to Pixhawk
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UAV Flight Testing:
LAD-GNSS vs. Standalone GPS
10
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Simulated vert for UAV
using LADGNSS error model
• vert for UAV is simulated during 24 hour applying LADGNSS error model
0 5 10 15 200.4
0.5
0.6
0.7
0.8
0.9
Time (hour)
vert
ical (
m)
Simulation
Condition
Satellite
constellation
GAD-B
error model
Standard Residual
Tropospheric Error Model of
GBAS
(60m from the ground)
AAD-A
model
GBAS model
RTCA 24
Constellation
Almanac
2 2 2 2 2
_ , , , ,i pr gnd i tropo i air i iono i
2
_ ,pr gnd i 2
,tropo i 2
,air i 2
,iono i
[M Kim. et al, ION GNSS 2014]
Will be used as
LAD-GNSS measurement error uncertainty
for simulation of sensor integration scenario
0.88m
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Outline
12
Local-Area Differential (LAD) GNSS for UAV Network Operations
• KAIST LAD-GNSS Test-bed Hardware Configuration
• UAV flight test to simulate vertical navigation error bounding
with LAD-GNSS
UAV vertical position error bounding for integrated sensors
• UAV navigation sensors and algorithms
• Error models for integrated sensors
• Simulation results using derived error models for each
sensor scenarios
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Navigation for UAV
13
Sensors used for UAV navigation
• GPS
• IMU sensors
• Barometer
• Magnetometer
• True airspeed
• Range finder (range to ground)
• Optical flow sensor
(optical and inertial sensor delta angles)
Algorithms used for UAV navigation
• Inertial navigation algorithm
• Extended Kalman Filter (EKF)
• Unscented Kalman filter (UKF)
• Particle filter etc
[Based on Pixhawk sensors]
[Pixhawk]
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Pixhawk EKF algorithm
Predict
states
Predict
Covariance
Matrix
Update
states
Update
Covariance
Matrix
Prediction Fusion
IMU data Measurements
GPS, Barometer,
(Magnetometer) Gyroscope, Accelerometer
Output states: Attitude, velocity, position, IMU error bias
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EKF covariance bounding
Predict
states
Predict
Covariance
Matrix
Update
states
Update
Covariance
Matrix
Prediction Fusion
IMU data Measurements
GPS, Barometer,
(Magnetometer) Gyroscope, Accelerometer
(Linearization error)
Measurement noise covariance Process noise covariance
[Z, Xing, 2010] Output states: Attitude, velocity, position, IMU error bias
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Bounding IMU process noise
error covariance
• IMU sensor bias model
• IMU sensor bias modeling methods
– : Constant bias is continuously estimated by EKF
– : sampling noise is modeled by white Gaussian noise
– : Correlated.noise Modeled by gauss-Markov process with
standard deviation and the time constant.
1( ) ( ) ( )o wb t b b t b t
ob
( )wb t
1( )b t
11 1
1( ) ( ) bb t b t w
Overbounded using CDF distribution to conservatively bound the white
Gaussian noise
Overbounded using autocorrelation plot
[D. GEBRE-EGZIABHER et al, 2003]
[Z. Xing, 2010]
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Example of modeling IMU sensor uncertainty
- Static gyroscope output
• 100Hz gyroscope data collect for 4 hour in static condition from
Pixhawk
0 0.5 1 1.5 2 2.5 3 3.5 4-5
0
5x 10
-3 Gyro (rad/s)
X
0 0.5 1 1.5 2 2.5 3 3.5 4-10
-5
0
5x 10
-3
Y
0 0.5 1 1.5 2 2.5 3 3.5 4-4
-2
0
2x 10
-3
Z
Time (hour)
Stable 3 hour dataset
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1 1.5 2 2.5 3 3.5 4-5
0
5x 10
-3 Constant bias removed gyro output(rad/s)
X
1 1.5 2 2.5 3 3.5 4-5
0
5x 10
-3
Y
1 1.5 2 2.5 3 3.5 4-5
0
5x 10
-3
Z
Time (hour)
Example of modeling IMU sensor uncertainty
- Constant bias removal
• This constant bias term b0 is continuously estimated with an
additional states on EKF
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Example of modeling IMU sensor uncertainty
- Wide band noise (Gyroscope)
0 0.5 1 1.5 2 2.5 3 3.5
x 10-3
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Gyro bias (rad/s)
X
Y
Z
=610-4 (rad/s)
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-3000 -2000 -1000 0 1000 2000 3000-0.5
0
0.5
1
1.5
2
2.5
x 10-8
Lags (second)
Find the exponential autocorrelation plot with variance and correlation time which
overbound actual data-driven autocorrelation plot (averaged every 1 sec)
Example of modeling IMU sensor uncertainty
- Correlated noise (Gyroscope)
=1.610-4 (rad/s)
=3000s
[J. Rife, 2007 ; Z. Xing, 2010]
/2( ) corr
xR e
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0 5 10 1510
20
30
40
50
60
Time (hour)
Alti
tud
e (
m)
Barometer sensor error
21
Altitude with default Mean Sea level
reference (1013.25hPa) set by
Pixhawk
GPS altitude from Pixhawk Ublox GPS receiver
Corrected altitude with pressure
information from nearest airports [NOAA aviation weather center]
Surveyed
Position
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Barometer error bounding Drift compensation
0 0.5 1 1.5 2 2.5 31014
1014.2
1014.4
1014.6
1014.8
Pre
ssu
re (
mb
ar)
Time (hour)
0 0.5 1 1.5 2 2.5 325
30
35
40
45
Altitu
de
(m
)
Time (hour)
Corrected altitude
Output altitude with default MSL
Interpolated Mean Sea Level
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Barometer altitude error bounding
0 1 2 3 4 5 6 7 810
-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Barometer error
CD
F
=1.5m
Many approaches for barometer drift compensation
could be considered. Further studies will be conducted for our UAV test
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Simulation results using
overbounded error noise covariance
Simulation
Condition
(bounded
noise covariance)
IMU sensor (prediction) – static situation Measurement sensor (update)
Acc Gyro Stand-
alone GPS Barometer
LAD-
GNSS
w=1.5*10-2 (m/s/s)
b1=3.7 10-3 (m/s/s)
=3300s
w=610-4 (rad/s)
b1=1.610-4 (rad/s)
=3000s
7.5m [spsps2008]
1.5m
0.88m
(max over
24 hours)
* Simulation is performed by modifying the EKF filter algorithm used by Pixhawk
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
Time (minute)
Altitu
de
err
or
bo
un
d
LADGNSS
Barometer
Stand-alone GPS
error bound=Kffmdoverbounded
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Conclusion
• LADGNSS error models for UAVs has been developed,
and UAV flight tests have been performed using
differential corrections from LADGNSS test-bed at KAIST
• Both process noise and measurement noise uncertainties
of integrated sensors were estimated and overbounded
to simulate vertical position error bounds
− LADGNSS when combined with IMU sensor reduced vertical
position error bounds significantly compared to stand-alone GPS
or barometer
• In this study, we derived sensor error models under static
conditions and assumed linear state transition for state
covariance bounding
– Future work is needed: bounding non-linearities in the state
transition matrix, error modeling in dynamic scenarios and
experimental flight-test validation