Sensing and Perception:
Localization and positioning
by
Isaac Skog
Outline
• Basic information sources and performance
measurements.
• Motion and positioning sensors.
• Positioning and motion tracking technologies.
• Information fusion techniques.
• Motion models and motion constraints.
• Cooperative positioning
Basic information sources
• Any measurable quantity that change with a
change in location or motion is a potential
source of navigation (positioning) information.
Exteroceptive
sensors
Proprioceptive
sensors
Motion models
&
constraints
Output:
Information
fusion
Position
Velocity
Attitude
Acceleration
Angular rate
+
Quality indicator(s)
Performance measures
Accuracy
Integrity
Availability
The degree of
conformity of
information concerning
position, velocity, etc.,
provided by the system
relative to actual values.
A measure of the trust
that can be put in the
information from the
navigation system, i.e.,
the likelihood of
undetected failures in
the specified accuracy of
the system.
A measure of the
percentage of the
intended coverage area
in which the navigation
system works.
In-Car Positioning and Navigation Technologies—A Survey, I. Skog and P. Händel, IEEE Transactions on Intelligent Transportation
Systems , 2009
Continuity of
service
The system’s probability
of continuously
providing information
without nonscheduled
interruptions during the
intended working
period.
SENSORS
Sensors
Any measurable quantity that change with a change in
location or motion is a potential source of navigation
(positioning) information.
• Electromagnetic radiation sensors
 Radio receivers, cameras, laser scanners, magnetic field sensors,
etc.
• Inertial sensors
 Accelerometers and gyroscopes
• Environmental & contact sensors
 Pressure, air flow, temperature sensors, wheel encoders, etc.
Extracted information can be used in multiple ways!
(Physical laws or feature mapping.)
Exteroceptive vs. proprioceptive
Exteroceptive sensors
GPS
Ultra sonic
Camera
Proprioceptive sensors
Accelerometer
Wheel encoder
• Measures values related to the
surrounding of the navigation platform,
e.g., radio signals
• Measure values internal to the
navigation platform, e.g., wheel
encoders.
• Generally provides absolute
information directly related to the
position and orientation of the system.
• Only provides information about the
motion and no absolute position and
orientation information.
• Requires dedicated infrastructure or
prior knowledge about the
surrounding.
• Requires no dedicated infrastructure
or prior knowledge about the
surrounding.
• Can be disturbed, jammed, spoofed,
etc.
• Can NOT be disturbed!
The frequency response of the
navigation process
Sensor
Position
ing
system
Sensor
Position
Orientation
Velocity
Acceleration
Angular rate
….
Exteroceptive sensor
Proprioceptive sensor
Frequency response of the sensor data to navigation state transformation
Motion dynamics to position
Position to motion dynamics
|H(f)|
|H(f)|
Low frequency
error amplification
f
High frequency
error amplification
f
The sensorization of the world
GNSS (GPS) receivers
1977
2015
Inertial sensors (accelerometer & gyroscopes)
2015
1960
Source: GNSS Market Report, Issue 4, copyright © European GNSS Agency, 2015
North
East
Positioning
techniques
Basic positioning techniques
Geometry based
positioning methods
Feature based
positioning methods
Dead reckoning
based positioning
methods
Trilateration (ToA)
Finger-printing
Dead reckoning
Multilateration (TDoA)
Terrain navigation
Inertial navigation
Triangulation (AoA)
Exteroceptive sensors
Proprioceptive sensors
Integrated navigation system
Feature based positioning
• Most basic form of positioning.
• Correlation of observed features (measured quantities) to an map
with a prior known locations of the features.
• Extension: Simultaneous localization and mapping
Terrain navigation
Signal strength finger printing
Indoor Localization Using Multi-Frequency RSS, M. A. Skoglund, G. Hendeby, J. Nygards, J. Rantakokko, G. Eriksson, Proc. IEEE/ION Position
Location and Navigation Symposium, 2016
Terrain navigation for underwater vehicles using the correlator method, I. Nygren, and M. Jansson, IEEE Journal of Oceanic Engineering, 2004
Ex: Magnetic fingerprinting
Simultaneous localization and mapping for pedestrians using only foot-mounted inertial sensors, P. Robertson, M. Angermann,
and B. Krach, Proc. of the 11th international conference on Ubiquitous computing, 2009
Accuracy of feature based
positioning
• The positioning accuracy
depends on several factors
• Accuracy of map
• Accuracy of the feature
measurements
• Uniqueness of the observed features
• The spatial density of the features
• The travel path
• The posterior Cramér-Rao bound
can be used to lower bound the
achievable position accuracy for
a given scenario, but also to plan
the path that optimize the
positioning accuracy.
Particle filters for positioning, navigation, and tracking, F. Gustafsson, et al, IEEE Transactions on Signal Processing, 2002
Posterior Cramer-Rao bounds for discrete-time nonlinear filtering, P. Tichavsky, C. H. Muravchik and A. Nehorai,
IEEE Transactions on Signal Processing, 1998
Geometry based positioning
• Range or angle measurements to objects with known positions can, using basic
geometry, be used for positioning.
• Range measurements can be obtained from e.g., time-of-flight or signal strength
measurements.
• Angular measurements can be obtained through directive antennas (antenna
arrays), rotating laser scanners, etc.
• Generally requires line-of-sight measurements to the objects
Trilateration
Triangulation
Accuracy of geometry based pos.
The accuracy depends on:
• The geometry and number of the objects (sources).
• The accuracy of the range or angle measurements, which depends on the
system noise, multi-path errors, clock jitter, etc.
Position uncertainty region
Position uncertainty region
Range estimate
Range estimate
Range estimate
Range uncertainty
Range estimate
Accuracy of geometry based pos.
Range uncertainty
Position uncertainty region
Range estimate
Range estimate
Range uncertainty
Depends only on direction to the sources
Ex: ToA – GNSS-receivers
• Global Navigation Satellite Systems (GNSS)
•
ToA radio positioning systems
•
Multiple systems: GPS, GLONASS, Galileo, Compass, etc.
•
Today 60 satellites, by 2030 approx. 120 satellites.
•
Accuracy:
Geometry
Ranging error
How many GNSS satellites are to many? G. Gao and P. Enge, IEEE Trans. Aerospace and Electronic Systems, Oct 2012.
Dead reckoning based positioning
Wheel
speed
sensor
Magnetic
field
sensor
Speed
R
Heading
• Integrative navigation process:
 Amplifies low frequency
measurement errors.
 Causes the position error to grow
without bound.
• Error sources:
1. Heading errors
2. Speed (distance errors)
3. Initial position and heading
errors
North
7
6
5
4
3
2
1
East
1
2
3
4
5
6
7
-2
2
0
-2
Mass
Stationary accelerometer
Mass
0
2
2
0
-2
Inertial navigation –
accelerometer
Mass
Accelerometer accelerating to the right,
and with the sensitivity axis orthogonal to
the gravity field.
Accelerometer stationary on the earth
and with the sensitivity axis aligned with
the gravity field.
The output of an accelerometer is called specific force and is the difference
between the inertial acceleration and the gravity acceleration.
Inertial navigation – gyroscope
• Measures angular rate with respect to inertial space.
• Several types of gyroscopes:
Spinning gyroscopes (Conversion of momentum)
Optical gyroscopes (Sagnac effect)
Vibratory gyroscopes (Coriolis force)
Nuclear Magnetic Resonance Gyroscopes (Larmor precession frequency)
z
y
D.E. Serrano, http://ieee-sensors2013.org/sites/ieeesensors2013.org/files/Serrano_Slides_Gyros2.pdf
x
Tuning fork gyroscope
using the Coriolis force
http://industrial.panasonic.com/ww/products/sensors/se
nsors/angular-rate-sensors
Stationary
Rotating
Tuning fork gyroscope
implemented on the
silicon of a MEMS sensor
Inertial measurement units
IMU
3 Accelerometers
3 Gyroscopes
IMU coordinate system
Platform coordinate system
Navigation coordinate system
Inertial Navigation System (INS)
Undisturbable
Environment independent
Infrastructure independent
Inertial navigation accuracy
• The positioning accuracy is mainly dependent on the gyroscope biases
(offsets).
• For systems using low-cost sensors the position error is approximately
given by
• For high-cost systems a Schuler feedback loop can be used and the
horizontal position error can be bounded; the vertical error is still
unbounded.
Information
fusion
Information fusion strategies
The objective of information fusion is to obtain more information than is present in any individual information
source by combining information from different sources. In practice, this means that by utilizing the
complementary properties of the different information sources, the information fusion tries to reduce ambiguities
in the measured information, thereby expanding the spatial and temporal coverage in which the system works and
enhancing the reliability of the system.
Fusion strategies & filter
algorithms
Sensor #1
Information
fusion
Sensor #2
Navigation state vector
Control input
Process noise
Observation noise
Particle filters for positioning, navigation, and tracking, F. Gustafsson, et al, IEEE Transactions on Signal Processing, 2002
Bayesian filtering for location estimation, V. Fox, J. Hightower, Lin Liao, D. Schulz and G. Borriello, IEEE Pervasive Computing, 2003
Direct & complimentary
Complimentary filtering
Direct
filter
Navigation
solution
Dead reckoning/INS
Navigation solution
h(x)
Complimentary
filter
+
Extroceptive
sensors
Sensor data
Stochastic motion model
Proprioceptive
sensors
Direct filtering
• Conceptually simple
•
Undisturbable sensor as backbone
• Hard to find generic motion model
that fits in a stochastic framework.
•
Error dynamics of the dead reckoning
process instead modelled.
• Difficult to handle attitude states
that are defined on a manifold
•
•
In-Car Positioning and Navigation Technologies—A Survey, I. Skog and P. Händel, IEEE Transactions on Intelligent Transportation
Systems , 2009
The Global Positioning System & Inertial Navigation, J.A. Farrell and M. Barth, McGraw-Hill, 1998.
Can often easier be fit in a stochastic
framework
Attitude errors are kept small and can be
approximated in R^3.
Centralized & decentralized
Centralized
Decentralized
• Minimal information loss and theoretical
optimal performance if given correct prior
information.
• Generally reduced computational
complexity.
• High computational complexity
• Fault detection and isolation may be tricky
• Simplified fault detection and isolation.
• Only optimal if correct estimation statistics
is propagated between the filters.
• Model complexity
• Communication complex
In-Car Positioning and Navigation Technologies—A Survey, I. Skog and P. Händel, IEEE Transactions on Intelligent Transportation
Systems , 2009
Ex: Camera aided INS
1
2
• By detecting and tracking
feature points between pictures,
displacement information can be
extracted and used to aid the
INS and reduce the error drift.
• By detecting feature points, e.g.,
QR tags, with known locations
absolute position estimates can
be obtained and used to bound
the error of the INS.
Ex: Camera aided INS (2)
IMU
Inertial
navigation
process
Navigation solution
Complimentary
filter
h(x)
+
Feature
point
extraction
Camera
• Complimentary filtering (Inertial navigation system used as backbone)
• Proprioceptive sensors: Accelerometers and gyroscopes
• Exteroceptive sensor: Camera
Camera-aided inertial navigation using epipolar points, D. Zachariah, and M. Jansson, IEEE/ION Position Location and
Navigation Symposium (PLANS), 2010
Motion
models
Motion models
• From an estimation-theoretical perspective, sensors and motion-model
information play an equivalent role in the estimation of the navigation
state.
Perfect sensor
Perfect motion model
Motion model not needed
Sensors not needed
Inertial sensor
assembly
Motion dynamics models & state
constraints
Ideally, the motion model is in-cooperated in your state-space model, but it may be hard to
combine hard constraints with a stochastic model or dead-reckoning (INS) equations.
Instead, include the motion model as a constraint on the state-vector in the filtering problem.
Filtering problem can be solved using for example:
•
•
•
Particle filter
Constraint Kalman filter theories
Pseudo observations:
Kalman filtering with state constraints: a survey of linear and nonlinear algorithms, D. Simon, IET Control Theory & Applications, 2010
Bayesian Estimation With Distance Bounds, D. Zachariah, I. Skog, M. Jansson, and P. Händel, IEEE Trans. SP, 2012
Ex: Zero-velocity aided INS (1)
Foot mounted INS
True
Estimated
Time period when
the system is
stationary, i.e., has
zero velocity.
Dead reckoning
R
h(x)
Velocity error that can be
used as an observation.
Time
Motion information
Complimentary
filter
+
0
The stationary period is
detected using a zerovelocity detector.
The periods when the system is stationary is commonly estimated using the data from
the proprioceptive sensors (accelerometers and gyroscope).
Zero-Velocity Detection—An Algorithm Evaluation, I. Skog, P. Händel, J. Nilsson, and J. Rantakokko, IEEE Trans. on Biomedical Engineering, 2010.
Evaluation of Zero-Velocity Detectors for Foot-Mounted Inertial Navigation Systems, I. Skog, J. Nilsson, and P. Händel,
IEEE International Conference on Indoor Positioning and Indoor Navigation, 2010.
Pseudo
observation
Velocity
Proprioceptive
sensors
Ex: Zero-velocity aided INS cont.
Ex: Zero-velocity aided INS cont.
INS
Step motion
+
Motion constraint
Estimated position
Foot-mounted INS for everybody - an open-source embedded implementation, J. Nilsson, I. Skog, P. Händel, and K.V.S Hari, IEEE/ION
Position Location and Navigation Symposium (PLANS), 2012
Ex: Map constraints
IMU
+
Motion model
+
Indoor PDR performance enhancement using minimal map information and particle filters, S. Beauregard, Widyawan and M. Klepal,
IEEE/ION Position Location and Navigation Symposium (PLANS), 2008
Cooperative
positioning
Basic idea
uncertainty
ellipse
North
7
Local
navigation
system
Local
navigation
system
6
5
4
Local
navigation
system
3
2
1
East
1
2
3
4
5
6
7
Special case of information fusion
Agent #1
Sensor #1
Sensor #N
Information
fusion
Agent #M
Sensor #1
Sensor #N
Practical problems:
• Limited communication recourses – what info. should be sent?
• High computational complexity – how should computations be
distributed?
• Robustness to varying network topologies – how to get stable results?
Example: First responder
positioning
Tactical Locator (TOR) system
Radio ranging units
Zero-velocity aided inertial
navigation is used to track the
relative motion of each user.
Commander in control center
Information
fusion for
cooperative
localization
Cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging, J.O. Nilsson, D. Zachariah, I. Skog, P. Händel,
EURASIP Journal on Advances in Signal Processing, 2013
Fire fighter with navigation display
TOR information fusion
Agent #1
Proprioceptive sensors +
constraints
Master filter
Zero-velocity aided INS #2
Extroceptive sensor
sensors
UWB ranging device
Agent #M
Proprioceptive sensors +
constraints
Zero-velocity aided INS #1
Zero-velocity aided INS #2
Extroceptive sensor
sensors
UWB ranging device
Joint navigation solution
Zero-velocity aided INS #1
Summary
Sensors
Information fusion
• Extroceptive sensors
• Filter algorithms
•
•
•
Absolute position & orientation
Easily disturbed
Require dedicated infrastructure or prior
information about the environment
•
• Filter structures
•
• Proprioceptive sensors
•
•
•
Depends on the structure of the state space
model and noise properties.
Only relative position information
Cannot be disturbed
Position error grows with time
•
Centralized & decentralized depending on
practical limitations and system
considerations.
Complementary filtering to handle the nature
of attitude estimates and easier state-space
modeling.
Motion models
Positioning methods
•
Feature based positioning methods
•
Geometry based positioning methods
•
Dead reckoning based positioning methods
•
State propagation model or state constraints
•
Can partially compensate for poor sensors
Cooperative positioning
•
Special case of multi-sensor positioning
constrained by practical aspects like computational
complexity and communication limitations.
Homework/Lab
GNSS positioning
GNSS aided INS
• GNSS position calculation
from pseudo range
measurements.
• Study the error growth in a
GNSS aided INS during GNSS
signal outages
• Study the effects of satellite
constellation on the obtainable
accuracy.
• Study the effects of a simple
vehicle model during GNSS
signal outages.
• Simulated data
• Study the effect of adding a
speedometer sensor.
• Real-world data
You are always welcome to mail me ([email protected] ) about the homework and lab.