Sensing and Perception: Localization and positioning. by Isaac Skog

Transcription

1 Sensing and Perception: Localization and positioning by Isaac Skog

2 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

3 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 Information fusion Output: Position Velocity Attitude Acceleration Angular rate + Quality indicator(s)

4 Performance measures Accuracy The degree of conformity of information concerning position, velocity, etc., provided by the system relative to actual values. Integrity 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. Availability A measure of the percentage of the intended coverage area in which the navigation system works. Continuity of service The system s probability of continuously providing information without nonscheduled interruptions during the intended working period. In-Car Positioning and Navigation Technologies A Survey, I. Skog and P. Händel, IEEE Transactions on Intelligent Transportation Systems, 2009

5 SENSORS

6 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.)

7 Exteroceptive vs. proprioceptive Exteroceptive sensors Proprioceptive sensors GPS Ultra sonic Camera Accelerometer Wheel encoder Measures values related to the surrounding of the navigation platform, e.g., radio signals Generally provides absolute information directly related to the position and orientation of the system. Requires dedicated infrastructure or prior knowledge about the surrounding. Can be disturbed, jammed, spoofed, etc. Measure values internal to the navigation platform, e.g., wheel encoders. Only provides information about the motion and no absolute position and orientation information. Requires no dedicated infrastructure or prior knowledge about the surrounding. Can NOT be disturbed!

8 The frequency response of the navigation process Sensor Sensor Position ing system Position Orientation Velocity Acceleration Angular rate. Exteroceptive sensor Proprioceptive sensor Frequency response of the sensor data to navigation state transformation Motion dynamics to position H(f) Position to motion dynamics H(f) Low frequency error amplification f High frequency error amplification f

9 The sensorization of the world GNSS (GPS) receivers Inertial sensors (accelerometer & gyroscopes) Source: GNSS Market Report, Issue 4, copyright European GNSS Agency, 2015

10 North East Positioning techniques

11 Basic positioning techniques Geometry based positioning methods Trilateration (ToA) Multilateration (TDoA) Triangulation (AoA) Feature based positioning methods Finger-printing Terrain navigation Dead reckoning based positioning methods Dead reckoning Inertial navigation Exteroceptive sensors Proprioceptive sensors Integrated navigation system

12 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

13 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

14 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

15 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

16 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 estimate Range uncertainty

17 Accuracy of geometry based pos. Range uncertainty Position uncertainty region Range estimate Range estimate Range uncertainty Depends only on direction to the sources

18 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.

19 Dead reckoning based positioning Wheel speed sensor Speed R North Magnetic field sensor Heading 7 6 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 East

20 Inertial navigation accelerometer Mass Mass Mass Stationary accelerometer 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.

21 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 x Tuning fork gyroscope using the Coriolis force nsors/angular-rate-sensors Stationary Rotating D.E. Serrano, Tuning fork gyroscope implemented on the silicon of a MEMS sensor

22 Inertial measurement units IMU 3 Accelerometers 3 Gyroscopes IMU coordinate system Platform coordinate system Navigation coordinate system

23 Inertial Navigation System (INS) Undisturbable Environment independent Infrastructure independent

24 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.

25 Information fusion

26 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.

27 Fusion strategies & filter algorithms Sensor #1 Sensor #2 Information fusion 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

28 Direct & complimentary Direct filtering Complimentary filtering Sensor data Stochastic motion model Direct filter Navigation solution Proprioceptive sensors Dead reckoning/ins Complimentary filter Navigation solution h(x) + Extroceptive sensors Conceptually simple Hard to find generic motion model that fits in a stochastic framework. Difficult to handle attitude states that are defined on a manifold Undisturbable sensor as backbone Error dynamics of the dead reckoning process instead modelled. Can often easier be fit in a stochastic framework Attitude errors are kept small and can be approximated in R^3. 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.

29 Centralized & decentralized Centralized Decentralized Minimal information loss and theoretical optimal performance if given correct prior information. High computational complexity Fault detection and isolation may be tricky Model complexity Communication complex Generally reduced computational complexity. Simplified fault detection and isolation. Only optimal if correct estimation statistics is propagated between the filters. In-Car Positioning and Navigation Technologies A Survey, I. Skog and P. Händel, IEEE Transactions on Intelligent Transportation Systems, 2009

30 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.

31 Ex: Camera aided INS (2) IMU Inertial navigation process Navigation solution h(x) Complimentary filter + 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

32

33 Motion models

34 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 Motion model not needed Perfect motion model Sensors not needed Inertial sensor assembly

35 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

36 Ex: Zero-velocity aided INS (1) Foot mounted INS

37 Ex: Zero-velocity aided INS cont. Velocity True Estimated Time period when the system is stationary, i.e., has zero velocity. Velocity error that can be used as an observation. Proprioceptive sensors Dead reckoning R Motion information h(x) Time Complimentary filter + 0 Pseudo observation 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, 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.

38 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

39 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

40 Cooperative positioning

41 Basic idea North uncertainty ellipse Local navigation system Local navigation system Local navigation system East

42 Special case of information fusion Agent #1 Sensor #1 Sensor #N Agent #M Sensor #1 Information fusion 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?

43 Example: First responder positioning

44 Tactical Locator (TOR) system Radio ranging units Commander in control center Zero-velocity aided inertial navigation is used to track the relative motion of each user. Information fusion for cooperative localization Fire fighter with navigation display 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

45 TOR information fusion Agent #1 Proprioceptive sensors + constraints Zero-velocity aided INS #1 Master filter Zero-velocity aided INS #2 Extroceptive sensor sensors UWB ranging device Agent #M Proprioceptive sensors + constraints Zero-velocity aided INS #1 Joint navigation solution Zero-velocity aided INS #2 Extroceptive sensor sensors UWB ranging device

46

47 Summary Sensors Extroceptive sensors Absolute position & orientation Easily disturbed Require dedicated infrastructure or prior information about the environment Proprioceptive sensors Only relative position information Cannot be disturbed Position error grows with time Positioning methods Feature based positioning methods Geometry based positioning methods Dead reckoning based positioning methods Information fusion Filter algorithms Depends on the structure of the state space model and noise properties. Filter structures 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 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.

48 Homework/Lab GNSS positioning GNSS position calculation from pseudo range measurements. Study the effects of satellite constellation on the obtainable accuracy. Simulated data GNSS aided INS Study the error growth in a GNSS aided INS during GNSS signal outages Study the effects of a simple vehicle model during GNSS signal outages. Study the effect of adding a speedometer sensor. Real-world data You are always welcome to mail me (skog@kth.se ) about the homework and lab.