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									Inertial Sensors and
Dead Reckoning

      Jonathan Friedman
      Yu Ching Chang
      Cheryl Buenaventura
      David Lee

      What is Inertial Navigation (INS)?
      Why use INS?
      Requirements
      Sensors
      Algorithms
      Errors
      Synchronization/Error Correction
      Conclusion
2003                 Friedman, Chang, Buenaventura, Lee   2
What is Inertial Navigation?
      Determining an object’s position based on sensors
       on the body
      Dead Reckoning
          Determining current position using acceleration/speed,
           orientation, and the old position as a reference point
          Px, current = Px, initial+ ΔPx
      Uses:
          Rockets (Military)
          Airplanes (Commercial)
          Cars (Personal)
          Wearable Computers (Personal)

2003                      Friedman, Chang, Buenaventura, Lee        3
Why Use INS?

      Sealed/Hostile Environments
      Unjammable (Combat Environments)
      Instantly Available (No Infrastructure
      Cheap (good for consumer
       applications like Wearable Computers)

2003               Friedman, Chang, Buenaventura, Lee   4
Requirements for an
Inertial Navigation System

      Calibration
          Starting reference point
          Sensors
      Sensors
          Accelerometers
          Magnetometers
          Gyroscopes

2003                  Friedman, Chang, Buenaventura, Lee   5
    Sensors: Accelerometers
   MEMS accelerometer
          measures acceleration
           through compression of
           cantilever beams
   Piezoelectric accelerometer
          consists of a charge-emitting
           crystal that is bonded to a
           mass inside
          Under a force, the mass                   Figure 1. Analog Devices iMEMS Accelerometer
           compresses the crystal,                          (source: http://www.analog.com)

           which emits a signal

    2003                       Friedman, Chang, Buenaventura, Lee                              6
    Sensors: Magnetometers
   Detects changes in Earth’s magnetic field
   Works like a compass in INS
   Complications
          Earth’s geographic north is not magnetic north
          Need to add or subtract appropriate declination angle for true
           geographic north

                         Figure 2. Declination chart for United States
    2003                     (source: http://www.honeywell.com)             7
    Sensors: Gyroscopes
   Measures Angular Velocity
   Two gyroscopes on gimbals are
    typically assembled with their
    axles at 90 degree angles
   Sensors are placed on the
    gimbals’ axles to detect
    changes in rotation
                                                   Figure 3. Analog Devices iMEMS Gyroscope
                                                        (source: http://www.analog.com)

    2003               Friedman, Chang, Buenaventura, Lee                              8
       Algorithms: Double Integration Method
                                                        Use accelerometers to
                                                         determine body’s
                                                         acceleration in x, y, z
                                                         direction relative to the body
                                                        Use gyroscopes to determine
                                                         the body’s orientation (roll,
                                                         pitch, yaw)
Figure 4. Acceleration and Angular Velocity in
                     x, y, z                            Or use magnetometers as a
       (source: http://www.electronic-
                                                         digital compass to determine
                                                         the direction the body’s
                                                         geographic orientation
                                                         (North, East, South, West)
       2003                                  Friedman, Chang, Buenaventura, Lee       9
    Algorithms: Double Integration Method
     Change in position = sx(t) = ∫∫ax(t) dt2
     Change in angle = φx = ∫ω(t) dt
     Px, current = Px, initial+ ∫∫ax(t) dt2
     Change in heading can simply be determined
      by digital compass (magnetometers)
     Depending on the application, acceleration is
      used with either change in angle information
      or changing in heading or both.

    2003             Friedman, Chang, Buenaventura, Lee   10
    Algorithms: Bounce and Stride Method
     Instead of measuring acceleration, use
      accelerometers to detect a “bounce”
     A bounce determines when a step has been
     When a step is taken, update the new position
      by one stride length
     Can attach accelerometer to hip or leg to
      determine when a bounce occurs

    2003             Friedman, Chang, Buenaventura, Lee   11
    Algorithms: Bounce and Stride Method
     Complications
          Stride is not constant
          Varies by ±40% from person to person
          Depends on leg length
          Varies by ±50% depending on how fast
           the person is walking
     α=θ
     Stride ≈ 2 x Bounce/α
     Distance ≈ (Amax – Amin)1/4 x n x k
          Amax=maximum acceleration in a single
           stride                                          Figure 5. Concept behind the bounce and
                                                                        stride method
          Amin=minimum acceleration in a single               (source: http://www.analog.com)
          n = number of steps walked
          K = length of one stride (ie. feet or

    2003                        Friedman, Chang, Buenaventura, Lee                               12
       Inertial sensors are very noisy
       Temperature can change accelerometer readings
       Accelerometer readings can have an error of a few mg
       For double integration method, the error of a few mg is
        made worse by the double integration
       Magnetometer must be parallel to the ground
       Magnetometer error can depend on where the person
        is on Earth
          In Mountain View, CA, 3º heading error/1º tilt
          In Greenland, 10º heading error/1º tilt
    2003                       Friedman, Chang, Buenaventura, Lee   13

      The magnetometer can experience
       interference from other magnetic field other
       than the Earth’s
      Gyroscope may experience Coriolis effect,
       causing a vibration orthogonal to the original
          In other words, over time, gyroscope can drift off
           actual value

2003                    Friedman, Chang, Buenaventura, Lee   14
Synchronization/Error Correction

      Must resynchronize INS periodically to
       correct for error
      External Syncs: receive external update
          GPS
          Light sensors
      Internal Syncs: update information stored on
       the inertial navigation system
          Map mapping

2003                       Friedman, Chang, Buenaventura, Lee   15
Synchronization/Error Correction: GPS

      GPS uses a system of 27 orbiting satellites to
       determine current position
      Each satellite orbits such that at least 4 satellites
       are “visible” in the sky
      In INS, a periodic signal from the GPS corrects
       the reference point of the INS
      Works great for outdoors
      Problems
          GPS signal could be blocked
          Does not work for indoors environment
2003                      Friedman, Chang, Buenaventura, Lee   16
    Synchronization/Error Correction:
    Light Sensors
   Similar to the infrared sensor on garage doors that
    prevents the door from closing on someone
   Light sensors are positioned in known places within an
   When the person crosses the light sensor and disrupts
    the beam, the position of the sensor is sent to the INS
   The INS updates its reference position to the position
    of the sensor
   Problems
          Requires a network of extra sensors
          Only feasible indoors or small areas

    2003                      Friedman, Chang, Buenaventura, Lee   17
    Synchronization/Error Correction:
    Map Mapping
   Fit the INS position to a legal place on the map (ie.
    not within an obstacle or off the road)

                         Figure 6. Concept behind Map Mapping
             (source: http://topo.epfl.ch/publications/paper_IAIN03_epfl.pdf)

    2003                         Friedman, Chang, Buenaventura, Lee             18
Synchronization/Error Correction:
Map Mapping
      Regular maps, like the Yahoo maps, works well for outdoors
       while the person is traveling along designated streets, but
       what about indoor maps?
      Take a CAD layout of the building and convert it to nodes
      Nodes consists of doors, rooms, points of interest
      Paths consists of hallways, walkways, and paths between

                                  Figure 7. CAD map to nodes
               (source: http://topo.epfl.ch/publications/paper_IAIN03_epfl.pdf)

2003                              Friedman, Chang, Buenaventura, Lee              19
    To determine a body’s position, INS requires inertial sensors on
     the body to gather information: accelerometer, magnetometer,
     and gyroscope.
    Two main methods of INS are 1) double integration and 2)
     bounce and stride
    Fairly inaccurate low-cost sensors
    Error is made worse by integration
    Need to correct for errors using periodic synchronization
    External Synchs are 1) GPS and 2) Light Sensors
    Internal Synch is Map mapping
    INS useful for a variety of pedestrian and object tracking

    2003                    Friedman, Chang, Buenaventura, Lee          20
1.     Cliff Randell, Chris Djiallis, Henk Muller, "Personal Position Measurement Using Dead
       Reckoning," Seventh IEEE International Symposium on Wearable Computers, October
       21 - 23, 2003, White Plains, New York, USA.
2.     Harvey Weinberg, "Using the ADXL202 in Pedometer and Personal Navigation
       Applications," Analog Devices.
3.     Kevin J. Walchko, Michael C. Nechyba, Eric Schwartz, and Antonio Arroyo. “Embedded
       Low Cost Inertial Navigation System,” Florida Conference on Recent Advances in
       Robotics, May 2003, Dania Beach, Florida, USA.
4.     Kevin J. Walchko. “Low Cost Inertial Navigation: Learning to Integrate Noise and Find
       Your Way.” University of Florida. 2002. http://homepage.mac.com/walchko/publications/
5.     Ladetto, Q.; Seeters, J. van; Sokolowski, S.; Sagan, Z.; and Merminod, B. “Digital
       Magnetic Compass and Gyroscope for Dismounted Soldier Position and Navigation.”
       EPFL. 2002.
6.     Peter Luethi, Thomas Moser, Marcus Uster. “Low Cost Inertial Navigation System”.
       2000. http://www.electronic-engineering.ch/study/ins/ins.html.
7.     Pierre-Yves Gilliéron, Bertrand Merminod, "Personal Navigation System for Indoor
       Application," 11th IAIN World Congress 21-24 octobre 2003, Berlin, Allemagne.

2003                            Friedman, Chang, Buenaventura, Lee                        21
8.     Seon-Woo Lee, Kenji Mase, "Personal Indoor Navigation System using
       Wearable Sensors," International Symposium of Mixed Reality , Yokohama,
       March 2001.
9.     Skaloud, J. and Limpach, P. "Synergy of CP-DGPS, Accelerometry and
       Magnetic Sensors for Precise Trajectography in Ski Racing". EPFL, 2003.
10.    Sensorland. "The Piezoelectric Accelerometer." Accessed November 21,
11.    How Stuff Works. "How Gyroscopes Work". Accessed November 21, 2003.

2003                        Friedman, Chang, Buenaventura, Lee               22

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