ZERODECOMPOSITION OF SPEECH FOR SOURCETRACT SEPARATION WITH APPLICATION TO GLOTTAL FLOW PARAMETER ES

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Workshop on State Estimation Heidelberg, Germany,
April 7-8, 2005
Robust Kalman Filtering Techniques Applied to
Train Positioning
Automatic Control Laboratory, FPMs Guillaume
Goffaux, Alain Vande Wouwer and Marcel Remy
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Outline

• Introduction
• Motivation Train positioning
• System description
• Evolution Equation
• Observation Equation
• Observability analysis
• State Estimation Techniques
• Kalman Filter
• Robust Filter
• Conclusion

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PIST Project

• PIST Intelligent and Secure Positioning in
  Transport (from 10/03 to 03/06)
• Position and velocity reconstruction with a high
  confident interval (10-12) in the context of a
  railway vehicle
• Objectives
• Preventing collisions
• Checking the respect of velocity limitations

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PIST Project
Disturbances/ Noises
Sensors
Outputs
Inputs
State variables
Measurement noises

• Classical sensors
• Odometers
• Radars
• Accelerometers
• Beacons

• Additional sensor
• GNSS (Global Navigation Satellite System)

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PIST Project

• Partnership
• Coordinator
• Pr. Joël Hancq (Circuit Theory and Signal
  Processing Department TCTS, FPMs Mons)
• Scientific partners
• Pr. Alain Vande Wouwer (Automatic Control
  Laboratory, FPMs Mons)
• Pr. Francis Grenez (Waves and Signals Department,
  ULB Brussels)
• Sub-contractor
• Multitel ASBL, Data Fusion Group
• Industrial Partner
• Alstom Transport Belgium

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PIST Project

• Planning
• Providing secure positioning by using classical
  sensors
• Incorporating GPS sensors
• Measurements in a Database
• Sensors embedded in a Pendolino train in Italy

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Outline

• Introduction
• Motivation Train positioning
• System description
• Evolution Equation
• Observation Equation
• Observability analysis
• State Estimation Techniques
• Kalman Filter
• Robust Filter
• Conclusion

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Train positioning

• Objective of this study
• Estimating position and velocity of the train by
  using classical sensors
• An odometer
• Radars
• An accelerometer
• State estimation methods
• Measurements from sensors
• Modelling of the vehicle and of the available
  sensors

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Train positioning

• Odometer
• Slotted disc spinning
• with the wheel axle
• Optical device
• Velocity sensor
• Sensitive to wheel spin and lock
• Placed in an axle which is neither braked nor
  towed

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Train positioning

• Radar
• Doppler principle
• Speed and position sensors
• Not sensitive to wheel
• spin and lock
• Sensitive to environmental
• conditions
• Status information on
• measurement quality

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Train positioning

• Accelerometer
• Acceleration sensor
• Pendulum principle
• Sensitive to the rail track
• gradient

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Outline

• Introduction
• Motivation Train positioning
• System description
• Evolution Equation
• Observation Equation
• Observability analysis
• State Estimation Techniques
• Kalman Filter
• Robust Filter
• Conclusion

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Modelling

• Evolution equation
• Kinematic modelling
• Discrete-time mode
• Constant acceleration between two measurement
  times
• One dimension

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Modelling

• Observation equation
• Discrete-time mode
• Asynchronous measurement time

• Observability analysis
• Which configuration of sensors allows to
  reconstruct state vectors ?

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Modelling

• Observability analysis
• Computing the observability matrix
• A position sensor is required
• Observable with only a position sensor

• Sensors used
• Speed sensors a Wiegand odometer and a Faiveley
  Doppler radar
• Position sensor a Deuta radar
• Acceleration a Sensorex accelerometer

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Modelling

• A Wiegand odometer
• 2 measurements every 0.1s

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Modelling

• A Faiveley Doppler radar
• Average sampling period 0.1 s

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Modelling

• A Deuta radar
• Average sampling period 0.1 s

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Modelling

• A Sensorex accelerometer
• Average sampling period 0.05 s

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Outline

• Introduction
• Motivation Train positioning
• System description
• Evolution Equation
• Observation Equation
• Observability analysis
• State Estimation Techniques
• Kalman Filter
• Robust Filter
• Conclusion

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Kalman Filter

• Estimation of
• Assumptions
• White noises and Gaussian statistics
• , ,
• Linear modelling

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Kalman Filter

• Recursive Filter
• Minimization of the mean-square estimation error.
• Conclusion
• Optimal filter
• Restrictive assumptions

• Prediction

• Correction

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Positioning example
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Outline

• Introduction
• Motivation Train positioning
• System description
• Evolution Equation
• Observation Equation
• Observability analysis
• State Estimation Techniques
• Kalman Filter
• Robust Filter
• Conclusion

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Robust Filter Mangoubi,98

• Nominal model P
• Uncertainties ?

?
?
y
r
P
x0

• Transforming the equations

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Robust Filter

• Objective

• Robust criterion reached with ? 1 in

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Robust Filter
Robust Discrete Filter Equations
Riccati equation in X from i to i-N
Riccati equation in P from i-N to i
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Robust Filter
Robust Theorem

• Assume that for a ? 1
• There exists a satisfying the Riccati
  equation in X in such that
  .
• There exists a satisfying the Riccati
  equation in P in such that
  .
• There exists so that .
• Then the robust performance condition is
  satisfied.

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Positioning example

• Uncertain system modelling
• Uncertainty on the acceleration measurement

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Positioning example
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Outline

• Introduction
• Motivation Train positioning
• System description
• Evolution Equation
• Observation Equation
• Observability analysis
• State Estimation Techniques
• Kalman Filter
• Robust Filter
• Conclusion

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Conclusion

• Reconstruction of position and velocity
• Biased output of the accelerometer due to the
  track slope
• Kalman Filter
• Optimal filter with restrictive assumptions
• Sensitive to model uncertainties
• Robust Filter
• Model uncertainties explicitly taken into account
• Min-max formulation
• Improved insensitivity to model uncertainties

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Acknowledgment
This work is performed in the framework of the
PIST project funded by the Walloon Region DGTRE
(Belgium). Database is property of Alstom
Transport Belgium.
Thank you for your attention!