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Karman filter and attitude estimation. Lin Zhong ELEC424, Fall 2010. Yaw, pitch, and roll angles. Inclination. How z is represented in the sensor coordinate XYZ : S z. Orientation (attitude).

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karman filter and attitude estimation

Karman filter and attitude estimation

Lin Zhong

ELEC424, Fall 2010

inclination
Inclination
  • How z is represented in the sensor coordinate XYZ: Sz
orientation attitude
Orientation (attitude)
  • How xyz is represented in the sensor coordinate XYZ: GSR=[ Sx, Sy, Sz]T

Ga = GSR·Sa

accelerometer
Accelerometer
  • Acceleration
  • Why is it not enough?
gyroscope
Gyroscope
  • Angular velocity
  • Why is it not enough?
kalman filter
Kalman filter
  • What does it do?
    • Estimate the internal state x of a linear dynamic system from noisy measurements
  • How does it estimate it?
    • Linearity of the system
    • Statistical properties of the system and measurement
    • Recursive (dynamic programming)
the target system
The target system
  • The system evolves in discrete time steps
    • Fk is the state transition model
    • Bk is the control-input model
    • wk is the process noise, assumed to a zero mean multivariable normal distribution wk~N(0, Qk)

http://en.wikipedia.org/wiki/Kalman_filter

the measurement
The measurement
  • The measurement (observation) of the state xk is a linear function of xk
    • Hk is the measurement model
    • vk is the measurement noise, a zero mean multivariable normal distribution vk~N(0, Rk)
discrete kalman filter
Discrete Kalman filter
  • Two variables are updated at each stage (k)
    • : state estimation given measurements up to and including time k
    • : error covariance matrix (how accurate is)
recursive estimation
Recursive estimation
  • At time 0, and are known
  • Given them at k-1, Predict and Update &

Measurement residual

Residual covariance

Optimal Kalman gain

slide12

A gyroscope measures a 3D angular velocity plus an offset and white measurement noise in the sensor co-ordinate frame

  • The spectrum of the gyroscope offset has a low cutoff frequency in comparison with the bandwidth of the kinematic signals that are to be measured
slide13

A 3D accelerometer measures acceleration minus gravity and a white noise component, all in the sensor co-ordinate frame

  • The acceleration of a body segment in the global system can be described as low pass filtered white noise
inclination estimated from gyroscope
Inclination estimated from gyroscope

Remove offset

Strapdown integration

GSRt

GSRt-1

inclination estimated from accelerometer
Inclination estimated from accelerometer

Remove body acceleration

SzA=Sgt/|Sgt|=

Predict

Rotate

GSR

what assumptions can we make
What assumptions can we make?
  • Offset of gyroscope and accelerometer can be calibrated, automatically.
  • Roll and pitch are small
  • Body acceleration is small (if engines are controlled properly)
  • Goal
    • Yaw should be constant
    • Roll and pitch should be small
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