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Karman filter and attitude estimation

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

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  1. Karman filter and attitude estimation Lin Zhong ELEC424, Fall 2010

  2. Yaw, pitch, and roll angles

  3. Inclination • How z is represented in the sensor coordinate XYZ: Sz

  4. Orientation (attitude) • How xyz is represented in the sensor coordinate XYZ: GSR=[ Sx, Sy, Sz]T Ga = GSR·Sa

  5. Accelerometer • Acceleration • Why is it not enough?

  6. Gyroscope • Angular velocity • Why is it not enough?

  7. 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)

  8. 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

  9. 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)

  10. 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)

  11. Recursive estimation • At time 0, and are known • Given them at k-1, Predict and Update & Measurement residual Residual covariance Optimal Kalman gain

  12. 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

  13. 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

  14. Inclination estimated from gyroscope Remove offset Strapdown integration GSRt GSRt-1

  15. Inclination estimated from accelerometer Remove body acceleration SzA=Sgt/|Sgt|= Predict Rotate GSR

  16. 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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