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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


Karman filter and attitude estimation


Karman filter and attitude estimation


Inclination estimated from gyroscope
Inclination estimated from gyroscope white noise component, all in the sensor co-ordinate frame

Remove offset

Strapdown integration

GSRt

GSRt-1


Inclination estimated from accelerometer
Inclination estimated from accelerometer white noise component, all in the sensor co-ordinate frame

Remove body acceleration

SzA=Sgt/|Sgt|=

Predict

Rotate

GSR


What assumptions can we make
What assumptions can we make? white noise component, all in the sensor co-ordinate frame

  • 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