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Karman filter and attitude estimation - PowerPoint PPT Presentation

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

Lin Zhong

ELEC424, Fall 2010

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

• How xyz is represented in the sensor coordinate XYZ: GSR=[ Sx, Sy, Sz]T

Ga = GSR·Sa

• Acceleration

• Why is it not enough?

• Angular velocity

• Why is it not enough?

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 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 (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

• Two variables are updated at each stage (k)

• : state estimation given measurements up to and including time k

• : error covariance matrix (how accurate is)

• At time 0, and are known

• Given them at k-1, Predict and Update &

Measurement residual

Residual covariance

Optimal Kalman gain

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 white noise component, all in the sensor co-ordinate frame

Remove body acceleration

SzA=Sgt/|Sgt|=

Predict

Rotate

GSR

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