Karman filter and attitude estimation

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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

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

Ga = GSR·Sa

Accelerometer
• Acceleration
• Why is it not enough?
Gyroscope
• 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 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 (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)
Recursive estimation
• At time 0, and are known
• Given them at k-1, Predict and Update &

Measurement residual

Residual covariance

Optimal Kalman gain

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

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

Remove offset

Strapdown integration

GSRt

GSRt-1

Inclination estimated from accelerometer

Remove body acceleration

SzA=Sgt/|Sgt|=

Predict

Rotate

GSR

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