DT Kalman filter - UBC Mechanical Engineering - University of ...
DT Kalman filter - UBC Mechanical Engineering - University of ...
DT Kalman filter - UBC Mechanical Engineering - University of ...
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Homework (Due Apr 8, 5pm)<br />
• (Last one!) 5-2: 5<br />
Consider the following<br />
continuous-time time system (oscillator):<br />
Design the <strong>Kalman</strong> <strong>filter</strong> for the discrete-time<br />
time<br />
system obtained by sampling the system above<br />
with sampling time 0.5:<br />
2008/09 MECH468/550P 29<br />
Homework (cont’d)<br />
• Assumptions<br />
• E{w}=<br />
}=E{v}=0,<br />
Rw=0.01,<br />
Rv=0.04<br />
• Initial value <strong>of</strong> error covariance matrix M=I2.<br />
• u[k] ] is a square-wave function defined in<br />
KFoscillator.m.<br />
• Task: Modify KFoscillator.m, , and design both<br />
time-varying and steady state <strong>Kalman</strong> <strong>filter</strong>s.<br />
(You do not have to follow the provided m-file.) m<br />
• Verify that your steady state <strong>Kalman</strong> <strong>filter</strong> gain<br />
matches with the time-varying gain after some time.<br />
• Compare the trajectories <strong>of</strong> the state estimates.<br />
2008/09 MECH468/550P 30<br />
8
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