Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
4.2 Simulation
− light blue curve: estimation rendered by a High-gain extended Kalman filter with θ = 7,
− red line: estimation done by the adaptive high-gain Kalman filter.
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Second scenario output signal
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Third scenario output signal
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Figure 4.12: Output signal for the two scenarios.
In the first scenario, when the perturbation occurs (at time 30), we see that, as expected,
the perturbation is detected by innovation, which crosses the y = m2 red line of Figure 4.17.
The high-gain parameter then increases and convergence is made more effective. We see
that when no perturbation occurs, innovation remains less than m2 and the behavior of the
observer is the same as the one of the extended Kalman filter 11 . The speed of convergence
after the perturbation is comparable to that of the high-gain extended Kalman filter modulo,
i.e., a small delay that corresponds to the time needed:
1. for the perturbation to have an effect on the output,
2. for the perturbation to be detected,
3. and for the high-gain to rise.
Notice that this delay depends also on the parameter δ, the sample time set for the computation
of the innovation. Since θ reacts on behalf of the innovation, its behavior can change
only every δ period of time.
11 Actually, the performance of the AEKF versus that of the EKF depends also on the level of the noise and
on the system under consideration. For example, if the noise level is really high, one would probably set the
matrix Q to a very low value thus rendering the EKF even slower. This very low value of Q has only a little
effect on the AEKF behavior in high-gain mode. Therefore the AEKF would be as quick to respond as in the
present situation and the EKF would be slower. In [21] and [22], the AEKF is used in some other examples
thus providing additional insight into the differences between EKF and AEKF.
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