Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
Parameter Value Role
Q diag(1, 10 −1 , 10 −2 ) Filtering
R 1 Filtering
θ1 1.25 High-gain
β 1664 π
e Adaptation*
m1 0.005 Adaptation*
m2 0.004 Adaptation
λ 100 Adaptation*
∆T 0.01 Adaptation*
d 0.1 Innovation
δ 0.1 Innovation*
Table 4.2: Final choice of parameters (*: Application-free parameters).
� ˙If = α(I − If )
Iused = I − If
where α fixes the maximum time that θ will remain fixed at its maximum value.
4.4 Conclusions
4.4 Conclusions
In this chapter, the adaptive high-gain extended Kalman filter was completely defined. A
sigmoid function allows us to take care of the influence of measurement noise on the final value
of innovation. We proposed a clear methodology in order to efficiently tune the parameters of
the observer. Its performance was compared to those of a pure high-gain and a non high-gain
observer in simulation.
In the second part of this chapter, the implementation of the observer, in a hard real-time
environment, on a simple process has been investigated in detail. The observer’s behavior is
as efficient as it is in simulations. The compliance to hard real-time constraints showed that
the effective use of this algorithm is not a mathematician’s mid-summer night’s dream.
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