Optimal Estimation of Dynamic Systems, 2nd Edition

200 Optimal Estimation of Dynamic Systems

valid, since filter matrices are evaluated with respect to estimated quantities. How-

ever, it can be assumed that the coupling aspects associated with the nonlinear filter

are small and can most times be ignored. Still, care must be taken to ensure that good

estimates are provided when applying nonlinear filters.

The constrained filter can also handle nonlinear constraints of the form:

36

d

k

= g

k

(x

k

) (3.269)

where g

k

(x

k

) is a continuous-differentiable nonlinear function. The approach to han-

dling the nonlinear constraint involves performing a linearization about the current

constrained state estimate:

d

k

≈ g

k

(

ˆ

x

k