  KKL (Kazantzis-Kravaris/Luenberger) observers are based on the idea of
immersing a given nonlinear system into a target system that is a linear stable
filter of the measured output. In the present paper, we extend this theory by
allowing this target system to be a nonlinear contracting filter of the output.
We prove, under a differential observability condition, the existence of these
new KKL observers. We motivate their introduction by showing numerically the
possibility of combining convergence speed and robustness to noise, unlike what
is known for linear filtering.
