The on-line estimation of unmeasured states in non-linear distributed systems faces considerable computational and implementation difficulties. In the present work an estimator is developed for a distributed system coupled through a highly non-linear term. The available secondary measurements and their time derivatives are used to preestimate the non-linear function. Then, the non-linearity is regarded as a known time dependent forcing term. The resulting estimation problem becomes linear, with a significant reduction of the computational scheme. The application of the method is illustrated with an example taken from the chemical industry; a tubular chemical reactor.