This work proposes an original method to estimate states in non-linear discrete-time systems with global convergence properties. The approach is based on the minimisation of a criterion (non-linear function, differentiable or not) that is the Euclidean norm of the difference between the estimated output and the measured output of the system over a considered time horizon. This method is based on an interval moving horizon state estimation method, called IMHSE, which is coupled to a technique of global optimisation of non-linear functions that uses interval arithmetic. The system states are described using a representation by interval numbers. The proposed technique is applied to biotechnological complex process models (solid substrate fermentation), and the results obtained through experimental and computer simulation demonstrate that this kind of estimator offers advantages over other observers and filters and can be easily implemented in an industrial context.