This paper proposes a moving horizon estimator for nonlinear systems with unknown inputs, which do not comply with the model structures proposed in the literature for the design of nonlinear observers. The estimator is designed as an optimization problem over a moving horizon, constrained to process model equations and considering the unknown inputs as random inputs among their operating bounds. This proposal is applied to the transport of mineral slurries among process units, typically present in chemical and biological processes. There, to have the slurry properties as online measurements is vital to an efficient control of those processing units. The performance of the proposed estimator is evaluated by simulation with data from a real processing plant, and its performance is compared with a linear estimator executing the same estimation task. Better results are obtained using the proposed estimator by considering the nonlinearities of the process.