This paper is devoted to the application of a simple machine learning technique for the design of a receding horizon state observer. The proposed approach is based on a neural network trained to learn the inverse problem consisting in deriving the current system state from past measurements and inputs. The training data is obtained from simple integrations of the system dynamics to be observed. The approach is here applied to the problem of estimating the car density on a highway online. A comparison with the solution of an receding horizon observer based on an adjoint method and used as reference demonstrates the effectiveness of the proposed approach.