This paper deals with guaranteed state estimation for a large class of nonlinear continuous-time systems in a bounded error context. The proposed observer is based on a guaranteed Linear Parameter-Varying (LPV) transformation of the original nonlinear model. The linearisation is justified since it is difficult to develop generic methods for computing a stable observer for a nonlinear system. The Luenberger structure is used and the observer gain is designed so that to satisfy the cooperativity property and the positivity of the observation error. This approach makes the observer less pessimistic than interval Taylor observers. The methodology is illustrated through simulations on a numerical example.