This paper proposes two novel methods for fault detection in non-linear processes. These methods apply a Gaussian process (GP) to model the underlying process, and then the extended Kalman filter (EKF) and square root cubature Kalman filter (SCKF) are used to detect faults. Accordingly, two approaches called the Gaussian process–extended Kalman filter (GP-EKF) and Gaussian process–square root cubature Kalman filter (GP-SCKF) are proposed. The most important characteristic of these proposed methods is that there is no need for an accurate model of the system. Therefore, these methods are considered non-parametric approaches of fault detection in non-linear systems. To illustrate the performance of these algorithms in fault detection, they have been used in a continuous stirred-tank reactor system (CSTR). Both proposed methods are able to detect sensor faults at an early stage.