The solid oxide fuel cell (SOFC) is an innovation power generation device in the form of an electric stack. The temperature distribution is crucial for the stable and safe operation of the system. Considering the difficulty of accurately measuring the internal temperature of the device

this paper proposes a temperature estimation method based on the Luenberger-sliding mode observer (L+S) and the Kalman filter (KF) observer. First

a discrete-time state-space model of the SOFC stack is established using a one-dimensional (1D) theoretical model that considers system noise. Secondly

the input variables of the observer are filtered and combined with the condition number of the measurement matrix to produce the optimal combination. The estimation performance of the model is enhanced through decoupling of error systems and vibration suppression. The Kalman filter observer model is constructed by combining the stack model with the Kalman filter (KF) algorithm. Then

the Luenberger-sliding mode observer model is constructed based on the theories of the Luenberger observer (L) and the sliding mode observer (S). The estimation performance of this model is enhanced through the decoupling of the error system and vibration suppression. The Kalman filter observer model is constructed by integrating the electric stack model with the Kalman filter (KF) algorithm. This method solves the time difference between the observed state and the actual system state by filtering noise to improve the estimation accuracy of the model. Finally

a multidimensional performance evaluation index system was established

and the estimation performance of various observer models was compared through simulation experiments and data analysis to verify the effectiveness of the temperature estimation model proposed in this article.