In this paper, the state profile estimation of a novel autothermal fixed-bed reactor (called circulation loop reactor, CLR), which can be operated as an autonomous periodic system, is studied. Since in autothermal operation the reactor shows sustained large oscillations, its dynamics have to be modelled as a strongly nonlinear distributed parameter system. The generally used lumping techniques (e.g. the orthogonal collocation method) for designing the state estimator of fixed-bed reactors are not applicable in this case. An approach for estimating the state profiles of the CLR based on a nonlinear distributed parameter observer is presented. To decrease the computational effort of the observer in real-time applications, the reduction of the detailed model of the CLR is investigated. In order to achieve asymptotic stability and fast convergence of the observer, the observability of the CLR is analysed, and use of features of the sustained oscillatory system and physical insight are made. A method based on exponential weighting functions is proposed to approximate the observation error profile. The temperature and concentration profiles are estimated from a small number of temperature measurements. The obtained observer was successfully tested with the dynamic simulator DIVA in the cases of errors in the initial condition and the model parameters, random noisy measurements, and unknown disturbances, also including the different choice of sensor locations, and different observer parameters. It shows excellent dynamic tracking of the reactor profiles, strong robustness, and easy tuning. It forms a basis for developing appropriate control strategies of the CLR.