<p>A Gaussian process extended Kalman filter is effective for a state estimation problem when the nonlinear functions of systems are unknown. However, the Gaussian process extended Kalman filter is not adequate for judging some patterns where outliers are included in the observed values and states of the systems. This paper proposes an extended risk-sensitive filter, which is based on Gaussian process regression. The proposed method approximates the unknown nonlinear systems by using Gaussian process regression and estimates the states of the nonlinear systems with various outliers by using the extended risk-sensitive filter. Numerical simulations show the effectiveness of the proposed method.</p>