This paper presents a robust model-based control in natural frame for a three-phase shunt active power filter. For the proposed control method a linear converter model is deduced. Then, this model is used in a Kalman filter in order to estimate the system state-space variables. Even though the states estimation do not match the variables of the real system, it has allowed to design three sliding mode controllers providing the following features to the closed loop system: a) robustness due to the fact that control specifications are met independently of any variation in the system parameters; b) noise immunity, since a Kalman filter is applied; c) a lower THD of the current delivered by the grid compared with the standard solution using measured variables; d) the fundamental component of the voltage at point of common coupling is estimated even in the case of a distorted grid; and e) a reduction in the number of sensors. Thanks to this solution the sliding surfaces for each controller are independent. This decoupling property of the three controllers allows using a fixed switching frequency algorithm that ensures a perfect current control. Finally, experimental results validate the propos