This paper presents an improved variable hysteresis-band current-control in natural frame for a three-phase shunt active power filter. The proposed control algorithm is based on three decoupled sliding-mode controllers combined with three independent Kalman filters. The use of Kalman filters instead of a non-adaptive state observer improves the quality of the estimated signals in presence of noise, increasing the immunity of the control loop in noisy environments and also reducing the THD of the current delivered to the grid. The overall control proposal has been fully integrated into a digital signal processor. Selected experimental results are introduced to validate the theoretical contributions of this paper.