The ever-increasing power capacities of wind turbines promote the use of tall and slender turbine towers. This poses a challenge from a fatigue loading perspective by the relocation of the first and lightly-damped tower side-side natural frequency into the turbine operating regime, promoting its excitation during nominal operation. The excitation of this resonance can be aggravated by periodic loading in the presence of rotor mass and/or aerodynamic imbalance. Earlier work already presented a method to prevent the side-side excitation using a combination of model demodulation and quasilinear parameter varying model predictive control techniques. However, the method does not incorporate features for active control for side-side load mitigations. Because the information of the beforementioned periodic side-side loading is unknown and unmeasurable in practical scenarios, this paper presents a Kalman filtering method for its estimation in a demodulated fashion. The Kalman filter employs an extended demodulated wind turbine model augmented with random walk models of the periodic load. The simulation result demonstrates the effectiveness of the proposed method in estimating the periodic load components along with unmeasurable tower states in their demodulated form. These estimates pose an opportunity for use in future advanced controller designs for active load reductions.