Active disturbance rejection control (ADRC) is widely used in airborne optoelectronic stabilization platforms due to its minimal reliance on the mathematical model of the controlled object. The extended state observer (ESO) is the core of ADRC, which treats internal parameter variations and external disturbances as total disturbances, observes the disturbances as extended states, and then compensates them into the control loop to eliminate their effects. However, the ESO can only achieve a precise estimation of constant or slowly varying disturbances. When the disturbance is periodically changing, satisfactory results cannot be obtained. In this paper, a generalized high-order extended state observer (GHOESO) is proposed to achieve the precise estimation of known frequency sinusoidal disturbance signals and improve disturbance suppression levels. Through numerical simulations, a traditional ESO and GHOESO are compared in terms of disturbance observation capability and disturbance suppression ability for single and compound disturbances based on our prior knowledge of disturbance frequency. The effectiveness of the proposed GHOESO method is verified. Finally, the algorithm is applied to an airborne optoelectronic stabilization platform for a 1°/1 Hz swing experiment on a space hexapod swing table. The experimental results demonstrate the superiority of the GHOESO proposed in this paper.