Abstract: To address the low-frequency drift problem in displacement estimation under unknown excitations, a structural response reconstruction method based on sparse acceleration measurements is proposed. A state-space model based on the Gillijns-De Moor filtering algorithm is established to simultaneously identify unknown excitations and estimate structural states. Subsequently, a compressed sensing algorithm is introduced to reduce the interference of measurement noise. During excitation identification, an inequality-constrained optimization model is established to improve the feasibility and physical plausibility of the obtained solutions. A pseudo-measurement technique is employed to efficiently solve the inequality-constrained optimization problem during excitation updates. Finally, based on the identified system states and unknown excitations, the full-field vibration responses, including displacement, velocity, and acceleration, are calculated using the modal superposition method. The proposed method is verified through numerical simulations and experimental tests on a simply supported beam structure. The results demonstrate that, under sparse acceleration measurement conditions, the proposed method can not only effectively reconstruct acceleration and velocity responses but also effectively suppress low-frequency drift in the reconstructed displacement, thereby improving the engineering applicability of response reconstruction techniques and providing a feasible solution for real-time structural health monitoring of large-scale infrastructure.