Displacements of structural systems under service loads can provide crucial performance and safety information. Nevertheless, measurement of displacements is a difficult and expensive task, because of the need for a stationary reference to which the measuring devices attached. Some methods have stemmed from developing indirect displacement estimation by converting measured accelerations into dynamic displacement. This research develops a new approach based on a generalized minimization problem with Tikhonov regularization, resulting in an efficient and stable FIR filter. In particular, the developed filter is suitable for suppressing low-frequency noise with little ripple and without adding phase distortion. The adequacy of the proposed reference-free displacement estimation method is demonstrated by numerical simulations using field accelerations and displacements of a railroad bridge under a test train, by laboratory experiments reproducing these field displacements with a servo-hydraulic motion simulator, and by a field test using actual displacements and accelerations records of a timber trestle bridge under revenue service traffic. All results show good agreement between the measured and estimated dynamic displacements, demonstrating the efficacy of this method estimates the dynamic displacements of structural systems.