Structures undergo some mechanical impacts during their life phase, which may create high vibration levels that induce damage and failure of the system itself. Hence, inverse methods are generally used to estimate the mechanical characteristics of these complex sources. Among all the existing methods, Kalman filtering provides a lightweight and elegant solution to solve force reconstruction problems in time domain. From the filters existing to solve the sequential input-state estimation problems, a unified Bayesian formulation is established. Through this general Bayesian framework, new filters can be derived by choosing different sets of hypotheses. In the present contribution, three particular filters are derived from this unifying vision. Their performances in terms of reconstruction accuracy are evaluated through a numerical experiment. Actually, it is shown that the proposed filters provide results that outperform those from the existing filters in terms of input estimation quality, as they remove the drift effect that causes important global error over time.