Numerical beam is an important structure type for replicating and idealizing several different real structures, such as bridges, high-rise structures etc. Towards development of damage detection approaches/ algorithms for bridge structure, present study has idealized it as a prismatic beam and an instance of localized structural damage is replicated as a through crack in the beam. The objective of this study is further to precisely localize the extent and location of such damages under severe ambient and model uncertainties. Particle filtering based structural health monitoring (SHM) approach has been employed in this study. Typical of such model-based algorithms, the real structural domain is discretized into finite elements with the damage attributed to any of these discrete elements, rendering the localization precision being dependent on the discretization resolution. Current study modelled the damage as an independent massless rotational spring in the beam attributing the local stiffness deterioration of the real structure through the decay in the spring stiffness. To localize and quantify the real damage in the beam, the goal of present estimation approach is therefore set as to locate the position of such spring and further estimate its residual spring stiffness. This enables localization of the damage with a resolution much beyond the discretization density, and thereby helping the algorithm to be supported with much less compute-intensive models. The algorithm is validated for its sensitivity against noise and damage severity. The results demonstrate the algorithm to be efficient, prompt and precise in detecting damage in a structure.