Structural health monitoring is the process of implementing a damage detection strategy for civil and mechanical engineering infrastructure. In this research, the structure’s health or the level of damage is monitored by identifying changes in structural parameters, by comparing the stiffness matrix of a structure with the undamaged model matrix. The two methods developed employ adaptive recursive least squares (RLS) filtering using measured or estimated structural responses and a reasonable estimate of the input force, such as an earthquake, to directly identify changes in structural stiffness for the ASCE benchmark structure health monitoring (SHM) problem. These methods focus on minimal computation to enable real-time implementation and are computationally simple, requiring 0.03 Mcycles of computation for a 4 degree of freedom (DOF) structure at a 100 Hz sampling rate and 520 Mcycles for 120-DOF at 100 Hz. These values assume no parallelisation for super-scalar digital signal processing chips and are within the capability of current digital signal processing devices. The identified changes in stiffness matrix converge to within 1.5% of the true value within 1.6 s, with an average of 0.56 s for the twelve 4-DOF and 12-DOF cases and damage patterns examined from the ASCE SHM benchmark problem.