Tensegrities are structural mechanisms, with dedicated compression (struts/bars) and tension members (cables). The compression members float inside the network of tension members. Tensegrities are characterized by the presence of at least one infinitesimal mechanism, which is stabilized by the pre-stress present in the members, to ensure the equilibrium of the structure. Under external load, tensegrity may change its form by altering its member pre-stress, thereby affecting its global stiffness even in the absence of damage. Moreover, tensegrities can have different stiffness properties under the same structural configuration in the absence of any damage or external load, if the pre-stress levels of the members are different. However, the changes in dynamic characteristics of tensegrities are not limited to the aforementioned causes only and is also affected by ambient uncertainties. A variation in temperature may alter the dynamic characteristics of a tensegrity by influencing its material (Young's modulus, etc.) and structural (boundary conditions, structural dimensions, etc.) properties. This can potentially lead to a false impression of tensegrity damage/health. Meanwhile, the prolonged usage of tensegrity may lead to loss of pre-stress in the cables, buckling of the bars, corrosion, and damage of the members, etc. Thus affecting the structural stiffness which leads to change in the measured dynamic properties of the tensegrity. To account for this actual damage in the tensegrity, all the mentioned major challenges that could lead to a false alarm need to be dealt with. The present study develops a vibration-based time-domain approach for tensegrity health monitoring in the presence of uncertainties due to ambient force, measurement noise, and varying temperature. An interacting filtering technique has been used, where the state variables are estimated by the Ensemble Kalman filter that resides inside the Particle filter which computes the health parameters.