Typically, for linear parameter varying systems, which can potentially get influenced by spatio-temporal external parameters, possible changes in their eigenstructure are not easy to be attributed conclusively to system faults or spatio-temporal parametric variations. Such spatio-temporal variations can although be estimated alongside, yet at the cost of making the estimable system dimension disproportionately large. Such augmented system dimension can thereby jeopardize tracking of the system evolution, either due to computational constraints or due to insufficient measurement channels (ill-posedness). This paper proposes a localized estimation approach wherein only a subdomain of the entire system is considered which reduces the dimension of the estimated model within manageable limits. To focus on the subdomain properties without knowledge of the rest of the model parameterization, a robust algorithm is developed through output injection using a simpler and sub-optimal version of Kitanidis filtering approach to induce robustness in the system parameter estimation against the boundary measurements. Finally, the subdomain model is estimated employing a marginalized filtering approach wherein a particle filter is employed for estimating both the eigenstructure and the controlling parameter while an ensemble Kalman filter estimates the states. The approach is demonstrated with the help of a mechanical system under spatial variation in temperature for which subdomain isolation necessitates the interface to be measured. In the context of the numerical application, the induced fault is due to damage, and the mechanical model is controlled and parameterized by the internal temperature, whose variations can be significant due to substantial external thermal variations inducing significant variations in the dynamic properties.