The purpose of model updating is to minimize the misfit between the structural response measurements and an assumed numerical model. In the context of damage quantification, this misfit is characterized by some features computed from the response data measured on the faulty structure, and its Finite Element (FE) model in the healthy condition. The FE model is parameterized so that the estimated features are related to the physical parameters of the model. Therein, the parameterization size may be large. As a consequence of low instrumentation, different parameters can have a similar effect on the estimated features, resulting in non uniqueness of the updating problem solutions, even taking into account the inherent uncertainty errors, originating both from the model and the measurements. In this paper a model updating-based damage quantification strategy is proposed. It involves the minimization of two Hankel matrices, one computed from the data and another from the optimized model. The difference between those two matrices is studied, in particular in the practical case where the ambient excitation is unknown. It yields a statistical residual, whose deviations from zero can be evaluated through a statistical test. The resulting optimization is based on the Generalized Likelihood Ratio test as an objective function and uses its 95 per cent quantile as a measure of closeness for a stopping criterion for the optimization. Moreover, the large size of the finite element model to optimize compared to the low instrumentation has to be taken into account by clustering the parameter space. This clustering is proceeded using the well known stochastic subspace-based damage localisation method. The proposed framework is validated on simulations of a simple mechanical system.