MPC of thermal systems usually results in robust operation with respect to uncertainties thanks to some key characteristics of the controller. However, the true limit until which these systems will actually be robust is rarely known explicitly. In this study a Hybrid Ground Coupled Heat Pump (HyGCHP) system with MPC is investigated, for which state estimation and disturbance prediction are highly uncertain, moreover, the system performance is highly sensitive to errors at these points. It has become popular to design control systems which perform explicit computations to assure robustness (e.g. min-max Robust MPC) but this framework is computationally demanding, therefore, not widely applied. An alternative is to perform robustness analysis of an MPC controlled system which is though generally avoided due to complicated theoretical formulations, implicitness and conservativeness of the approach. To tackle these issues an existing framework for robustness analysis is extended and applied to the case of a HyGCHP system with MPC to analyze robustness with respect to state estimation uncertainty. This paper presents an approach to use the original formulation, suggested for regulation/stabilization in order to analyze robustness for the case of set point tracking. The results show that the maximum allowed state estimation uncertainty found by robustness analysis of the regulation problem is confirmed by the simulated HyGCHP system with MPC, which performs set point tracking. In conclusion, the method gives a reliable guarantee for the degree of state estimation uncertainty, up to which the HyGCHP system investigated remains robust. Future research can extend the robustness analysis method towards disturbance prediction uncertainty.