However, both methods lead to high overestimation. Therefore, it is necessary to bisect often to obtain very small intervals in order to be able to prove the injectivity. Furthermore, the provided and presented solver ITVIA only allows determining the injectivity of functions mapping \(\mathbb{R}\rightarrow\mathbb{R}^{2}\) or \(\mathbb{R}^{2}\rightarrow\mathbb{R}^{2}\)[10]. Thereby, the verification of injectivity is impracticable, especially since the number of required Lie derivatives is unknown and cannot be easily varied. In [11], [PERSON] and [PERSON] analyze the observability of nonlinear systems. The authors use automatic differentiation to determine the Taylor coefficients of Lie derivatives. The resulting observability matrix is checked on full rank by singular value decomposition. The smallest singular value over time gives the authors information about whether a nonlinear system is observable. The method is capable of determining whether a nonlinear system might be observable. However, it is not able to identify the observable states or which areas are not distinguishable. In [12] interval arithmetic routines are used to verify the controllability and observability of the states in case of uncertain dynamic systems. For this purpose the observability matrix is constructed using automatic differentiation and the rank is checked. Therefore, the observability can only be verified locally. However, the importance of taking the reachability and observability of states into account for choosing the structures for control laws and state observers in the earliest design stages are shown. A different approach to prove local as well as global observability of nonlinear systems is presented in [13]. The method considers polynomial systems with a one-dimensional output equation \(\mathbb{R}^{n}\rightarrow\mathbb{R}\). The authors [PERSON] and [PERSON] use the method of quantor elimination [14] to determine the injectivity of the observability matrix or the observability function, respectively. Depending on the number of Lie derivatives, a binary decision about observability of the system is possible. If the system states are defined as free variables, thus they are not bound to a quantor, it is also possible to specify the restrictions if the algorithm returns false as a result. Thereby, constraints can be specified for which the states are distinguishable. However, this does not allow the exact assignment about which state is indistinguishable from which other state. The advantage of the method presented in [13] is that the nonlinear state space representation can be parameter-dependent. The parameters are also considered as free variables. Therefore, constraints can be found for which the observability of the nonlinear system can be proven. All of these methods do not provide the determination of indistinguishable states. However, this information may be of particular interest. It would be usable to design a controller such that the system is stabilized while its states remain in the observable domain. Motivated by these issues, the aim of this work is to contribute a method to analyze the observability of nonlinear systems. The determination of indistinguishable states is provided by the work [15]. This approach is enhanced by system uncertainties in [16], which will be presented in the following. Therefore, this work provides an iterative algorithm based on interval arithmetics to determine whether the nonlinear system (1), (2) is observable. In case that the system is not globally observable, the subset for which observability has been proven is given even if the subset is of a complex structure. Additionally, the information about the indistinguishable states is provided. This is uniquely for this method and allows insight on how to modify an output function to achieve global observability of a nonlinear system. Thus, a method is available, which allows the user to check the observability of a nonlinear system with system uncertainties, whereby only the knowledge of the system equation is required.