Modern power systems are cyber-physical systems with increasing relevance and influence of information and communication technology. This influence comprises all processes, functional, and non-functional aspects like functional correctness, safety, security, and reliability. An example of a process is the data acquisition process. Questions focused in this paper are, first, how one can trust in process data in a data acquisition process of a highly-complex cyber-physical power system. Second, how can the trust in process data be integrated into a state estimation to achieve estimated results in a way that it can reflect trustworthiness of that input?We present the concept of an anomaly-sensitive state estimation that tackles these questions. The concept is based on a multi-faceted trust model for power system network assessment. Furthermore, we provide a proof of concept by enriching measurements in the context of the IEEE 39-bus system with reasonable trust values. The proof of concept shows the benefits but also the limitations of the approach.