## 2 Methods for Industrial Data Fusion at Sensor, Feature and Decision Level  
Efficiency, repeatability, robustness, and quality of manufacturing processes are of great importance in today's production sites. Monitoring systems enable to capture parameters and system states in real time, allowing to effectively control manufacturing processes. The quality and performance of these automation systems stand and fall with the reliability and precision of available information. As a result, robust and accurate process measurements are of crucial relevance to satisfy higher-quality requirements. A common approach to tackle these issues is a fast developing and huge research field called sensor fusion. The scope of data fusion, also known as sensor fusion, multi-sensor data fusion, multi-sensor integration, data combination or data aggregation is to obtain improved information with higher accuracy by merging multiple information sources. It fosters the robustness, reliability and confidence of the analysed information and improves the temporal and spatial resolution [8]. Initial developments of sensor-fusion-based systems go back to the military industry, where the authentication and tracking of dynamic objects is of crucial importance. Recently, further sectors such as the automotive sector experience a strong increase in sensor fusion for autonomous vehicles to accurately map their environment. There have been multiple attempts to define a definition and framework for sensor data fusion. One of the most popular definitions has been presented by the Joint Directors of Laboratories (JDL) [9] describing sensor fusion as a multi-level process handling the association, correlation and combination of data and information from single and multiple sources. This section focuses on the application of AI-based algorithms for industrial data fusion. For a deeper insight in further data fusion architectures, the reader is referred to [10; 11; 12]. To capitalize on the benefits of sensor data fusion, some challenges must be overcome for a successful implementation. There are various data properties affecting the feasibility and success of the data fusion process. The main challenges of data fusion arise from the heterogeneity of data sources and individual imperfections of each data source such as uncertainty, imprecision or granularity. An overview of typical data fusion issues is displayed in Figure 3.  
Depending on the considered data type and its fusion issues, suitable fusion algorithms must be selected. Today's available algorithms only address a subset of these aspects. Due to the multitude of applications and available algorithms, the following section does not claim to be complete, but identifies promising methodologies for applications in industrial control solutions. Furthermore, there are many ways to classify fusion algorithms. [PERSON] et al. [13] presented the algorithms according to their abstraction level as signal level, feature level and decision level, whereas [PERSON] et al. [14] divides fusion approaches in probabilistic models, least-square techniques and intelligent fusion. Figure 3: Taxonomy describing data-fusion-related issues. On a _signal level_, the most intuitive and easiest way to increase the signal-to-noise ratio of redundant sources is to apply the weighted average or the least squares method on captured data. A more sophisticated and widespread method is the Kalman Filter. The Kalman Filter considers the statistical characteristics of the measurements while still allowing for real-time processing of the data. Kalman filtering is a discrete and time invariant approach and only holds for linear models. Unfortunately, practical problems often have strong non-linear relations. To overcome these limitations, Extended Kalman Filter (EKF) [15], Unscented Kalman Filter (UKF) or the Particle Filter (PF) [16] also known as Sequential Monte Carlo (SMC) have been developed to handle non-linear relationships. A drawback of the latter method is the increasing computational effort and rising amount of required data.