This paper compares the integration of measurement data with the data-fusion of the same set of data, and shows the superiority of the data-fusion by applying certain information functions and additional transformations to the covariance matrices. The algorithm to be used is the linear Kalman-Filter where the covariances can be computed without any measurement data. The improvement of the data-fusion algorithm will be demonstrated by partitioning the system into a canonical form (independent subsystems), which allows the processing of every set of data on its own (integration of data). In a further algorithm we evaluate the same sets of data, but this time the system models consists of the real physical relationships of the variables and therefore combines the different measurements to the desired estimates (data-fusion). In a first step we compare the estimates of both algorithms and their variances to understand that data fusion leads to more exact estimates. This is because the different measurement variables do not only contain information of the value of 'their own' state variable, but also of the values of other state variables. So this information leads to more exact estimates. To demonstrate the information gain we use Shannon's entropy, which provides a scalar measure of the whole additional information contained in the measurement variables. To obtain the gained information of every single state variable an additional transformation is necessary. This transformation (Karhunen-Loeve) and the fact that Shannon's entropy depends on the coordinate system, finally demonstrates the improvement of the data-fusion algorithm for every single state variable.
"Information gained by data fusion", Proc. SPIE 2784, Vision Systems: Sensors, Sensor Systems, and Components, (21 August 1996); doi: 10.1117/12.248528; https://doi.org/10.1117/12.248528