# Data Fusion Analysis and Synthesis Framework for Improving Disaster Situation Awareness
## 6 Objectives and the Effects of Data Fusion
### Calculating the Effect of Data Fusion  
The estimated effect of fusion of a set of data sources depends on the contribution of each data source if they are attached to the same element. The effect must be estimated according to one of the objectives defined in the previous section. For determining the effectiveness values, depending on the characteristics of the geographical elements, prospective data sources, and the size and structure of the fusion, one may use different models of computation. Arithmetical formulas, statistical methods [19], Bayesian networks [20], Markov models, [60] etc., are typical examples. We observe, however, three determining factors: First, the model of computation must match the physical properties of the fusion. Second, it must be computationally efficient since these computations may need to be carried out many times especially during a synthesis process. Third, a library of alternative algorithms must be available if desired. This will give flexibility to the user in deciding the best algorithm for a particular case. In this article, the unit of calculation is based on one of the element types within a geographical area such as a residence. Basically, there are two cases:  
1. **Effectiveness of fusion of data sources with no contribution to each other**. In this case, the effectiveness value of the data source with the highest value is considered. For example, in Appendix B Table A4, it is estimated that the data sources of UAV cameras, motion-based collapse detectors, seismic detectors, and cameras of the face recognizers have no contribution to a GPS tracker. 2. **Effectiveness of fusion of data sources with some contribution two each other**. The effectiveness value of the fusion must be computed. In the following, we define three alternative formulas; Weak, Average, and Strong Contributions:  
* **Weak contribution:** Per effectiveness objective, the selected \(N\) data sources are ranked according to their effectiveness value from \(1..N\), where \(1\) represents the data source with the highest effectiveness value and \(N\) is the lowest. The effectiveness of data fusion of the element \(k\in K\) which is denoted as \(E_{k}\) with respect to objective \(j\in J\) which is denoted as \(O_{j}\) is calculated using the following formula: \[EF(E_{k},O_{j})=  
* **Medium contribution:** This formula uses the same parameters as the Equation (1). The only difference is, in Equation (2), \((1-e_{m})\) the component of the formula is not squared. \[EF(E_{k},O_{j})=e_{1}+\sum_{n=2}^{N}\prod_{m=1}^{n-1}(1-e_{m})\cdot{e_{n}}^{2}\] (2)
* **Strong contribution:** This formula uses the same parameters as the Equation (2). The only difference is, in Equation (3), the \(e_{n}\) component of the formula is not squared. \[EF(E_{k},O_{j})=e_{1}+\sum_{n=2}^{N}\prod_{m=1}^{n-1}(1-e_{m})\cdot e_{n}\] (3)  
The effects of the three formulas are illustrated in the Figure 4. Here, the green, orange, and blue lines display the weak, medium, and strong contributions, respectively. This figure is drawn with the assumption that every additional data source has the effectiveness value 0.5. It can be seen that green contribution has an upper bound of approximately 0.6. **Example 2**. : _Let us assume that the following data sources are to be considered for the residence \(R\):_  
* _A UAV-camera is dispatched to the geographical area._
* _There is a base station in the geographical area._
* _One collapse detector is installed at the ground floor._
* _There exists a registration database._
* _There is a face recognizer at the entrance of the building._
* _The camera of the face recognizer is used also as a collapse detector._  
Based on Appendices A and B, the objective values are computed as follows:  
**Objective 1 (effectiveness)**: To estimate the effectiveness value for this objective, using the Tables A1 and A2 from Appendix A and based on the mean values of the distribution functions, the data sources under consideration are ranked:  
1. Collapse detector (0.7). 2. UAV-camera (0.7). 3.