## 2 Materials and Methods
### Information Fusion in Chain-Based IOT Platform using Proposed Method
#### 2.8.2 Method of Performance Evaluation  
We conduct a series of simulations using OMNeT++ 5.1 academic edition software platform to evaluate the performance of the proposed statistical information fusion approach comparing the testing parameter with results of AVG fusion and Estimation Based Diffusion Kalman Filter method of fusion. Both fusion accuracy and network life time are considered. OMNeT++ is an open source object-oriented modular discrete event network simulation framework having a generic architecture [54]. In [55], the authors compared the performance of OMNeT++ and Network Simulator 2(NS2), and concluded that OMNeT++ performs better than NS2 for large WSN. As our simulations also contain sensor nodes containing 20 to 240 nodes, we selected OMNeT++ for simulations. As it is impractical to simulate all three algorithms of data fusion at the same time, they were simulated separately in OMNeT++ environment and some final results of three fusion techniques were exported separately to MATLAB environment for graphical analysis, while some were integrated in the OMNeT++ environment appropriately. A stationary, time invariant chain-based network topology is generated by deploying nodes in equal distances. We assume that MICA2 wireless sensor nodes are used in the network as IoT end devices. The BER of each link is determined based on the analytical model given in [56]. We set the transmission power \(P_{t}=0\) dBm, reference distance \(d_{0}=1\) m, power loss at reference distance \(PL(d_{0})=55\) dBm, the noise floor \(P(n)=-115\) dBm and the parameters for path loss exponent \((n)\), and shadowing effects \((\sigma)\) in Equation (29)) are set to 3.3 and 4. The modulation scheme selected for wireless communication was Non-Coherent Frequency Shift Keying so that \(BER(P_{e})\) is given by Equation (28) [56]. \[P_{e}=\frac{exp^{\frac{-\gamma(d)}{2}}}{2} \tag{28}\]  
where \(\gamma(d)\) is the signal to noise ratio at distance d from the source which is given in dB by Equation (29) as,  
\[\gamma(d)indB=P_{t}-(PL(d_{0})-10*n*log_{10}\frac{d}{d_{0}}+X_{\sigma})-P_{n} \tag{29}\]  
All other parameters are as specified in [56]. Unless otherwise specified, the \(L_{k}\) is set to 8. Heterogeneous measurement noise variances are considered and they are generated for all fusion techniques as given in Equation (30) subjected to an upper bound for fair comparison of three different fusion techniques. \[\sigma_{s_{k}}^{2}=R_{k,i}=b_{0}+{a_{0}}^{2}\chi^{2}(1) \tag{30}\]  
Here, \(\chi^{2}(1)\) is the chi squared distribution with degree of freedom 1, \(b_{0}\) represents the network wide noise variance threshold, and \(a_{0}\) gives the underlying variation from the nominal minimum. Noise variance is calculated in this manner to create heterogeneous sensing conditions between sensors of the same network and to create heterogeneous network conditions among initializations. This variance is calculated at the initialization of the network for each node and will be a constant there after. Gaussian distribution is used to generate instantaneous noise (\(n_{k}\)) of a particular sensor node. This noise is added to the actual parameter to get the sensor measurement as shown in Equation (1). The Gaussian distribution's mean is set to zero and variance is set to the value generated at the network initialization using Equation (30) for a particular sensor node. Note that different sensor nodes of the same network will have different noise variances as they are generated from Chi-Square distribution as it was shown in Equation (30). For a particular sensor of a given network, the variance generated using Equation (30) is a constant. That means each time a particular sensor node takes a measurement; the noise is generated using the same Gaussian distribution. However, when a network is initialized again, Equation (30) will make sure that a particular sensor will get a different value for variance making the PDF of sensor measurements different.