## 3 Results and Discussion
### Simulations for Chain-Based Network
Thus, the proposed statistical method is able to maintain the network mean square error less than 0.29 for the considered BER range. Diffusion techniques do not differentiate between the parent and child nodes; they identify both child nodes and the parent as neighbors. For chain structure employing diffusion techniques, the number of neighbors of the intermediate nodes is always equal to two, whereas the number of  
Figure 4: Performance comparison among the proposed statistical, EBDKF, and AVG information fusion methods in a chain-based IoT platform for different BER. neighbors of the first and sink node is equal to one. The number of child nodes per network and the sink node for a WSN employing the proposed statistical method and the AVG fusion techniques are always equal to one. Therefore, the accuracy of the information fusion for network and the sink node will be similar for networks employing AVG and the proposed method, as is evident from the results obtained in Figure 4. When the number of nodes is high, so is the number of intermediate nodes. Therefore, the average number of neighbors for a network employing EBDKF is equivalent to two. But, the sink node will definitely have only one neighbor. The performance gap of EBDKF for network MSE error and MSE of sink node observed in Figure 4 must be due to this difference in number of neighbors of the sink node and the network. For low BER values, the network MSE has been lower than sink node's MSE. That is because an estimate produced by a diffusion technique becomes more accurate when the number of neighbors is higher under low communication errors. However, the higher number of neighbors will greatly reduce the accuracy under high communication errors for diffusion techniques. That is why the sink having only one neighbor outperforms its network having two neighbors for high BER values. However, still, we can observe that the proposed method's sink node's MSE is lesser than MSE of sink node employing EBDKF for BERs higher than 0.025. However, the accuracy of the sink node of EBDKF fusion technique is always lesser than accuracy of a sink node with Average data fusion for all BER s.  
To have a very good understanding about the network's estimate of the system parameter under different BER for different information fusion schemes, we plot the mean value of the estimate at each node and the mean value of each node's 95% confidence interval limits as illustrated in Figure 5.  
Figure 5: Network Mean estimate and 95% confidence interval limits for a true state of 1.80 compared among the proposed statistical, EBDKF and AVG information fusion methods in a chain-based IoT platform for different BER. When analyzing the results obtained in Figure 5, it can be seen that for low BER values, the network mean estimate is very close to the system state of 1.8 for all fusion techniques. However, the performance in terms of accuracy is different due to difference in the variance of the estimates of different fusion techniques. This variance can be identified by looking at the size of the 95% confidence interval in Figure 5. In very low BER conditions (\(<\)10\({}^{-5}\)), the 95% confidence interval is also narrow and its width is in decreasing order for Average, EBDKF, and proposed method proving the previous result obtained for network MSE for very low probability of communication errors. This is because we can say that when the confidence interval for the results is higher, so is the network mean square error. The mean estimate of the proposed method decreases slightly and remains very close to the real value of 1.8 when BER increases outperforming the accuracy of mean estimate of other two fusion techniques. However, the mean value tends to deviate more from real value of 1.8 when BER increases for other two data fusion techniques where the AVG method having a moderate deviation and EBDKF having the highest deviation.