## 3 Results and Discussion
### Simulations for Chain-Based Network
The reason for observing high network MSE for high BER for average and EBDKF can be explained by looking at the increasing size of the 95% confidence interval for those two methods as evident from Figure 5. In contrast, the proposed method's confidence interval is only slightly increased with increasing BER, so that it is showing least network MSE for high BER. Further, the average method's accuracy approaches that of proposed method when \(0.001<BER<0.002\) as seen from the confidence interval and observable in Figure 4 as well. We further analyze the impact of the transmission errors on each individual bit in a data frame/packet. Figure 6 depicts how each individual bit in a data frame/packet experience two different BER conditions. Here, we compare the mean value of bit wise accuracy of the quantized output of fused result of each node with the quantized value of the system parameter. We set 100% error if a bit is altered and 0% error if the particular bit of the quantized fused output is same as the corresponding bit of the quantized value of system parameter. Here, we get the mean of the results for particular bit considering all the nodes to obtain the network bit level performance for first five most significant bits. The significant bits can drastically change the final value from the true value. For example, the impact of MSB is higher than the total combination of next four significant bits. When BER is 0.005, the average error probabilities of first five significant bits of EBDKF is lesser than both AVG and proposed method. The percentage error of first two Significant bits for proposed and AVG methods remain at very low values but higher than EBDKF. The decreasing order of magnitude of percentage error in first two most significant bits are in the order of AVG, proposed method, and EBDKF. Therefore, this proves why it is seen a high network MSE and high width of 95% confidence interval in Figures 4 and 5, respectively, in decreasing order as AVG, proposed method and EBDKF when BER is 0.005. However, when BER is 0.05, the preceding order changes to EBDKF, AVG, and the proposed method proving that proposed method shows lower error probabilities for the first two most significant bits compared to AVG and EBDKF as seen in Figure 6. When observing the size of the confidence intervals at a BER of 0.05, only the proposed method's interval is small as seen in Figure 5. The size of the confidence interval is moderately large for Average and very large for EBDKF. Same order is observed for first two MSB s for BER of 0.05 in Figure 6. Therefore, we can use the proposed method to protect these most significant bits successfully under high communication error environments. This explains why we observe a significant performance gap among the three different fusion schemes at BER 0.05 in Figures 4 and 5. It can also be observed from Figure 6 that the percentage error of both third and fourth significant bits of all considered fusion schemes have increased when BER is 0.05 compared to BER of 0.005. However, the percentage error of first two significant bits for proposed method is reduced by a very small amount and that for Average and EBDKF have been significantly increased as the BER is increased. Redundant node deployment can be used to improve the accuracy of fusion schemes. We simulate the information fusion process in chain-based network by varying the number of nodes. Here, the distance between the sink node and the furthest node is kept constant at 2500 m. Figure 7 shows the  
Figure 6: Bit level error performance comparison among the proposed statistical, EBDKF, and AVG information fusion methods in a chain-based IoT platform for (**a**) BER of 0.005 and (**b**) BER of 0.05.  
number of nodes required for AVG, EBDKF, and proposed statistical methods to maintain a given network mean square error. It is evident from Figure 7 that when more sensor nodes are added, the network MSE of all the aggregation schemes decrease. However, the rate of decrement of MSE depends on the aggregation method.