## 3 Results and Discussion
### Simulations for Hierarchical Tree Structured 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 (decreasing nodes), so that it is showing least network MSE for high BER. It is very important to understand the impact of number of data gathering cycles on the accuracy of the estimate. Therefore, we plot the network MSE vs. the number of data gathering cycles as shown in Figure 14.  
Average bit error rate of 0.05 corresponds to 38 nodes and that of 0.0003 corresponds to 200 nodes in tree structure. We selected these two BER values because when BER is 0.05, the accuracy of proposed method is higher than EBDKF and vice versa for BER of 0.0003 for 600 data gathering cycles as proven in Figure 12. Indeed, all the results generated so far corresponded to 600 data gathering cycles. As it is evident from Figure 14, the previous argument is unchanged for any data gathering cycle. Only the MSE gap is changed with data gathering cycles. For all fusion methods, the network MSE for high communication errors is always higher than that for low communication errors for any data gathering cycle. The proposed method shows the least deviation and thus the highest stability on the network MSE against number of data gathering cycles. It shows higher fluctuations of network MSE for initial data gathering cycles (for up to about 50 cycles) for both BER s than when number of data cycles are much higher. Similar variation with data cycles is observed in AVG method, but its variations are higher than proposed method and it consumes a higher number of data cycles for the network MSE to get stabilized. However, in contrast, the MSE performance with data cycles is different for data fusion scheme EBDKF under high communication errors. As proved by Figure 14, the variation of proposed method with data cycles even for high communication errors is almost same as that for low communication errors. When it comes to the diffusion technique, the network MSE is always lesser than 1.0 until first 28 data gathering cycles for BER of 0.05 case. After that, the network MSE value is often greater than 1.0. On the other hand, for low communication error scenario, EBDKF tend to be less accurate for initial data gathering cycles. That is because we can observe a big spike at 20 data cycles and a smaller spike at 120 and no spike after that with highly stable MSE for the graph of EBDKF for BER of  
Figure 13: 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 tree-based IoT platform for different number of sensor nodes. 0.0003 in Figure 14. Therefore, it can be deduced that accuracy of diffusion technique is better for low data gathering cycles under high communication errors and vice versa. The proposed method has clearly outperformed both AVG and EBDKF under BER of 0.05 for any data gathering cycle as it was concluded for 600 data gathering cycles before. We further analyze the impact of BER on bit level error characteristics in Figure 4.0  
Two networks are simulated where network one has 38 nodes and network two has 98 nodes corresponding approximately to average BER of 0.05 and 0.005, respectively. These values are selected in order to have a fair comparison of the bit level accuracy among tree and chain topologies. When the proposed statistical information fusion method is employed, the most significant 4 bits are successfully recovered in both networks. The bit flipping in the most significant bits significantly change the accuracy of the fused value. In network two (\(\text{BER}=0.005\)), the average error probabilities of most significant bits show lower values for both Average and proposed methods, in which the proposed method has a slightly lesser value.