## 3 Results and Discussion
### Simulations for Hierarchical Tree Structured Network  
2.1 Simulations for Data Accuracy of a Deterministic Constant (Slowly Varying) Parameter Having Bounded Sensor Noise  
In this section, the mean square error of the network is analyzed by considering different network sizes that vary from 20 to 240 in steps of 20 nodes. The heterogeneous measurement noise variances are generated by setting \(b_{0}=0.3\) and \(a_{0}=0.1\). Figure 12 shows the network MSE comparison among three different fusion techniques for the considered network sizes. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Fusion Function** & **Latency for Zig Bee (ms)** & **Latency for WCDMA (ms)** \\ \hline Average & 32.004(N\(-\)1) & 6.97(N\(-\)1) \\ Proposed Method & 8.008(N\(-\)1) & 1.74(N\(-\)1) \\ EBDKF & 98.42 & 23.316 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Network Latency of different information fusion functions for chain-based network. When observing the results in Figure 12, it can be seen that the accuracy of the sink node and network using proposed method is always higher than that of conventional average method and the performance gap between these two approaches reduces with the number of nodes. The accuracy of those two methods become almost same when the number of nodes is greater than 120 for both network and the sink node. When we increase the number of nodes in the network, sensor nodes become closer to each other as the area in which sensor nodes are placed is maintained constant. Therefore, the average link distance is reduced, even though the individual link distances vary, making the resultant BER values of links in the network to be reduced. For example, when the number of nodes is increased from 20 to 240, the BER of a link is reduced from 0.2289 to 0.000002 following the shape similar to an inverse square law function. When the BER reduces, the performance gap of all three fusion methods for sink node's accuracy approaches a very low value, but the accuracy is in the decreasing order of EBDKF, proposed method and average having a very low accuracy gap between each of them. EBDKF fusion technique has the highest accuracy out of all the methods when the number of nodes is greater than 60 for both sink node and the network. The average BER value, when number of nodes is equal to 60, is 0.0173. Therefore, the proposed method shows highest accuracy when the average BER of a link is higher than 0.0173. When the number of Nodes is less than or equal to 40, i.e., when average BER of a link is greater than 0.0455, the EBDKF fusion's accuracy degrades resulting least accuracy out of the three methods. The performance gap between the network and the sink node accuracy is very low. This can be explained as a result of both the network and the sink nodes having equivalent number (1.87 exactly as derived in following section on complexity) of average neighbors and since all nodes act as aggregating nodes. For chain-based network, the accuracy of sink node and network almost overlapped as seen in Figure 4. However, in contrast, for tree-based network the accuracy of the sink node had been always better than the network for proposed statistical method. The performance gap of the accuracy of network and sink node for proposed method reduces as the  
Figure 12: Accuracy comparison among the proposed statistical, AVG, and EBDKF information fusion methods in a tree-based IoT platform. BER is increased. Lower accuracy of the network can be explained as a result of 47% (refer section on complexity evaluation) non-aggregating leaf nodes present in tree networks which do not use any fusion technique, but only transmit the measurement to immediate node. In tree network, the network MSE performance of the average method is higher than that of the chain-based network. The reason for this can be predicted as the increment of the average number of child nodes for a given node in tree-based network.