## 4 Conclusions  
Measurement errors, quantization errors, and transmission errors are the three major sources of errors that affect the information fusion performance of IoT platforms in smart grids. We incorporate the statistical properties of these errors to information fusion to improve the information accuracy. The proposed statistical information fusion function not only shows highest information accuracy on popular information fusion structures, namely, chain and tree, but also in ad hoc networks under high communication errors (\(BER>0.0175\)) when compared with AVG and EBDKF fusion methods. Further, for chain network EBDKF outperformed the proposed method's accuracy for \(10^{-5}<BER<10^{-2}\) and for tree structure and ad hoc-type networks when \(BER<0.017\). The accuracy of EBDKF fusion method varies having a high deviation for initial data gathering cycles under high communication errors while network MSE performance of all fusion techniques are considerably stable under low channel errors. The computational complexity of fusion techniques is always in the increasing order of AVG, proposed and EBDKF methods, respectively. When retransmissions are not allowed, simulation results prove that the proposed method achieves a network lifetime similar to AVG method and outperform the diffusion techniques for any BER. Fusion functions use different techniques such as retransmissions and redundant node deployment to improve the information accuracy under high communication errors. As the proposed statistical approach does not require these supporting techniques, it not only saves a large amount of energy and results in a longest network life time, but also leads to least network latency in HANs for both structured and unstructured networks and FANs in ad hoc-type networks outperforming both AVG and EBDKF in retransmission allowed networks. Further, the proposed method satisfies the maximum tolerable network latency requirement of 300 ms for SG applications targeted in this context for both FANs and WANs in all types of networks. When proposed method is used in structured FANs such as chain and tree, EBDKF outperformed the latency of proposed method when the link length is high. Therefore, under smart grid communication conditions, the proposed method is having the highest accuracy and network lifetime for all chain, tree and graph networks. When the effect of all the factors such as information accuracy, fusion complexity, latency and energy efficiency are combined, even under low communication errors, the overall performance  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Fusion Function** & **Latency for Zig Bee (ms)** & **Latency for WCDMA (ms)** \\ \hline Average & 8.034(K + 1) + 0.00375 & 1.775(K + 1) + 0.00375 \\ Proposed Method & 8.034(K + 1) + 0.01125 & 1.775(K + 1) + 0.01125 \\ EBDKF & 49.202(K + 1) + 0.0867 & 11.65(K + 1) + 0.0867 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Network latency of different information fusion functions for non-hierarchical sensor network.  
of the proposed method can be considered to be higher than other fusion techniques considered in this context.  
Conceptualization, H.L. and C.S.; methodology, C.S., P.A.D.S.N.W., and H.L.; software, P.A.D.S.N.W. and C.S.; validation, P.A.D.S.N.W.; formal analysis,P.A.D.S.N.W. and C.S.; investigation, H.L., C.S., and P.A.D.S.N.W.; resources, P.A.D.S.N.W.; data curation, P.A.D.S.N.W.; writing--original draft preparation, P.A.D.S.N.W. and C.S.; writing--review and editing, H.L.; visualization, P.A.D.S.N.W. and C.S; supervision, H.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
We show our gratitude to [PERSON], Head of the Department of Electrical and Information Engineering for approving the research conducted by second author during working hours in Faculty of Engineering, University of Ruhuna, Galle, Sri Lanka.  
The authors declare no conflict of interest.