## 1 Introduction
### Review of Data Aggregation  
Conventional information fusion functions, which can be incorporated irrespective of parallel of serial information fusion, are type-sensitive, and type threshold symmetric functions such as Average (AVG), Maximum (MAX), Minimum (MIN), Mode, mean of k largest values, etc. [25]. For single bit quantization of data, for instance in the case of decision fusion; OR, AND, K out of N, MAJORITY functions has been used where the performance of information accuracy depended on the measurement frequency and number of nodes [26; 27; 28]. The Chair Varnish Rule has been presented as the optimum one-bit fusion technique, but in this technique, it is needed to know the probability of detection and failure for all sensor nodes at the fusion center which is a major drawback [29; 30]. These information fusion functions combine the information frames/packets from multiple nodes to a single frame/packet. Thus, redundant data transmission can be minimized. Although it is beneficial in terms of energy consumption, this might reduce the accuracy. For example, a single erroneous data can add a biased to the resultant average value when AVG is employed as the information fusion function. Furthermore, MAX and MIN choose only extreme values in information fusion process and do not combine different information to reduce the noise level. Thus, there is a high possibility to vary the fused information from the true value at intermediate devices. It can lead to huge failures in power delivery and stability of SGs due to the unreliable information. In centralized/parallel estimation, the fusion estimate is produced at a single fusion center where all the sensor nodes transmit their local observations. The major drawback of this aggregation mechanism is that network lifetime is shorter than decentralized approach, as the distant nodes consuming larger amount of energy for direct transmission to the fusion center [22]. An improved version of AVG known as support degree fusion had been used as one of the data fusion techniques for centralized estimation. In this algorithm, the support degree is the amount by which the measurements by each sensor are close to each other. At the fusion center, measurements from each sensor are weighted by the support degree to obtain the estimate using the power average operator without the awareness of any probability distribution [31; 32; 33]. Decentralized estimation under distributed detection has been a research area over the last few decades. Linear state estimation fusion techniques such as Maximum Likelihood Estimate, Linear Minimal Variance Estimate, and Best Linear Unbiased Estimate (BLUE) had been invented in 1990s [34; 35; 36; 37; 38]. These fusion techniques use local estimates and covariance between local estimates to compute a global estimate. More recent trend is to use Kalman Filtering. During the first decade of the 21 st century, consensus-based Kalman filter fusion techniques have been proposed [39; 40; 41; 42]. Consensus refers to the general agreement among the sensors. In the preceding algorithm, sensors exchange local information or state estimates among the neighbors during each observation period to reach a consensus on the global estimate known as Consensus Estimation. In between consensus estimates, information is broadcasted to neighbors and fused where state estimates and error covariances are updated. Therefore, broadcasting with neighbors takes place iteratively in between consensus estimations, this algorithm will consume more energy and is less suitable to SG environments. Diffusion strategies had been developing since early 2010s, which show faster convergence and lower mean square error than consensus strategies [43]. Diffusion strategies shown in [44; 45] include standard Kalman filtering update, diffusion update step, and a time update step. At every time instant, a given node will broadcast local observations for Kalman filter update and intermediate estimate for diffusion update.