Incorrect sensor readings can cause serious problems in Wireless Sensor Networks (WSNs), potentially disrupting the operation of the entire system. As shown in the literature, they can arise from various reasons; therefore, addressing this issue has been a significant challenge for the scientific community over the past few decades. In this paper, we examine the applicability of seven distributed consensus gossip-based algorithms for sensor fusion (namely, the Randomized Gossip algorithm, the Geographic Gossip algorithm, three initial configurations of the Broadcast Gossip algorithm, the Push-Sum protocol, and the Push-Pull protocol) to compensate for incorrect data in WSNs. More specifically, we consider a scenario where the sensor-measured data (measured by a set of independent sensor nodes) are skewed due to Gaussian noise with a various standard deviation $\sigma$, resulting in discrepancies between the measured values and the true value of observed physical quantities. Subsequently, the aforementioned algorithms are employed to mitigate this skewness in order to improve the accuracy of the measured data. In this paper, WSNs are modeled as random geometric graphs with various connectivity, and the performance of the algorithms is evaluated using two metrics (specifically, the mean square error (MSE) and the number of sent messages required for an algorithm to be completed). Based on the presented results, it is identified that all the examined algorithms can significantly suppress incorrect sensor readings (MSE without sensor fusion = −0.42 dB if $\sigma$ = 1, and MSE without sensor fusion = 14.05 dB if $\sigma$ = 5), and the best performance is achieved by PS in dense graphs and by GG in sparse graphs (both algorithms achieve the maximum precision MSE = −24.87 dB if $\sigma$ = 1 and MSE = −21.02 dB if $\sigma$ = 5). Additionally, the performance of the analyzed distributed consensus gossip algorithms is compared to the best deterministic consensus algorithm applied for the same purpose.

In recent decades, distributed consensus-based algorithms for data aggregation have been gaining in importance in wireless sensor networks since their implementation as a complementary mechanism can ensure sensor-measured values with high reliability and optimized energy consumption in spite of imprecise sensor readings. In the presented article, we address the average consensus algorithm over bipartite regular graphs, where the application of the maximum-degree weights causes the divergence of the algorithm. We provide a spectral analysis of the algorithm, propose a distributed mechanism to detect whether a graph is bipartite regular, and identify how to reconfigure the algorithm so that the convergence of the average consensus algorithm is guaranteed over bipartite regular graphs. More specifically, we identify in the article that only the largest and the smallest eigenvalues of the weight matrix are located on the unit circle; the sum of all the inner states is preserved at each iteration despite the algorithm divergence; and the inner states oscillate between two values close to the arithmetic means determined by the initial inner states from each disjoint subset. The proposed mechanism utilizes the first-order forward and backward finite-difference of the inner states (more specifically, five conditions are proposed) to detect whether a graph is bipartite regular or not. Subsequently, the mixing parameter of the algorithm can be reconfigured the way it is identified in this study whereby the convergence of the algorithm is ensured in bipartite regular graphs. In the experimental part, we tested our mechanism over randomly generated bipartite regular graphs, random graphs, and random geometric graphs with various parameters, thereby identifying its very high detection rate and proving that the algorithm can estimate the arithmetic mean with high precision (like in error-free scenarios) after the suggested reconfiguration.

Consensus-based data aggregation in d-regular bipartite graphs poses a challenging task for the scientific community since some of these algorithms diverge in this critical graph topology. Nevertheless, one can see a lack of scientific studies dealing with this topic in the literature. Motivated by our recent research concerned with this issue, we provide a comparative study of frequently applied consensus algorithms for distributed averaging in d-regular bipartite graphs in this paper. More specifically, we examine the performance of these algorithms with bounded execution in this topology in order to identify which algorithm can achieve the consensus despite no reconfiguration and find the best-performing algorithm in these graphs. In the experimental part, we apply the number of iterations required for consensus to evaluate the performance of the algorithms in randomly generated regular bipartite graphs with various connectivities and for three configurations of the applied stopping criterion, allowing us to identify the optimal distributed consensus algorithm for this graph topology. Moreover, the obtained experimental results presented in this paper are compared to other scientific manuscripts where the analyzed algorithms are examined in non-regular non-bipartite topologies.