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.

Determining the network size is a critical process in numerous areas (e.g., computer science, logistic, epidemiology, social networking services, mathematical modeling, demography, etc.). However, many modern real-world systems are so extensive that measuring their size poses a serious challenge. Therefore, the algorithms for determining/estimating this parameter in an effective manner have been gaining popularity over the past decades. In the paper, we analyze five frequently applied distributed consensus gossip-based algorithms for network size estimation in multi-agent systems (namely, the Randomized gossip algorithm, the Geographic gossip algorithm, the Broadcast gossip algorithm, the Push-Sum protocol, and the Push-Pull protocol). We examine the performance of the mentioned algorithms with bounded execution over random geometric graphs by applying two metrics: the number of sent messages required for consensus achievement and the estimation precision quantified as the median deviation from the real value of the network size. The experimental part consists of two scenarios—the consensus achievement is conditioned by either the values of the inner states or the network size estimates—and, in both scenarios, either the best-connected or the worst-connected agent is chosen as the leader. The goal of this paper is to identify whether all the examined algorithms are applicable to estimating the network size, which algorithm provides the best performance, how the leader selection can affect the performance of the algorithms, and how to most effectively configure the applied stopping criterion.

Efficient data aggregation is crucial for mobile wireless sensor networks, as their resources are significantly constrained. Over recent years, the average consensus algorithm has found a wide application in this technology. In this paper, we present a weight matrix simplifying the average consensus algorithm over mobile wireless sensor networks, thereby prolonging the network lifetime as well as ensuring the proper operation of the algorithm. Our contribution results from the theorem stating how the Laplacian spectrum of an undirected simple finite graph changes in the case of adding an arbitrary edge into this graph. We identify that the mixing parameter of Best Constant weights of a complete finite graph with an arbitrary order ensures the convergence in time-varying topologies without any reconfiguration of the edge weights. The presented theorems and lemmas are verified over evolving graphs with various parameters, whereby it is demonstrated that our approach ensures the convergence of the average consensus algorithm over mobile wireless sensor networks in spite of no edge reconfiguration.

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.

This paper addresses the regression modeling of local environmental pollution levels for electric power industry needs, which is fundamental for the proper design and maintenance of high-voltage transmission lines and insulators in order to prevent various hazards, such as accidental flashovers due to pollution and the resultant power outages. The primary goal of our study was to increase the precision of regression models for this application area by exploiting additional input attributes extracted from satellite imagery and adjusting the modeling methodology. Given that thousands of different attributes can be extracted from satellite images, of which only a few are likely to contain useful information, we also explored suitable feature selection procedures. We show that a suitable combination of attribute selection methods (relief, FSRF-Test, and forward selection), regression models (random forest models and M5P regression trees), and modeling methodology (estimating field-measured values of target variables rather than their upper bounds) can significantly increase the total modeling accuracy, measured by the correlation between the estimated and the true values of target variables. Specifically, the accuracies of our regression models dramatically rose from 0.12–0.23 to 0.40–0.64, while their relative absolute errors were conversely reduced (e.g., from 1.04 to 0.764 for the best model).