The Pseudo-Pascal Triangle of Maximum Deng Entropy

PPascal triangle (known as Yang Hui Triangle in Chinese) is an important model in mathematics while the entropy has been heavily studied in physics or as uncertainty measure in information science. How to construct the the connection between Pascal triangle and uncertainty measure is an interesting topic. One of the most used entropy, Tasllis entropy, has been modelled with Pascal triangle. But the relationship of the other entropy functions with Pascal triangle is still an open issue. Dempster-Shafer evidence theory takes the advantage to deal with uncertainty than probability theory since the probability distribution is generalized as basic probability assignment, which is more efficient to model and handle uncertain information. Given a basic probability assignment, its corresponding uncertainty measure can be determined by Deng entropy, which is the generalization of Shannon entropy. In this paper, a Pseudo-Pascal triangle based the maximum Deng entropy is constructed. Similar to the Pascal triangle modelling of Tasllis entropy, this work provides the a possible way of Deng entropy in physics and information theory

Accurate range-free localization for anisotropic wireless sensor networks

Journal ArticlePosition information plays a pivotal role in wireless sensor network (WSN) applications and protocol/ algorithm design. In recent years, range-free localization algorithms have drawn much research attention due to their low cost and applicability to large-scale WSNs. However, the application of range-free localization algorithms is restricted because of their dramatic accuracy degradation in practical anisotropic WSNs, which is mainly caused by large error of distance estimation. Distance estimation in the existing range-free algorithms usually relies on a unified per hop length (PHL) metric between nodes. But the PHL between different nodes might be greatly different in anisotropic WSNs, resulting in large error in distance estimation. We find that, although the PHL between different nodes might be greatly different, it exhibits significant locality; that is, nearby nodes share a similar PHL to anchors that know their positions in advance. Based on the locality of the PHL, a novel distance estimation approach is proposed in this article. Theoretical analyses show that the error of distance estimation in the proposed approach is only one-fourth of that in the state-of-the-art pattern-driven scheme (PDS). An anchor selection algorithm is also devised to further improve localization accuracy by mitigating the negative effects from the anchors that are poorly distributed in geometry. By combining the locality-based distance estimation and the anchor selection, a range-free localization algorithm named Selective Multilateration (SM) is proposed. Simulation results demonstrate that SM achieves localization accuracy higher than 0.3r, where r is the communication radius of nodes. Compared to the state-of-the-art solution, SM improves the distance estimation accuracy by up to 57% and improves localization accuracy by up to 52% consequently.This work is partially supported by the National Science Foundation of China (61103203, 61173169, 61332004, and 61420106009), the Hong Kong RGC General Research Fund (PolyU 5106/11E), the International Science & Technology Cooperation Program of China (2013DFB10070), and the EU FP7 QUICK project (PIRSES-GA-2013-612652)

Joint Frequency and DOA Estimation with Automatic Pairing Using the Rayleigh–Ritz Theorem

This paper presents a novel scheme for joint frequency and direction of arrival (DOA) estimation, that pairs frequencies and DOAs automatically without additional computations. First, when the property of the Kronecker product is used in the received array signal of the multiple-delay output model, the frequency-angle steering vector can be reconstructed as the product of the frequency steering vector and the angle steering vector. The frequency of the incoming signal is then obtained by searching for the minimal eigenvalue among the smallest eigenvalues that depend on the frequency parameters but are irrelevant to the DOAs. Subsequently, the DOA related to the selected frequency is acquired through some operations on the minimal eigenvector according to the Rayleigh–Ritz theorem, which realizes the natural pairing of frequencies and DOAs. Furthermore, the proposed method can not only distinguish multiple sources, but also effectively deal with other arrays. The effectiveness and superiority of the proposed algorithm are further analyzed by simulations

Development an accurate and stable range-free localization scheme for anisotropic wireless sensor networks

With the high-speed development of wireless radio technology, numerous sensor nodes are integrated into wireless sensor networks, which has promoted plentiful location-based applications that are successfully applied in various fields, such as monitoring natural disasters and post-disaster rescue. Location information is an integral part of wireless sensor networks, without location information, all received data will lose meaning. However, the current localization scheme is based on equipped GPS on every node, which is not cost-efficient and not suitable for large-scale wireless sensor networks and outdoor environments. To address this problem, research scholars have proposed a rangefree localization scheme which only depends on network connectivity. Nevertheless, as the representative range-free localization scheme, Distance Vector-Hop (DV-Hop) localization algorithm demonstrates extremely poor localization accuracy under anisotropic wireless sensor networks. The previous works assumed that the network environment is evenly and uniformly distributed, ignored anisotropic factors in a real setting. Besides, most research academics improved the localization accuracy to a certain degree, but at expense of high communication overhead and computational complexity, which cannot meet the requirements of high-precision applications for anisotropic wireless sensor networks. Hence, finding a fast, accurate, and strong solution to solve the range-free localization problem is still a big challenge. Accordingly, this study aspires to bridge the research gap by exploring a new DV-Hop algorithm to build a fast, costefficient, strong range-free localization scheme. This study developed an optimized variation of the DV-Hop localization algorithm for anisotropic wireless sensor networks. To address the poor localization accuracy problem in irregular C-shaped network topology, it adopts an efficient Grew Wolf Optimizer instead of the least-squares method. The dynamic communication range is introduced to refine hop between anchor nodes, and new parameters are recommended to optimize network protocol to balance energy cost in the initial step. Besides, the weighted coefficient and centroid algorithm is employed to reduce cumulative error by hop count and cut down computational complexity. The developed localization framework is separately validated and evaluated each optimized step under various evaluation criteria, in terms of accuracy, stability, and cost, etc. The results of EGWO-DV-Hop demonstrated superior localization accuracy under both topologies, the average localization error dropped up to 87.79% comparing with basic DV-Hop under C-shaped topology. The developed enhanced DWGWO-DVHop localization algorithm illustrated a favorable result with high accuracy and strong stability. The overall localization error is around 1.5m under C-shaped topology, while the traditional DV-Hop algorithm is large than 20m. Generally, the average localization error went down up to 93.35%, compared with DV-Hop. The localization accuracy and robustness of comparison indicated that the developed DWGWO-DV-Hop algorithm super outperforms the other classical range-free methods. It has the potential significance to be guided and applied in practical location-based applications for anisotropic wireless sensor networks

Enhancing sensor duty cycle in environmental wireless sensor networks using Quantum Evolutionary Golden Jackal Optimization Algorithm

Environmental wireless sensor networks (EWSNs) are essential in environmental monitoring and are widely used in gas monitoring, soil monitoring, natural disaster early warning and other fields. EWSNs are limited by the sensor battery capacity and data collection range, and the usual deployment method is to deploy many sensor nodes in the monitoring zone. This deployment method improves the robustness of EWSNs, but introduces many redundant nodes, resulting in a problem of duty cycle design, which can be effectively solved by duty cycle optimization. However, the duty cycle optimization in EWSNs is an NP-Hard problem, and the complexity of the problem increases exponentially with the number of sensor nodes. In this way, non-heuristic algorithms often fail to obtain a deployment solution that meets the requirements in reasonable time. Therefore, this paper proposes a novel heuristic algorithm, the Quantum Evolutionary Golden Jackal Optimization Algorithm (QEGJOA), to solve the duty cycle optimization problem. Specifically, QEGJOA can effectively prolong the lifetime of EWSNs by duty cycle optimization and can quickly get a deployment solution in the face of multi-sensor nodes. New quantum exploration and exploitation operators are designed, which greatly improves the global search ability of the algorithm and enables the algorithm to effectively solve the problem of excessive complexity in duty cycle optimization. In addition, this paper designs a new sensor duty cycle model, which has the advantages of high accuracy and low complexity. The simulation shows that the QEGJOA proposed in this paper improves by 18.69, 20.15 and 26.55 compared to the Golden Jackal Optimization (GJO), Whale Optimization Algorithm (WOA) and the Simulated Annealing Algorithm (SA)

Distributed localisation algorithm for wireless ad hoc networks of moving nodes

Existing ad hoc network localisation solutions rely either on external location references or network-wide exchange of information and centralised processing and computation of location estimates. Without these, nodes are not able to estimate the relative locations of other nodes within their communication range. This thesis defines a new distributed localisation algorithm for ad hoc networks of moving nodes. The Relative Neighbour Localisation (RNL) algorithm works without any external localisation signal or systems and does not assume centralised information processing. The idea behind the location estimates produced by the RNL algorithm is the relationship between the relative locations of two nodes, their mobility parameters and the signal strengths measured between them. The proposed algorithm makes use of the data available to each node to produce a location estimate. The signal strength each node is capable of measuring is used as one algorithm input. The other input is the velocity vector of the neighbouring node, composed of its speed and direction of movement, which each node is assumed to periodically broadcast. The relationship between the signal strength and the mobility parameters on one, and the relative location on the other side can be analytically formulated in an ideal case. The limitations of a realistic scenario complicate this relationship, making it very difficult to formulate analytically. An empirical approach is thus used. The angle and the distance estimates are individually computed, together forming a two-dimensional location estimate. The performance of the algorithm was analysed in detail using simulation, showing a median estimate error of under 10m, and its application was tested through design and evaluation of a distributed sensing coverage algorithm, showing RNL location estimates can provide 90% of the coverage achievable with true locations being known