Robust multi-task distributed estimation based on generalized maximum correntropy criterion

False data injection(FDI) attacks are common in the distributed estimation of multi-task network environments, so an attack detection strategy is designed by combining the generalized maximum correntropy criterion. Based on this, we propose a diffusion least-mean-square algorithm based on the generalized maximum correntropy criterion(GMCC-DLMS)for multi-task networks. The algorithm achieves gratifying estimation results. Even more, compared to the related work,it has better robustness when the number of attacked nodes increases. Moreover, the assumption about the number of attacked nodes is relaxed, which is applicable to multi-task environments. In addition, the performance of the proposed GMCC-DLMS algorithm is analyzed in the mean and mean-square senses. Finally, simulation experiments confirm the performance and effectiveness against FDI attacks of the algorithm.

Distributed Dynamic Load in Structural Dynamics by the Impulse-Based Force Estimation Algorithm

This paper proposes a novel approach for identifying distributed dynamic loads in the time domain.Using polynomial andmodal analysis,the load is transformed intomodal space for coefficient identification.This allows the distributed dynamic load with a two-dimensional form in terms of time and space to be simultaneously identified in the form of modal force,thereby achieving dimensionality reduction.The Impulse-based Force Estimation Algorithm is proposed to identify dynamic loads in the time domain.Firstly,the algorithm establishes a recursion scheme based on convolution integral,enabling it to identify loads with a long history and rapidly changing forms over time.Secondly,the algorithm introduces moving mean and polynomial fitting to detrend,enhancing its applicability in load estimation.The aforementioned methodology successfully accomplishes the reconstruction of distributed,instead of centralized,dynamic loads on the continuum in the time domain by utilizing acceleration response.To validate the effectiveness of the method,computational and experimental verification were conducted.

Distributed Secure State Estimation of Multi-Agent Systems Under Homologous Sensor Attacks

This paper addresses the problem of distributed secure state estimation for multi-agent systems under homologous sensor attacks.Two types of secure Luenberger-like distributed observers are proposed to estimate the system state and attack signal simultaneously.Specifically,the proposed two observers are applicable to deal with the cases in the presence and absence of time delays during network communication.It is also shown that the proposed observers can ensure the attack estimations from different agents asymptotically converge to the same value.Sufficient conditions for guaranteeing the asymptotic convergence of the estimation errors are derived.Simulation examples are finally provided to demonstrate the effectiveness of the proposed results.

Distributed Estimation of Oscillations in Power Systems: An Extended Kalman Filtering Approach

Online estimation of electromechanical oscillation parameters provides essential information to prevent system instability and blackout and helps to identify event categories and locations.We formulate the problem as a state space model and employ the extended Kalman filter to estimate oscillation frequencies and damping factors directly based on data from phasor measurement units.Due to considerations of communication burdens and privacy concerns,a fully distributed algorithm is proposed using diffusion extended Kalman filter.The effectiveness of proposed algorithms is confirmed by both simulated and real data collected during events in State Grid Jiangsu Electric Power Company.

Distributed Estimation in Sensor Networks with Repetition Coding

This paper considers the distributed estimation of a source parameter using quantized sensor observations in a wireless sensor network with noisy channels. Repetition codes are used to transmit quantization bits of sensor observations and a quasi best linear unbiased estimate is constructed to estimate the source parameter. Simulations show that the estimation scheme achieves a better power and spectral efficiency than the previous scheme.

Universal Distributed Estimation Scheme for a Bandwidth Constrained Ad Hoc Sensor Network

This paper describes a distributed estimation scheme （DES） for a bandwidth constrained ad hoc sensor network. The DES is universal in the sense that operations on all sensors are identical and independent of noise distribution. The scheme requires each sensor to transmit just a 1-bit message per observation. Simulation results show that the scheme achieves much better mean-squares error （MSE） performance than the simplified isotropic universal DES and even outperforms the isotropic universal DES which requires more than twice the bandwidth of this scheme.

Distributed Estimation for Sensor Networks with Channel Estimation Errors

This paper describes the effect of channel estimation error （CEE） on the performance of distributed estimations of an unknown parameter in a wireless sensor network. Both the classical and Bayesian estimators are derived to mitigate the adverse effects caused by the CEE. Power scheduling among sensors and the power ratio between the training and data transmission at each individual node are optimized by directly minimizing the final average mean squared error to compensate for the CEE. A closed-form power scheduling policy is given for a homogeneous environment, which shows that more than 50% of the power should be allocated to sensor observation transmissions. For an inhomogeneous environment, a multilevel waterfilling type solution is developed for the power scheduling among sensors for only the sum power constraint with a ＂cave＂ waterfilling solution for both the sum and individual power constraints. Simulations show that the proposed power scheduling schemes achieve better performance than the equal power scheduling scheme.

Distributed computations for large-scale networked systems using belief propagation

This paper introduces several related distributed algorithms,generalised from the celebrated belief propagation algorithm for statistical learning.These algorithms are suitable for a class of computational problems in largescale networked systems,ranging from average consensus,sensor fusion,distributed estimation,distributed optimisation,distributed control,and distributed learning.By expressing the underlying computational problem as a sparse linear system,each algorithm operates at each node of the network graph and computes iteratively the desired solution.The behaviours of these algorithms are discussed in terms of the network graph topology and parameters of the corresponding computational problem.A number of examples are presented to illustrate their applications.Also introduced is a message-passing algorithm for distributed convex optimisation.

An Ellipsoidal Set-Membership Approach to Distributed Joint State and Sensor Fault Estimation of Autonomous Ground Vehicles

This paper is concerned with the problem of distributed joint state and sensor fault estimation for autonomous ground vehicles subject to unknown-but-bounded(UBB)external disturbance and measurement noise.In order to improve the estimation reliability and performance in cases of poor data collection and potential communication interruption,a multisensor network configuration is presented to cooperatively measure the vehicular yaw rate,and further compute local state and fault estimates.Toward this aim,an augmented descriptor vehicle model is first established,where the unknown sensor fault is modeled as an auxiliary state of the system model.Then,a new distributed ellipsoidal set-membership estimation approach is developed so as to construct an optimized bounding ellipsoidal set which guarantees to contain the vehicle’s true state and the sensor fault at each time step despite the existence of UBB disturbance and measurement noises.Furthermore,a convex optimization algorithm is put forward such that the gain matrix of each distributed estimator can be recursively obtained.Finally,simulation results are provided to validate the effectiveness of the proposed approach.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

Efficient Distributed Estimation of High-dimensional Sparse Precision Matrix for Transelliptical Graphical Models

In this paper,distributed estimation of high-dimensional sparse precision matrix is proposed based on the debiased D-trace loss penalized lasso and the hard threshold method when samples are distributed into different machines for transelliptical graphical models.At a certain level of sparseness,this method not only achieves the correct selection of non-zero elements of sparse precision matrix,but the error rate can be comparable to the estimator in a non-distributed setting.The numerical results further prove that the proposed distributed method is more effective than the usual average method.

Distributed Privacy-Preserving Fusion Estimation Using Homomorphic Encryption

The privacy-preserving problem for distributed fusion estimation scheme is concerned in this paper.When legitimate user wants to obtain consistent information from multiple sensors,it always employs a fusion center(FC)to gather local data and compute distributed fusion estimates(DFEs).Due to the existence of potential eavesdropper,the data exchanged among sensors,FC and user imperatively require privacy preservation.Hence,we propose a distributed confidentiality fusion structure against eavesdropper by using Paillier homomorphic encryption approach.In this case,FC cannot acquire real values of local state estimates,while it only helps calculate encrypted DFEs.Then,the legitimate user can successfully obtain the true values of DFEs according to the encrypted information and secret keys,which is based on the homomorphism of encryption.Finally,an illustrative example is provided to verify the effectiveness of the proposed methods.

Distributed Trimmed Hill Estimator

Proceeded from trimmed Hill estimators and distributed inference, a new distributed version of trimmed Hill estimator for heavy tail index is proposed. Considering the case where the number of observations involved in each machine can be either the same or different and either fixed or varying to the total sample size, its consistency and asymptotic normality are discussed. Simulation studies are particularized to show the new estimator performs almost in line with the trimmed Hill estimator.

Adaptive Multisensor Tracking Fusion Algorithm for Air－borne Distributed Passive Sensor Network

Single passive sensor tracking algorithms have four disadvantages: bad stability, longdynamic time, big bias and sensitive to initial conditions. So the corresponding fusion algorithm results in bad performance. A new error analysis method for two passive sensor tracking system is presented and the error equations are deduced in detail. Based on the equations, we carry out theoretical computation and Monte Carlo computer simulation. The results show the correctness of our error computation equations. With the error equations, we present multiple 'two station'fusion algorithm using adaptive pseudo measurement equations. This greatly enhances the tracking performance and makes the algorithm convergent very fast and not sensitive to initial conditions.Simulation results prove the correctness of our new algorithm.

Average Convergence for Directed&Undirected Graphs in Distributed Systems

Consensus control of multi-agent systems is an innovative paradigm for the development of intelligent distributed systems.This has fascinated numerous scientific groups for their promising applications as they have the freedom to achieve their local and global goals and make their own decisions.Network communication topologies based on graph and matrix theory are widely used in a various real-time applications ranging from software agents to robotics.Therefore,while sustaining the significance of both directed and undirected graphs,this research emphases on the demonstration of a distributed average consensus algorithm.It uses the harmonic mean in the domain of multi-agent systems with directed and undirected graphs under static topologies based on a control input scheme.The proposed agreement protocol focuses on achieving a constant consensus on directional and undirected graphs using the exchange of information between neighbors to update their status values and to be able to calculate the total number of agents that contribute to the communication network at the same time.The proposed method is implemented for the identical networks that are considered under the directional and non-directional communication links.Two different scenarios are simulated and it is concluded that the undirected approach has an advantage over directed graph communication in terms of processing time and the total number of iterations required to achieve convergence.The same network parameters are introduced for both orientations of the communication graphs.In addition,the results of the simulation and the calculation of various matrices are provided at the end to validate the effectiveness of the proposed algorithm to achieve consensus.

Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields

This paper presents a Markov random field （MRP） approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields （DEUM）. DEUM is a subclass of estimation of distribution algorithms （EDAs） where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are： 1） use of MRF models, 2） fitness modeling approach to estimating the parameter of the model and 3） Monte Carlo approach to sampling from the model.

Cramer-Rao bound and signal-to-noise ratio gain in distributed coherent aperture radar

This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent aperture radar （DCAR）. Firstly, three architectures of signal processing in the DCAR are introduced. Secondly, the closed-form Cramer-Rao bound （CRB） of the CPP estimation is derived and compared. Then, the closed-form CRB is verified by numerical simulations. Finally, when the next generation radar works in a fully coherent mode, the closed-form signal-to-noise ratio （SNR） gain of the three architectures is presented.

Combinations of Estimation of Distribution Algorithms and Other Techniques

This paper summaries our recent work on combining estimation of distribution algorithms （EDA） and other techniques for solving hard search and optimization problems： a） guided mutation, an offspring generator in which the ideas from EDAs and genetic algorithms are combined together, we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem, b） evolutionary algorithms refining a heuristic, we advocate a strategy for solving a hard optimization problem with complicated data structure, and c） combination of two different local search techniques and EDA for numerical global optimization problems, its basic idea is that not all the new generated points are needed to be improved by an expensive local search.

An improved estimation of distribution algorithm for multi-compartment electric vehicle routing problem

The multi-compartment electric vehicle routing problem(EVRP)with soft time window and multiple charging types(MCEVRP-STW&MCT)is studied,in which electric multi-compartment vehicles that are environmentally friendly but need to be recharged in course of transport process,are employed.A mathematical model for this optimization problem is established with the objective of minimizing the function composed of vehicle cost,distribution cost,time window penalty cost and charging service cost.To solve the problem,an estimation of the distribution algorithm based on Lévy flight(EDA-LF)is proposed to perform a local search at each iteration to prevent the algorithm from falling into local optimum.Experimental results demonstrate that the EDA-LF algorithm can find better solutions and has stronger robustness than the basic EDA algorithm.In addition,when comparing with existing algorithms,the result shows that the EDA-LF can often get better solutions in a relatively short time when solving medium and large-scale instances.Further experiments show that using electric multi-compartment vehicles to deliver incompatible products can produce better results than using traditional fuel vehicles.

Archimedean copula estimation of distribution algorithm based on artificial bee colony algorithm

The artificial bee colony （ABC） algorithm is a com- petitive stochastic population-based optimization algorithm. How- ever, the ABC algorithm does not use the social information and lacks the knowledge of the problem structure, which leads to in- sufficiency in both convergent speed and searching precision. Archimedean copula estimation of distribution algorithm （ACEDA） is a relatively simple, time-economic and multivariate correlated EDA. This paper proposes a novel hybrid algorithm based on the ABC algorithm and ACEDA called Archimedean copula estima- tion of distribution based on the artificial bee colony （ACABC） algorithm. The hybrid algorithm utilizes ACEDA to estimate the distribution model and then uses the information to help artificial bees to search more efficiently in the search space. Six bench- mark functions are introduced to assess the performance of the ACABC algorithm on numerical function optimization. Experimen- tal results show that the ACABC algorithm converges much faster with greater precision compared with the ABC algorithm, ACEDA and the global best （gbest）-guided ABC （GABC） algorithm in most of the experiments.