Distributed Estimation Method Research Articles

Prescribed‐time distributed direct estimation under relative state measurements

AbstractThe distributed estimation technology is prevalently utilized to solve the leader‐following multi‐agent tracking problem. This technology poses a challenge in practice, since it generally relies on the available absolute state measurements. For this reason, a novel distributed estimation approach based on relative state measurements is developed in this article. The proposed method directly estimates the tracking error between the leader and each follower, rather than using an existing indirect way of estimating and making subtraction under absolute state measurements. Specifically, a distributed directed estimation is first studied to complete estimation tasks within prescribed time under the known directed networks. Then, a fully distributed directed estimation problem is considered under the unknown directed networks. Both distributed and fully distributed results are extended to the robustness cases to resist external disturbances. Simulation examples, including numerical examples and a multiship coordination example, are provided to demonstrate the effectiveness and advantages of the proposed distributed estimation method.

Comparison of different estimation methods for the inverse power perk distribution with applications in engineering and actuarial sciences

Introducing the Inverse Power Perk distribution, this paper presents a versatile probability distribution designed to model positively skewed data with unprecedented flexibility. Building upon the Perk distribution, it accommodates a wide range of shapes including right-skewed, J-shaped, reversed J-shaped, and nearly symmetric densities, as well as hazard rates exhibiting various patterns of increase and decrease. The paper delves into the mathematical properties of this novel distribution and offers a comprehensive overview of estimation techniques, including maximum likelihood estimators, ordinary least square estimators, percentile-based estimators, maximum product of spacing estimators, Cramer-von Mises, weighted least squares estimators, and Anderson-Darling estimators. To assess the performance of these estimation methods across different sample sizes, Monte Carlo simulations are conducted. Through comparisons of average absolute error and mean squared error, the efficacy of each estimator is evaluated, shedding light on their suitability for both small and large samples. In a practical application, three real datasets, including insurance data, are employed to demonstrate the versatility of the current model, when comparing to existing alternatives. The IPP distribution offers significant advantages over traditional distributions, particularly in its superior ability to model tail risks, making it an invaluable tool for practitioners dealing with extreme values and rare events. Its computational efficiency further sets it apart, enabling more robust and faster analysis in large-scale datasets.This empirical analysis further underscores the utility and adaptability of the Inverse Power Perk model in capturing the nuances of diverse datasets, thereby offering valuable insights for practitioners in various fields.

Comparison Of Some Estimation Methods For The Estimators Of Marshall Olkin Distribution With Simulation

The research comprised multiple simulated tests to determine the relationship between (sample size, distribution parameter value, estimation method, and pollution indivuduales). The experimental findings indicate that the estimator is influenced by sample size, the value of distribution parameter, estimation method, and pollution indivuduales. The results of the mean square error analysis indicate that (robust estimation method) produces the best results with the lowest mean square error, and the best estimation method was (191) of (243) simulation experiments. Additional statistical distributions with additional factors can be performed to demonstrate additional results.

Distributed Consensus Estimation for Networked Multi-Sensor Systems under Hybrid Attacks and Missing Measurements.

Cyber-security research on networked multi-sensor systems is crucial due to the vulnerability to various types of cyberattacks. For the development of effective defense measures, attention is required to gain insight into the complex characteristics and behaviors of cyber attacks from the attacker's perspective. This paper aims to tackle the problem of distributed consensus estimation for networked multi-sensor systems subject to hybrid attacks and missing measurements. To account for both random denial of service (DoS) attacks and false data injection (FDI) attacks, a hybrid attack model on the estimator-to-estimator communication channel is presented. The characteristics of missing measurements are defined by random variables that satisfy the Bernoulli distribution. Then a modified consensus-based distributed estimator, integrated with the characteristics of hybrid attacks and missing measurements, is presented. For reducing the computational complexity of the optimal distributed estimation method, a scalable suboptimal distributed consensus estimator is designed. Sufficient conditions are further provided for guaranteeing the stability of the proposed suboptimal distributed estimator. Finally, a simulation experiment on aircraft tracking is executed to validate the effectiveness and feasibility of the proposed algorithm.

Hybrid-attack-resistant distributed state estimation for nonlinear complex networks with random coupling strength and sensor delays

In this paper, a recursive distributed hybrid-attack-resistant state estimation (SE) scheme is proposed for a class of time-varying nonlinear complex networks (NCNs) subject to random coupling strength (RCS) and random sensor delays (RSDs) under hybrid attacks. A hybrid-attack model is considered to characterize the random occurrence of denial-of-service (DoS) attacks and deception attacks. The objective of the problem to be solved is to develop a recursive distributed estimation method such that, in the presence of RCS, RSDs and hybrid attacks, a locally optimized upper bound (UB) on the estimation error covariance (EEC) is ensured. By employing the mathematical induction method, a UB is firstly derived on the EEC. Subsequently, the obtained UB is minimized by appropriately designing the estimator gain (EG). Furthermore, a sufficient criterion guaranteeing the exponential boundedness (EB) of SE error is elaborated in the mean square sense (MSS). Finally, simulation experiments with localization applications of multiple mobile indoor robots are conducted to illustrate the applicability of the proposed SE scheme.

Solving Contextual Stochastic Optimization Problems through Contextual Distribution Estimation

Stochastic optimization models always assume known probability distributions about uncertain parameters. However, it is unrealistic to know the true distributions. In the era of big data, with the knowledge of informative features related to uncertain parameters, this study aims to estimate the conditional distributions of uncertain parameters directly and solve the resulting contextual stochastic optimization problem by using a set of realizations drawn from estimated distributions, which is called the contextual distribution estimation method. We use an energy scheduling problem as the case study and conduct numerical experiments with real-world data. The results demonstrate that the proposed contextual distribution estimation method offers specific benefits in particular scenarios, resulting in improved decisions. This study contributes to the literature on contextual stochastic optimization problems by introducing the contextual distribution estimation method, which holds practical significance for addressing data-driven uncertain decision problems.

Comparison of some Bayesian estimation methods for type-I generalized extreme value distribution with simulation

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimating the scale parameter of the Weibull distribution. To evaluate their performance, we generate simulated datasets with different sample sizes and varying parameter values. A technique for pre-estimation shrinkage is suggested to enhance the precision of estimation. Simulation experiments proved that the Bayesian shrinkage estimator and shrinkage pre-estimation under the squared loss function method are better than the other methods because they give the least mean square error. Overall, our findings highlight the advantages of shrinkage Bayesian estimation methods for the proposed distribution. Researchers and practitioners in fields reliant on extreme value analysis can benefit from these findings when selecting appropriate Bayesian estimation techniques for modeling extreme events accurately and efficiently.

Comparing some estimation methods for Frechet Distribution (Simulation)

The Frechet distribution, widely utilized in various fields such as hydrology, finance, and environmental sciences, poses challenges in parameter estimation, This study aims to compare several estimation methods for the Frechet distribution under scenarios with outlier observations. We consider both classical and robust estimation techniques, including ( Maximum Likelihood Estimation (MLE), Method of Moments (MOM), Least Squares Estimation (LSE), and Robust Regression methods(RRE)). To evaluate the performance of these methods, extensive simulation studies are conducted under different sample sizes and intial parameter values .mean squared error, are employed to assess the accuracy and robustness of each method under varying conditions. Our findings provide insights into the effectiveness and limitations of different estimation approaches for the Frechet distribution when simulation parameters are present, aiding practitioners in selecting suitable methods for robust parameter estimation in practical applications. Simulation results show that estimation method effected with (sample size, initial parameter values and evaluation criteria) , Bayesian estimation methods can be compared with Non-Bayesian estimation methods for Frechet distribution.

Comparison of item response theory ability and item parameters according to classical and Bayesian estimation methods

This research aims to compare the ability and item parameter estimations of Item Response Theory according to Maximum likelihood and Bayesian approaches in different Monte Carlo simulation conditions. For this purpose, depending on the changes in the priori distribution type, sample size, test length, and logistics model, the ability and item parameters estimated according to the maximum likelihood and Bayesian method and the differences in the RMSE of these parameters were examined. The priori distribution (normal, left-skewed, right-skewed, leptokurtic, and platykurtic), test length (10, 20, 40), sample size (100, 500, 1000), logistics model (2PL, 3PL). The simulation conditions were performed with 100 replications. Mixed model ANOVA was performed to determine RMSE differentiations. The prior distribution type, test length, and estimation method in the differentiation of ability parameter and RMSE were estimated in 2PL models; the priori distribution type and test length were significant in the differences in the ability parameter and RMSE estimated in the 3PL model. While prior distribution type, sample size, and estimation method created a significant difference in the RMSE of the item discrimination parameter estimated in the 2PL model, none of the conditions created a significant difference in the RMSE of the item difficulty parameter. The priori distribution type, sample size, and estimation method in the item discrimination RMSE were estimated in the 3PL model; the a priori distribution and estimation method created significant differentiation in the RMSE of the lower asymptote parameter. However, none of the conditions significantly changed the RMSE of item difficulty parameters.

Distributed state estimation for leak detection in water supply networks

In this paper, we focus on observer-based approaches of leak detection and isolation in pipeline networks, which has the potential to be extended to large-scale water supply network systems, while in previous studies only single pipeline scenario is considered. Due to several disadvantages of implementing centralized state estimation for large-scale systems, the distributed Kalman filter algorithm has been applied in this paper. The observers are designed on the basis of a set of nonlinear fluid models of pipelines, pumps and other hydraulic accessories, with uncertainties in leak position and magnitude. The approach assumes only flow and pressure measurements at the ends of each duct. Simulation results with a water transmission line are presented to assess the efficiency of the proposed distributed state estimation method while comparing with its centralized counterpart.

Toward Data Integrity Attacks Against Distributed Dynamic State Estimation in Smart Grid

With the continuous expansion of the power grid nodes scale, traditional centralized state estimation method shows certain limitations in estimation efficiency and accuracy. Recently, some power grids adopt a distributed state estimation method, in which each partition independently estimates the partial state information by partitioning the entire power system. However, the deviation of the state estimation in certain partition will result in the deviation of the estimation results in the entire power grid system. In this paper, we propose the attack strategy against the distributed state estimation in smart grids from two perspectives, i.e. the attack against local physical measurement value of the power system partition and the attack against the measurement value of coordination center. Moreover, the theoretical analysis of the state estimation deviation caused by the proposed data integrity attack and the propagation processes of proposed attack vectors in measurement calculations are formalized. The effectiveness of the proposed attack strategy is verified in the IEEE-30 bus and IEEE-118 bus systems. Simulation results show that attacking against a certain partition of a distributed system can indirectly affect the state estimation results of other partitions and attacking against the measurement value of coordination center can directly threaten the state estimation results of the entire power grid. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes two attack strategies against the distributed state estimation of power grid from two perspectives, i.e. the attack against local physical measurement value of the power system partition and the attack against the measurement value of coordination center. Most of the previous works fail to formalize the state estimation deviation of both partial and entire state estimation results of power grid after the attacker launches the attack against the distributed state estimation. We formalize the state estimation deviation caused by the proposed data integrity attack and the propagation processes of proposed attack vectors in measurement calculations. The effectiveness of the proposed attack strategy against the state estimation of power grid is verified in the IEEE-30 bus and IEEE-118 bus systems. Simulation results show that attacking against a certain partition of power grid can indirectly cause the deviation in the state estimation results of entire power grid and attacking against the measurement value of the coordination center can directly threaten the state estimation results of the entire power grid. In conclusion, the proposed attack strategies are helpful for the research community to design detection strategies in a targeted manner and can be conveniently applied to the real-world security management system of smart grid.

Locally Masked Convolutional Models for Anomalous Sound Detection by Deep Learning

Anomalous Sound Detection by Deep Learning could be used to automatically detect malfunctions in mechanical products from their operating sounds. With many normal sounds but very few anomalous sounds available for training, one-class classification methods applied to sound spectrograms are the most suitable methods. Among them, the Masked Autoencoder for Distribution Estimation (MADE) method showed state-of-the-art results with transient anomalous sounds but poor results with sustained anomalous sounds. The loss of the spectro-temporal structure in the inputs possibly explaining this issue, we have modified a method recently designed for 2D image completion, taking advantage of the full spectro-temporal structure of the inputs. When evaluated on industrial data, this new method outperforms a baseline Autoencoder method and the original MADE method.

Modeling Climate data using the Quartic Transmuted Weibull Distribution and Different Estimation Methods

Modeling Climate data using the Quartic Transmuted Weibull Distribution and Different Estimation Methods

Overall particle size distribution estimation method based on kinetic modeling and transformer prediction

Estimating the overall particle size distribution (PSD) on the conveyor is one of the most important means of monitoring blast furnace production. Due to the harsh production environment and limited detection conditions, existing online detection methods can only estimate part of the PSD, but it is difficult to predict the overall PSD. Unlike segmentation methods that can only obtain surface PSD, we propose an overall PSD estimation method based on mechanistic modeling and local–global fused prediction networks. First, we constructed a kinetic mechanism model of particle accumulation, from which global field distribution features such as coordination number, moment of inertia, and spatial distribution were extracted. Then, a particle segmentation model is trained using surface images collected by detection means such as cameras to obtain surface PSDs as local surface features. Next, to predict the overall PSD, we propose a Local surface and Global field distribution feature Fusion-based Transformer network (LGFT). Among them, in order to better aggregate local and global features, we introduce orthogonal fusion and point cloud extractors in the encoder. Finally, we verify the accuracy and efficiency of our method through extensive ablation experiments.

Survival Analysis and Hazard of Log Logistic Distribution on Type I Censored Data Parametrically

Survival Analysis is a research method that examines the survival time of individuals or experimental units in relation to events such as death, disease, recovery, or other experiences. This study utilizes a parametric survival analysis model with a 2 parameter log logistic distribution and Maximum Likelihood Estimation (MLE) method to analyze the survival of students during their study period. The log logistic distribution is chosen due to its ability to capture early or late failure patterns. The objective of this research is to analyze type I censored survival data using the log logistic distribution applied to secondary data on student study duration. The dataset consists of 98 observations. The calculated values for the β and γ parameters of the 2 parameters log logistic distribution are 2.12831 and 0.0918891, respectively. The probability of students completing their studies by semester 8 (hazard function h(8)) is 0.370102, while the probability of students continuing their studies in semester 9 (survival function s(9)) is 0.320817.

Distributed security state estimation-based carbon emissions and economic cost analysis for cyber–physical power systems under hybrid attacks

Sustainable cyber–physical power systems (CPPSs) significantly reduce carbon emissions due to climate change. However, when the data exchange in CPPSs suffers from hybrid attacks, the distributed state estimation and optimal power flow (OPF) analysis will inevitably be compromised, leading to inadequate or faulty scheduling of clean energy and thermal power generations and further affecting the total carbon emissions and economic cost. To address these problems, this paper proposes a novel consensus-based distributed security state estimation (DSSE) method for CPPSs, which is used to analyze the impact of hybrid attacks on carbon emissions and economic cost. Firstly, the incomplete and non-authentic data features caused by hybrid attacks are described, and their influence on distributed state estimation model is analyzed. A new residual-based attack detection method is then constructed in each subregion, where secure and non-secure sets are employed to describe whether the subregion is attacked and the compensation mechanism is designed for the non-secure set. Secondly, considering data compensation, distributed state estimation model is reconstructed, and a distributed security state estimation method under hybrid attacks is proposed while its convergence condition is derived. Thirdly, the impacts of hybrid attacks on carbon emissions and economic costs are analyzed based on the proposed DSSE method. Finally, experimental results confirm the validity of the theoretic analysis.

3-D Localization of Multiagent Systems Under Random Environments Based on Iterative Learning

This work addresses the localization of dynamic multi-agent systems (MASs) in three-dimensional (3-D) space under random environments (i.e., random packet loss, measurement noise and simultaneous communication noise). It is more practical yet challenging to deal with than static systems under ideal environments. Barycentric coordinates based on the relative-distance are used to characterize the positions between agents. The sign coefficients are introduced to guarantee that the sum of barycentric coordinates is equal to one, thus eliminating the constraint that the agent needs to be located in the convex hull. Using the newly designed iteration-varying gains, a robust distributed estimation method based on iterative learning is proposed. The key to accurate localization is to construct an appropriate approximator via introducing two iterative-varying gains into the localization scheme. The convergence in the sense of mathematical expectation is proved. The simulation examples and experimental results verify the effectiveness of the proposed approach.

Regular Vehicle Spatial Distribution Estimation Based on Machine Learning

For the mixed traffic flow, obtaining the distribution of connected vehicles (CVs) and regular vehicles (RVs) is of great significance for road network analysis and cooperative control in intelligent transportation systems (ITSs). However, whether it is based on fixed sensors or based on CVs and traffic mechanism to estimate the spatial distribution of RVs, the implementation complexity and low estimation accuracy are the points that need to be improved. This paper proposes a regular vehicle spatial distribution estimation method using adjacent connected vehicles as mobile sensors. First, to investigate the hidden relationship between the interaction information of adjacent CVs and the spatial distribution of RVs among CVs, the Gaussian mixture model-hidden Markov model (GMM-HMM) is selected as the identification method. Then, three sets of experiments were designed to study the influence of observed features on the identification capability of the model, generalization capability validation, and comparison with other methods, respectively. Finally, the proposed method is verified by the dataset generated by the car-following model. The experimental results show that selecting the relative position and time headway as observed features can effectively reflect the regular vehicle spatial distribution between adjacent CVs. The average accuracy of the proposed method to identify the regular vehicle spatial distribution is over 93.7%, which can provide valuable suggestions for the Internet of Vehicles application.

Freight trip distribution using spatiotemporal aggregate data: A modified collective flow diffusion model-based approach

The estimation of freight trip distribution is an important issue in freight transport studies, and collecting data on the spatiotemporal aggregated number of freight vehicles without trip information is relatively easy and inexpensive. In this paper, we propose a new model for freight distribution estimation, referred to as “TripCFDM.” Unlike the traditional collective flow diffusion model (CFDM), which solely relies on aggregate data, TripCFDM relies on aggregate data along with a small amount of trip data. CFDM estimates the probability of latent zonal freight trips based on aggregate data corresponding to the number of vehicles in each zone and time step. The use of the aggregate and small amounts of trip data ensures a realistic data acquisition environment. Our model is applied to freight trips in the Tokyo Metropolitan Area using the National Survey of Roads and Streets Traffic Conditions (Road Traffic Census). The results reveal that TripCFDM yields a significant improvement in the estimated probability compared with CFDM, particularly for intrazonal freight trips. However, the estimation results of interzonal trips obtained by CFDM and TripCFDM tend to be similar, suggesting that CFDM alone may be adequate to estimate the probability of interzonal trips with a sufficient degree of accuracy; nevertheless, TripCFDM is a better method for freight trip distribution estimation, including for intrazonal trips. The results of CFDM are not significantly affected by the time steps in the input data, whereas TripCFDM can yield higher accuracies with longer time steps. Regarding the number of zones and zone size, sufficient zone aggregation may be effective in improving the estimation accuracy because a detailed zonal division leads to a small probability of origin–destination trips with extensive computations. Based on this modified CFDM approach, origin and destination matrices for freight transport can be generated without large-scale surveys.

A distributed multi-area power system state estimation method based on generalized loss function

For power system state estimation, the measurement noise is usually assumed to follow the Gaussian distribution, and the widely used estimator is the weighted least squares (WLS). However, the Gaussian distribution assumption is not always true, and the performance of WLS becomes bad when the measurement noise is non-Gaussian. In this paper, a new distributed state estimation (SE) method is proposed for multi-area power systems. The proposed distributed method is based on the generalized loss function so that it can reduce the influence of non-Gaussian noise and bad data. Further, thanks to the matrix-splitting technology, the proposed distributed method can be implemented in a distributed way so that the computation time in each local area can be reduced. The simulation results carried out in the IEEE 30-bus and 118-bus systems verify the robustness and effectiveness of the proposed distributed SE method.