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distributed parameter estimation with Gaussian observation noises in time-varying digraphs

AUTOMATICA 2025年 176卷

作者： Yan, Jiaqi Ishii, Hideaki Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Univ Tokyo Dept Informat Phys & Comp Tokyo 1138656 Japan

In this paper, we consider the problem of distributed parameter estimation in sensor networks. Each sensor makes successive observations of an unknown d-dimensional parameter, which might be subject to Gaussian random noises. The sensors aim to infer the true value of the unknown parameter by cooperating with each other. To this end, we first generalize the so-called dynamic regressor extension and mixing (DREM) algorithm to stochastic systems, with which the problem of estimating a d-dimensional vector parameter is transformed to that ofd scalar ones: one for each of the unknown parameters. For each of the scalar problem, both combine-then-adapt (CTA) and adapt-then-combine (ATC) diffusion-based estimation algorithms are given, where each sensor performs a combination step to fuse the local estimates in its in-neighborhood, alongside an adaptation step to process its streaming observations. Under weak conditions on network topology and excitation of regressors, we show that the proposed estimators guarantee that each sensor infers the true parameter, even if any individual of them cannot by itself. Specifically, it is required that the union of topologies over an interval with fixed length is strongly connected. Moreover, the sensors must collectively satisfy a cooperative persistent excitation (PE) condition, which relaxes the traditional PE condition. Numerical examples are finally provided to illustrate the established results. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： distributed parameter estimation Cooperative persistent excitation Diffusion strategies Stochastic systems

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On Collaboration in distributed parameter estimation With Resource Constraints

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IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT 2025年第1期22卷 151-167页

作者： Chen, Yu-Zhen Janice Menasche, Daniel S. Towsley, Don Univ Massachusetts Amherst Manning Coll Informat & Comp Sci Amherst MA 01002 USA Univ Fed Rio de Janeiro Inst Comp BR-21941901 Rio de Janeiro Brazil

Effective resource allocation in sensor networks, IoT systems, and distributed computing is essential for applications such as environmental monitoring, surveillance, and smart infrastructure. Sensors or agents must optimize their resource allocation to maximize the accuracy of parameter estimation. In this work, we consider a group of sensors or agents, each sampling from a different variable of a multivariate Gaussian distribution and having a different estimation objective. We formulate a sensor or agent's data collection and collaboration policy design problem as a Fisher information maximization (or Cramer-Rao bound minimization) problem. This formulation captures a novel trade-off in energy use, between locally collecting univariate samples and collaborating to produce multivariate samples. When knowledge of the correlation between variables is available, we analytically identify two cases: (1) where the optimal data collection policy entails investing resources to transfer information for collaborative sampling, and (2) where knowledge of the correlation between samples cannot enhance estimation efficiency. When knowledge of certain correlations is unavailable, but collaboration remains potentially beneficial, we propose novel approaches that apply multi-armed bandit algorithms to learn the optimal data collection and collaboration policy in our sequential distributed parameter estimation problem. We illustrate the effectiveness of the proposed algorithms, DOUBLE-F, DOUBLE-Z, UCB-F, UCB-Z, through simulation.

关键词： Collaboration estimation Data collection Correlation distributed databases parameter estimation Optimization Vectors Wireless sensor networks Resource management distributed parameter estimation sequential estimation sensor selection vertically partitioned data Fisher information multi-armed bandit (MAB) Kalman filter

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distributed parameter estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第6期58卷 3575-3605页

作者： Kar, Soummya Moura, Jose M. F. Ramanan, Kavita Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA Brown Univ Div Appl Math Providence RI 02912 USA

The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy intersensor communication. It introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation. It studies two distributed estimation algorithms in separably estimable models, the NU (with its linear counterpart LU) and the NLU. Their update rule combines a consensus step (where each sensor updates the state by weight averaging it with its neighbors' states) and an innovation step (where each sensor processes its local current observation). This makes the three algorithms of the consensus + innovations type, very different from traditional consensus. This paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value), efficiency, and asymptotic unbiasedness. For LU and NU, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms LU and NU are analyzed in the framework of stochastic approximation theory;algorithm NLU exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in this paper.

关键词： Asymptotic normality consensus consensus plus innovations consistency distributed parameter estimation Laplacian separable estimable spectral graph theory stochastic approximation unbiasedness

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distributed parameter estimation in unreliable WSNs: Quantized communication and asynchronous intermittent observation

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INFORMATION SCIENCES 2015年 309卷 11-25页

作者： Wang, Huiwei Liao, Xiaofeng Huang, Tingwen Chen, Guo Southwest Univ Coll Elect & Informat Engn Chongqing 400715 Peoples R China Texas A&M Univ Qatar Doha 5825 Qatar Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

Motivated by the application of wireless sensor networks, we study a class of distributed learning algorithms for estimating an unknown deterministic parameter. In such networks, each sensor activates in an unreliable network environment which admits new nodes joining and old nodes leaving the network, and can tolerate link failures and noisy interference. Additionally, sensors operate under limited computational, bandwidth and energy resources. In order to overcome these constraints, we propose a novel algorithm to reliably estimate the unknown parameter associated with a linear measurement function based on its noisy samples occasionally made at local sensors. Each local sensor processes its observation, updates its estimate through local information exchange and sends its quantized estimate to its one-hop neighbors. Based on the theory of matrix decomposition and stochastic approximation, we show that the studied algorithm converges almost surely to the unknown parameter with probability one, and the sensor estimate is, in expectation, equal to the unknown parameter. Specifically, we further provide the upper bounds on the mean square error and epsilon-convergence time. Finally, we present a numerical example to assess and compare the communication cost with several similar scheme algorithms to achieve a given performance. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Asynchronous intermittent observation distributed parameter estimation Quantized communication Unreliable network environment

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distributed parameter estimation in unreliable sensor networks via broadcast gossip algorithms

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NEURAL NETWORKS 2016年 73卷 1-9页

作者： Wang, Huiwei Liao, Xiaofeng Wang, Zidong Huang, Tingwen Chen, Guo Southwest Univ Coll Elect & Informat Engn Chongqing 400715 Peoples R China Brunel Univ Dept Informat Syst & Comp Uxbridge UB8 3PH Middx England Texas A&M Univ Qatar Doha 5825 Qatar Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia King Abdulaziz Univ Fac Engn Jeddah 21589 Saudi Arabia

In this paper, we present an asynchronous algorithm to estimate the unknown parameter under an unreliable network which allows new sensors to join and old sensors to leave, and can tolerate link failures. Each sensor has access to partially informative measurements when it is awakened. In addition, the proposed algorithm can avoid the interference among messages and effectively reduce the accumulated measurement and quantization errors. Based on the theory of stochastic approximation, we prove that our proposed algorithm almost surely converges to the unknown parameter. Finally, we present a numerical example to assess the performance and the communication cost of the algorithm. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Broadcast gossip algorithm distributed parameter estimation Quantized communication Unreliable sensor networks

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distributed parameter estimation in wireless sensor networks using fused local observations

Distributed parameter estimation in wireless sensor networks...

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Conference on Wireless Sensing, Localization and Processing VII

作者： Fanaei, Mohammad Valenti, Matthew C. Schmid, Natalia A. Alkhweldi, Marwan M. W Virginia Univ Lane Dept Comp Sci & Elect Engn Morgantown WV 26506 USA

ISBN: (纸本)9780819490827

The goal of this paper is to reliably estimate a vector of unknown deterministic parameters associated with an underlying function at a fusion center of a wireless sensor network based on its noisy samples made at distributed local sensors. A set of noisy samples of a deterministic function characterized by a finite set of unknown parameters to be estimated is observed by distributed sensors. The parameters to be estimated can be some attributes associated with the underlying function, such as its height, its center, its variances in different directions, or even the weights of its specific components over a predefined basis set. Each local sensor processes its observation and sends its processed sample to a fusion center through parallel impaired communication channels. Two local processing schemes, namely analog and digital, are considered. In the analog local processing scheme, each sensor transmits an amplified version of its local analog noisy observation to the fusion center, acting like a relay in a wireless network. In the digital local processing scheme, each sensor quantizes its noisy observation before transmitting it to the fusion center. A flat-fading channel model is considered between the local sensors and fusion center. The fusion center combines all of the received locally-processed observations and estimates the vector of unknown parameters of the underlying function. Two different well-known estimation techniques, namely maximum-likelihood (ML), for both analog and digital local processing schemes, and expectation maximization (EM), for digital local processing scheme, are considered at the fusion center. The performance of the proposed distributed parameter estimation system is investigated through simulation of practical scenarios for a sample underlying function.

关键词： distributed parameter estimation maximum likelihood (ML) expectation maximization (EM) analog/digital local processing local quantization integrated mean-squared error flat-fading channel fusion center wireless sensor networks

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distributed parameter estimation in Sensor Networks Based on Stochastic Approximation 34

Distributed Parameter Estimation in Sensor Networks Based on...

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34th Chinese Control Conference (CCC)

作者： Lei, Jinlong Chen, Han-Fu Chinese Acad Sci Acad Math & Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China

ISBN: (纸本)9789881563897

A distributed stochastic approximation algorithm with expanding truncations (DSAAWET) is proposed to estimate the unknown parameter linearly appearing in the sensor networks. Each agent updates its local estimate by averaging its neighbors' estimates with weights and by processing its local current observation. The estimates are shown to converge to the true parameter with probability one. A numerical example is given to demonstrate the obtained theoretic result.

关键词： distributed parameter estimation sensor networks stochastic approximation linear observation model

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distributed parameter estimation Under Event-triggered Communications 38

Distributed Parameter Estimation Under Event-triggered Commu...

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38th Chinese Control Conference (CCC)

作者： He, Xingkang Liu, Qian Wu, Junfeng Johansson, Karl Henrik KTH Royal Inst Technol ACCESS Linnaeus Ctr Sch Elect Engn & Comp Sci Stockholm Sweden Chinese Acad Sci LSC Acad Math & Syst Sci Beijing Peoples R China Univ Chinese Acad Sci Beijing Peoples R China Zhejiang Univ Coll Control Sci & Engn Hangzhou Zhejiang Peoples R China

ISBN: (纸本)9789881563972

In this paper, we study a distributed parameter estimation problem with an asynchronous communication protocol over multi-agent systems. Different from traditional time-driven communication schemes, in this work, data can be transmitted between agents intermittently rather than in a steady stream. First, we propose a recursive distributed estimator based on an event-triggered communication scheme, through which each agent can decide whether the current estimate is sent out to its neighbors or not. With this scheme, considerable communications between agents can be effectively reduced. Then, under mild conditions including a collective observability, we provide a design principle of triggering thresholds to guarantee the asymptotic unbiasedness and strong consistency. Furthermore, under certain conditions, we reveal that, with probability one, for every agent the time interval between two successive triggering instants goes to infinity as time goes to infinity. Finally, we provide a numerical simulation to validate the theoretical results of this paper.

关键词： distributed parameter estimation Event-triggered communications Strong consistency

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Differentially Private distributed parameter estimation

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Journal of Systems Science & Complexity 2023年第1期36卷 187-204页

作者： WANG Jimin TAN Jianwei ZHANG Ji-Feng School of Automation and Electrical Engineering University of Science and Technology BeijingBeijing 100083China Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Data privacy is an important issue in control systems,especially when datasets contain sensitive information about *** this paper,the authors are concerned with the differentially private distributed parameter estimation problem,that is,we estimate an unknown parameter while protecting the sensitive information of each ***,the authors propose a distributed stochastic approximation estimation algorithm in the form of the differentially private consensus+innovations(DP-CI),and establish the privacy and convergence property of the proposed ***,it is shown that the proposed algorithm asymptotically unbiased converges in mean-square to the unknown parameter while differential privacy-preserving holds for finite number of ***,the exponentially damping step-size and privacy noise for DP-CI algorithm is *** estimate approximately converges to the unknown parameter with an error proportional to the step-size parameter while differential privacy-preserving holds for all *** tradeoff between accuracy and privacy of the algorithm is effectively ***,a simulation example is provided to verify the effectiveness of the proposed algorithm.

关键词： Differential privacy distributed parameter estimation stochastic approximation

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Privacy-preserving distributed parameter estimation for probability distribution of wind power forecast error

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RENEWABLE ENERGY 2021年 163卷 1318-1332页

作者： Jia, Mengshuo Huang, Shaowei Wang, Zhiwen Shen, Chen Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China State Key Lab Power Syst Beijing 100084 Peoples R China Bytedance Engn & Efficiency Beijing 100084 Peoples R China

Building the conditional probability distribution of wind power forecast errors benefits both wind farms (WFs) and independent system operators (ISOs). Establishing the joint probability distribution of wind power and the corresponding forecast data of spatially correlated WFs is the foundation for deriving the conditional probability distribution. Traditional parameter estimation methods for probability distributions require the collection of historical data of all WFs. However, in the context of multi-regional interconnected grids, neither regional ISOs nor WFs can collect the raw data of WFs in other regions due to privacy or competition considerations. Therefore, based on the Gaussian mixture model, this paper first proposes a privacy-preserving distributed expectation-maximization algorithm to estimate the parameters of the joint probability distribution. This algorithm consists of two original methods: (1) a privacy-preserving distributed summation algorithm and (2) a privacy-preserving distributed inner product algorithm. Then, we derive each WF's conditional probability distribution of forecast error from the joint one. By the proposed algorithms, WFs only need local calculations and privacy-preserving neighboring communications to achieve the whole parameter estimation. These algorithms are verified using the wind integration data set published by the NREL. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Wind power forecast error Probability distribution distributed parameter estimation Data privacy Gaussian mixture model Expectation-maximization algorithm

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