arXiv subjects

Haitao Fang

Publications and source records attributed to Haitao Fang.

12 recordsLinked to original sources

arXiv2025

Theoretical Guarantees for AOA-based Localization: Consistency and Asymptotic Efficiency

We study the problem of signal source localization using angle of arrival (AOA) measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model's asymptotic localizability. Then we establish the consistency and asymptotic efficiency of the maximum likelihood (ML) estimator. However, obtaining the ML estimator is challenging due to its association with a non-convex optimization problem. To address this, we propose an asymptotically efficient two-step estimator that matches the ML estimator's asymptotic properties while achieving low computational complexity (linear in the number of measurements). The primary challenge lies in obtaining a consistent estimator in the first step. To achieve this, we construct a linear least squares problem through algebraic operations on the measurement nonlinear model to first obtain a biased closed-form solution. We then eliminate the bias using the data to yield an asymptotically unbiased and consistent estimator. In the second step, we perform a single Gauss-Newton iteration using the preliminary consistent estimator as the initial value, achieving the same asymptotic properties as the ML estimator. Finally, simulation results demonstrate the superior performance of the proposed two-step estimator for large sample sizes.

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arXiv2025

RSS-Based Localization: Ensuring Consistency and Asymptotic Efficiency

We study the problem of signal source localization using received signal strength measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model's asymptotic localizability. Then we establish the consistency and asymptotic efficiency of the maximum likelihood (ML) estimator. However, computing the ML estimator is challenging due to its reliance on solving a non-convex optimization problem. To overcome this, we propose a two-step estimator that retains the same asymptotic properties as the ML estimator while offering low computational complexity, linear in the number of measurements. The main challenge lies in obtaining a consistent estimator in the first step. To address this, we construct two linear least-squares estimation problems by applying algebraic transformations to the nonlinear measurement model, leading to closed-form solutions. In the second step, we perform a single Gauss-Newton iteration using the consistent estimator from the first step as the initialization, achieving the same asymptotic efficiency as the ML estimator. Finally, simulation results validate the theoretical property and practical effectiveness of the proposed two-step estimator.

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arXiv2023

Community Structure Recovery and Interaction Probability Estimation for Gossip Opinion Dynamics

We study how to jointly recover the community structure and estimate the interaction probabilities of gossip opinion dynamics. In this process, agents randomly interact pairwise, and there are stubborn agents never changing their states. Such a model illustrates how disagreement and opinion fluctuation arise in a social network. It is assumed that each agent is assigned with one of two community labels, and the agents interact with probabilities depending on their labels. The considered problem is to jointly recover the community labels of the agents and estimate interaction probabilities between the agents, based on a single trajectory of the model. We first study stability and limit theorems of the model, and then propose a joint recovery and estimation algorithm based on a trajectory. It is verified that the community recovery can be achieved in finite time, and the interaction estimator converges almost surely. We derive a sample-complexity result for the recovery, and analyze the estimator's convergence rate. Simulations are presented for illustration of the performance of the proposed algorithm.

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arXiv2021

Distributed Design of Robust Kalman Filters over Corrupted Channels

We study distributed filtering for a class of uncertain systems over corrupted communication channels. We propose a distributed robust Kalman filter with stochastic gains, through which upper bounds of the conditional mean square estimation errors are calculated online. We present a robust collective observability condition, under which the mean square error of the distributed filter is proved to be uniformly upper bounded if the network is strongly connected. For better performance, we modify the filer by introducing a switching fusion scheme based on a sliding window. It provides a smaller upper bound of the conditional mean square error. Numerical simulations are provided to validate the theoretical results and show that the filter scales to large networks.

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arXiv2020

Community Detection for Gossip Dynamics with Stubborn Agents

We consider a community detection problem for gossip dynamics with stubborn agents in this paper. It is assumed that the communication probability matrix for agent pairs has a block structure. More specifically, we assume that the network can be divided into two communities, and the communication probability of two agents depends on whether they are in the same community. Stability of the model is investigated, and expectation of stationary distribution is characterized, indicating under the block assumption, the stationary behaviors of agents in the same community are similar. It is also shown that agents in different communities display distinct behaviors if and only if state averages of stubborn agents in different communities are not identical. A community detection algorithm is then proposed to recover community structure and to estimate communication probability parameters. It is verified that the community detection part converges in finite time, and the parameter estimation part converges almost surely. Simulations are given to illustrate algorithm performance.

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arXiv2019

Recursive Network Estimation From Binary-Valued Observation Data

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which agents exchange and display binary outputs. Sufficient conditions are given to ensure stability of the observation sequence and identifiability of the system parameters. It is shown that stability and identifiability can be guaranteed under the assumption of independent standard Gaussian disturbances. Via a maximum likelihood approach, the estimation problem is transformed into an optimization problem, and it is verified that its solution is the true parameter vector under the independent standard Gaussian assumption. A recursive algorithm for the estimation problem is then proposed based on stochastic approximation techniques. Its strong consistency is established and convergence rate analyzed. Finally, numerical simulations are conducted to illustrate the results and to show that the proposed algorithm is insensitive to small unmodeled factors.

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arXiv2019

Distributed Filtering for Uncertain Systems Under Switching Sensor Networks and Quantized Communications

This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and interval-quantized messages from neighboring sensors successively, an extended state based distributed Kalman filter (DKF) is proposed for simultaneously estimating both system state and uncertain dynamics. To alleviate the effect of observation biases, an event-triggered update based DKF is presented with a tighter mean square error bound than that of the time-driven one by designing a proper threshold. Both the two DKFs are shown to provide the upper bounds of mean square errors online for each sensor. Under mild conditions on systems and networks, the mean square error boundedness and asymptotic unbiasedness for the proposed two DKFs are proved. Finally, the numerical simulations demonstrate the effectiveness of the developed filters.

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arXiv2019

Network Weight Estimation for Binary-Valued Observation Models

This paper studies the estimation of network weights for a class of systems with binary-valued observations. In these systems only quantized observations are available for the network estimation. Furthermore, system states are coupled with observations, and the quantization parts are unknown inherent components, which hinder the design of inputs and quantizers. To fulfill the estimation, we propose a recursive algorithm based on stochastic approximation techniques. More precisely, to deal with the temporal dependency of observations and achieve the recursive estimation of network weights, a deterministic objective function is constructed based on the likelihood function by extending the dimension of observations and applying ergodic properties of Markov chains. It is shown that this function is strictly concave and has unique maximum identical to the true parameter vector. Finally, the strong consistency of the algorithm is established. Our recursive algorithm can be applied to online tasks like real-time decision-making and surveillance for networked systems. This work also provides a new scheme for the identification of systems with quantized observations.

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arXiv2019

Distributed Kalman Filters with State Equality Constraints: Time-based and Event-triggered Communications

In this paper, we investigate a distributed estimation problem for multi-agent systems with state equality constraints (SEC). First, under a time-based consensus communication protocol, applying a modified projection operator and the covariance intersection fusion method, we propose a distributed Kalman filter with guaranteed consistency and satisfied SEC. Furthermore, we establish the relationship between consensus step, SEC and estimation error covariance in dynamic and steady processes, respectively. Employing a space decomposition method, we show the error covariance in the constraint set can be arbitrarily small by setting a sufficiently large consensus step. Besides, we propose an extended collective observability (ECO) condition based on SEC, which is milder than existing observability conditions. Under the ECO condition, through utilizing a technique of matrix approximation, we prove the boundedness of error covariance and the exponentially asymptotic unbiasedness of state estimate, respectively. Moreover, under the ECO condition for linear time-invariant systems with SEC, we provide a novel event-triggered communication protocol by employing the consistency, and give an offline design principle of triggering thresholds with guaranteed boundedness of error covariance. More importantly, we quantify and analyze the communication rate for the proposed event-triggered distributed Kalman filter, and provide optimization based methods to obtain the minimal (maximal) successive non-triggering (triggering) times. Two simulations are provided to demonstrate the developed theoretical results and the effectiveness of the filters.

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arXiv2019

Asymptotic Properties of Distributed Social Sampling Algorithm

Social sampling is a novel randomized message passing protocol inspired by social communication for opinion formation in social networks. In a typical social sampling algorithm, each agent holds a sample from the empirical distribution of social opinions at initial time, and it collaborates with other agents in a distributed manner to estimate the initial empirical distribution by randomly sampling a message from current distribution estimate. In this paper, we focus on analyzing the theoretical properties of the distributed social sampling algorithm over random networks. Firstly, we provide a framework based on stochastic approximation to study the asymptotic properties of the algorithm. Then, under mild conditions, we prove that the estimates of all agents converge to a common random distribution, which is composed of the initial empirical distribution and the accumulation of quantized error. Besides, by tuning algorithm parameters, we prove the strong consistency, namely, the distribution estimates of agents almost surely converge to the initial empirical distribution. Furthermore, the asymptotic normality of estimation error generated by distributed social sampling algorithm is addressed. Finally, we provide a numerical simulation to validate the theoretical results of this paper.

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arXiv2018

Distributed Kalman Filter for A Class of Nonlinear Uncertain Systems: An Extended State Method

This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the original state and the nonlinear dynamics is constructed. By analyzing the extended system, we provide a design method for the filtering gain and fusion matrices, leading to the extended state distributed Kalman filter. It is shown that the proposed filter can provide the upper bound of estimation covariance in real time, which means the estimation accuracy can be evaluated online.It is proven that the estimation covariance of the filter is bounded under rather mild assumptions, i.e., collective observability of the system and jointly strong connectedness of network topologies. Numerical simulation shows the effectiveness of the proposed filter.

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arXiv2017

Consistent distributed state estimation with global observability over sensor network

This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter, since it requires each sensor to have global information which is usually forbidden in large networks. Then, a sub-optimal distributed Kalman filter (DKF) is proposed by employing the covariance intersection (CI) fusion strategy. It is proven that the proposed DKF is of consistency, that is, the upper bound of error covariance matrix can be provided by the filter in real time. The consistency also enables the design of adaptive CI weights for better filter precision. Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the sub-system with local sensor's measurements to be unobservable. Meanwhile, to keep the covariance of the estimation error bounded, the proposed DKF does not require the system matrix to be nonsingular at each moment, which seems to be a necessary condition in the main DKF designs under global observability. Finally, simulation results of two examples show the effectiveness of the algorithm in the considered scenarios.

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