arXiv subjects

Peihu Duan

Publications and source records attributed to Peihu Duan.

16 recordsLinked to original sources

arXiv2026

Multi-Domain Iterative Detection for Massive Connectivity in LEO Satellite Networks

Grant-Free (GF) random access is promising for low Earth orbit satellite Internet due to its reduced access latency. However, existing schemes suffer from poor performance in massive connectivity scenarios. To address this challenge, we firstly propose an iterative residual feedback multi-measurement vector approximate message passing algorithm. This algorithm leverages multi-domain synergistic sparsity in the spatial-frequency and angular-delay domains to alternately perform active user terminal detection (AUD) and channel estimation (CE). Additionally, a residual feedback mechanism is incorporated to suppress error accumulation, thereby enhancing AUD performance. Furthermore, conventional data detection (DD) methods significantly degrade when active user terminals are spatially close or outnumber the satellite's receive antennas, making the demodulation problem rank-deficient or underdetermined. To mitigate this, we design a data modulation scheme via joint spatial-frequency multi-domain spreading, which utilizes observations from both spatial and frequency domains to facilitate multi-domain DD. Simulation results demonstrate that the proposed scheme significantly outperforms existing GF methods in terms of AUD accuracy, CE precision, and bit error rate, especially under conditions of low effective pilot length and practical signal-to-noise ratios.

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arXiv2026

Data-Driven Moving Horizon Estimators for Linear Systems with Sample Complexity Analysis

This paper investigates the state estimation problem for linear systems subject to Gaussian noise, where the model parameters are unknown. By formulating and solving an optimization problem that incorporates both offline and online system data, a novel data-driven moving horizon estimator (DDMHE) is designed. We prove that the expected 2-norm of the estimation error of the proposed DDMHE is ultimately bounded. Further, we establish an explicit relationship between the system noise covariances and the estimation error of the proposed DDMHE. Moreover, through a sample complexity analysis, we show how the length of the offline data affects the estimation error of the proposed DDMHE. We also quantify the performance gap between the proposed DDMHE using noisy data and the traditional moving horizon estimator with known system matrices. Finally, the theoretical results are validated through numerical simulations.

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arXiv2025

Secure State Estimation of Cyber-Physical Systems via Gaussian Bernoulli Mixture Model

The implementation of cyber-physical systems in real-world applications is challenged by safety requirements in the presence of sensor threats. Most cyber-physical systems, especially multi-sensor systems, struggle to detect sensor attacks when the attack model is unknown. In this paper, we tackle this issue by proposing a Gaussian-Bernoulli Secure (GBS) estimator, which transforms the detection problem into an optimal estimation problem concerning the system state and observation indicators. It encompasses two theoretical sub-problems: sequential state estimation with partial observations and estimation updates with disordered new observations. Within the framework of Kalman filter, we derive closed-form solutions for these two problems. However, due to their computational inefficiency, we propose the iterative approach employing proximal gradient descent to update the estimation in less time. Finally, we conduct experiments from three perspectives: computational efficiency, detection performance, and estimation error. Our GBS estimator demonstrates significant improvements over other methods.

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arXiv2025

An Autocovariance Least-Squares-Based Data-Driven Kalman Filter for Unknown Systems

This article investigates the problem of data-driven state estimation for linear systems with both unknown system dynamics and noise covariances. We propose an Autocovariance Least-squares-based Data-driven Kalman Filter (ADKF), which provides a unified framework for simultaneous system identification and state estimation by utilizing pre-collected input-output trajectories and estimated initial states. Specifically, we design a SDP-based algorithm for estimating the noise covariances. We quantify the impact of model inaccuracy on noise covariances estimation using this identification algorithm, and introduce a feedback control mechanism for data collection to enhance the accuracy and stability of noise covariance estimation. The estimated noise covariances account for model inaccuracy, which are shown to be more suitable for state estimation. We also quantify the performance gap between the ADKF and the traditional Kalman filter with known system dynamics and noise covariances, showing that this gap decreases as the number and length of pre-collected trajectories increase. Finally, numerical simulations validate the robustness and effectiveness of the proposed ADKF.

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arXiv2025

Robust Data-Driven Kalman Filtering for Unknown Linear Systems using Maximum Likelihood Optimization

This paper investigates the state estimation problem for unknown linear systems subject to both process and measurement noise. Based on a prior input-output trajectory sampled at a higher frequency and a prior state trajectory sampled at a lower frequency, we propose a novel robust data-driven Kalman filter (RDKF) that integrates model identification with state estimation for the unknown system. Specifically, the state estimation problem is formulated as a non-convex maximum likelihood optimization problem. Then, we slightly modify the optimization problem to get a problem solvable with a recursive algorithm. Based on the optimal solution to this new problem, the RDKF is designed, which can estimate the state of a given but unknown state-space model. The performance gap between the RDKF and the optimal Kalman filter based on known system matrices is quantified through a sample complexity bound. In particular, when the number of the pre-collected states tends to infinity, this gap converges to zero. Finally, the effectiveness of the theoretical results is illustrated by numerical simulations.

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arXiv2024

Performance Analysis of Distributed Filtering under Mismatched Noise Covariances

This paper systematically investigates the performance of consensus-based distributed filtering under mismatched noise covariances. First, we introduce three performance evaluation indices for such filtering problems,namely the standard performance evaluation index, the nominal performance evaluation index, and the estimation error covariance. We derive difference expressions among these indices and establish one-step relations among them under various mismatched noise covariance scenarios. We particularly reveal the effect of the consensus fusion on these relations. Furthermore, the recursive relations are introduced by extending the results of the one-step relations. Subsequently, we demonstrate the convergence of these indices under the collective observability condition, and show this convergence condition of the nominal performance evaluation index can guarantee the convergence of the estimation error covariance. Additionally, we prove that the estimation error covariance of the consensus-based distributed filter under mismatched noise covariances can be bounded by the Frobenius norms of the noise covariance deviations and the trace of the nominal performance evaluation index. Finally, the effectiveness of the theoretical results is verified by numerical simulations.

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arXiv2024

On the Effects and Optimal Design of Redundant Sensors in Collaborative State Estimation

The existence of redundant sensors in collaborative state estimation is a common occurrence, yet their true significance remains elusive. This paper comprehensively investigates the effects and optimal design of redundant sensors in sensor networks that use Kalman filtering to estimate the state of a random process collaboratively. The paper presents two main results: a theoretical analysis of the effects of redundant sensors and an engineering-oriented optimal design of redundant sensors. In the theoretical analysis, the paper leverages Riccati equations and Symplectic matrix theory to unveil the explicit role of redundant sensors in cooperative state estimation. The results unequivocally demonstrate that the addition of redundant sensors enhances the estimation performance of the sensor network, aligning with the principle of ``more is better". Moreover, the paper establishes a precise sufficient and necessary condition to assess whether the inclusion of redundant sensors improves the overall estimation performance. Moving towards engineering-oriented design optimization, the paper proposes a novel algorithm to tackle the optimal design problem of redundant sensors, and the convergence of the proposed algorithm is guaranteed. Numerical simulations are provided to demonstrate the results.

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arXiv2024

A Framework on Fully Distributed State Estimation and Cooperative Stabilization of LTI Plants

How to realize high-level autonomy of individuals is one of key technical issues to promote swarm intelligence of multi-agent (node) systems with collective tasks, while the fully distributed design is a potential way to achieve this goal. This paper works on the fully distributed state estimation and cooperative stabilization problem of linear time-invariant (LTI) plants with multiple nodes communicating over general directed graphs, and is aimed to provide a fully distributed framework for each node to perform cooperative stabilization tasks. First, by incorporating a novel adaptive law, a consensus-based estimator is designed for each node to obtain the plant state based on its local measurement and local interaction with neighbors, without using any global information of the communication topology. Subsequently, a local controller is developed for each node to stabilize the plant collaboratively with performance guaranteed under mild conditions. Specifically, the proposed method only requires that the communication graph be strongly connected, and the plant be collectively controllable and observable. Further, the proposed method can be applied to pure fully distributed state estimation scenarios and modified for noise-bounded LTI plants. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.

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arXiv2023

Cooperative Control of Multi-Channel Linear Systems with Self-Organizing Private Agents

Cooperative behavior design for multi-agent systems with collective tasks is a critical issue in promoting swarm intelligence. This paper investigates cooperative control for a multi-channel system, where each channel is managed by an agent expected to self-organize a controller to stabilize the system collaboratively by communicating with neighbors in a network. Integrating a state decomposition technique and a fusion approach, a fully distributed privacy-preserving mechanism is proposed to shield agents' private information from neighbors' eavesdropping. Moreover, the cost of introducing the privacy-preserving mechanism and the benefit of adding more channels to the system are quantitatively analyzed. Finally, comparative simulation examples are provided to demonstrate the effectiveness of the theoretical results.

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arXiv2023

Harmonic-Copuled Riccati Equations and its Applications in Distributed Filtering

The coupled Riccati equations are cosisted of multiple Riccati-like equations with solutions coupled with each other, which can be applied to depict the properties of more complex systems such as markovian systems or multi-agent systems. This paper manages to formulate and investigate a new kind of coupled Riccati equations, called harmonic-coupled Riccati equations (HCRE), from the matrix iterative law of the consensus on information-based distributed filtering (CIDF) algortihm proposed in [1], where the solutions of the equations are coupled with harmonic means. Firstly, mild conditions of the existence and uniqueness of the solution to HCRE are induced with collective observability and primitiviness of weighting matrix. Then, it is proved that the matrix iterative law of CIDF will converge to the unique solution of the corresponding HCRE, hence can be used to obtain the solution to HCRE. Moreover, through applying the novel theory of HCRE, it is pointed out that the real estimation error covariance of CIDF will also become steady-state and the convergent value is simplified as the solution to a discrete time Lyapunov equation (DLE). Altogether, these new results develop the theory of the coupled Riccati equations, and provide a novel perspective on the performance analysis of CIDF algorithm, which sufficiently reduces the conservativeness of the evaluation techniques in the literature. Finally, the theoretical results are verified with numerical experiments.

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arXiv2023

Observation of Periodic Systems: Bridge Centralized Kalman Filtering and Consensus-Based Distributed Filtering

Compared with linear time invariant systems, linear periodic system can describe the periodic processes arising from nature and engineering more precisely. However, the time-varying system parameters increase the difficulty of the research on periodic system, such as stabilization and observation. This paper aims to consider the observation problem of periodic systems by bridging two fundamental filtering algorithms for periodic systems with a sensor network: consensus-on-measurement-based distributed filtering (CMDF) and centralized Kalman filtering (CKF). Firstly, one mild convergence condition based on uniformly collective observability is established for CMDF, under which the filtering performance of CMDF can be formulated as a symmetric periodic positive semidefinite (SPPS) solution to a discrete-time periodic Lyapunov equation. Then, the closed form of the performance gap between CMDF and CKF is presented in terms of the information fusion steps and the consensus weights of the network. Moreover, it is pointed out that the estimation error covariance of CMDF exponentially converges to the centralized one with the fusion steps tending to infinity. Altogether, these new results establish a concise and specific relationship between distributed and centralized filterings, and formulate the trade-off between the communication cost and distributed filtering performance on periodic systems. Finally, the theoretical results are verified with numerical experiments.

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arXiv2023

Sensor Scheduling Design for Complex Networks under a Distributed State Estimation Framework

This paper investigates sensor scheduling for state estimation of complex networks over shared transmission channels. For a complex network of dynamical systems, referred to as nodes, a sensor network is adopted to measure and estimate the system states in a distributed way, where a sensor is used to measure a node. The estimates are transmitted from sensors to the associated nodes, in the presence of one-step time delay and subject to packet loss. Due to limited transmission capability, only a portion of sensors are allowed to send information at each time step. The goal of this paper is to seek an optimal sensor scheduling policy minimizing the overall estimation errors. Under a distributed state estimation framework, this problem is reformulated as a Markov decision process, where the one-stage reward for each node is strongly coupled. The feasibility of the problem reformulation is ensured. In addition, an easy-to-check condition is established to guarantee the existence of an optimal deterministic and stationary policy. Moreover, it is found that the optimal policies have a threshold, which can be used to reduce the computational complexity in obtaining these policies. Finally, the effectiveness of the theoretical results is illustrated by several simulation examples.

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arXiv2022

Stochastic Event-triggered Variational Bayesian Filtering

This paper proposes an event-triggered variational Bayesian filter for remote state estimation with unknown and time-varying noise covariances. After presetting multiple nominal process noise covariances and an initial measurement noise covariance, a variational Bayesian method and a fixed-point iteration method are utilized to jointly estimate the posterior state vector and the unknown noise covariances under a stochastic event-triggered mechanism. The proposed algorithm ensures low communication loads and excellent estimation performances for a wide range of unknown noise covariances. Finally, the performance of the proposed algorithm is demonstrated by tracking simulations of a vehicle.

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arXiv2022

Consensus-Based Distributed Filtering with Fusion Step Analysis

For consensus on measurement-based distributed filtering (CMDF), through infinite consensus fusion operations during each sampling interval, each node in the sensor network can achieve optimal filtering performance with centralized filtering. However, due to the limited communication resources in physical systems, the number of fusion steps cannot be infinite. To deal with this issue, the present paper analyzes the performance of CMDF with finite consensus fusion operations. First, by introducing a modified discrete-time algebraic Riccati equation and several novel techniques, the convergence of the estimation error covariance matrix of each sensor is guaranteed under a collective observability condition. In particular, the steady-state covariance matrix can be simplified as the solution to a discrete-time Lyapunov equation. Moreover, the performance degradation induced by reduced fusion frequency is obtained in closed form, which establishes an analytical relation between the performance of the CMDF with finite fusion steps and that of centralized filtering. Meanwhile, it provides a trade-off between the filtering performance and the communication cost. Furthermore, it is shown that the steady-state estimation error covariance matrix exponentially converges to the centralized optimal steady-state matrix with fusion operations tending to infinity during each sampling interval. Finally, the theoretical results are verified with illustrative numerical experiments.

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arXiv2021

Linear Quadratic Regulator Design for Multi-input Systems with A Distributed Cooperative Strategy

In this paper, a cooperative Linear Quadratic Regulator (LQR) problem is investigated for multi-input systems, where each input is generated by an agent in a network. The input matrices are different and locally possessed by the corresponding agents respectively, which can be regarded as different ways for agents to control the multi-input system. By embedding a fully distributed information fusion strategy, a novel cooperative LQR-based controller is proposed. Each agent only needs to communicate with its neighbors, rather than sharing information globally in a network. Moreover, only the joint controllability is required, which allows the multi-input system to be uncontrollable for every single agent or even all its neighbors. In particular, only one-time information exchange is necessary at every control step, which significantly reduces the communication consumption. It is proved that the boundedness (convergence) of the controller gains is guaranteed for time-varying (time-invariant) systems. Furthermore, the control performance of the entire system is ensured. Generally, the proposed controller achieves a better trade-off between the control performance and the communication overhead, compared with the existing centralized/decentralized/consensus-based LQR controllers. Finally, the effectiveness of the theoretical results is illustrated by several comparative numerical examples.

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arXiv2021

A Distributed Optimization Scheme for State Estimation of Nonlinear Networks with Norm-bounded Uncertainties

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach, the estimation problem is reformulated as an optimization problem, solving for a solution in a distributed way by utilizing a decoupling technique. Then, based on this solution, a class of estimators is designed to handle the system dynamics and constraints. A novel feature of this design lies in the unified modeling of uncertainties and nonlinearities, the decoupling of nodes, and the construction of recursive approximate covariance matrices for the optimization problem. Furthermore, the feasibility of the proposed estimators and the boundedness of the mean-square errors are ensured under a developed criterion, which is easier to check than some typical estimation strategies including the linear matrix inequalities-based and the variance-constrained ones. Finally, the effectiveness of the theoretical results is verified by a numerical simulation.

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