arXiv subjects

Jieming Ke

Publications and source records attributed to Jieming Ke.

8 recordsLinked to original sources

arXiv2026

Asymptotically Efficient Recursive Identification Under One-Bit Communications Achieving Original CRLB

This paper develops an asymptotically efficient recursive identification algorithm for autoregressive systems with exogenous inputs under one-bit communications. In particular, the proposed method asymptotically achieves the Cramer-Rao lower bound (CRLB) based on the original data before quantization (original CRLB), whereas existing approaches typically attain only the CRLB corresponding to the quantized observations. The primary reason is that the existing methods quantize only the current system output, resulting in non-negligible information loss under one-bit quantization. To overcome this challenge, we present a novel quantization method that integrates both current and historical system outputs and inputs to provide richer parameter information in one-bit data, allowing the information loss caused by quantization to become a minor term relative to the original CRLB. Based on this technique, a corresponding remote estimation algorithm is further proposed. To address the convergence analysis challenge posed by the non-independence of the one-bit data, we establish a new framework that analyzes the tail probability of integrated data formed by combining current and historical system outputs and inputs before quantization, thereby eliminating the need for the traditional independence assumption on the quantized data. It is proven that the remote estimate achieves asymptotic normality, and the error covariance matrix converges to the original CRLB, confirming its asymptotic efficiency. Compared to existing identification algorithms under one-bit data, this method reduces the asymptotic mean squared error by at least 36%. Several numerical examples are simulated to show the effectiveness of the proposed algorithm.

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arXiv2026

Recursive Binary Identification with Differential Privacy and Data Tampering Attacks

In this paper, we consider the parameter estimation in a bandwidth-constrained sensor network communicating through an insecure medium. The sensor performs a local quantization, and transmits a 1-bit message to an estimation center through a wireless medium where the transmission of information is vulnerable to attackers. Both eavesdroppers and data tampering attackers are considered in our setting. A differential privacy method is used to protect the sensitive information against eavesdroppers. Then, a recursive projection algorithm is proposed such that the estimation center achieves the almost sure convergence and mean-square convergence when quantized measurements, differential privacy, and data tampering attacks are considered in a uniform framework. A privacy analysis including the convergence rate with privacy or without privacy is given. Further, we extend the problem to multi-agent systems. For this case, a distributed recursive projection algorithm is proposed with guaranteed almost sure and mean square convergence. A simulation example is provided to illustrate the effectiveness of the proposed algorithms.

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arXiv2026

Privacy-Preserving Distributed Estimation with Limited Data Rate

This paper focuses on the privacy-preserving distributed estimation problem with a limited data rate, where the observations are the sensitive information. Specifically, a binary-valued quantizer-based privacy-preserving distributed estimation algorithm is developed, which improves the algorithm's privacy-preserving capability and simultaneously reduces the communication costs. The algorithm's privacy-preserving capability, measured by the Fisher information matrix, is dynamically enhanced over time. Notably, the Fisher information matrix of the output signals with respect to the sensitive information converges to zero at a polynomial rate, and the improvement in privacy brought by the quantizers is quantitatively characterized as a multiplicative effect. Regarding the communication costs, each sensor transmits only 1 bit of information to its neighbours at each time step. Additionally, the assumption on the negligible quantization error for real-valued messages is not required. While achieving the requirements of privacy preservation and reducing communication costs, the algorithm ensures that its estimates converge almost surely to the true value of the unknown parameter by establishing a co-design guideline for the time-varying privacy noises and step-sizes. A polynomial almost sure convergence rate is obtained, and then the trade-off between privacy and convergence rate is established. Numerical examples demonstrate the main results.

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arXiv2025

Privacy-Preserving Cram\'er-Rao Lower Bound

This paper establishes the privacy-preserving Cramer-Rao lower bound (CRLB) theory, characterizing the fundamental limit of identification accuracy under privacy constraint for general stochastic obfuscation mechanisms. An identifiability criterion under privacy constraint is derived by using Fisher information matrix as the privacy metric. In the identifiable case, a precise privacy-preserving CRLB is established with an explicit expression, which quantifies the privacy cost without unspecified constant factors. Considering computational efficiency, recursive formulas are developed to compute the privacy-preserving CRLB for multi-measurement systems, reducing the computational burden caused by direct high-dimensional matrix inversion. To demonstrate the tightness of the lower bound, a Gaussian-mechanism-based privacy-preserving RLS algorithm is shown to exactly attain the bound under Gaussian measurement noises, and a maximum-likelihood-based privacy-preserving identification algorithm is proposed to attain the bound in the sense of convergence rates under non-Gaussian measurement noises. For applicability, the proposed theory can be extended to dynamic model state estimation, distributed estimation, and average consensus. Experimental results are provided to demonstrate the privacy-preserving CRLB and show the effectiveness of the proposed algorithms.

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arXiv2025

Asymptotic Efficiency Analysis of the Recursive Least-Squares Algorithm for ARX Systems Without Projection

This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the parameter estimates, which may diverge to infinity. Previous approaches addressed this issue by assuming that both the true parameter and the RLS estimates remain confined within a known compact set, thereby ensuring uniform boundedness throughout the analysis. In contrast, we propose a new analytical framework that eliminates the need for such a boundness assumption. Specifically, we establish a quantitative relationship between the bounded moment conditions of quasi-stationary input/output signals and the convergence rate of the tail probability of the RLS estimation error. Based on this technique, we prove that when system inputs/outputs have bounded twentieth-order moments, the RLS algorithm achieves asymptotic normality and the covariance matrix of the RLS algorithm converges to the Cramér-Rao lower bound (CRLB), confirming its asymptotic efficiency. These results demonstrate that the RLS algorithm is an asymptotically optimal identification algorithm for ARX systems, even without the projection operators to ensure that parameter estimates reside within a prior known compact set.

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arXiv2025

Signal-Comparison-Based Distributed Estimation Under Decaying Average Data Rate Communications

The paper investigates the distributed estimation problem under low bit rate communications. Based on the signal-comparison (SC) consensus protocol under binary-valued communications, a new consensus+innovations type distributed estimation algorithm is proposed. Firstly, the high-dimensional estimates are compressed into binary-valued messages by using a periodic compressive strategy, dithered noises and a sign function. Next, based on the dithered noises and expanding triggering thresholds, a new stochastic event-triggered mechanism is proposed to reduce the communication frequency. Then, a modified SC consensus protocol is applied to fuse the neighborhood information. Finally, a stochastic approximation estimation algorithm is used to process innovations. The proposed SC-based algorithm has the advantages of high effectiveness and low communication cost. For the effectiveness, the estimates of the SC-based algorithm converge to the true value in the almost sure and mean square sense. A polynomial almost sure convergence rate is also obtained. For the communication cost, the local and global average bit rates for communications decay to zero at a polynomial rate. The trade-off between the convergence rate and the communication cost is established through event-triggered coefficients. A better convergence rate can be achieved by decreasing event-triggered coefficients, while lower communication cost can be achieved by increasing event-triggered coefficients. A simulation example is given to demonstrate the theoretical results.

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arXiv2025

Recursive Identification of Binary-Valued Systems under Uniform Persistent Excitations

This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or truncations is proposed. The algorithm overcomes the limitations of the existing empirical measurement method and the recursive projection method, where the former requires periodic inputs, and the latter requires projections to restrict the search region in a compact set.To analyze the convergence property of the algorithm, the distribution tail of the estimation error is proved to be exponentially convergent through an auxiliary stochastic process. Based on this key technique, the SA-based algorithm appears to be the first to reach the almost sure convergence rate of $ O(\sqrt{\ln\ln k/k}) $ theoretically in the non-periodic input case. Meanwhile, the mean square convergence is proved to have a rate of $ O(1/k) $, which is the best one even under accurate observations. A numerical example is given to demonstrate the effectiveness of the proposed algorithm and theoretical results.

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arXiv2023

Differentially Private Bipartite Consensus over Signed Networks with Time-Varying Noises

This paper investigates the differentially private bipartite consensus algorithm over signed networks. The proposed algorithm protects each agent's sensitive information by adding noise with time-varying variances to the cooperative-competitive interactive information. In order to achieve privacy protection, the variance of the added noise is allowed to be increased, and substantially different from the existing works. In addition, the variance of the added noise can be either decaying or constant. By using time-varying step-sizes based on the stochastic approximation method, we show that the algorithm converges in mean-square and almost-surely even with an increasing privacy noise. We further develop a method to design the step-size and the noise parameter, affording the algorithm to achieve asymptotically unbiased bipartite consensus with the desired accuracy and the predefined differential privacy level. Moreover, we give the mean-square and almost-sure convergence rate of the algorithm, and the privacy level with different forms of the privacy noises. We also reveal the algorithm's trade-off between the convergence rate and the privacy level. Finally, a numerical example verifies the theoretical results and demonstrates the algorithm's superiority against existing methods.

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