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Event-Triggered Resilient Filtering for 2-D Systems with Asynchronous-Delay: Handling Binary Encoding Decoding with Probabilistic Bit Flips

Yu Chen, Wei Wang

TL;DR

The paper tackles resilient state estimation for $2$-D systems with asynchronous delays transmitted over binary-encoded channels susceptible to probabilistic bit flips. It proposes a dynamic event-triggered mechanism that determines transmission instants and a measurement reconstruction approach to exploit delayed decoded data, enabling a delay-free perspective for estimation. An $N+1$-step recursive filter is developed using reconstructed measurements, with estimation gains derived by minimizing an upper bound on the filtering error covariance; the authors also prove monotonicity of the filtering performance with respect to triggering parameters. Collectively, the work reduces network load while maintaining estimation accuracy, and provides rigorous design rules for triggering and gains under binary EDSs in the presence of asynchronous delays and channel noise.

Abstract

In this paper, the event-triggered resilient filtering problem is investigated for a class of two-dimensional systems with asynchronous-delay under binary encoding-decoding schemes with probabilistic bit flips. To reduce unnecessary communications and computations in complex network systems, alleviate network energy consumption, and optimize the use of network resources, a new event-triggered mechanism is proposed, which focuses on broadcasting necessary measurement information to update innovation only when the event generator function is satisfied. A binary encoding-decoding scheme is used in the communication process to quantify the measurement information into a bit stream, transmit it through a memoryless binary symmetric channel with a certain probability of bit flipping, and restore it at the receiver. In order to utilize the delayed decoded measurement information that a measurement reconstruction approach is proposed. Through generating space equivalence verification, it is found that the reconstructed delay-free decoded measurement sequence contains the same information as the original delayed decoded measurement sequence. In addition, resilient filter is utilized to accommodate possible estimation gain perturbations. Then, a recursive estimator framework is presented based on the reconstructed decoded measurement sequence. By means of the mathematical induction technique, the unbiased property of the proposed estimator is proved. The estimation gain is obtained by minimizing an upper bound on the filtering error covariance. Subsequently, through rigorous mathematical analysis, the monotonicity of filtering performance with respect to triggering parameters is discussed.

Event-Triggered Resilient Filtering for 2-D Systems with Asynchronous-Delay: Handling Binary Encoding Decoding with Probabilistic Bit Flips

TL;DR

The paper tackles resilient state estimation for -D systems with asynchronous delays transmitted over binary-encoded channels susceptible to probabilistic bit flips. It proposes a dynamic event-triggered mechanism that determines transmission instants and a measurement reconstruction approach to exploit delayed decoded data, enabling a delay-free perspective for estimation. An -step recursive filter is developed using reconstructed measurements, with estimation gains derived by minimizing an upper bound on the filtering error covariance; the authors also prove monotonicity of the filtering performance with respect to triggering parameters. Collectively, the work reduces network load while maintaining estimation accuracy, and provides rigorous design rules for triggering and gains under binary EDSs in the presence of asynchronous delays and channel noise.

Abstract

In this paper, the event-triggered resilient filtering problem is investigated for a class of two-dimensional systems with asynchronous-delay under binary encoding-decoding schemes with probabilistic bit flips. To reduce unnecessary communications and computations in complex network systems, alleviate network energy consumption, and optimize the use of network resources, a new event-triggered mechanism is proposed, which focuses on broadcasting necessary measurement information to update innovation only when the event generator function is satisfied. A binary encoding-decoding scheme is used in the communication process to quantify the measurement information into a bit stream, transmit it through a memoryless binary symmetric channel with a certain probability of bit flipping, and restore it at the receiver. In order to utilize the delayed decoded measurement information that a measurement reconstruction approach is proposed. Through generating space equivalence verification, it is found that the reconstructed delay-free decoded measurement sequence contains the same information as the original delayed decoded measurement sequence. In addition, resilient filter is utilized to accommodate possible estimation gain perturbations. Then, a recursive estimator framework is presented based on the reconstructed decoded measurement sequence. By means of the mathematical induction technique, the unbiased property of the proposed estimator is proved. The estimation gain is obtained by minimizing an upper bound on the filtering error covariance. Subsequently, through rigorous mathematical analysis, the monotonicity of filtering performance with respect to triggering parameters is discussed.
Paper Structure (15 sections, 10 theorems, 90 equations, 1 figure)

This paper contains 15 sections, 10 theorems, 90 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. System description
  4. Dynamic event-triggered mechanisms
  5. Encoding-decoding schemes
  6. PRELIMINARIES
  7. The internal dynamic variable properties
  8. Effects of binary encoding-decoding schemes
  9. Original decoded measurement description
  10. Reconstruction of the decoded measurement
  11. MAIN RESULTS
  12. Filter development
  13. Design of estimation gain parameters
  14. Monotonicity of triggering parameters
  15. Conclusion

Key Result

Lemma 1

Let the parameters satisfies $\rho_{(s)}\geq \frac{1}{\alpha_{(s),1}}, \rho_{(s)}\geq \frac{1}{\alpha_{(s),2}},$$0<\alpha_{(s),1},\alpha_{(s),2},\sigma_{(s)}^{\gamma}<1$ for any $\gamma\in[1,m]$. Then, we have $\xi_{(s)}^{\gamma}(i,j)\geq0$ for $i,j\in[0,\wp]$.

Figures (1)

  • Figure 1: Framework of ETMs and EDSs for 2-D systems estimation.

Theorems & Definitions (21)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • ...and 11 more