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Event-Triggered State Estimation Through Confidence Level

Wei Liu

TL;DR

This work addresses state estimation for discrete-time linear systems in wireless-sensor-network settings under an event-triggered scheme. It introduces a novel confidence-level-based trigger using the chi-square distribution, enabling a direct link between the innovation covariance, the trigger threshold, and communication rate. A recursive MMSE estimator is developed under this scheme, along with two algorithms to estimate the communication rate, one using one-step delay and another using two-step delay. Demonstrated on a target-tracking problem, the SECL estimator achieves superior tracking performance for a given average communication rate, with Pa2 providing the most accurate rate estimates among the approaches.

Abstract

This paper considers the state estimation problem for discrete-time linear systems under event-triggered scheme. In order to improve performance, a novel event-triggered scheme based on confidence level is proposed using the chi-square distribution and mild regularity assumption. In terms of the novel event-triggered scheme, a minimum mean squared error (MMSE) state estimator is proposed using some results presented in this paper. Two algorithms for communication rate estimation of the proposed MMSE state estimator are developed where the first algorithm is based on information with one-step delay, and the second algorithm is based on information with two-step delay. The performance and effectiveness of the proposed MMSE state estimator and the two communication rate estimation algorithms are illustrated using a target tracking scenario.

Event-Triggered State Estimation Through Confidence Level

TL;DR

This work addresses state estimation for discrete-time linear systems in wireless-sensor-network settings under an event-triggered scheme. It introduces a novel confidence-level-based trigger using the chi-square distribution, enabling a direct link between the innovation covariance, the trigger threshold, and communication rate. A recursive MMSE estimator is developed under this scheme, along with two algorithms to estimate the communication rate, one using one-step delay and another using two-step delay. Demonstrated on a target-tracking problem, the SECL estimator achieves superior tracking performance for a given average communication rate, with Pa2 providing the most accurate rate estimates among the approaches.

Abstract

This paper considers the state estimation problem for discrete-time linear systems under event-triggered scheme. In order to improve performance, a novel event-triggered scheme based on confidence level is proposed using the chi-square distribution and mild regularity assumption. In terms of the novel event-triggered scheme, a minimum mean squared error (MMSE) state estimator is proposed using some results presented in this paper. Two algorithms for communication rate estimation of the proposed MMSE state estimator are developed where the first algorithm is based on information with one-step delay, and the second algorithm is based on information with two-step delay. The performance and effectiveness of the proposed MMSE state estimator and the two communication rate estimation algorithms are illustrated using a target tracking scenario.
Paper Structure (14 sections, 6 theorems, 95 equations, 8 figures, 1 table, 2 algorithms)

This paper contains 14 sections, 6 theorems, 95 equations, 8 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. System Description
  4. Event-Triggered Scheme based on Confidence Level
  5. MMSE State Estimation
  6. Communication Rate Estimation
  7. Simulation Example
  8. Performance Evaluation of the Proposed Results
  9. Comparison with SEHI
  10. Conclusion
  11. Proof of Lemmas \ref{['lemfGh']}$-$\ref{['lemfOm']}
  12. Proof of Theorem \ref{['Theorem1']}
  13. Proof of Theorem \ref{['Theorem2']}
  14. Proof of Algorithm \ref{['Pa2']}

Key Result

Lemma 1

Under the assumption that $f(x_{k-1}|\textrm{I}_{k-1})$ is Gaussian, it holds that: 1). $f(x_{k}|\textrm{I}_{k-1})$ is Gaussian. 2). $f(y_{k}|\textrm{I}_{k-1})$ is Gaussian.

Figures (8)

  • Figure 1: Structure of event-triggered state estimation.
  • Figure 2: RMS Position errors of SECL for three different cases.
  • Figure 3: RMS velocity errors of SECL for three different cases.
  • Figure 4: Communication rates of SECL, Algorithm \ref{['Pa1']} and Algorithm \ref{['Pa2']} at Case 1.
  • Figure 5: Communication rates of SECL, Algorithm \ref{['Pa1']} and Algorithm \ref{['Pa2']} at Case 2.
  • ...and 3 more figures

Theorems & Definitions (17)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Lemma 1
  • Remark 5
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • Remark 6
  • ...and 7 more