Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Yunxiao Ren, Zhisheng Duan, Peihu Duan, Ling Shi

TL;DR

The paper investigates redundant sensors in collaborative Kalman filtering, combining Riccati-equation analysis and symplectic geometry to quantify how redundancy affects steady-state error covariances. It proves that adding redundant sensors can only improve estimation, and it derives a strict condition for when the improvement is guaranteed for all state elements. An optimization framework with an algorithm (Algorithm 1) and convergence guarantees is introduced to design redundant sensors in a plug-and-play manner, along with a sufficiency condition and a practical convex-set constraint. Numerical simulations validate the theoretical findings and demonstrate the algorithm’s effectiveness and scalability. The work provides actionable insights for robust sensor-network design in industrial and engineering systems where redundancy is common and redesign is costly.

Abstract

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.

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

TL;DR

The paper investigates redundant sensors in collaborative Kalman filtering, combining Riccati-equation analysis and symplectic geometry to quantify how redundancy affects steady-state error covariances. It proves that adding redundant sensors can only improve estimation, and it derives a strict condition for when the improvement is guaranteed for all state elements. An optimization framework with an algorithm (Algorithm 1) and convergence guarantees is introduced to design redundant sensors in a plug-and-play manner, along with a sufficiency condition and a practical convex-set constraint. Numerical simulations validate the theoretical findings and demonstrate the algorithm’s effectiveness and scalability. The work provides actionable insights for robust sensor-network design in industrial and engineering systems where redundancy is common and redesign is costly.

Abstract

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.
Paper Structure (13 sections, 15 theorems, 97 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 15 theorems, 97 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. Problem Formulation and Preliminaries
  5. Modeling Formulation
  6. Problem Statement
  7. Preliminaries
  8. The Effects of Redundant Sensors
  9. The Optimal Design of the Redundant Sensors
  10. Simulation Examples
  11. The effects of redundant sensors
  12. The effectiveness of Algorithm 1
  13. Conclusion

Key Result

Lemma 1

If Assumptions assum:inver holds. For process eq:process, and two different sensor networks SN1, SN2 with output matrices and noise covariance matrices $(C_{1},R_{1})$ and $(C_{2},R_{2})$ respectively, denote the corresponding priori and poesteriori covariance matrices as $P_{1}$, $P_{p,1}$ and $P_{

Figures (6)

  • Figure 1: The model and research problem concerned.
  • Figure 2: The distributions and corresponding error ellipsoids of $n_{i}$.
  • Figure 3: Probability distributions of the estimate errors of $\bar{C}$ and $C_{r1}$.
  • Figure 4: Probability distributions of the estimate errors of $\bar{C}$ and $C_{r2}$.
  • Figure 5: The evolution of $\gamma^{j}$ with iteration step $j$.
  • ...and 1 more figures

Theorems & Definitions (20)

  • Remark 1
  • Lemma 1
  • Corollary 1
  • Remark 2
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • Theorem 1
  • ...and 10 more