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Fast and Robust State Estimation and Tracking via Hierarchical Learning

Connor Mclaughlin, Matthew Ding, Deniz Erdogmus, Lili Su

TL;DR

This paper proposes two ``consensus + innovation'' algorithms, both of which rely on a novel hierarchical push-sum consensus component and characterize their convergence rates under a linear local observation model and minimal technical assumptions.

Abstract

Fast and reliable state estimation and tracking are essential for real-time situation awareness in Cyber-Physical Systems (CPS) operating in tactical environments or complicated civilian environments. Traditional centralized solutions do not scale well whereas existing fully distributed solutions over large networks suffer slow convergence, and are vulnerable to a wide spectrum of communication failures. In this paper, we aim to speed up the convergence and enhance the resilience of state estimation and tracking for large-scale networks using a simple hierarchical system architecture. We propose two ``consensus + innovation'' algorithms, both of which rely on a novel hierarchical push-sum consensus component. We characterize their convergence rates under a linear local observation model and minimal technical assumptions. We numerically validate our algorithms through simulation studies of underwater acoustic networks and large-scale synthetic networks.

Fast and Robust State Estimation and Tracking via Hierarchical Learning

TL;DR

This paper proposes two ``consensus + innovation'' algorithms, both of which rely on a novel hierarchical push-sum consensus component and characterize their convergence rates under a linear local observation model and minimal technical assumptions.

Abstract

Fast and reliable state estimation and tracking are essential for real-time situation awareness in Cyber-Physical Systems (CPS) operating in tactical environments or complicated civilian environments. Traditional centralized solutions do not scale well whereas existing fully distributed solutions over large networks suffer slow convergence, and are vulnerable to a wide spectrum of communication failures. In this paper, we aim to speed up the convergence and enhance the resilience of state estimation and tracking for large-scale networks using a simple hierarchical system architecture. We propose two ``consensus + innovation'' algorithms, both of which rely on a novel hierarchical push-sum consensus component. We characterize their convergence rates under a linear local observation model and minimal technical assumptions. We numerically validate our algorithms through simulation studies of underwater acoustic networks and large-scale synthetic networks.
Paper Structure (34 sections, 8 theorems, 75 equations, 8 figures, 2 algorithms)

This paper contains 34 sections, 8 theorems, 75 equations, 8 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Hierarchical algorithms
  4. Fault-tolerant algorithms
  5. Comparison with Previous Work
  6. Problem Formulation
  7. System Model
  8. Threat Model
  9. State Dynamics and Local Observation Models
  10. State dynamics
  11. Local observation
  12. Hierarchical Average Consensus in the Presence of Packet-dropping Failures
  13. State Estimation
  14. State Tracking
  15. Numerical Results
  16. ...and 19 more sections

Key Result

Theorem 1

Choose $\Gamma = BD^*$. Suppose that Assumptions ass: link reliability and ass: connectivity hold, and that $t\ge 2\Gamma$. Then where $\gamma = 1-\frac{1}{4M^2} \left( \min_{i\in [M]}\beta_i \right)^{2D^*B}$.

Figures (8)

  • Figure 1: The System Architecture of Hierarchical Learning
  • Figure 2: Network Configurations
  • Figure 3: State Estimation on Small Network Configuration.
  • Figure 4: Comparison of Synchronization Frequency on Large Network Configuration.
  • Figure 5: Ablation on System Robustness ($B, \bar{\sigma}$) on Large Network Configuration.
  • ...and 3 more figures

Theorems & Definitions (16)

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