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NDKF: A Neural-Enhanced Distributed Kalman Filter for Nonlinear Multi-Sensor Estimation

Siavash Farzan

TL;DR

NDKF tackles distributed nonlinear state estimation by learning both system dynamics and measurement mappings with neural networks and fusing local estimates via a consensus mechanism, thereby reducing communication and avoiding a central fusion node. The method preserves a Kalman-like prediction-update structure using neural models and operates in a fully distributed fashion with information-form fusion, supported by a stability analysis under Lipschitz and bounded-Jacobian assumptions. Empirical results on a 2D multi-sensor setup show substantial RMSE reductions over a mis-specified distributed EKF, highlighting improved scalability, robustness, and accuracy in nonlinear environments. The work thus offers a principled, data-driven alternative for large-scale distributed estimation, with potential extensions to online learning, adaptive noise tuning, and more robust fusion schemes.

Abstract

We propose a Neural-Enhanced Distributed Kalman Filter (NDKF) for multi-sensor state estimation in nonlinear systems. Unlike traditional Kalman filters that rely on explicit, linear models and centralized data fusion, the NDKF leverages neural networks to learn both the system dynamics and measurement functions directly from data. Each sensor node performs local prediction and update steps using these learned models and exchanges only compact summary information with its neighbors via a consensus-based fusion process, which reduces communication overhead and eliminates a single point of failure. Our theoretical convergence analysis establishes sufficient conditions under which the local linearizations of the neural models guarantee overall filter stability and provides a solid foundation for the proposed approach. Simulation studies on a 2D system with four partially observing nodes demonstrate that the NDKF significantly outperforms a distributed Extended Kalman Filter. These outcomes, as yielded by the proposed NDKF method, highlight its potential to improve the scalability, robustness, and accuracy of distributed state estimation in complex nonlinear environments.

NDKF: A Neural-Enhanced Distributed Kalman Filter for Nonlinear Multi-Sensor Estimation

TL;DR

NDKF tackles distributed nonlinear state estimation by learning both system dynamics and measurement mappings with neural networks and fusing local estimates via a consensus mechanism, thereby reducing communication and avoiding a central fusion node. The method preserves a Kalman-like prediction-update structure using neural models and operates in a fully distributed fashion with information-form fusion, supported by a stability analysis under Lipschitz and bounded-Jacobian assumptions. Empirical results on a 2D multi-sensor setup show substantial RMSE reductions over a mis-specified distributed EKF, highlighting improved scalability, robustness, and accuracy in nonlinear environments. The work thus offers a principled, data-driven alternative for large-scale distributed estimation, with potential extensions to online learning, adaptive noise tuning, and more robust fusion schemes.

Abstract

We propose a Neural-Enhanced Distributed Kalman Filter (NDKF) for multi-sensor state estimation in nonlinear systems. Unlike traditional Kalman filters that rely on explicit, linear models and centralized data fusion, the NDKF leverages neural networks to learn both the system dynamics and measurement functions directly from data. Each sensor node performs local prediction and update steps using these learned models and exchanges only compact summary information with its neighbors via a consensus-based fusion process, which reduces communication overhead and eliminates a single point of failure. Our theoretical convergence analysis establishes sufficient conditions under which the local linearizations of the neural models guarantee overall filter stability and provides a solid foundation for the proposed approach. Simulation studies on a 2D system with four partially observing nodes demonstrate that the NDKF significantly outperforms a distributed Extended Kalman Filter. These outcomes, as yielded by the proposed NDKF method, highlight its potential to improve the scalability, robustness, and accuracy of distributed state estimation in complex nonlinear environments.

Paper Structure

This paper contains 18 sections, 1 theorem, 44 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. NDKF Framework
  3. System Setup
  4. Neural Network for System and Measurement Modeling
  5. Kalman Filter with Neural Network Integration
  6. Prediction Step
  7. Local Measurement Update
  8. Distributed Fusion Mechanism
  9. Initialization and Parameter Tuning
  10. Scalability and Computational Complexity
  11. Convergence and Stability Analysis
  12. Assumptions
  13. Local Error Dynamics
  14. Sufficient Conditions for Stability
  15. Results and Discussion
  16. ...and 3 more sections

Key Result

Theorem 1

Under assumptions (i)--(iii), suppose that there exist constants $\alpha,\beta \in (0,1)$ such that for all time indices $k$ and for each node $i$, Then, there exists a neighborhood $\mathcal{E}$ around the true state such that if $\| \mathbf{e}_{0|0,i} \| < \delta$, the estimation error $\mathbf{e}_{k|k,i}$ converges exponentially fast (in mean-square sense) to a bounded region determined by the

Figures (2)

  • Figure 1: True state, individual node estimates, and the fused NDKF estimate.
  • Figure 2: Measurement innovation residuals for Node 1.

Theorems & Definitions (2)

  • Theorem 1: Stability of NDKF
  • proof