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Environment-Aware Learning of Smooth GNSS Covariance Dynamics for Autonomous Racing

Y. Deemo Chen, Arion Zimmermann, Thomas A. Berrueta, Soon-Jo Chung

TL;DR

This work develops a learning-based framework, LACE, capable of directly modeling the temporal dynamics of GNSS measurement covariance, and model the covariance evolution as an exponentially stable dynamical system where a deep neural network learns to predict the system's process noise from environmental features through an attention mechanism.

Abstract

Ensuring accurate and stable state estimation is a challenging task crucial to safety-critical domains such as high-speed autonomous racing, where measurement uncertainty must be both adaptive to the environment and temporally smooth for control. In this work, we develop a learning-based framework, LACE, capable of directly modeling the temporal dynamics of GNSS measurement covariance. We model the covariance evolution as an exponentially stable dynamical system where a deep neural network (DNN) learns to predict the system's process noise from environmental features through an attention mechanism. By using contraction-based stability and systematically imposing spectral constraints, we formally provide guarantees of exponential stability and smoothness for the resulting covariance dynamics. We validate our approach on an AV-24 autonomous racecar, demonstrating improved localization performance and smoother covariance estimates in challenging, GNSS-degraded environments. Our results highlight the promise of dynamically modeling the perceived uncertainty in state estimation problems that are tightly coupled with control sensitivity.

Environment-Aware Learning of Smooth GNSS Covariance Dynamics for Autonomous Racing

TL;DR

This work develops a learning-based framework, LACE, capable of directly modeling the temporal dynamics of GNSS measurement covariance, and model the covariance evolution as an exponentially stable dynamical system where a deep neural network learns to predict the system's process noise from environmental features through an attention mechanism.

Abstract

Ensuring accurate and stable state estimation is a challenging task crucial to safety-critical domains such as high-speed autonomous racing, where measurement uncertainty must be both adaptive to the environment and temporally smooth for control. In this work, we develop a learning-based framework, LACE, capable of directly modeling the temporal dynamics of GNSS measurement covariance. We model the covariance evolution as an exponentially stable dynamical system where a deep neural network (DNN) learns to predict the system's process noise from environmental features through an attention mechanism. By using contraction-based stability and systematically imposing spectral constraints, we formally provide guarantees of exponential stability and smoothness for the resulting covariance dynamics. We validate our approach on an AV-24 autonomous racecar, demonstrating improved localization performance and smoother covariance estimates in challenging, GNSS-degraded environments. Our results highlight the promise of dynamically modeling the perceived uncertainty in state estimation problems that are tightly coupled with control sensitivity.
Paper Structure (19 sections, 2 theorems, 21 equations, 9 figures, 1 table)

This paper contains 19 sections, 2 theorems, 21 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Definition
  3. Method
  4. Preprocessing
  5. Spatial Embedding and Attention Mechanism
  6. Core Model
  7. Smoothness through LACE
  8. Data-efficient Implementation
  9. Loss Function
  10. Contraction Stability Analysis
  11. Results
  12. Datasets
  13. Training
  14. Exponential Convergence
  15. Track Prediction
  16. ...and 4 more sections

Key Result

Theorem 1

Let $A(t)\in\mathbb{R}^{n\times n}$ be time-varying with eigenvalues $\{\lambda_i(t)\in \mathbb{C}\}_{i=1}^n$ and let $R(t)\in\mathbb{S}_{++}^n$ be differentiable. If the eigenvalues of $A(t)$ are constrained such that for all $t\geq 0$, there is a $\lambda_{\min} < 0$, such that: then choosing $\lambda_{\min} \geq -\,r_{\max}/(2n)$ satisfies the smoothness constraint from eq:smoothness.

Figures (9)

  • Figure 1: LACE applied to IAC racecars. Top: Illustration of the learned GNSS covariance evolution as the racecar passes under a concrete bridge at Laguna Seca Raceway. The structure degrades GNSS measurement quality, causing the covariance to broaden. For clarity, the covariance distribution is visualized in 2D. Bottom: Caltech IAC AV-24 racecar.
  • Figure 2: LACE architecture overview. The core model produces a symmetric positive-definite matrix, while during both training and inference, LACE propagates this output through its dynamical model to guarantee stability and enforce temporal smoothness.
  • Figure 3: Illustration of the robot’s position $x(t)$, reparameterized into arc-length coordinates $s(t)$ and processed by a low-temperature attention mechanism to capture localized environmental features.
  • Figure 4: Dense LiDAR map of the Laguna Seca Raceway from running offline FGO based SLAM framework with color coded by altitude.
  • Figure 5: Train and evaluation loss of our method (LACE) and MLP, yellow stars indicate the lowest part of the evaluation loss. LACE shows a much faster training convergence rate.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof