Visual-inertial state estimation based on Chebyshev polynomial optimization

TL;DR

This work introduces a continuous-time visual–inertial state estimator built on Chebyshev polynomial optimization, modeling attitude and velocity with finite-order Chebyshev expansions to obtain continuous poses over a time interval $[t_0,t_M]$. By combining a compelling IMU measurement model, a visual BA residual, and a jointly optimized objective, the method preserves the quasi-Gaussian nature of measurements and enables asynchronous sensor fusion without repeated IMU re-integration. The approach uses Chebyshev collocation, Clenshaw–Curtis quadrature, and EFH interpolation to transform the problem into a nonlinear least-squares optimization over polynomial coefficients, solved via augmented Lagrangian and Levenberg–Marquardt. Empirical results on simulations and EuRoC MAV data show substantial improvements in velocity and position accuracy (≈30–50% RMSE reductions) and about 50% reduction in runtime cost compared with discrete preintegration, highlighting the practical potential of continuous-time VINS. Future work includes adaptive polynomial-order selection and sliding-window extensions for real-time deployment.

Abstract

This paper proposes an innovative state estimation method for visual-inertial fusion based on Chebyshev polynomial optimization. Specifically, the pose is modeled as a Chebyshev polynomial of a certain order, and its time derivatives are used to calculate linear acceleration and angular velocity, which, along with inertial measurements, constitute dynamic constraints. This is coupled with a visual measurement model to construct a visual-inertial bundle adjustment formulation. Simulation and public dataset experiments show that the proposed method has better accuracy than the discrete-form preintegration method.

Figures (35)

• Figure 1: Circular trajectory.
• Figure 2: Attitude errors of Chebyshev polynomial optimization and preintegration across 50 Monte-Carlo runs.
• Figure 3: Velocity errors of Chebyshev polynomial optimization and preintegration across 50 Monte-Carlo runs.
• Figure 4: Position errors of Chebyshev polynomial optimization and preintegration across 50 Monte-Carlo runs.
• Figure 5: Average attitude errors across 50 Monte-Carlo runs for Chebyshev polynomial optimization and preintegration.