Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning-based Attitude Estimation with Noisy Measurements and Unknown Gyro Bias

Parham Oveissi, Mohammad Mirtaba, Ankit Goel

TL;DR

The paper addresses attitude estimation on $SO(3)$ under noisy measurements and unknown gyro bias by introducing the Retrospective Cost Attitude Estimator (RCAE), a learning-based method that learns a multiplicative correction via retrospective cost optimization. RCAE updates the attitude with a scalar RCAC-driven term, avoiding Jacobians and covariance propagation while rejecting constant gyro bias without explicit bias estimation. The approach is validated through numerical simulations and physical experiments, showing competitive accuracy with lower computational load than the MEKF. The work offers a practical, data-driven alternative for real-time attitude estimation in robotics and navigation.

Abstract

This paper introduces a learning-based, data-driven attitude estimator, called the retrospective cost attitude estimator (RCAE), for the SO(3) attitude representation. RCAE is motivated by the multiplicative extended Kalman filter (MEKF). However, unlike MEKF, which requires computing a Jacobian to compute the correction signal, RCAC uses retrospective cost optimization that depends only on the measured data. Moreover, due to the structure of the correction signal, RCAE does not require explicit estimation of gyro bias. The performance of RCAE is verified and compared with MEKF through both numerical simulations and physical experiments.

Learning-based Attitude Estimation with Noisy Measurements and Unknown Gyro Bias

TL;DR

The paper addresses attitude estimation on under noisy measurements and unknown gyro bias by introducing the Retrospective Cost Attitude Estimator (RCAE), a learning-based method that learns a multiplicative correction via retrospective cost optimization. RCAE updates the attitude with a scalar RCAC-driven term, avoiding Jacobians and covariance propagation while rejecting constant gyro bias without explicit bias estimation. The approach is validated through numerical simulations and physical experiments, showing competitive accuracy with lower computational load than the MEKF. The work offers a practical, data-driven alternative for real-time attitude estimation in robotics and navigation.

Abstract

This paper introduces a learning-based, data-driven attitude estimator, called the retrospective cost attitude estimator (RCAE), for the SO(3) attitude representation. RCAE is motivated by the multiplicative extended Kalman filter (MEKF). However, unlike MEKF, which requires computing a Jacobian to compute the correction signal, RCAC uses retrospective cost optimization that depends only on the measured data. Moreover, due to the structure of the correction signal, RCAE does not require explicit estimation of gyro bias. The performance of RCAE is verified and compared with MEKF through both numerical simulations and physical experiments.
Paper Structure (11 sections, 1 theorem, 34 equations, 11 figures)

This paper contains 11 sections, 1 theorem, 34 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Retrospective Cost Attitude Estimator
  4. Attitude Error
  5. Attitude Estimator
  6. Retrospective Cost Optimization
  7. Experimental Verification and Performance Comparison
  8. Numerical Simulation
  9. Physical Experiment
  10. Conclusions and Future Work
  11. Attitude Measurement

Key Result

Proposition III.1

Consider eq:RetCost_def, where $\theta_0 \in {\mathbb R}^{l_\theta}$ and $P_0 \in {\mathbb R}^{l_\theta \times l_\theta}$ is positive definite. For all $k\ge0$, denote the minimizer of $J_k$ given by eq:RetCost_def by Then, for all $k\ge0$, $\theta_{k+1}$ is given by where and

Figures (11)

  • Figure 1: Retrospective cost attitude estimator architecture.
  • Figure 2: True and measured angular velocities.
  • Figure 3: 3-2-1 Euler angles corresponding to the true orientation ${\mathcal{O}}_{\rm B/A}^k,$ measured orientation ${\mathcal{O}}_{\rm B_m/A}^k,$ and estimated orientation ${\mathcal{O}}_{\rm \hat{B}/A}^k$ using RCAE.
  • Figure 4: Retrospective cost attitude estimation. a) shows the signal $u_k$ computed by RCAE, and b) shows the estimator gain $\theta_k$ optimized by RCAE.
  • Figure 5: True and estimated frames corresponding to the true orientation ${\mathcal{O}}_{\rm B/A}^k$ and estimated orientation ${\mathcal{O}}_{\rm \hat{B}/A}^k.$
  • ...and 6 more figures

Theorems & Definitions (2)

  • Proposition III.1
  • proof