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Pitot-Aided Attitude and Air Velocity Estimation with Almost Global Asymptotic Stability Guarantees

Melone Nyoba Tchonkeu, Soulaimane Berkane, Tarek Hamel

TL;DR

This work addresses the problem of estimating the attitude $R \in SO(3)$ and the body-frame air velocity $V_a \in \mathbb{R}^3$ for fixed-wing UAVs using IMU data, Pitot measurements, and magnetometer readings. It introduces a two-stage cascade observer: first, a Riccati-type filter on a linear time-varying model jointly estimates $V_a$ and the gravity-direction tilt $z=R^\top e_3$ under a uniform observability (and persistent excitation) condition, then an $SO(3)$-based nonlinear observer fuses the tilt with magnetometer information to recover the full attitude with AGAS guarantees. Theoretical results show global exponential convergence of the reduced-state errors and almost global asymptotic stability for the complete attitude estimator, while experiments on a wind-affected UAV validate accurate air velocity and full attitude estimation and demonstrate the observability gains from a zero-sideslip constraint. The approach provides a rigorous Pitot-aided estimation framework suitable for GNSS-denied or highly dynamic flight regimes, with practical implications for robust UAV navigation and control.

Abstract

This paper investigates the problem of attitude and air velocity estimation for fixed-wing unmanned aerial vehicles (UAVs) using IMU measurements and at least one Pitot tube measurement, with almost global asymptotic stability (AGAS) guarantees. A cascade observer architecture is developed, in which a Riccati/Kalman-type filter estimates the body-fixed frame air velocity and the vehicle's tilt using IMU data as inputs and Pitot measurements as outputs. Under mild excitation conditions, the resulting air velocity and tilt estimation error dynamics are shown to be uniformly observable. The estimated tilt is then combined with magnetometer measurements in a nonlinear observer on SO(3) to recover the full attitude. Rigorous analysis establishes AGAS of the overall cascade structure under the uniform observability (UO) condition. The effectiveness of the proposed approach is demonstrated through validation on real flight data.

Pitot-Aided Attitude and Air Velocity Estimation with Almost Global Asymptotic Stability Guarantees

TL;DR

This work addresses the problem of estimating the attitude and the body-frame air velocity for fixed-wing UAVs using IMU data, Pitot measurements, and magnetometer readings. It introduces a two-stage cascade observer: first, a Riccati-type filter on a linear time-varying model jointly estimates and the gravity-direction tilt under a uniform observability (and persistent excitation) condition, then an -based nonlinear observer fuses the tilt with magnetometer information to recover the full attitude with AGAS guarantees. Theoretical results show global exponential convergence of the reduced-state errors and almost global asymptotic stability for the complete attitude estimator, while experiments on a wind-affected UAV validate accurate air velocity and full attitude estimation and demonstrate the observability gains from a zero-sideslip constraint. The approach provides a rigorous Pitot-aided estimation framework suitable for GNSS-denied or highly dynamic flight regimes, with practical implications for robust UAV navigation and control.

Abstract

This paper investigates the problem of attitude and air velocity estimation for fixed-wing unmanned aerial vehicles (UAVs) using IMU measurements and at least one Pitot tube measurement, with almost global asymptotic stability (AGAS) guarantees. A cascade observer architecture is developed, in which a Riccati/Kalman-type filter estimates the body-fixed frame air velocity and the vehicle's tilt using IMU data as inputs and Pitot measurements as outputs. Under mild excitation conditions, the resulting air velocity and tilt estimation error dynamics are shown to be uniformly observable. The estimated tilt is then combined with magnetometer measurements in a nonlinear observer on SO(3) to recover the full attitude. Rigorous analysis establishes AGAS of the overall cascade structure under the uniform observability (UO) condition. The effectiveness of the proposed approach is demonstrated through validation on real flight data.
Paper Structure (9 sections, 2 theorems, 38 equations, 8 figures, 1 algorithm)

This paper contains 9 sections, 2 theorems, 38 equations, 8 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARY MATERIAL
  3. PROBLEM DESCRIPTION
  4. PROPOSED OBSERVER DESIGN
  5. Tilt and Air Velocity Estimation
  6. Full Attitude Estimation on $\mathrm{SO}(3)$
  7. Discrete-Time Implementation
  8. EXPERIMENTS
  9. CONCLUSION

Key Result

Lemma 1

Assume that the angular velocity $\boldsymbol{\omega}(t)$ is continuous and bounded. If the matrix $\Sigma(t)$ is persistently exciting (PE) in the sense that there exist $\bar{\delta}, \bar{\mu} > 0$ such that $\forall t \ge 0$, then the pair $(A(t), C)$ is uniformly observable, and the equilibrium $\tilde{x} = 0_{6\times1}$ is globally uniformly exponentially stable (GES).

Figures (8)

  • Figure 1: A fixed-wing UAV equipped with an IMU, a Pitot tube measuring the air velocity $V_a$.
  • Figure 2: Two-stage observer architecture: a Riccati observer fuses IMU and Pitot tube data to estimate tilt and air velocity, followed by an $\mathrm{SO}(3)$ observer combining tilt, gyro, and magnetometer to estimate $\hat{R}$.
  • Figure 3: Onboard Air-velocity Components.
  • Figure 4: Comparison between measurement of $V_{a,1}$ (Red) and $\bar{V}_{a,1}$ (Blue) in the real flight data set.
  • Figure 5: Air Velocity components and error: Configuration 1 (Red) and Configuration 2 (Blue).
  • ...and 3 more figures

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Theorem 1
  • proof