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UAV attitude estimation using Unscented Kalman Filter and TRIAD
Hector Garcia de Marina, Fernando J. Pereda, Jose Marina Giron-Sierra, Felipe Espinosa
TL;DR
UAV attitude estimation must support closed-loop control despite noisy and biased sensor signals. The paper proposes a quaternion AHRS combining UKF filtering with TRIAD observations, and reports better UKF simulation performance, encouraging field results, and real-time microcontroller implementation.
Problem
Noisy, biased, and vibration-affected sensor signals make accurate three-angle UAV attitude estimation necessary for closing autonomous control loops.
Method
The paper develops a quaternion-based AHRS using a UKF with TRIAD as the observation model and MEMS gyrometers, magnetometers, and accelerometers as inputs.
Results
Simulations show better UKF performance than EKF, while field experiments with independent sensors report good estimation results.
Takeaways & Limitations
The estimator is easy to implement, runs on an onboard microcontroller, and supports future integration with a closed-loop controller.
Abstract
from arXiv · showhide
A main problem in autonomous vehicles in general, and in \acp{UAV} in particular, is the determination of the attitude angles. A novel method to estimate these angles using off-the-shelf components is presented. This paper introduces an \ac{AHRS} based on the \ac{UKF} using the \ac{TRIAD} algorithm as the observation model. The performance of the method is assessed through simulations and compared to an \ac{AHRS} based on the \ac{EKF}. The paper presents field experiment results using a real fixed-wing \ac{UAV}. The results show good real-time performance with low computational cost in a microcontroller.
I. INTRODUCTION
The paper addresses noisy, biased attitude sensing for UAV control by proposing a UKF-based AHRS using TRIAD measurements and quaternion attitude representation. Simulations and field experiments report better UKF performance than EKF, satisfactory fixed-wing UAV estimation, and low-cost real-time implementation.
- Motivation: Accurate three-angle attitude estimation is needed for closing autonomous UAV control loops despite vibration, sensor noise, and bias.The onboard system uses MEMS accelerometers, gyrometers, magnetometers, and GPS on a small fixed-wing UAV.
- Motivation: The EKF was unsatisfactory on experimental signals, with sometimes excessive estimation errors or divergence.These behaviors are described as inappropriate for control loops.
- Evaluation: The simulation framework uses X-Plane 9 with high-frequency noise and sensor latencies added to simulated measurements.The framework combines a six-degree-of-freedom aerodynamic model, X-Plane plug-in code, and a sensor model.
- Evaluation: Under maximum-error requirements of 1.0° for pitch and roll and 4.0° for yaw, the UKF shows better performance than the EKF.The requirements are described as standard in the industry and were assessed across many simulation cases.
- Evaluation: Field experiments on a real fixed-wing UAV show good estimation quality using independent sensors, with implementation feasible on an onboard microcontroller.The authors identify closed-loop controller integration as future experimental work.
- Approach: The proposed AHRS uses a UKF with the TRIAD algorithm as its observation model and gyrometers, magnetometers, and accelerometers as inputs.The attitude is formulated with quaternions, which avoid gimbal lock and are easier to propagate numerically than angles.
III. PROBLEM FORMULATION
The problem formulation represents UAV attitude kinematics independently of aircraft coefficients, using Euler angles, quaternion components, and a quaternion-derived direction cosine matrix. Quaternion propagation is preferred to avoid instability and gimbal lock while relating sensor angular rates to attitude.
- III. PROBLEM FORMULATION: The AHRS problem is formulated for a UAV with three-axis gyrometer, accelerometer, and magnetometer measurements.The kinematic model determines Euler angles independently of the UAV’s dynamical coefficients.
- A. AHRS kinematic model: Euler angles describe body-axis orientation in north-east-down coordinates: θ is pitch, φ is roll, and ψ is yaw.The body-frame angular rates are P, Q, and R for roll, pitch, and yaw.
- A. AHRS kinematic model: Quaternion propagation is preferred because direct integration can be numerically unstable and may encounter gimbal lock.The quaternion norm is constrained to 1, and quaternion components are related to half-angles φ′, θ′, and ψ′.
- A. AHRS kinematic model: The quaternion components are constructed from trigonometric combinations of the half-angle Euler variables.Equations (3)–(6) define q0 through q3 using φ′, θ′, and ψ′.
- A. AHRS kinematic model: Figure 2 defines the coordinate axes used by the Euler-angle and kinematic formulations.Its coordinate convention is the north-east-down frame described in the surrounding model.
- A. AHRS kinematic model: The kinematic relation between body-frame angular rates and Earth-frame attitude rates can be rewritten linearly using quaternion components.The formulation uses the rate transformation associated with P, Q, and R.
- A. AHRS kinematic model: The direction cosine matrix is expressed from quaternion components, and Euler angles are recovered from its terms.This provides a matrix-based representation alongside the quaternion state.
3. Then,
Gyroscope integration is affected by bias and quaternion-norm drift. The formulation models slowly varying bias, corrects measured angular rates, and uses a norm-preserving integration approach under constant-rate discretization.
- B. Gyros integration problem: Gyroscopes measure angular velocity, but integrating biased measurements causes error to grow at every step.The angular velocity vector is ω = (P, Q, R).
- B. Gyros integration problem: Under normal MEMS conditions, gyroscope bias can be modeled as constant or very slowly varying during the UAV mission.The assumption excludes extreme temperature or pressure variation.
- B. Gyros integration problem: Measured angular velocities are corrected by subtracting the modeled gyroscope bias.The relation is expressed as ω = ωs − b.
- B. Gyros integration problem: Quaternion integration must preserve unit norm; otherwise, Euler angles computed from the quaternion are wrong.The paper presents an integrating factor as an alternative to normalizing after every integration step.
- B. Gyros integration problem: The discrete propagation assumes angular velocities remain constant over the interval dt.The discretization includes the squared rate-increment terms and the identity matrix I.
C. The TRIAD algorithm
TRIAD is a deterministic attitude-determination method that computes the direction cosine matrix from paired reference and observed vectors. Because the first pair has greater influence, the more accurate vector pair should be assigned first according to flight conditions.
- C. The TRIAD algorithm: TRIAD determines spacecraft attitude from two reference unit vectors and their corresponding observed unit vectors.The method computes the direction cosine matrix from these vector pairs.
- C. The TRIAD algorithm: The TRIAD algorithm uses an explicit expression to determine the direction cosine matrix.Observation vectors are denoted oi and reference vectors ri.
- C. The TRIAD algorithm: The first vector pair has more influence on the computed matrix because part of the second pair’s information is discarded.The paper therefore assigns the more accurate pair to (W1, V1), with criteria based on flight circumstances.
IV. UNSCENTED KALMAN FILTER DESIGN
The proposed UKF estimates quaternion attitude components and gyrometer biases in a two-step propagator/corrector filter, with propagation at 100 Hz and correction at 1 Hz. It uses TRIAD information in the correction loop and avoids Jacobians or Hessians.
- The UKF estimates quaternion components and gyrometer biases for UAV attitude estimation.
- The filter uses a propagator/corrector structure, with propagation limited to 100 Hz and correction limited by the 1 Hz GPS sample rate.
- TRIAD information feeds the correction step in the algorithm’s two main loops.
- The UKF uses the unscented transformation to estimate statistics after nonlinear transformations under an additive, zero-mean sensor-noise assumption.
- The UKF computation starts by generating sigma points for quaternion components and gyrometer biases, then evaluates the process model on them.
- The process-noise covariance combines quaternion and gyrometer-bias covariance blocks, with Qq close to but different from zero and Qb set to the 3x3 zero matrix.
B. Correction equations and observation model
The observation model uses TRIAD-derived attitude information from accelerometer and magnetometer vector pairs, with GPS velocity helping remove centrifugal acceleration. Measurement reliability determines which vector pair is prioritized or whether correction is skipped.
- Only four of TRIAD’s nine DCM terms are used to calculate the Euler angles in the observation function.
- Pitch and roll use X and Y components of the Z earth vector, whereas yaw uses X and Y components of the X body vector in Earth coordinates.
- TRIAD computes DCM terms from magnetic-field and acceleration observation-reference vector pairs.
- GPS speed supplies the dominant body-frame forward velocity component used to subtract centrifugal acceleration.
- The correction step prioritizes accelerometers during stationary flight and magnetometers during coordinated turns, based on acceleration magnitude.
- Correction is skipped when magnetic measurements are unreliable or when the aircraft is assumed to be acrobatic.
V. SIMULATIONS RESULTS
The simulations combine an X-Plane six-degree-of-freedom aircraft model with realistic sensor models to study noise, bias, and latency effects. The evaluation imposes attitude-error tolerances aligned with stated industry standards.
- The simulation framework combines X-Plane 9, plug-in code, and a sensor model for integrated aircraft and sensor simulation.
- The sensor model focuses on GPS delay, gyrometer bias and white noise, accelerometer bias and high-frequency colored noise, and magnetometer bias and white noise.
- The simulations study estimator tolerance to sensor bias and noise magnitude using maximum errors of 1.0o for pitch and roll and 4.0o for yaw.
A. Error tolerances and comparison of estimators
Monte Carlo simulations compare UKF and EKF tolerance to sensor biases and noise. Both estimators are especially sensitive to yaw-rate bias, while the UKF is generally less sensitive and is preferred.
- Monte Carlo experiments vary bias and noise magnitudes drawn from Gaussian distributions.
- UKF and EKF results are reported separately in Tables I and II.
- Both algorithms are more sensitive to errors in R than to errors in P and Q because yaw information comes only from the magnetometer.
- The EKF is generally more sensitive to biases and noise than the UKF, particularly to bias in R, so the UKF is preferred.
B. Simulation using real error values
Using typical MEMS bias and noise values, the simulation evaluates whether the EKF tolerances are met and finds that some errors exceed EKF limits, excluding EKF use in this case.
- Some typical MEMS errors fall outside the EKF tolerances, so the EKF cannot be used in this case.The comparison uses values from the typical MEMS and EKF tolerance tables.
- The simulation uses real bias and noise magnitudes extracted from the IMU datasheet.
- The roll-angle simulation is evaluated using MEMS parameters.
- The resulting simulation provides confidence in the UKF-based AHRS and supports proceeding to field experiments.
VI. FIELD EXPERIMENT RESULTS
Field experiments assess attitude-angle estimation on a small fixed-wing UAV using independent validation systems for roll and yaw. The comparisons are reported as satisfactory, with environmental and pitch-validation constraints noted.
- Experimental setup: Experiments assess the three attitude angles through attempted single-mode excitations and coordinated turns on a small fixed-wing UAV.Pure roll, pitch, and yaw could not be isolated completely because the motions are coupled.
- Roll validation: Roll estimation is validated against a computer-vision system that measures horizon slope, with an uncertainty of ±3o.
- Roll validation: The roll comparison between the vision system and UKF estimation is reported as clearly satisfactory.
- Yaw validation: GPS velocity provides an independent yaw-validation reference because it is used only to subtract the centrifugal accelerometer contribution.
- Yaw validation: During crosswind, the estimated yaw angle and GPS heading diverge because the UAV does not move in the direction it points.
- Pitch validation: No independent pitch measurement is available, so pitch correctness is inferred from the assumed coupling of pitch with correctly estimated roll and yaw.
VII. CONCLUSIONS.
The paper develops a quaternion-based UAV attitude estimator combining a UKF with TRIAD and evaluates it in simulation and field experiments. It reports better UKF performance than EKF, good experimental estimation quality, and microcontroller implementation.
- Quaternion formulation supports attitude representation for the onboard AHRS.
- The proposed AHRS estimates UAV attitude with a UKF, TRIAD observation model, and MEMS gyrometers, magnetometers, and accelerometers.
- TRIAD enables selection of more reliable sensors across different acrobatic and non-acrobatic flight phases.
- Simulation results show better UKF performance than EKF, leading to UKF use in the final AHRS.
- Field experiments with independent sensors report good estimation results, supporting future closed-loop controller testing.
- Complete experimental data confirm good estimation quality, while the algorithm remains suitable for implementation on an onboard microcontroller.