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Open Access Publications from the University of California

A Comparison of Attitude Propagation and Parameterization Methods for Low-Cost UAVs

  • Author(s): Casey, Robert Taylor
  • Advisor(s): Elkaim, Gabriel H.
  • et al.

Unmanned aerial vehicles (UAVs) represent an increasingly important and prolific technology in today's world,

finding use in myriad applications across multiple domains, including civil, commercial, military, and research

environments. Control of these aircraft requires fundamental information on the vehicle's position and orientation in

space. Attitude determination algorithms calculate this spatial orientation by propagating the attitude kinematic

equations that estimate the current attitude based on previous estimates along with information about the vehicle's angular

velocities. Within the domain of low-cost UAVs, numerous options exist for the choice of 1) propagation algorithms,

2) attitude representation, and 3) the assumptions about the behavior of the angular velocity vector between samples within

the discrete-time hardware of the embedded system typically running the estimation algorithms. This thesis examines the

impact of these three variables upon propagated

attitude estimates with respect to accuracy, computational efficiency, and noise response. Noise response is evaluated in

terms of the algorithm's ability to track an underlying clean signal in spite of inputs corrupted by additive Gaussian

noise. Various propagation methods are evaluated across four attitude representations: the direction cosine matrix, Euler

angles, quaternions, and the angle-axis or eigen-axis parameterization. Lastly, the nature of angular velocity (constant,

linear, and quadratic) is evaluated in terms of accuracy, computational efficiency, and noise resilience.

The algorithms were tested using simulated angular velocity inputs from analytic functions as well as flight test data from

low-cost, fixed wing UAVs. Implementation was done in Matlab as well as Simulink-based test modules to evaluate algorithm


The quaternion parameterization proved most beneficial across all three test metrics, though the

DCM representation was only slightly deficient in terms of computational load. Matrix exponential propagation methods

offered higher accuracy and better noise response than direct integration using the first-order

Euler method, though the latter offered better computational efficiency. For low-cost UAV applications, where MEMS-based

sensors have large noise on the gyros, a DCM parameterization

using the matrix exponential with linear fit to the data gives the best results for reasonable computation. This is

especially true when using either magnetometer or accelerometer feedback into the attitude filter for bias


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