Autonomous UAV Algorithm Handbook

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Complementary Filter ​

Problem Statement ​

Low-cost IMU attitude estimation suffers from gyroscope drift and accelerometer noise. The complementary filter combines high-frequency gyroscope integration with low-frequency gravity alignment to produce stable orientation estimates for downstream control.

Model and Formulation ​

Let \omega_m be measured angular rate and a_m the measured acceleration. The roll/pitch estimate is propagated by integrating rates, then corrected with an accelerometer-derived attitude:

$$ \theta_k = \alpha \left(\theta_{k-1} + \omega_{m,k}\Delta t\right) + (1-\alpha)\theta_{acc,k} $$

where \alpha \in (0, 1) defines the crossover between gyro and accelerometer trust.

Algorithm Procedure ​

  1. Integrate gyroscope rates to obtain predicted orientation.
  2. Compute gravity-consistent roll and pitch from accelerometer measurements.
  3. Blend the two estimates using the complementary gain \alpha.
  4. Output attitude estimate to attitude and position controllers.

Tuning Guidance ​

  • \alpha near 0.98 works well when IMU rates are high (>= 100 Hz).
  • Increase accelerometer weighting when gyro bias grows over long flights.
  • Reduce accelerometer weighting in aggressive maneuvers where linear acceleration contaminates gravity direction.

Failure Modes and Diagnostics ​

  • Sustained acceleration can be misinterpreted as tilt, causing attitude bias.
  • Poor gyro bias handling leads to slow heading/attitude drift.
  • Check innovation between gyro-integrated and accelerometer attitude; persistent bias indicates gain mismatch.

Implementation and Execution ​

bash
python -m uav_sim.simulations.estimation.complementary_filter

Evidence ​

Complementary Filter

References ​