The "Toilet Bowl" Effect

Diagnosis

You switch to Loiter. The drone holds for a moment, then starts to circle. The circle gets wider and faster with every revolution. This is the Toilet Bowl Effect (TBE). It is a classic instability in the position control loop.

The Mechanics of Failure

TBE is caused by a disagreement between the drone's Heading (where it thinks it is pointing) and its Track (where the GPS says it is moving).

The Vector Rotation

The flight controller calculates a position error vector ($\vec{E}$) to correct drift.
$$ \vec{E} = \vec{P}{target} - \vec{P}{current} $$

It then attempts to apply a correction acceleration ($\vec{A}$) by rotating this error vector into the body frame using the Compass Heading ($\psi$).
$$ \vec{A}{body} = R(\psi) \cdot \vec{E}{NED} $$

The Error

If your Compass is rotated by $\theta = 90^\circ$ (due to magnetic interference):

1. Drift: The drone drifts North.
2. GPS: Reports "Moving North".
3. FC Logic: "To stop moving North, I must lean South."
4. Reality: Because $\psi$ is wrong, "South" in the body frame is actually West.
5. Result: The drone leans West. It accelerates sideways.
6. Loop: The GPS now sees Westward drift. The FC tries to correct... and pushes South. The error vector rotates continuously, driving the drone into a widening spiral.

Virtual GPS Specifics

Indoor environments are notoriously bad for compasses. Steel beams, reinforced concrete, and electrical wiring create magnetic fields that warp the Earth's field, changing $\psi$ dynamically as you fly past pillars.

The Solution: Mag-Less Flight

If you have a solid Virtual GPS fix, you might not need a compass at all.

• GPS Heading: If the drone is moving, the EKF can infer heading from the velocity vector (EK3_MAG_CAL options).
• External Yaw: If your positioning system provides Yaw (e.g., Visual Odometry or Dual Antenna GPS), you can inject this via the yaw field in GPS_INPUT (centidegrees) and disable the internal compass.

Source Code Reference

• State Prediction: libraries/AP_NavEKF3/AP_NavEKF3_core.cpp - See UpdateStrapdownEquationsNED where the attitude quaternion rotates accelerations.
• Fusion Logic: libraries/AP_NavEKF3/AP_NavEKF3_PosVelFusion.cpp - See FuseVelPosNED.