Estimating gyroscope bias for attitude IMU sensor fusion with an unscented Kalman filter

I’m trying to use a UKF as the attitude estimator for a drone with just a gyroscope and accelerometer as sensors. So far, it’s going well and after some tuning appears to perform basically as well as a Madgwick filter in simulated testing. However, when the drone is stationary on the ground, the UKF accumulates a much greater error in its attitude estimate than the Madgwick filter which seems to be caused by gyro bias (note that the bias of the simulated gyro is not even that large and a dead-reckoning estimator only accumulates about a 10 degree error after 10 seconds).

All this has led me to try adding gyro bias to the state vector of the UKF which seems like a common strategy in Kalman filtering land for mitigating sensor bias. Unfortunately, adding this term to the state and incorporating it in the gyro sensor model for the update step has completely broken the UKF making its attitude estimate seem basically random. It seems to come up with unrealistically large estimates of the bias that change very quickly which is obviously not correct.

It feels like adding this bias to the state makes it hard for the UKF to differentiate how much of a measurement should count as bias vs what is actually real. Anyway, what can I try to fix this? Is there some trick to tuning the process/measurement model covariance or is this simply a case of there not being enough information available to estimate the gyro bias? I suspect I’m just doing something wrong as I would expect a UKF to outperform Madgwick when set up correctly.