How to use output of Indirect Kalman Filter(=error state kalman filter)

I would like to measure true degree from IMU sensor by using indirect kalman filter(IKF). I can calculate error of angle and error of the bias of gyro from indirect kalman filter as attached image. However, i can not remove the bias of gyro despite using error of bias calculated from IKF like a attached image. I would like to know how to use IKF's output. Please let me know if you have any solution. In this article they use a Kalman filter to estimate the bias of the rate gyro and then subtract it from the true rate but they are running the states with only rate gyro info:

so their rate states are:

$$x_k =\begin{bmatrix} \theta_k \\ \dot{\theta_k} \end{bmatrix}$$

then they subtract the bias from the new rate:

rate = newRate - bias;
angle += dt * rate;

In this other article when they combine the two they use a fraction of each the accelerometer and rate gyro.

angle = 0.98 *(angle+gyro*dt) + 0.02*acc

Hope this helps.

One thing I'd like to add is this works for a 6DOF sensor, but its better to have add a magnetometer so then you have a solid (well as long as you can trust magnetic north) sensor updating your rates.