the complementary filter architecture described in DT0060 is the following:
1. start with the current best estimate of the orientation
2. update this using gyro data and obtain a new estimate (estimate 1)
3. obtain another estimate from acc and mag data (estimate 2)
4. combine the two estimates to get a new best estimate, usually estimate 1 from gyro is given a large weight (99%) and estimate 2 from acc and mag is given a small weight (1%)
The weight can also be set based on sensor data: for example if acc norm is close to 1g it is probably measuring only gravity, and gyro output is close to 0 we are probably static, and mag norm is close to expected value there is no mag anomaly, then one can give more weight to estimate 2 from acc and mag, leading to a faster recovery of the gyro integration error when motion stops.
Note that estimate 2 is always needed because otherwise the gyro integration error will accumulate over time. Having estimate 2 at a lower rate is ok, when you have it just mix this in with estimate 1 from gyro. If you only have estimate 1 then that counts 100% of course.
Gyro bias (the non-zero output when angular velocity is zero) must be calibrated and compensated. This is typically done measuring the non-zero output in static conditions, recording it, and subtracting it from gyro output before it is integrated.
Magnetometer hard-iron (the spurious offset) must be calibrated and compensated (see DT0059). Suitable motion must be executed by the user to get a successful calibration. Hard-iron is the most important error to compensate, there are other known as soft-iron which matter less but can also be compensated.
All this is no small task: better to use our off-the-shelf fusion MotionFX which comes in X-Cube-MEMS1 package. MotionFX does gyro bias compensation and magnetic calibration automatically, moreover is based on Kalman filter more advanced with respect to complementary filter.
