Attitude estimation problem in the presence of acceleration (MPU6050, etc....)

Hello, I am using popular IMU sensors such as MPU6050, MPU6050+HMC5883L, ITG3205+ADXL345, etc And I also use general open source code between Arduino and the sensors.

In the code, I understand that Roll and pitch angle are calculated by trigonometric function with accX, accY, and accZ. Since then, Complimentary filter, Kalman filter, and some other filters are used with acceleration data and gyro data for more exact estimation.

However, I find that if there are some big acceleration in moving object, then roll and pitch angle have some offset or inexact values. (Of course, If without big acceleration, roll and pitch are generally accurate.)

Is it difficult or impossible to predict attitude values in the presence of acceleration more than certain value using the sensors or Am I misunderstanding?

May I ask for your advice? Thank you.

Is it difficult or impossible to predict attitude values in the presence of acceleration

Yes, and the higher the acceleration, the more difficult the problem.

Then you need to adjust your Kalman filter parameters. Short term acceleration should not have a big affect on the attitude estimation. The gyros should be providing that. The acceleration should only be supplying a small correction to take out the slow drift of the gyros.