A Robust Indirect Kalman Filter Based on the Gradient Descent Algorithm for Attitude Estimation During Dynamic Conditions

The real-time response and accuracy of the attitude (i.e., roll and pitch) estimation from low-cost inertial measurement unit (IMU) have become the key issues restricting related applications. This paper proposes a robust attitude estimation scheme which can perform well under dynamic conditions. When only accelerometers are used to calculate and correct the attitude, the external acceleration becomes the main source of attitude estimation errors. Moreover, the truncation error in the linearization process of the nonlinear system also affects the attitude estimation. As our first contribution, the external acceleration is modeled as a first-order Gauss Markov model, and its value is calculated under the indirect Kalman filter (IKF) framework. The measurement noise covariance matrix of the IKF is adaptively adjusted to enhance its robustness and reduce the negative impact caused by inaccurate modeling. In the second part of our work, the two-step cascade filter method is used for attitude estimation. The attitude obtained from the gravity field based on the gradient descent (GD) algorithm shows fast response capabilities, and hence, it is embedded as a measurement in the IKF by using the chain-derivation rule. The truncation error introduced into the linearization process of the nonlinear system is effectively avoided. Both simulation and experiments are carried out to verify the feasibility and accuracy of the proposed algorithm. The results show that the approach proposed in this paper can meet the accuracy requirements of consumer products.