The work is devoted to the application of a linear Kalman filter (KF) for estimating the roll angle of a quadcopter with structural asymmetry, under which the control input contains a nonzero constant component. This violates the standard assumption of zero mathematical expectation and reduces the efficiency of traditional KF implementations. A filter synthesis method is proposed based on the optimization of the covariance matrices ratio using a criterion that accounts for both the mean square error and the transient response time. The effectiveness of the approach is confirmed by simulation and experimental studies conducted on a setup with an IMU-6050 and an Arduino Nano. The obtained results demonstrated that the proposed Kalman filter provides improved accuracy in estimating the angle and angular velocity, thereby simplifying its tuning for asymmetric dynamic systems.

Keywords: Kalman filter, quadcopter with asymmetry, optimization of covariance matrices, functional with mean square error and process time, complementary filter, roll and pitch control