The motion state of a quadruped robot in operation changes constantly. Due to the drift caused by the accumulative error, the function of the inertial measurement unit (IMU) will be limited. Even though multi-sensor fusion technology is adopted, the quadruped robot will lose its ability to respond to state changes after a while because the gain tends to be constant. To solve this problem, this paper proposes a strong tracking mixed-degree cubature Kalman filter (STMCKF) method. According to system characteristics of the quadruped robot, this method makes fusion estimation of forward kinematics and IMU track. The combination mode of traditional strong tracking cubature Kalman filter (TSTCKF) and strong tracking is improved through demonstration. A new method for calculating fading factor matrix is proposed, which reduces sampling times from three to one, saving significantly calculation time. At the same time, the state estimation accuracy is improved from the third-degree accuracy of Taylor series expansion to fifth-degree accuracy. The proposed algorithm can automatically switch the working mode according to real-time supervision of the motion state and greatly improve the state estimation performance of quadruped robot system, exhibiting strong robustness and excellent real-time performance. Finally, a comparative study of STMCKF and the extended Kalman filter (EKF) that is commonly used in quadruped robot system is carried out. Results show that the method of STMCKF has high estimation accuracy and reliable ability to cope with sudden changes, without significantly increasing the calculation time, indicating the correctness of the algorithm and its great application value in quadruped robot system.

The traditional Cubature Kalman Filter (CKF) and its derived algorithms cannot work without the two hypotheses of Kalman Filter (KF), one is that the system model is accurate and the other is the system is only influenced by independent white noise with known statistical characteristics. However, it is difficult to fully guarantee the above hypotheses in actual operation. The presence of multiplicative noise undermines the first hypothesis, while the additive noise correlation undermines the second hypothesis. Given invalid hypotheses, the estimated performances of CKF and its derivative algorithms are degraded drastically. To solve this issue, this paper proposes Multiplicative Noises and Additive Correlated Noises Cubature Kalman Filter (MACNCKF), which solves state estimation problems involving multiplicative noise and additive noise while maintaining CKF advantages. Moreover, this algorithm has been testified to be correct and easy to be transplanted to CKF and its derivative algorithm after strict mathematical derivation. When the system lacks multiplicative noise and additive noise, the algorithm is degraded to corresponding algorithm in a general form, which helps extend the application environment of CKF and its derivative algorithms, thus improving robustness. Numerical simulation and experiments on quadruped robot system indicate that MACNCKF can effectively solve state estimation problem involving both multiplicative noise and additive noise. Given time consumption in MACNCKF basically comparable to that in CKF, MACNCKF has improved estimation accuracy, robustness and reliability.