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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 article 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.

A Multiplicative Noises and Additive Correlated Noises Cubature Kalman Filter and Its Application in Quadruped Robot