Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise

Mobile robots are often subject to multiplicative noise in the target tracking tasks, where the multiplicative measurement noise is correlated with additive measurement noise. In this paper, first, a correlation multiplicative measurement noise model is established. It is able to more accurately represent the measurement error caused by the distance sensor dependence state. Then, the estimated performance mismatch problem of Cubature Kalman Filter (CKF) under multiplicative noise is analyzed. An improved Gaussian filter algorithm is introduced to help obtain the CKF algorithm with correlated multiplicative noise. In practice, the model parameters are unknown or inaccurate, especially the correlation of noise is difficult to obtain, which can lead to a decrease in filtering accuracy or even divergence. To address this, an adaptive CKF algorithm is further provided to achieve reliable state estimation for the unknown noise correlation coefficient and thus the application of the CKF algorithm is extended. Finally, the estimated performance is analyzed theoretically, and the simulation study is conducted to validate the effectiveness of the proposed algorithm.