关键词: 非线性滤波, 平方根容积卡尔曼滤波, 高斯过程回归, 状态估计, 状态转移模型, 量测模型, 模型增强

Abstract:

In many applications, the parametric models of dynamical systems (including the process and measurement of noise statistics) are difficult to obtain or are insufficiently accurate, which results in the serious deterioration or even divergence of the filtering of cubature Kalman filter (CKF). In this paper, the Gaussian process regression (GPR) method is used to learn the training data to obtain the transition and measurement GPR models and their noise statistics of dynamical systems. These GPR models are used to replace or enhance the primary system models and integrate them into the square-root CKF (SRCKF), which yields a model-free Gaussian process SRCKF (MFGP-SRCKF) algorithm and a model-enhanced Gaussian process SRCKF (MEGP-SRCKF) algorithm. Simulation results show that, by improving the accuracy of the models of dynamical systems and adjusting adaptively the noise covariance real-time, the two new adaptive filters alleviate the problem of unknown or insufficiently accurate system models in the classical filters. Meanwhile, in the case that an insufficiently accurate parametric model is given and the limited training data do not fill all over the estimated state space, MEGP-SRCKF can yield higher filtering accuracy than MFGP-SRCKF.

Key words: nonlinear filtering, square-root cubature Kalman filter, Gaussian process regression, state estimation, state transition model, measurement model, model enhancement