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与传统算法一样,动态系统的参数化模型(含噪声统计特性)未知或不够准确易导致容积卡尔曼滤波(CKF)效果严重下降,甚至滤波结果发散。为此,利用高斯过程回归(GPR)方法对训练数据进行学习,得到动态系统的状态转移GPR模型和量测GPR模型以及噪声统计特性,用以替代或增强原有动态系统模型,并将其融入到平方根容积卡尔曼滤波(SRCKF)中,分别提出了无模型高斯过程SRCKF(MFGP-SRCKF)和模型增强高斯过程SRCKF(MEGP-SRCKF)两种算法。仿真结果表明:这两种新的自适应滤波算法提高了动态系统模型精度,且实时自适应调整噪声的协方差,克服了传统算法滤波性能易受系统模型限制的问题;与MFGP-SRCKF相比,在给定一个不够准确的参数化模型,且有限的训练数据未能遍布估计状态空间的情况下,MEGP-SRCKF具备更高的滤波精度。
As with traditional algorithms, the parametric model of dynamic system (including noise statistics) is unknown or inaccurate, which leads to the serious effect of volumetric Kalman filter (CKF), even the filtering results diverge. Therefore, by using the method of Gaussian process regression (GPR) to study the training data, the state transition GPR model and the measured GPR model of the dynamic system and the statistical properties of the noise are obtained to replace or enhance the original dynamic system model and integrate it into To the square root volume Kalman filter (SRCKF), two algorithms of model-free Gaussian process SRCKF (MFGP-SRCKF) and model-enhanced Gaussian process SRCKF (MEGP-SRCKF) are proposed respectively. The simulation results show that these two new adaptive filtering algorithms improve the accuracy of the dynamic system model and adaptively adjust the covariance of the noise in real time, thus overcoming the problem that the filtering performance of the traditional algorithm is easily limited by the system model. Compared with MFGP-SRCKF , MEGP-SRCKF has higher filtering accuracy given a less accurate parametric model, and limited training data can not be found in the estimation state space.