基于高斯过程回归的平方根UPF算法

针对系统动力学模型不准确可能导致滤波精度下降,以及系统状态协方差阵可能出现的负定性问题,提出一种新的高斯过程回归平方根分解无迹粒子滤波(Gaussian process regression square-root decomposition unscented particle filter,GPSR-UPF)算法。在该算法中,采用高斯过程回归求取UPF的重要性密度函数。当系统模型不准确时,通过高斯过程回归学习训练数据,进而获取系统的回归模型及系统噪声协方差,同时引入平方根变换抑制系统状态协方差阵的负定性。将提出的GPSR- UPF算法应用到捷联惯导/全球定位系统(strapdown inertial navigation system / global positioning system, SINS/GPS)组合导航系统中进行仿真验证。结果表明,所提出滤波算法的性能优于基本的无迹粒子滤波算法,能提高组合导航系统的解算精度。

Square-root unscented particle filter based on Gaussian process regression

In view of the uncertainty of the system dynamic model may reduce the filtering effect and the system state covariance matrix is negative definiteness, a new unscented particle filter(UPF) based on Gaussian process regression and square-root decomposition(GPSR) is proposed. The importance density function of UPF is gotten by Gaussian process regression. When the system model and observation model are inaccurate, Gaussian process regression is used to learn the training data, the regression models and noise covariance of the dynamic system are gotten; square-root decomposition is used to restrain the negative definiteness of the system state covariance matrix. The proposed algorithm is applied to the integrated navigation system of strapdown inertial navigation system / global positioning system (SINS/GPS). The simulation results show that the proposed algorithm is better than UPF, and also effectively improves the positioning precision of the navigation system.