基于SRCKF 的自适应高斯和状态滤波算法

针对非线性非高斯离散动态系统中的状态估计问题，基于高斯和递推关系，提出一种高斯和状态估计算法GSSRCKF.首先将状态噪声、观测噪声及滤波初值均表示为高斯和的形式，以平方根容积卡尔曼滤波为子滤波器分别估计各高斯子项对应的系统状态；然后结合各子项对应的权值实现全局估计；最后设计高斯子项对应权值的自适应策略，并采用约简控制法降低计算复杂度.仿真结果验证了所提出的算法在滤波稳定性方面的优越性.

Adaptive Gaussian sum method based on squared-root cubature Kalman filter for state estimation

For the state estimation of nonlinear non-Gaussian discrete dynamic systems, based on the Gaussian sum recursive relations, a Gaussian sum squared-root cubature Kalman filter (GSSRCKF) for state estimation is proposed. On the assumption that the probability density functions of process noises, measurement noises and initial condition are denoted by a Gaussian sum or approximated by a Gaussian sum, a bank of squared-root cubature Kalman filters (SRCKF) are used as the Gaussian sub-filters to estimate the state of the system respectively in GSSRCKF. Then, the different filtering results are combined to the global state estimation according to the corresponding weights, which are set as adaptive process parameters at each filtering time. And the effective reduction method is adopted to reduce the computational complexity. The simulation results verify the superiority of the proposed method on filter consistency.