条件线性高斯状态空间模型的GSF-KF滤波算法

算法将模型中的条件线性状态方程代入观测方程,并融合线性状态的过程噪声和观测噪声,再与非线性状态方程联立,由高斯和滤波器(Gaussian sum filter,GSF)获得非线性状态的估计;然后将估计值代入线性状态方程与观测方程,由卡尔曼滤波器(Kalman Filter,KF)获得线性状态的估计.此外,获得的非线性状态估计的方差还用于修正线性状态的估计.将GSF-KF算法应用于目标跟踪的仿真结果表明,与现有Rao-Black-wellized粒子滤波器(Rao-Blackwellized ParticleFilter,RBPF)相比,新方法在保证精度的同时,明显提高了实时性,计算时间仅约为RBPF的7%.

GSF-KF Algorithm for Conditionally Linear Gaussian State Space Models

In the Gaussian sum filter-Kalman filter (GSF-KF) algorithm, the conditional linear state equation was first inserted into the measurement equation, which fused the linear state process noise and the original measurement noise. And the GSF was applied to the new measurement and nonlinear state equations to estimate the nonlinear states. Then the estimations of the nonlinear states were inserted into the linear state equation and the original measurement equation to estimate the linear states by the KF. Moreover, the variances of the nonlinear states estimations were fed back to modify the estimations of the linear states. The simulation results of the proposed GSF-KF applying to target tracking show that the proposed algorithm only consumes about 7% the computing time required by the Rao-Blackwellized particle filter (RBPF), while the consistent filtering performance is kept.