一种新的SPKF算法-GSPKF算法

提出了一种SPKF算法的改进算法,称之为GSPKF。该算法中Sigma点权值由选择该Sigma点的概率决定。此时,Sigma点权值物理意义明确、计算简单、恒大于零,协方差矩阵物理意义明确,可以实现全局拟合,GSPKF算法的物理意义更加明确。可以证明,两种算法对期望和协方差的准确估计精度是相同的,但是,GSPKF算法可以渐进拟合非线性函数真实的期望和协方差,GSPKF算法的滤波效果至少不低于现有SPKF算法。它们的滤波效果由仿真进行了验证。

Novel SPKF-GSPKF

Mended algorithms called as the global SPKF(GSPKF)were proposed.In the GSPKF,the weights of Sigma-Points are decided by the probabilities at which they are chosen,and they have explicitly physical meanings,and they are always positive which can guarantee the covariance matrix is positive.The Sigma-Points in the GSPKF can achieve the global imitation,and the GSPKF have clearer physical meanings than the SPKF.In theory,the GSPKF have the same accuracy of exact approximations to the expectation and covariance of a non-linear function with the SPKF,but the GSPKF gradually imitate them,therefore the effects of the GSPKF are no less than those of the SPKF.At last,the effects of filters were compared by simulations.