Approximating statistics of stochastic variables after non-linear transformation with high-accuracy
ZHAO Dong-ming,WU Xiao-ping(Srveying and Mapping Institute of Information Engineering University,Zhengzhou 450052,China)
This paper first pointed out that the first step of the application of the Extended Kalman Filter in state estimation of non-linear systems is to make linearization to the system dynamic equations,which cause errors in state estimation. Then through series expansion of the non-linear transformation function,formulae of the true mean and covariance of the stochastic variable resulting from the non-linear transformation are obtained,which also lead to the form of the first-order linearization. Finally a transform method with higher accuracy is introduced. And it is proved that the transform method can approximate the true mean and covariance better than the linearization method does. Both theoretical analysis and numerical experiment prove that the new method is not only more accurate than linearization but also easier to implement.