Curvature Measures of the Nonlinearity Degree of the Nonlinear Filtering and Its Application

A quantitative measure approach to the degree of nonlinearity of the nonlinear filtering problems using the differential geometry based measures of nonlinearity such as parameter-effect curvature and intrinsic curvature is given.The simulation test using the extended Kalman filtering and the unscented Kalman filtering is implemented.The results verify that these curvatures indeed can measure the degree of the nonlinearity of the nonlinear filtering problem,and simultaneously can tell the state estimation performance of the nonlinear filtering algorithms.