Nonlinear Filtering Based on Taylor Differential Algebra

The problem of nonlinear filtering represents a crucial issue in celestial mechanics. In this paper a high-order filter based on differential algebra is presented. The proposed filtering algorithm is based on nonlinear mapping of statistics and a linear update scheme, in which only the probability density function of the measurement errors are constrained to be Gaussian. No hypothesis on the state probability density function is made. The case of an Earth-orbiting spacecraft in a two-body problem frame is considered as an example to demonstrate the general feature and performance of the filter. A comparison with the extended and unscented Kalman filters is also included.