Backward-Smoothing Extended Kalman Filter

The principle of the iterated extended Kalman filter has been generalized to create a new filter that has superior performance when the estimation problem contains severe nonlinearities. The new filter is useful when nonlinearities might significantly degrade the accuracy or convergence reliability of other filters. The new filter solves a nonlinear smoothing problem for the current and past sample intervals using iterative numerical techniques. This approach retains the nonlinearities of a fixed number of stages that precede the stage of interest, and it processes information from earlier stages in an approximate manner. The algorithm has been simulation tested on a difficult spacecraft attitude estimation problem that includes sensing of fewer than three axes and significant dynamic model uncertainty. The filter compensates for this uncertainty via simultaneous estimation of moment of inertia parameters. The new filter exhibits markedly better convergence reliability and accuracy than an extended Kalman filter and an unscented Kalman filter for estimation problems that start with large initial attitude or attitude rate errors.