A sigma-points fixed-interval smoothing algorithm has been derived from first principles and tested using data from a truth-model simulation. This smoothing algorithm extends the use of sigma-points estimation methods, which have benefited the practice of discrete-time nonlinear filtering, into the realm of discrete-time nonlinear smoothing, where similar benefits are expected. Two equivalent forms of the algorithm have been developed based on Bayesian analysis of smoothing. One form is easier to derive and gives rise to the simplest equations, whereas the other form develops insight into the smoothing calculations by deriving them as a nonlinear pseudomeasurement update that is executed using sigma-points methods. Both forms of the algorithm use data from a forward pass of a sigma-points filter, and the result is a sigma-points adaptation of the Rauch-Tung-Striebel smoother. The algorithm has been tested using a truth-model simulation of a difficult gyroless attitude determination problem that uses only magnetometer data and that simultaneously estimates moment-of-inertia parameters to improve its Eider dynamics propagation of its attitude-rate estimates. The sigma-points smoother produces smaller estimation errors than an extended Kalman smoother, and its accuracy is comparable to that of a nonlinear batch smoother on some test cases.
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