Abstract

A new Rauch-tung-striebel form of the fixed-lag cubature Kalman smoother has been developed for nonlinear state-space models by adopting cubature transformation for optimal smoothing. This new smoother differs from the previously proposed fixed-interval cubature Kalman smoother, in which the current step's smoothing calculation is based on the current step's filtering estimate and the next step's smoothing estimate. In this research, we introduce a fixed-lag cubature Kalman smoother that uses all filtering estimates from step k-n to k to correct the estimate in step k-n by backward iteration, given that n is the lag, and k is the current step. Derived smoothing equations here are approximated to the formal Bayesian optimal smoothing equations. The effect of different n values on smoothing estimate is investigated and an example is used to demonstrate the new algorithm's performance.

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