A square-root version of the divided difference Rauch-Tung-Striebel (RTS) smoother is proposed in this paper. The square-root variant essentially propagates the square roots of the covariance matrices and can consistently improve the numerical stability because all the resulting covariance matrices are guaranteed to stay positive semi-definite. Furthermore, the square-root form ensures reliable implementation in an embedded system with fixed or limited precision although it is algebraically equivalent to the standard form. The new smoothing algorithm is tested in a challenging two-dimensional maneuvering target tracking problem with unknown and time-varying turn rate, and its performance is compared with that of other de-facto standard filters and smoothers. The simulation results indicate that the proposed RTS smoother markedly outperforms the associated filters and gives slightly smaller error than an unscented-based RTS smoother.
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