Square-root divided difference Rauch-Tung-Striebel smoother

TANG Xiao-jun¹, WEI Jian-li², CHEN Kai²

1.School of Aeronautics, Northwestern Polytechnical University, Xi¡¯an 710072, China;2.School of Astronautics, Northwestern Polytechnical University, Xi¡¯an 710072, China



Abstract:

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.ª¤

Key words:  Gaussian Rauch-Tung-Striebel smoother  square-root divided difference filter  fixed-interval smoothing  state estimationª¤

DOI£º10.11916/j.issn.1005-9113.2012.05.006

Clc Number:O211.64

Fund: