Abstract
A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously. Moreover, the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems. Finally, the lower bound is evaluated by a typical example in target tracking. It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques, and the colored noise has a significantly effect on the lower bound and the performance of filters.
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This paper was supported in part by the Open Research Funds of BACC-STAFDL of China under Grant No. 2015afdl010, the National Natural Science Foundation of China under Grant No. 61673282 and the PCSIRT16R53.
This paper was recommended for publication by Editor CHEN Jie.
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Wang, Z., Shen, X. & Zhu, Y. Posterior Cramér-Rao Bounds for Nonlinear Dynamic System with Colored Noises. J Syst Sci Complex 32, 1526–1543 (2019). https://doi.org/10.1007/s11424-019-7310-5
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DOI: https://doi.org/10.1007/s11424-019-7310-5