Ieee Transactions on Signal Processing, Vol. X, No. X, X X 1 a Basic Convergence Result for Particle Filtering
Ieee Transactions on Signal Processing, Vol. X, No. X, X X 1 a Basic Convergence Result for Particle Filtering
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通讯作者：
Xiao-Li Hu;Thomas B. Schön;L. Ljung
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作者：
Xiao-Li Hu;Thomas B. Schön;L. Ljung
—考虑动力系统的基本非线性滤波问题。通过粒子滤波方法来近似最佳滤波器估计可能已成为近年来最常见和最有用的方法。人们已经提出了粒子滤波器的许多变体，并且有大量关于近似质量的理论方面的文献。仍然缺乏一个明确的结果，即当粒子数量趋于无穷大时，无界函数的近似解会收敛到真正的最优估计。本贡献的目的是为一类相当一般的无界函数给出这样的基本收敛结果。此外，还给出了一个通用框架，包括许多作为特殊情况的粒子滤波算法。
—The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result for a rather general class of unbounded functions. Furthermore, a general framework, including many of the particle filter algorithms as special cases, is given.