Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters

• 成果类型: Article
• 署名作者: Le Gland, F; Oudjane, N
• 署名单位: Inria; Electricite de France (EDF)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2004
• 页码: 144-187
• 关键词: Exponential stability; ergodicity

摘要

We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective metric. These stability results are then used to prove, under some mixing assumption, the uniform convergence to the optimal filter of several particle filters, such as the interacting particle filter and some other original particle filters.