A note on the memory length of optimal nonlinear filters

✍ Scribed by Rami Atar; Ofer Zeitouni

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 86 KB
• Volume: 35
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(98)00045-0

✦ Synopsis

Consider the one-dimensional ÿltering problem with state di usion coe cient and observation noise coe cient 1-, where 1 2 ¡ ¡1 is ÿxed. In the regime → 0, we provide an example of state dynamics and a corresponding asymptotically optimal ÿlter whose memory length is short in a strong sense. This stands in contrast with the behavior of the correlation memory length, proposed in [7], which stays bounded away from zero as → 0.