Expressing stochastic filters via number sequences

被引：8

作者：

Capponi, A. ^{[1
]}

Farina, A. ^{[2
]}

Pilotto, C. ^{[1
]}

机构：

[1] CALTECH, Dept Comp Sci, Pasadena, CA 91125 USA

[2] SELEX Sistemi Integrati SpA, Business Unit Large Syst, Rome, Italy

来源：

SIGNAL PROCESSING | 2010年 / 90卷 / 07期

关键词：

Kalman filter; Benes filter; Fibonacci sequence; Padovan sequence; Filtering gain;

D O I：

10.1016/j.sigpro.2010.01.011

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

We generalize the results presented in [1] regarding the relation between the Kalman filter and the Fibonacci sequence. We consider more general filtering models and relate the finite dimensional Kalman and Benes filters to the Fibonacci sequence and to the Golden Section. We also prove that Fibonacci numbers may be expressed as the convolution of the Fibonacci and Padovan sequence, thus extending the connection between stochastic filtering and Fibonacci sequence to the Padovan sequence. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：2124 / 2132

页数：9

共 12 条

[1]

[Anonymous], 2006, GENERATINGFUNCTIONOL

[2]

[Anonymous], 1999, FERMATS LAST THEOREM

[3] Fibonacci sequence, golden section, Kalman filter and optimal control [J].