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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Recursive least squares filter ： ウィキペディア英語版 Recursive least squares filter The Recursive least squares (RLS) is an adaptive filter which recursively finds the coefficients that minimize a weighted linear least squares cost function relating to the input signals. This is in contrast to other algorithms such as the least mean squares (LMS) that aim to reduce the mean square error. In the derivation of the RLS, the input signals are considered deterministic, while for the LMS and similar algorithm they are considered stochastic. Compared to most of its competitors, the RLS exhibits extremely fast convergence. However, this benefit comes at the cost of high computational complexity. ==Motivation== RLS was discovered by Gauss but laid unused or ignored until 1950 when Plackett rediscovered the original work of Gauss from 1821. In general, the RLS can be used to solve any problem that can be solved by adaptive filters. For example, suppose that a signal d(n) is transmitted over an echoey, noisy channel that causes it to be received as :$x(n)=\backslash sum\_^q\; b\_n(k)\; d(n-k)+v(n)$ where $v(n)$ represents additive noise. We will attempt to recover the desired signal $d(n)$ by use of a $p+1$-tap FIR filter, $\backslash mathbf$: :$\backslash hat(n)\; =\; \backslash sum\_^\; w\_n(k)x(n-k)=\backslash mathbf\_n^\backslash mathit\; \backslash mathbf\_n$ where $\backslash mathbf\_n=(x(n-1)\backslash quad\backslash ldots\backslash quad\; x(n-p))^T$ is the vector containing the $p+1$ most recent samples of $x(n)$. Our goal is to estimate the parameters of the filter $\backslash mathbf$, and at each time ''n'' we refer to the new least squares estimate by $\backslash mathbf\_n$. As time evolves, we would like to avoid completely redoing the least squares algorithm to find the new estimate for $\backslash mathbf\_$, in terms of $\backslash mathbf\_n$. The benefit of the RLS algorithm is that there is no need to invert matrices, thereby saving computational power. Another advantage is that it provides intuition behind such results as the Kalman filter. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Recursive least squares filter」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.