法国数学家勒让德于1806年首次发表最小二乘理论。 德国的高斯于1794年已经应用这一理论推算了谷神星的轨 道，但迟至1809年才正式发表。 CH6 LS Method RLS Algorithm RLS procedure is derived from least squares estimation theory. The LMS algorithm may then be viewed as a pruned version of the RLS algorithm. In contrast to the usual approach in which the LMS algorithm is derived from Wiener filter theory,based on steepest-descent optimization and instantaneous estimates of the process statistics
CH6 LS Method & RLS Algorithm RLS procedure is derived from least squares estimation theory. The LMS algorithm may then be viewed as a pruned version of the RLS algorithm. In contrast to the usual approach in which the LMS algorithm is derived from Wiener filter theory, based on steepest-descent optimization and instantaneous estimates of the process statistics. 法国数学家勒让德于1806年首次发表最小二乘理论。 德国的高斯于1794年已经应用这一理论推算了谷神星的轨 道，但迟至1809年才正式发表
Contents o S1.Introduction o S2.LS Method o S3.RLS algorithm o S4.Examples 2020-01-18 2
2020-01-18 2 Contents S1. Introduction S2. LS Method S3. RLS algorithm S4. Examples
S1.Introduction o 'given statistics'case Wiener filter theory:Probabilistic cost function statistical information on the stochastic processes involved is available. The Wiener-Hopf equations may be solved if the correlation matrix and cross-correlation vector are given. o‘given data'case In most applications,however,only data sequences are given,so that the process statistics have to be estimated from these data. Data based cost function. 2020-01-18 3
2020-01-18 3 S1. Introduction ‘given statistics’ case Wiener filter theory：Probabilistic cost function statistical information on the stochastic processes involved is available. The Wiener-Hopf equations may be solved if the correlation matrix and cross-correlation vector are given. ‘given data’ case In most applications, however, only data sequences are given, so that the process statistics have to be estimated from these data. Data based cost function
Self-designing filter o The filter is supplemented with an adaptation algorithm, ● monitor the environment (process statistics) vary the filter transfer function accordingly. 2020-01-18 4
2020-01-18 4 Self-designing filter The filter is supplemented with an adaptation algorithm, monitor the environment (process statistics) vary the filter transfer function accordingly
Detour:probabilistic machinery 0 In the 'given data'case,time averaging represents a practical means for the estimation of the process statistics (after invoking stationarity and ergodicity). o RLS algorithm may be derived starting from Wiener filter theory and employing time averaged estimates of the statistical parameters. o Viewing signals as realizations of stochastic processes,and then trying to estimate the corresponding process statistics is somewhat of a detour,which to some extent can be avoided. 2020-01-18 5
2020-01-18 5 Detour: probabilistic machinery In the ‘given data’ case, time averaging represents a practical means for the estimation of the process statistics (after invoking stationarity and ergodicity). RLS algorithm may be derived starting from Wiener filter theory and employing time averaged estimates of the statistical parameters. Viewing signals as realizations of stochastic processes, and then trying to estimate the corresponding process statistics is somewhat of a detour, which to some extent can be avoided