Direct approach o Data based cost function. A valid alternative to the probabilistic detour leads to comparable results (e.g.the RLS procedure) without having to rely on all the probabilistic machinery (stationarity, ergodicity,etc.) 2020-01-18 6
2020-01-18 6 Direct approach Data based cost function. A valid alternative to the probabilistic detour leads to comparable results (e.g. the RLS procedure) without having to rely on all the probabilistic machinery (stationarity, ergodicity, etc.)
True adaptive filtering O F Batch-mode processing ● a complete batch of data is available to design the optimal filter (i.e.the least squares parameter estimation problem). o True adaptive filtering:RLS The algorithm starts from a set of initial conditions,which may correspond to complete ignorance about the environment, ● And then adapts itself while doing the filtering operation. 2020-01-18 7
2020-01-18 7 True adaptive filtering Batch-mode processing a complete batch of data is available to design the optimal filter (i.e. the least squares parameter estimation problem). True adaptive filtering: RLS The algorithm starts from a set of initial conditions, which may correspond to complete ignorance about the environment, And then adapts itself while doing the filtering operation
S2.LS Method o The basic set-up of the filter o Data based cost function o LS estimation versus WF design o LS versus Orthogonal Principle o The sufficient-order problem o SVD solution o WLS,TLS,IRWLS... 2020-01-18 8
2020-01-18 8 S2. LS Method The basic set-up of the filter Data based cost function LS estimation versus WF design LS versus Orthogonal Principle The sufficient-order problem SVD solution WLS, TLS, IRWLS…
(1)basic set-up of the filter o Similar to WF o But the filter is fed by true data sequences instead of stochastic processes o The filter is fed by an input sequence either the FIR case or the linear combiner case o The error signal is e欧=d-w吸=康-ufW 1≤k≤L. 2020-01-18 9
2020-01-18 9 (1) basic set-up of the filter Similar to WF But the filter is fed by true data sequences instead of stochastic processes The filter is fed by an input sequence either the FIR case or the linear combiner case The error signal is
Matrix form ey d 吲 e d 吗 M 三 : : WN-1 eL dL 吲 W d U 2020-01-18 10
2020-01-18 10 Matrix form