H2 Design of Adaptation Laws with Constant Gains.
European Control Conference,
Porto, Portugal, Sept. 4-7 2001. © EUCA 2001
We present a method for optimizing
adaptation laws that are generalizations of
the LMS algorithm.
The proposed technique has been applied
successfully for designing estimators of
rapidly time-varying mobile radio channels.
The estimators apply time-invariant
filtering on the instantaneous gradient.
of linear regression models are estimated
in situations where
the regressors are stationary or have slowly
time-varying properties. The structure and gains
of these adaptation laws are
optimized in MSE for time-variations
modeled as correlated stochastic processes.
The aim is to systematically use such
prior information to provide filtering,
prediction or fixed lag smoothing estimates for
Our design method is based on a novel transformation
that recasts the adaptation problem into a
Wiener filter design problem.
The filter works in open loop
for slow parameter variations
while a time-varying closed loop is important
for fast variations.
In closed loop, the filter
design is performed iteratively.
The solution at one iteration can be obtained
by a bilateral Diophantine polynomial matrix
equation and a spectral factorization.
For white noise, the Diophantine equation
has a closed-form solution. When one filter
is known, a set of predictors and smoothers,
up to a predefined prediction
horizon or smoothing lag,
is obtained by analytical expressions.
of the general constant-gain adaptation algorithms. (Complete report,
of stability and performance, for slow and fast variations.
The Wiener LMS
adaptation algorithm, a special case with low complexity.
A Case Study on IS-136 channels.
PhD Thesis by Lars Lindbom, 1995.
Robust Design of adaptation laws,
based on uncertain models of the properties of time-variations.
(IFAC Como 2001).
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