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In is study, two hierarchical methods are investigated, one
is for determining the optimal adaptive forgetting
factor for the recursive least squares filter algorithm,
the other is for constructing this factor adjusting
hierarchical structure. It is required that for a given required
resolution about the forgetting factor, the number of
developed branches of the factor adjusting hierarchical
structure should be minimized. For
observation and comparison, three fading memory recursive least
squares filtering algorithms are constructed. The first one is
called the method of parallel exhausting search, in which 20
parallel filters are constructed, each has a different
forgetting factor ranged from 0.05 to 1.0 with an increment of
0.05 at each time stage. The filter has best performance is
chosen. The second one is the method of hierarchical search of
this study. The third one called themethod of estimated optimal
uses the forgtting factor determined by the estimated
nonstationary to noise ratio. Essentially, the method of
parallel exhausting search is optimal in nature, and the
method of estimated optimal willprovide the optimal forgetting
factor if the nonstationary to noise ratio has been correctly
estimated. The method of hierarchical search can expect a
similarresult as that of parallel exhausting search, but with
much less computation requirement. Simulation results can
support the above arguments.
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