On Stepsize of Fast Subspace Tracking Methods

Adjusting stepsize between convergence rate and steady state error level or stability is a problem in some subspace tracking schemes. Methods in DPM or Oja class may sometimes show sparks in their steady state error, even with a rather small stepsize. By a study on the schemes’ updating routine, it is found that the update does not happen to all of basis vectors but to a specific vector, if a proper basis is chosen to describe the estimated subspace. The vector moves only in a plane which is defined by the new input and pervious estimation. Through analyzing the vectors relationship in that plane, the movement of that vector is constricted to a reasonable range as an amendment on the algorithms to fix the sparks problem. The simulation confirms it eliminates the sparks.

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