Stochastic parallel model adaptation: theory and applications to active noise cancelling, feedforward control, IIR filtering and identification

The authors consider general stochastic parallel model adaptation problems which consist of an unknown linear time invariant system and a partially or wholly tunable system connected in parallel, with a common input. The goal of adaptation is to tune the partially tunable system so that its output matches that of the unknown system despite the presence of any disturbance which is stochastically uncorrelated with the input. This general formulation of stochastic parallel adaptation schemes allow applications to adaptive feedforward control and adaptive active noise canceling with input contamination, in addition to output error identification and adaptive IIR (infinite impulse response) filtering. It is shown that in all the applications, the goal of adaptation is met whenever a matching conditions and a positive real condition are satisfied. A special case of the results resolves the long-standing problem of the convergence and the unbiasedness of the output error identification scheme in the presence of colored noise