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A new set of multichannel adaptive filtering algorithms containing a feedback convergence function is described. The algorithms represent an extension of the Kalman filtering approach to the linearly constrained multichannel adaptive filtering. In essence, the convergence function in the adaptive filtering algorithm, which is designed to control stability and rate of adaptation, is modified to fashion the Kalman gain structure. Through adaptive feedback schemes, the algorithms are capable of tracking not only the prediction errors with respect to the input multichannel signals, but also the performance errors in the estimated filter weights by means of updating the error covariance matrix. Thus, with double monitoring capability, the revised adaptive filtering algorithm is shown to be more effective in suppressing coherent noises than the previous one, and is well suited for processing the highly time-varying nonstationary data.