The LMK algorithm with time-varying forgetting factor for adaptive system identification in additive output-noise

Adaptive algorithms are susceptible to noise signals due to the perturbation of the gradient direction. Depending upon the statistics of the noise, various cost functions can be minimised. The least mean kurtosis (LMK) adaptive algorithm is a stochastic gradient approach that uses the kurtosis of the error signal. Depending upon the noise distribution, the forgetting factor used in the LMK algorithm must be chosen optimally. A version of the LMK is presented, in which the forgetting factor is made time-varying such that if the output-noise distribution is unknown, which is almost always the case in practice, the algorithm will tune its forgetting factor in sympathy with the noise distribution. Hence the proposed algorithm is more flexible than the least mean square (LMS) and least mean fourth (LMF) adaptive algorithms under noisy conditions