Sayın, Muhammed O.Vanlı, N. DenizcanKozat, Süleyman S.2016-02-082016-02-082014-05http://hdl.handle.net/11693/26775Date of Conference: 4-9 May 2014Conference name: 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)We present a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error amount. We introduce the least mean logarithmic square (LMLS) algorithm that achieves comparable convergence performance with the least mean fourth (LMF) algorithm and overcomes the stability issues of the LMF algorithm. In addition, we introduce the least logarithmic absolute difference (LLAD) algorithm. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interference and outperforms the sign algorithm (SA). © 2014 IEEE.EnglishLogarithmic cost functionRobustness against impulsive noiseStable adaptive methodAdaptive algorithmsAbsolute differenceAdaptive filtering algorithmsAdaptive methodsConvergence performanceImproved convergenceImpulsive interferenceLeast mean square algorithmsNoise environmentsSignal processingConference Paper10.1109/ICASSP.2014.6854456