We present an adaptive log domain filter with integrated learning rules for model reference estimation. The system is a first order low pass filter based on a log domain topology that incorporates multiple input floating gate transistors to implement on-line learning of gain and time constant. Adaptive dynamical system theory is use to derive robust learning rules for both gain and time-constant adaptation in a system identification task. The adaptive log domain filters have simulated cutoff frequencies above 100KHz with power consumption of 23/spl mu/W and show robust adaptation of the estimated gain and time constant as the parameters of the reference filter are changed.