Natural gradient algorithm occupies an important position in blind source separation due to its good separation performance

but when the algorithm is based on a fixed-step size

a good balance will impossibly be achieved between the convergence rate and steady-state error.This article drew PID (Proportion Integration Differentiation) algorithm of automation control as a reference and proposed an algorithms in variable-step learning rate closely integrated with the state of separation.Due to the fact the cumulative amount of the signal kurtosis was an intrinsic value after the complete separation

there arose a gradually decreasing error value between the cumulative amount of the signal kurtosis of the separation process and the inherent value.The exponential function value of e in the algorithm was applied to reflect the error value.Then the error was used to constitute proportional differential variable-step algorithm

among which the initial value of the step was equivalent to proportional value of the error control

and the differential term of the error gained the adjusted values in acceleration.The simulation results show that corresponding to a maximum and a minimum of step initial value

the number of iterations of the algorithm in two times was lower than that of iterations with fixed-step algorithm

and the difference between the two iterations was about 10 to 40 times for signals of different type

however

the steady-state error of the two algorithms was the same.