Title :
The stability of LMS
Author_Institution :
Dept. of Stat., Macquarie Univ., North Ryde, NSW, Australia
fDate :
12/1/1997 12:00:00 AM
Abstract :
New and weak conditions are given under which the LMS algorithm is exponentially convergent with probability one in a stochastic setting. These results show that LMS works under very broad conditions: a small gain, input signal with finite fourth moments; time varying persistence of excitation; and weak assumptions on the correlation structure of the input signal. Previous results at this level of generality linked convergence to peak signal amplitude rather than average amplitude. Under the same conditions stochastic boundedness of a forced LMS system is also established
Keywords :
convergence of numerical methods; least mean squares methods; probability; signal processing; stability; stochastic processes; LMS algorithm; LMS stability; average amplitude; convergence; finite fourth moments; input signal; peak signal amplitude; probability; small gain; stochastic boundedness; stochastic setting; time varying excitation persistence; Algorithm design and analysis; Convergence; Eigenvalues and eigenfunctions; Helium; Least squares approximation; Stability; Stochastic processes; Stochastic resonance; Stochastic systems; White noise;
Journal_Title :
Signal Processing, IEEE Transactions on
