Title :
On asymptotic convergence of the stochastic least squares algorithm
Author :
Xue, Ping ; Liu, Bede
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., NJ, USA
Abstract :
The asymptotic convergence of the least-squares (LSs) algorithm is investigated for stochastic inputs. It is shown that, when a forgetting factor is applied to the past data, the convergence is bounded exponentially, and prediction coefficients fluctuate around the LS coefficients in the steady state. A small forgetting factor increases the convergence rate, but results in a larger fluctuation. It is also shown that if there is no data forgetting, the convergence is O(1/T) and the coefficient fluctuation vanishes as T→∞
Keywords :
adaptive filters; convergence of numerical methods; filtering and prediction theory; asymptotic convergence; convergence rate; fluctuation; forgetting factor; stochastic inputs; stochastic least squares algorithm; Convergence; Equations; Filtering algorithms; Finite impulse response filter; Fluctuations; Kalman filters; Least squares methods; Signal processing algorithms; Steady-state; Stochastic processes;
Conference_Titel :
Circuits and Systems, 1991., IEEE International Sympoisum on
Print_ISBN :
0-7803-0050-5
DOI :
10.1109/ISCAS.1991.176393
