TY - JOUR
T1 - Exponential convergence of recursive least squares with exponential forgetting factor
AU - Johnstone, Richard M.
AU - Richard Johnson, C.
AU - Bitmead, Robert R.
AU - Anderson, Brian D.O.
PY - 1982/8
Y1 - 1982/8
N2 - This paper demonstrates that, provided the system input is persistently exciting, the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent. Further, it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary. The result holds for stable finite-dimensional, linear, time-invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail.
AB - This paper demonstrates that, provided the system input is persistently exciting, the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent. Further, it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary. The result holds for stable finite-dimensional, linear, time-invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail.
KW - Exponential convergence
KW - Exponential data weighting
KW - Forgetting factor.
KW - Recursive estimation
UR - http://www.scopus.com/inward/record.url?scp=0007347550&partnerID=8YFLogxK
U2 - 10.1016/S0167-6911(82)80014-5
DO - 10.1016/S0167-6911(82)80014-5
M3 - Article
AN - SCOPUS:0007347550
SN - 0167-6911
VL - 2
SP - 77
EP - 82
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 2
ER -