| Title |
Determination of Minimum Eigenvalue in a Continuous-time Weighted Least Squares Estimator |
| Authors |
Kim, Sung-Duck(Kim, Sung-Duck) |
| Keywords |
하중최소자승 앨고리즘 ; 최소고유치 ; 지속여기 ; 수렴 유계값 Weighted Least Squares Algorithm ; Minimum Eigenvalue ; Persistent Excitation ; Convergence Bounded Value |
| Abstract |
When using a least squares estimator with exponential forgetting factor to identify continuous-time deterministic system, the problem of determining minimum eigenvalue is described in this paper. It is well known fact that the convergence rate of parameter estimates relies on various factors consisting of the estimator and especially, theirproperties can be directly affected by all eigenvalues in the parameter error differential equation. Fortunately, there exists only one adjusting eigenvalue in the given estimator and then, the parameter convergence rates depend on this minimum eigenvalue. In this note, a new result to determine the minimum eigenvalue is proposed. Under the assumption that the input has as many spectral lines as the number of parameter estimates, it can be proven that the minimum eigenvalue converges to a constant value, which is a function of the forgetting factor and the parameter estimates number. |