1. Parametric Methods 指導教授：黃文傑 W.J. Huang 學生：蔡漢成 H.C. Tsai

2. Outline DML (Deterministic Maximum Likelihood) SML (Stochastic Maximum Likelihood) Subspace-Based Approximations

3. DML (Deterministic Maximum Likelihood)-1 Performance of spectral- … is not sufficient Coherent signal increase the difficulties Noise independent Noise as a Gaussian white, whereas the signal … deterministic and unknown

4. DML-2 Skew-symmetric cross-covariance x(t) is white Gaussian with mean PDF of one measurement vector x(t) x(t) is white Gaussian with mean PDF of one measurement vector x(t)

5. DML-3 Likelihood function is obtained as Unknown parameters Solved by

6. DML-4 By solving the following minimization

7. DML-5 X(t) are projected onto subspace orthogonal to all signal components Power measurement Remove all true signal on projected subspace ， energy ↓

8. SML (Stochastic Maximum Likelihood) -1 Signal as Gaussian processes Signal waveforms be zero-mean with second-order property

9. SML-2 Vectorx(t) is white, zero-mean Gaussian random vector with covariance matrix Vector x(t) is white, zero-mean Gaussian random vector with covariance matrix -log likelihood function ( l SML ) is proportional to

10. SML-3 For fixed,minima l SML to find the

11. SML-4 SML have a better large sample accuracy than the corresponding DML estimates,in low SNR and highly correlated signals SML attain the Cramer-Rao lower bound (CRB)

12. Subspace-Based Approximations MUSIC estimates with a large-sample accuracy as DML Spectral-based method exhibit a large bias in finite samples, leading to resolution problems,especially for high source correlation Parametric subspace-based methods have the same statistical performance as the ML methods Subspace Fitting methods

13. Subspace Fitting-1 The number of signal eigenvector is M’ U s will span an M’ – dimentional subspace of A

14. Subspace Fitting-2 Form the basis for the Signal Subspace Fitting (SSF)

15. Subspace Fitting-3 and T are unknown, solve U s =AT T is “ nuisance parameter ” instead Distance between AT and

16. Subspace Fitting-4 For fix unknown A, concentrated Introduce a weighting of the eigenvectors

17. WSF (Weighting SF)-1 Projected eigenvectors W should be a diagonal matrix containing the inverse of the covariance matrix of

18. WSF -2 WFS and SML methods also exhibit similar small sample behaviors Another method,

19. NSF(Noise SF)-1 V is some positive define weighting matrix

20. NSF-2 For V =I NSF method can reduce to the MUSIC is a quadratic function of the steering matrix A