Parametric Methods

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# Parametric Methods - PowerPoint PPT Presentation

Parametric Methods. 指導教授： 黃文傑 W.J. Huang 學生： 蔡漢成 H.C. Tsai. Outline. DML (Deterministic Maximum Likelihood) SML (Stochastic Maximum Likelihood) Subspace-Based Approximations. DML (Deterministic Maximum Likelihood)-1. Performance of spectral- … is not sufficient

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## PowerPoint Slideshow about 'Parametric Methods' - kerry-chase

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### Parametric Methods

Outline
• DML (Deterministic Maximum Likelihood)
• SML (Stochastic Maximum Likelihood)
• Subspace-Based Approximations
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
DML-2
• Skew-symmetric cross-covariance
• x(t) is white Gaussian with meanPDF of one measurement vector x(t)
DML-3
• Likelihood function is obtained as
• Unknown parameters
• Solved by
DML-4
• By solving the following minimization
DML-5
• X(t) are projected onto subspace orthogonal to all signal components
• Power measurement
• Remove all true signal on projected subspace ， energy ↓
SML (Stochastic Maximum Likelihood) -1
• Signal as Gaussian processes
• Signal waveforms be zero-mean with second-order property
SML-2

Vectorx(t) is white, zero-mean Gaussian random vector with covariance matrix

-log likelihood function (lSML) is proportional to

SML-3
• For fixed ,minima lSML to find the
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)
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
Subspace Fitting-1
• The number of signal eigenvector is M’
• Us will span an M’–dimentional subspace of A
Subspace Fitting-2

Form the basis for the Signal Subspace Fitting (SSF)

Subspace Fitting-3
• and T are unknown , solve Us=AT
• T is “nuisance parameter ”

Distance between AT and

Subspace Fitting-4
• For fix unknown A ,
• concentrated

Introduce a weighting of the eigenvectors

WSF (Weighting SF)-1
• Projected eigenvectors
• W should be a diagonal matrix containing the inverse of the covariance matrix of
WSF -2
• WFS and SML methods also exhibit similar small sample behaviors
• Another method,
NSF(Noise SF)-1

V is some positive define weighting matrix

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