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Quality of
Estimation
Classical
PSD Estimation
Quality of Estimation
Why not take the
Theoretical result?
It's perfect, ideal, accurate ... ,
so it's physically unavailable! L
What is Estimation?
All
measurements are Random Processes,
the
approximations to the Theoretical results.
Observation
= Theoretical Value + Noise
x[n]
= θ + w[n]
A
simplest Estimation:
Mean , Variance, MSE(均方误差):
Biaslessness(无偏性)
Effectiveness(有效性)
Consistency(一致性)
It is equivalent to:
Other Estimations
Least MSE Estimation will minimize the MSE.
Bayes Estimation will minimize the Mean of
the following Cost:
 , or 
Maximum Likelihood Estimation (MLE) will maximize
the Likelihood Probability Density Function:
f(x1, x2,
..., xN|θ )
Least Square
Estimation (LSE) minimizes the
sum of
square of residual:
 where 
Classical
PSD Estimation
Autocorrelation自相关 method
Wiener-Khinchin Theorem
Periodogram周期图 method
Averaged平均Periodogram method
Smoothed Periodogram
method
w[m]: Anti-Leakage Window
More Methods:
Matlab Signal Processing Toolbox
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