Digital Signal Processing Reference
In-Depth Information
1
0.9
Standard Deviation of the ML Estimation
Square Root of e Accurate CRLB
Square Root of e Approximate CRLB
0.8
0.7
0.6
0.5
0.4
0.3
0.2
10
20
30
40
50
60
70
80
90
100
Number of sub−estimation periods, Q
(a)
1
0.9
Standard Deviation of the ML Estimation
Square Root of e Accurate CRLB
Square Root of e Approximate CRLB
0.8
0.7
0.6
0.5
0.4
q
0.3
0.2
10
20
30
40
50
60
70
80
90
100
Length of sub−estimation periods, Q
(b)
FIgure 7.7
Comparison of CRLB and the estimation variance of the ML estimator of {θ
k
}
k
=1
(a)
N
= 8,
K
k
= 5,
M
= 1,
L
q
= 10; (b)
N
= 8,
K
k
= 5,
M
= 1,
Q
= 10. (Reproduced from Kim et al., 2006.
© 2006, IEEE. With permission.)
shows the square root of the CRLB and the standard deviation of the ML estimator of
{θ
k
}
k
=1
, when {θ
k
}
k
=1
are generated randomly from [0,2π) and ϕ
q
= (
q
/
Q
)2π. One can see
that the standard deviation of the DOA estimation algorithm is very close to the CRLB.
This agrees with the theory that the proposed ML estimator of DOAs is asymptotically
a minimum variance estimator.
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