Geoscience Reference
In-Depth Information
6. The results
To prove the procedures were presented in this Chapter, several different tests have been
conducted. The results are divided into two categories. At first, the proposed method
for estimating the joint time delay and Doppler is examined and compared with other
conventional methods. Then, the efficiency of this method in the tracking of the maneuver
target is also investigated.
6.1 Parameter estimation results
To
estimate
the
time
delay
and
Doppler
parameters,
the
following
assumptions
are
considered:
The transmitted desired signal follows a trimodal Gaussian mixture distribution presented
in equation (6) with the following mean and standard deviation related to the three modes:
σ s 1 = σ s 2 = σ s 3 =
1,
μ s 1 =
2,
μ s 2 =
5,
μ s 3 =
8,
And the probability distribution of the modes is considered as below:
p 1 =
0.3, p 2 =
0.3, p 3 =
0.4 .
The observation time of the signal is considered 1 millisecond.
The time delay can be within the observation time of the signal, and in here, it is assumed
300 microseconds.
ω ε =
Doppler value,
2
πε
, is a number between 0 and 2
π
that provides a 2
π
rotation for
the frequency shift. Now, Doppler is assumed 0.8
π
.
The test is done for different SNR values from -10dB to +10dB, and for each SNR, the operation
is performed 1000 times. The figure (4) depicts the error existed in the estimation of the time
delay for the conventional methods and the proposed moment one. This error is depicted as
MSE, calculated from 1000 times of simulation implementation, versus SNR. We have used
normalized MSE in our results:
E ˆ
2 ,
τ − τ
τ
τ ) =
MSE
(
ˆ
(37)
where
is the estimated value of this parameter. The
conventional methods are WV [Chassande-Mottin & Pai, 2005], wavelet method [Niu et al.,
1999] and FLOAF [Ma & Nikias, 1996].
τ
is the actual time delay, and
τ
ˆ
As shown in Figure (4), all methods are convincing in high SNRs, but in low SNRs, especially
negative ones, WV and FLOAF methods are completely unable to estimate the time delay.
Wavelet method also has relatively unsuitable results, so that it presents very little reduction
in MSE value from SNR=-10dB to SNR=0dB. But the moment method in the both high and
low SNRs provides precise answers.
 
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