Geoscience Reference
In-Depth Information
for the use of the narrowband(wideband) WV transformation for detecting a deterministic
signal with unknown delay-Doppler(-scale) parameters. WV's practical usage is limited
by the presence of non-negligible cross-terms, resulting from interactions between signal
components. Alternative approaches are proposed for eliminating or at least suppressing the
cross-terms [Chassande-Mottin & Pai, 2005; Orr et al., 1992; Tan & Sha'ameri, 2008]. Generally
speaking, cross-term suppression may be divided into two categories: signal-independent and
signal-dependent paradigm. Coupling the Gabor transformation with the WV distribution
is a signal-independent procedure that reveals a cross-term suppression approach through
exploitation of partial knowledge about signals to be encountered [Orr et al., 1992]. For
signal-dependent method, it is possible to apply an adaptive window over WV distribution
where the kernel parameters are determined automatically from the parameters of the
input signal. This kernel is capable of suppressing the cross-terms and maintain accurate
time-frequency resolution [Tan & Sha'ameri, 2008]. Besides the WV method, there are other
time-frequency techniques such as wavelet transform. Wavelet approach combines the noise
filtering and scaling together, yielding a reduction in complexity [Niu et al., 1999]. There
is also another procedure using the fractional lower order ambiguity function (FLOAF)
for joint time delay and Doppler estimation [Ma & Nikias, 1996]. Now another view is
presented. It is assumed that the transmitted signal follows an
N
-mode Gaussian mixture
model (GMM). GMM can be used for different transmitted signals. Especially, it presents
an accurate modeling for actual signals transmitted in the sonar and radar systems [Bilik
et al., 2006]. The received signal is affected by the noise, time delay and Doppler where
the conglomerate effects on the signal cause peculiar changes on the moments of received
signal. Using moments is a powerful procedure which is used for different applications,
specially in parameter estimation. Some people use the moment method to estimate the
parameters of a Gaussian mixture in an environment without noise [Fukunaga et al., 1983].
Some apply the method for better parameter estimation in a faded signal transmitted through
a communication channel which is suffered from multipath. The method can be implemented
using a non-linear least-squares algorithm to represent a parameterized fading model for
the instantaneous received path power which accounts for both wide-sense stationary
shadowing and small-scale fading [Bouchereau & Brady, 2008]. The most prominent and
novel models for the envelope of a faded signal are Rician and Nakagami. There are
estimators for the Nakagami-m parameter based on real sample moments. The estimators
present an asymptotic expansion which provides a generalized closed-form expression for
the Nakagami-m parameter without the need for coefficient optimization for different ratios
of real moments [Gaeddert & Annamalai, 2005]. There are also approaches that show the
K-factor in Rician model is an exact function of moments estimated from time-series data
[Greenstein et al., 1999].
In this chapter, we analyze the effect of noise, time delay, and Doppler on the moments of
received signal and exploit them for estimating the position and velocity of the target. We note
that in the new method, the noise power is assumed unknown which is estimated along with
the time delay and Doppler shift. The new approach exhibits accurate results compared to the
existing methods even in very low SNR and long tailed noise. Then, the estimated parameters
are used for tracking a maneuvering target's position and velocity. There exist other practical
methods for tracking targets such as Kalman filtering [Park & Lee, 2001]. However, when
the target motion is nonlinear and/or clutter and/or noise are non-Gaussian, this approach
fails to be effective. Instead, unscented Kalman filter (UKF) and extended Kalman filter (EKF)
come into use [Jian et al., 2007]. However, in long tailed noise, Kalman filtering results are
