a la physique de l'information - Lisa - Université d'Angers

estimation improvement ratio G est
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
−20 −15 −10 −5 0
SNRin dB
Fig. 3a
estimation improvement ratio Gest
6
5
4
3
2
1
−20 −15 −10
SNRin dB
−5 0
Fig.3b
Fig. 3. Estimation improvement ratio Gest as a function of
the input signal to noise ratio SNRin (dB). (◦) stands for
the numerical evaluation of Gest, solid line is only a guide
for the eye, and the dash-dotted line at the top stands for
the asymptotic estimation improvement ratio G0 given in
Eq. (26) under the weak signal assumption. In panel (a), the
noise η is a mixture of Gaussian with α = 0.6 and β = 4,
the signal correlation decay parameter ζ = 0.5. In panel (b),
same conditions as in Fig. 3a but the noise has generalized
Gaussian density with exponent p = 0.5.
SNRin (dB) −20 −10 −4 0
Wiener £lter 0.14 0.40 0.62 0.73
Quantizer–estimator 0.21 0.50 0.64 0.69
Table 1. Values of the correlations Corsˆs for the Wiener
£lter and Cors˜s for the quantizer–estimator corresponding
to some points in Fig. 3a.
5. CONCLUSION
In this paper, we have introduced a new nonlinear estimator
capable of doing better than the conventional linear Wiener
£lter for shape estimation of weak signals buried in additive
non-Gaussian noise. We have assessed the performance of
this nonlinear estimator both theoretically and numerically
for non-Gaussian noise relevant for applications in underwater
acoustic. In addition to providing an improved estimation,
this nonlinear estimator composed of a 3–level
symmetric quantizer followed by the Wiener £lter presents
the advantage of being almost as simple as the Wiener £lter.
A conceptually and practically interesting result of this
study is that working with a parsimonious representation of
SNRin (dB) −20 −10 −4 0
Wiener £lter 0.17 0.47 0.67 0.76
Quantizer–estimator 0.35 0.57 0.66 0.70
Table 2. Values of the correlations Corsˆs and Cors˜s corresponding
to some points in Fig. 3b.
the observable signal (here it was only a 3–level representation)
can sometimes be more ef£cient for information processing
than seeking a faithful representation of the original
signal from the physical environment. Various perspectives
and extensions of this work can be pursued, like considering
other non-Gaussian noise distributions of practical
interest, testing other types of simple nonlinear preprocessors
(for example the array of quantizers studied in [6]) or
even applying these nonlinear preprocessors to other signal
processing tasks (for example enhancing the Kalman £lter
for nonstationary signal estimation buried in non-Gaussian
noise).
6. REFERENCES
[1] S. Kay, “Fundamentals of Statistical Signal Processing,
Vol. 1: Estimation Theory”, Prentice Hall, Englewood
Cliffs, 1993.
[2] F.W. Machell, C. S. Penrod, and G.E. Ellis, “Statistical
Characteristics of Ocean Acoustic Noise Processes”,
Topics in Non-Gaussian Signal Processing, Springer,
Wegman, E. J. and Schwartz, S. C. and Thomas, J. B.,
Berlin, 1989, pp. 29–57.
[3] F. Chapeau-Blondeau, “Periodic and Aperiodic
Stochastic Resonance with Output Signal-to-noise Ratio
Exceeding that at the Input”, International Journal
of Bifurcation and Chaos, 1999, Vol. 9, pp. 267–272.
[4] A. Saha, G. V. Anand, “Design of Detectors Based
on Stochastic Resonance”, Signal Processing, 2003,
Vol. 83, pp. 1193–1212.
[5] V. G. Guha, “Detection of Weak Signals in Non-
Gaussian Noise Using Stochastic Resonance”, M. Sc.
(Engg.) Thesis, Department of Electrical Communication
Engineering, Indian Institute of Science, Bangalore,
2002.
[6] D. Rousseau, F. Chapeau-Blondeau, “Suprathreshold
Stochastic Resonance and Signal-to-noise Ratio Improvement
in Arrays of Comparators”, Physics Letters
A, 2004, Vol. 321, pp. 280–290.
113/197