Abstract: Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.
Abstract: The Maximum entropy principle in spectral analysis
was used as an estimator of Direction of Arrival (DoA) of
electromagnetic or acoustic sources impinging on an array of sensors,
indeed the maximum entropy operator is very efficient when the
signals of the radiating sources are ergodic and complex zero mean
random processes which is the case for cosmic sources. In this paper,
we present basic review of the maximum entropy method (MEM)
which consists of rank one operator but not a projector, and we
elaborate a new operator which is full rank and sum of all possible
projectors. Two dimensional Simulation results based on Monte
Carlo trials prove the resolution power of the new operator where the
MEM presents some erroneous fluctuations.
Abstract: This paper addresses the problem of how one can
improve the performance of a non-optimal filter. First the theoretical question on dynamical representation for a given time correlated
random process is studied. It will be demonstrated that for a wide class of random processes, having a canonical form, there exists
a dynamical system equivalent in the sense that its output has the
same covariance function. It is shown that the dynamical approach is more effective for simulating and estimating a Markov and non-
Markovian random processes, computationally is less demanding,
especially with increasing of the dimension of simulated processes.
Numerical examples and estimation problems in low dimensional
systems are given to illustrate the advantages of the approach. A very useful application of the proposed approach is shown for the
problem of state estimation in very high dimensional systems. Here a modified filter for data assimilation in an oceanic numerical model
is presented which is proved to be very efficient due to introducing
a simple Markovian structure for the output prediction error process
and adaptive tuning some parameters of the Markov equation.
Abstract: Real world Speaker Identification (SI) application
differs from ideal or laboratory conditions causing perturbations that
leads to a mismatch between the training and testing environment
and degrade the performance drastically. Many strategies have been
adopted to cope with acoustical degradation; wavelet based Bayesian
marginal model is one of them. But Bayesian marginal models
cannot model the inter-scale statistical dependencies of different
wavelet scales. Simple nonlinear estimators for wavelet based
denoising assume that the wavelet coefficients in different scales are
independent in nature. However wavelet coefficients have significant
inter-scale dependency. This paper enhances this inter-scale
dependency property by a Circularly Symmetric Probability Density
Function (CS-PDF) related to the family of Spherically Invariant
Random Processes (SIRPs) in Log Gabor Wavelet (LGW) domain
and corresponding joint shrinkage estimator is derived by Maximum
a Posteriori (MAP) estimator. A framework is proposed based on
these to denoise speech signal for automatic speaker identification
problems. The robustness of the proposed framework is tested for
Text Independent Speaker Identification application on 100 speakers
of POLYCOST and 100 speakers of YOHO speech database in three
different noise environments. Experimental results show that the
proposed estimator yields a higher improvement in identification
accuracy compared to other estimators on popular Gaussian Mixture
Model (GMM) based speaker model and Mel-Frequency Cepstral
Coefficient (MFCC) features.
Abstract: Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.
Abstract: The bridge vibration due to traffic loading has been a
subject of extensive research during the last decades. A number of
these studies are concerned with the effects of the unevenness of
roadways on the dynamic responses of highway bridges. The road
unevenness is often described as a random process that constitutes
of different wavelengths. Thus, the study focuses on examining
the effects of the random description of roadways on the dynamic
response and its variance. A new setting of variance based sensitivity
analysis is proposed and used to identify and quantify the
contributions of the roadway-s wavelengths to the variance of the
dynamic response. Furthermore, the effect of the vehicle-s speed on
the dynamic response is studied.