Abstract: In Secondary Surveillance Radar (SSR) systems, it is
more difficult to locate and recognise aircrafts in the neighbourhood of civil airports since aerial traffic becomes greater. Here, we propose to apply a recent Blind Source Separation (BSS) algorithm based
on Time-Frequency Analysis, in order to separate messages sent by different aircrafts and falling in the same radar beam in reception. The above source separation method involves joint-diagonalization
of a set of smoothed version of spatial Wigner-Ville distributions.
The technique makes use of the difference in the t-f signatures of the nonstationary sources to be separated. Consequently, as the SSR sources emit different messages at different frequencies, the above fitted to this new application. We applied the technique in simulation to separate SSR replies. Results are provided at the end
of the paper.
Abstract: A multi-rate discrete-time model, whose response
agrees exactly with that of a continuous-time original at all sampling
instants for any sampling periods, is developed for a linear system,
which is assumed to have multiple real eigenvalues. The sampling
rates can be chosen arbitrarily and individually, so that their ratios
can even be irrational. The state space model is obtained as a
combination of a linear diagonal state equation and a nonlinear output
equation. Unlike the usual lifted model, the order of the proposed
model is the same as the number of sampling rates, which is less than
or equal to the order of the original continuous-time system. The
method is based on a nonlinear variable transformation, which can be
considered as a generalization of linear similarity transformation,
which cannot be applied to systems with multiple eigenvalues in
general. An example and its simulation result show that the proposed
multi-rate model gives exact responses at all sampling instants.
Abstract: In this paper, many techniques for blind identification of moving average (MA) process are presented. These methods utilize third- and fourth-order cumulants of the noisy observations of the system output. The system is driven by an independent and identically distributed (i.i.d) non-Gaussian sequence that is not observed. Two nonlinear optimization algorithms, namely the Gradient Descent and the Gauss-Newton algorithms are exposed. An algorithm based on the joint-diagonalization of the fourth-order cumulant matrices (FOSI) is also considered, as well as an improved version of the classical C(q, 0, k) algorithm based on the choice of the Best 1-D Slice of fourth-order cumulants. To illustrate the effectiveness of our methods, various simulation examples are presented.
Abstract: This paper addresses the problem of blind source separation
(BSS). To recover original signals, from linear instantaneous
mixtures, we propose a new contrast function based on the use of a
double referenced system. Our approach assumes statistical independence
sources. The reference vectors will be incrusted in the cumulant
to evaluate the independence. The estimation of the separating matrix
will be performed in two steps: whitening observations and joint
diagonalization of a set of referenced cumulant matrices. Computer
simulations are presented to demonstrate the effectiveness of the
suggested approach.