Alexandru Serbanescu

On exact Kalman filtering of polynomial systems

A closed-form state estimator for some polynomial nonlinear systems is derived in this paper. Exploiting full Taylor series expansion we first give exact matrix expressions to compute mean and covariance of any random variable distribution that has been transformed through a polynomial function. An original discrete-time Kalman filtering implementation relying on this exact polynomial transformation is proposed. The important problem of chaotic synchronization of Chebyshev maps is then considered to illustrate the significance of these results. Mean square error between synchronized signals and consistency criteria are chosen as performance measures under various signal-to-noise ratios. Comparisons to the popular extended Kalman filter and to the recent unscented Kalman filter are also conducted to show the pertinence of our filtering formulation

A complete receiver solution for a chaotic direct-sequence spread spectrum communication system

This paper is devoted to receiver design in a chaotic direct-sequence spread spectrum (CD3S) digital communication system. The demodulation is achieved through chaos synchronization in an efficient manner thanks to dual unscented Kalman filtering. The problem of carrier phase recovery, frequently neglected in chaos-based communication systems, is addressed either through Costas loop prior to demodulation or by dual estimation of the code, symbol and phase in baseband. The input signal power fluctuations, which often causes large errors in synchronizing chaotic waveforms, is also taken into account. Numerical simulations are provided to show the significance of the proposed receiver for both additive white Gaussian noise (AWGN) channel and a nonstationary channel.

A vector approach to transient signal processing

The detection and characterization of burst signals are challenging tasks for time-frequency analysis, due to their very short duration. This paper investigates in this context the recurrence plot analysis (RPA) method, from which it derives the vector samples processing (VeSP) concept. The paper shows that VeSP is a generic framework that unifies signal processing concepts like histogram and autocorrelation, which it also generalizes and extends. Results of VeSP based tools are provided, concerning detection of transient signals, noise reduction, and frequency estimation.

Time-frequency-phase tracking approach : Application to underwater signals in a passive context

One of the most challenging applications of time-frequency representations deals with the analysis of the signal issued from natural environment. Recently, the interest for passive underwater context increased, basically due to the rich information carried out by the natural signals. Taken into account the non-linear multi-component time-frequency behavior of such signals, their analysis is a complex problem. In this paper we introduce a new time-frequency analysis concept that aims to extract the non-linear time-frequency components. The main feature of this technique is the joint use of time-amplitude, time-frequency and time-phase information. This is materialized by a short-time polynomial phase modeling and the fusion of local information according to the best locally matches of local cubic frequency modulations. Tests provided on real data illustrate the benefits of the proposed approach.

On the recurrence plot analysis method behaviour under scaling transform

In the last decade, the applications of the recurrence plot analysis method make it a valuable alternative to the time-frequency and time-scale tools. As it was initially developed for the study of dynamical systems, and was later used in nonlinear time series analysis, the question of using it as a signal processing tool has not been put into discussion yet. In this field the projective techniques are largely used, with good results. Nevertheless, they also have some limitations — especially regarding transient signal processing. But this kind of signals are ubiquitous in real world. In addition, propagation through various media as well as on multiple paths lead to delayed, attenuated and dilated versions of the original transients. In this paper we study the behaviour of the recurrence plot analysis method in the context of analyzing some finite duration signals being subject to rescalings of the amplitude and time axes. This study is a starting point in employing the analysis of recurrences in investigations of a large class of real world signals.

Optimization of partial discharge detection in high voltage cables based on advanced signal processing techniques

In this paper we approach the challenges of partial discharges (PD) detection in high voltage cables using signal processing techniques based on time frequency methods combined with Recurrence Plot Analysis (RPA) and high order spectrum analysis (HOSA). Detection of PD poses many problems in terms of speed of calculation, selection criteria and multitude of causes which lead to the occurrence of PD. In order to overcome these drawbacks, we have developed an algorithm which uses the spectrogram to perform a fast detection of parts from the signal which are susceptible of PD activity. The second stage calculates for each zone a detection curve using the HOSA concept of bispectrum and RPA. The latter has been applied in many non-linear systems in order to characterize the process on the basis of the recurrence matrix obtained from a time series given by the system.

Recent Advances in Non-stationary Signal Processing Based on the Concept of Recurrence Plot Analysis

This work concerns the analysis of non-stationary signals using Recurrence Plot Analysis concept. Non-stationary signals are present in real-life phenomena such as underwater mammal’s vocalizations, human speech, ultrasonic monitoring, detection of electrical discharges, transients, wireless communications, etc. This is why a large number of approaches for non-stationary signal analysis are developed such as wavelet analysis, higher order statistics, or quadratic time-frequency analysis. Following the context, the methods defined around the concept of Recurrence Plot Analysis (RPA) constitute an interesting way of analyzing non-stationary signals and, particularly, the transient ones. Starting from the phase space and the recurrence matrix, new approaches [the angular distance, recurrence-based autocorrelation function (ACF), average-magnitude difference function (AMDF) and time-distributed recurrence (TDR)] are introduced in order to extract information about the non-stationary signals, specific to different applications. Comparisons with existing analysis methods are presented, proving the interest and the potential of the RPA-based approaches.

A time-distributed phase space histogram for detecting transient signals

Burst-type signals constitute an important class of transient signals, being used especially in the investigation of various physical environments by electric or acoustic means. An important issue in the analysis of this type of signals is their detection in time. In this paper, we propose a detection method that is based on the histogram of the phase space distributed over time. The method consists in representing the analyzed signal in phase space and, then, quantifying the recurrences of the trajectory obtained in this space. In this way, we derive a time - recurrence radius representation for the signal, that allows identification of positions and durations of the transients. Afterwards, we propose a method to obtain a detection curve starting from this representation of the signal. We also present here some results concerning the performance of our method in the presence of noise on both synthetic and real signals.

Applications of nonlinear time-series analysis in unstable periodic orbits identification - Chaos control in buck converter

Recently, there has been an extensive interest in research on the analysis and control of chaotic behavior in nonlinear systems. Various control problems can be defined for such systems, such as targeting the trajectories to a desired point, stabilizing unstable periodic orbits etc. The recurrence plot is a two dimensional representation technique that brings out distance correlations in a time series and make it instantly apparent whether a system is periodic or chaotic. In this paper, the proposed method is applied to control chaos in buck converter. In particular, the resonant parametric perturbation in the perturbing signal is studied.

Multipath combining in chaotic direct-sequence spread spectrum communications through dual estimation

The aim of the present paper is to increase the reliability of a Kalman filter-based DS-SS receiver by considering in the state space models the multipath coefficients and associated delays. The objective being to operate at very low SNRs in shallow water (to achieve furtive transmissions) and with the need of a limited computational cost, the implementation relies on the Unscented Kalman Filter, which is known to be more robust than the popular Extended Kalman Filter. The proposed receiver schemes are discussed and compared using experimental data.