SPTM-5.1

Signal compression by piecewise linear non-interpolating approximation
Ranveig Nygaard, John H Husoy, Dag Haugland, Sven O Aase (Hogskolen i Stavanger)

In this paper we present a signal compression scheme based on coding linear segments approximating the signal. Although the approach is useful for many types of signals, we focus in this paper on compression of ElectroCardioGram (ECG) signals. ECG signal compression has traditionally been tackled by heuristic approaches. However, it has recently been demonstrated that exact optimization algorithms outclass these heuristic approaches by a wide margin with respect to reconstruction error. The exact optimization algorithm extracts signal samples from the original signal by formulating the sample selection problem as a graph theory problem. Thus known optimization theory can be applied in order to yield optimal compression. This paper generalizes the exact optimization scheme by removing the interpolation restriction when applying piecewise linear approximation. This guarantees a lower reconstruction error with respect to the number of extracted signal samples. The method shows superior performance compared to traditional ECG compression methods.

SPTM-5.2

Non-linear Instantaneous Least Squares and its High SNR Analysis
Jakob �ngeby, Mats Viberg (Chalmers University of Technology, Department of Signals and Systems), Tony Gustafsson (Signal Processing group, Chalmers University of Technology, Department of Signals and Systems)

A novel approach for signal parameter estimation, named the Non-Linear Instantaneous Least Squares (NILS) estimator, is proposed and a high SNR statistical analysis of the estimates is presented. The algorithm is generally applicable to deterministic signal in noise models. However, it is of particular interest in applications where the ``conventional'' non-linear least squares criterion suffers from numerous local minima. The key idea here is to apply a sliding window to estimate the instantaneous amplitude, which is then used in a separable least squares criterion-function. Hereby the radius of attraction of the global minimum is under the control of the user, which makes the NILS approach advantegous to use in practical applications.

SPTM-5.3

Level Estimation in Nonlinearly Distorted Hidden Markov Models Using Statistical Extremes
Kutluyil Dogancay (Inst. of Info. Sciences & Technology, Massey University, Palmerston North, New Zealand), Vikram Krishnamurthy (Dept. of Electrical & Electronic Engineering, The University of Melbourne, Parkville, Australia)

Estimation of the state levels of a discrete-time, finite-state Markov chain hidden in coloured Gaussian noise and subjected to unknown nonlinear distortion is considered. If the nonlinear distortion has almost linear behaviour for small values near zero or for large values, extreme value theory can be applied to the level estimation problem, resulting in simple estimation algorithms. The extreme value-based level estimator is computationally inexpensive and has potential applications in data measurement systems where inaccuracies are introduced by dead zones or saturation in sensor characteristics. The effectiveness of the new level estimator is demonstrated by way of computer simulations.

SPTM-5.4

Combating channel distortions for chaotic signals
Naresh Sharma, Edward Ott (University of Maryland, College Park)

Over the past several years, there have been various proposals for communication with chaotic signals. But the issue of compensating the distortions introduced by the physical channel like noise, time varying fading and multi-path has not been fully addressed. In this paper, we first describe a noise reduction method for chaotic signals corrupted by an additive noise. The method uses the phenomenon of chaos synchronization to approximate the maximum likelihood (ML) decoder for the AWGN channel. Further we use the synchronizing receiver to nullify slowly time varying fading and multi-path. We find the region of operation for such a receiver and show how the time varying parameters characterizing such channels can be tracked at the receiver.

SPTM-5.5

Adaptive Identification of Bilinear Systems
Zhiwen Zhu (Communications Research Laboratory, McMaster University, Hamilton, Ontario, Canada L8S 4K1), Henry Leung (Surface Radar Section, Defence Research Establishment Ottawa, Ottawa, Ontario, Canada K1A 0Z4)

The paper considers the adaptive identification of bilinear systems using the equation-error approach. An improved least squares (ILS) objective function is presented to reduce the bias of coefficient estimation in the case of large measurement noise when the standard least squares (LS) technique is used. An adaptive algorithm based on the ILS criterion is proposed for the identification of the bilinear system. Numerical simulations are given to demonstrate the effectiveness of the adaptive ILS algorithm. Compared with the least mean squares (LMS) technique, the proposed algorithm has superior identification performance.

SPTM-5.6

Analysis of stochastic gradient identification of polynomial nonlinear systems with memory
Patrick Celka (Swiss Federal Institute of Technology), Neil J Bershad (University of California Irvine), Jean-Marc Vesin (Swiss Federal Institute of Technology)

This paper present analytical, numerical and experimental results for a stochastic gradient adaptive scheme which identifies a polynomial-type nonlinear system with memory for noisy output observations. The analysis includes the computation of the stationary points, the mean square error surface, and the mean behavior of the algorithm for Gaussian data. Monte Carlo simulations confirm the theoretical predictions which show a small sensitivity to the observation noise.

SPTM-5.7

Performance analysis of the mutual information function for nonlinear and linear signal processing
Hans-Peter Bernhard (Institute for Communications and Radio-Frequency Engineering, Vienna University of Technology), Georges A Darbellay (Institute of Information Theory and Automation, AV CR Prague)

Nonlinear signal processing is now well established both in theory and applications. Nevertheless, very few tools are available for the analysis of nonlinear systems. We introduce the mutual information function (MIF) as a nonlinear correlation function and describe the practicalities of estimating it from data. Even if an estimator is consistent, it is of great interest to check what the bias and variance are with a finite sample. We discuss these questions, as well as the computational efficiency, for two estimators. Both algorithms are of the complexity N log_2 N, where N is the sample length, but they use different methods to find the histogram for the estimation of the mutual information. An efficient implementation makes it possible to apply the algorithm on real time signal processing problems where the linear correlation analysis breaks down. Current applications are: mobile radio channels, load curve forecasting, speech processing, nonlinear systems theory.

SPTM-5.8

A Novel Channel Equalizer for Chaotic Digital Communications Systems
Mahmut Ciftci, Douglas B Williams (Georgia Institute of Technology)

In recent years, a variety of communications systems based on chaos and nonlinear dynamics have been proposed. However, most of these algorithms fail to work under realistic channel conditions. This paper presents a channel equalization scheme for chaotic communication systems based on a family of archetypal chaotic maps. The symbolic-dynamic representation of these maps is exploited to allow a straightforward and efficient implementation. Equalizer filter coefficients are updated using appropriately modified versions of decision-directed and decision-feedback equalization algorithms with adaptation based on the NLMS algorithm.

SPTM-5.9

A Recursive Prediction Error Algorithm for Identification of Certain Time-Varying Nonlinear Systems
Anders E. Nordsjo, Lars H. Zetterberg (Royal Institute of Technology)

The tracking problem in identification of certain classes of time-varying nonlinear systems is addressed. In particular, a Hammerstein type system which consists of a nonlinear part, given on a state space description, followed by a time-varying linear part is considered. A Recursive Prediction Error Method, RPEM combined with a method for on-line adjustment of the forgetting factor is proposed. This algorithm does not require estimation of the statistics of the noise and the dynamics of the true system. It is shown how the proposed scheme can be used for identification of certain nonlinear time varying acoustic echo paths. Thus, the suggested algorithm is applicable to for instance, conference telephony and mobile telephone handsfree.

SPTM-5.10

Nonlinear System Identification of Hydraulic Actuator Friction Dynamics using a Finite-State Memory Model
Byung-Jae Kwak, Andrew E Yagle (University of Michigan), Joel A Levitt (Ford Motor Co.)

We present a finite-state memory model for parametric system identification of the lip seal friction process in a hydraulic actuator. The performance of the finite state memory model is compared to two Hammerstein type models using experimental results.

SPTM-5.11

Nonlinear Filtering by Kringing, with Application to System Inversion
Costa Jean-Pierre, Pronzato Luc, Thierry Eric (Laboratoire I3S, CNRS-UNSA)

Prediction by kringing does not rely on any specific model structure, and is thus much more flexible than approaches based on parametric behavioural models. Since accurate predictions are obtained for extremely short training sequences, it generally performs better than prediction methods using parametric models. Application to nonlinear system inversion is considered.

< SPTM-4 SPTM-6 >

Last Update: February 4, 1999 Ingo Höntsch