Chaotic dynamics of sea clutter

Abstract

The notion that a deterministic nonlinear dynamical system (with relatively few degrees of freedom) can display aperiodic behavior has a strong bearing on sea clutter characterization: random-looking sea clutter may be the outcome of a chaotic process. This new approach envisages deterministic rules for the underlying sea clutter dynamics, in contrast to the stochastic approach where sea clutter is viewed as a random process with a large number of degrees of freedom. In this paper, we demonstrate, convincingly for the first time, the chaotic dynamics of sea clutter. We say so on the basis of results obtained using radar data collected from a series of extensive and thorough experiments, which have been carried out with ground-truthed sea clutter data sets at three different sites. The study includes correlation dimension analysis (based on the maximum likelihood principle) and Lyapunov spectrum analysis. The Lyapunov (Kaplan-Yorke) dimension, which is a byproduct of Lyapunov spectrum analysis, shows that it is indeed a good estimator of the correlation dimension. The Lyapunov spectrum also reveals that sea clutter is produced by a coupled system of nonlinear differential equations of order five or six. (c) 1997 American Institute of Physics.

On modeling sea clutter by noisy chaotic dynamics

“…Recently, their conclusion has been challenged by a number of researchers [3][4][5][6][7][8][9]. In particular, Unsworth et al [6,7] have demonstrated that the two main invariants used by Haykin et al [1,2], namely the "maximum likelihood of the correlation dimension estimate" and the "false nearest neighbors" are problematic in the analysis of measured sea clutter data, since both invariants may interpret stochastic processes as chaos. They have also tried an improved method, which is based on the correlation integral of Grassberger and Procaccia [10] and has been found to be effective in distinguishing stochastic processes from chaos.…”

“…Since the complicated sea clutter signals are functions of complex (sometimes turbulent) wave motions on the sea surface, while wave motions on the sea surface clearly have their own dynamical features that are not readily described by simple statistical features, it is very appealing to understand sea clutter by considering some of their dynamical features. In the past decade, Haykin et al have carried out analysis of some sea clutter data using chaos theory [1,2], and concluded that sea clutter was generated by an underlying chaotic process. Recently, their conclusion has been challenged by a number of researchers [3][4][5][6][7][8][9].…”

Detection of Low‐Flying Target under the Sea Clutter Background Based on Volterra Filter

“…They experimented and observed the correlation dimension of sea clutter time series and found the chaotic characteristics of sea clutter. Subsequently, Haykin et al analyzed the x-band radar data of McMaster University in Canada firstly and verified the chaotic characteristics of sea clutter by calculating the correlation dimension, Kolmogorov entropy, and Lyapunov exponent [19,20]. The famous scientist Vito Volterra proposed the breakthrough concept of Volterra series in the discussion of nonlinear analytic functional; he proved that Volterra series can approach nonlinear systems [21].…”

Multi-scale Modeling Approach for Detecting LowObservable Targets within Sea Clutter

“…Despite these extensive studies, however, the nature of sea clutter is still poorly understood. For example, whether sea clutter is chaotic or not is still a much debated issue [6][7][8][9][10][11][12][13][14][15]. As a result, the important problem of target detection within sea clutter remains a tremendous challenge.…”