Limitations of nonlinear chaotic dynamics in predicting sea clutter returns

Nonlinear Modeling and Simulation of Radar Clutter

“…The study on clutter using the chaos theory has experienced only a short time, only about a decade, and there still exists some different opinions and doubts cast on its application on radar clutter modeling and simulation, for example [6], M.McDonald and A.Damini show that the commonly used chaotic invariant measures of correlation dimension and Lyapunov exponent are incapable of uniquely identifying chaotic processes, and produce similar results for measured sea clutter returns and simulated stochastic processes. Professor Simon Haykin also pointed that the discovery that a real-world experimental time series is chaotic has a risk of being a self-fulfilling prophecy, because the influence of dynamic and measurement noise [8].…”

“…But it is found that, in small sample problems, minimum-error can not always produce a good prediction result, and in some cases, it even makes the actual risk increasing. Statistical learning theory analyzes the relationship between empirical risk and actual risk, and finds that the empirical risk emp R and actual risk ) (w R satisfy the inequality as in (6) with the probability η − 1 at least.…”

A Novel Method of Small Target Detection in Sea Clutter

“…To describe the sea clutter characteristics, chaotic process seems to be also an important approach [6]. However, the chaotic invariant measurements have been disputed by researchers interested in the field [7]. Making use of neural network trained, such as Radial Basis Function (RBF) network and Back Propagation (BP) network, to compare the difference between predicted value and the real data being tested is a very popular way to solve the detection problem focus on the sea surface with small targets recently [8].…”

On modeling sea clutter by noisy chaotic dynamics

“…To test this possibility, McDonald and Damini [12] have tried a series of low-pass filters to remove noise; but again they have failed to find any chaotic features. Furthermore, they have found that the commonly used invariant measures of chaos, the correlation dimension and the largest positive Lyapunov exponent, computed by conventional methods, cannot be used to distinguish measured sea clutter data from simulated stochastic processes, and that a nonlinear predictor shows little improvement over linear prediction.…”