Sea clutter, the radar backscatter from the ocean surface, is highly complicated and non-stationary, due to multipath
propagation of the radar returns and multiscale interactions at the air-sea interface. To facilitate robust detection of low
observable targets within sea clutter, which is an important issue in coastal security, navigation safety and environmental
monitoring, we propose a systematic multiscale approach to the modeling of sea clutter. Specifically, we (i) develop new
methods to better fit non-stationary and non-Gaussian sea clutter, (ii) fully characterize the correlation structure of sea
clutter on multiple time scales, (iii) develop a highly accurate cascade model for sea clutter, and (iv) develop accurate
and readily implementable methods to detect low observable targets within sea clutter.
Sea clutter, the radar backscatter from the ocean surface, has been observed to be highly non-Gaussian. K distribution
is among the best distributions proposed to fit non-Gaussian sea clutter data. Using diffusive models, K distributed sea
clutter can be casted as a Gaussian speckle, with a de-correlation time of 0.1 s, modulated by a Gamma distribution,
with a de-correlation time of about 1 s, characterizing the large scale structures of the sea surface. Our analyses of large
amounts of real sea clutter data suggest that between the time scales for the Gaussian speckle and large scale structures
on the sea surface to de-correlate, sea clutter can be characterized as multifractal 1/f processes. This is the feature that
is not captured by diffusive models and underlies why K distribution cannot fit real sea clutter data sufficiently well.
We surmise that by combining K distribution and associated diffusive models with multifractal formalism, the many
different physical processes underlying sea clutter can be more comprehensively characterized.
Modeling sea clutter by chaotic dynamics has been an exciting yet heatedly debated topic. To resolve controversies
associated with this approach, we use the scale-dependent Lyapunov exponent (SDLE) to study sea clutter. The SDLE
has been shown to be able to unambiguously distinguish chaos from noise. Our analyses of almost 400 sea clutter
datasets measured by Professor Simon Haykin suggest that on very short time scales, sea clutter may be classified as
noisy chaos, characterized by a parameter γ, which characterizes the speed of information loss. It is shown that γ can be used to very effectively detect low observable targets within sea clutter.
Enterprise networks are facing ever-increasing security threats from Distributed Denial of Service (DDoS) attacks, worms, viruses, intrusions, Trojans, port scans, and network misuses, and thus effective monitoring approaches to quickly detect these activities are greatly needed. In this paper, we employ chaos theory and propose an interesting phase space method to detect Internet worms.
An Internet worm is a self-propagating program that automatically replicates itself to vulnerable systems and spreads across the Internet. Most deployed worm-detection systems are signature-based. They look for specific byte sequences (called attack signatures) that are known to appear in the attack traffic. Conventionally, the
signatures are manually identified by human experts through careful analysis of the byte sequence from captured attack traffic. We propose to embed the traffic sequence to a high-dimensional phase space using chaos theory. We have observed that the signature sequence of a specific worm will occupy specific regions in the phase space, which may be appropriately called the invariant subspace of the worm. The invariant subspace of the worm separates itself widely from the subspace of the normal traffic. This separation allows us to construct three simple metrics, each of which completely separates 100 normal traffic streams from 200 worm traffic streams, without training in the conventional sense. Therefore, the method is at least as accurate as any existing methods. More importantly, our
method is much faster than existing methods, such as based on expectation maximization and hidden Markov models.
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