This paper deals with the problem of detecting a radar target signal against correlated non-Gaussian clutter, which is modeled by the compound-Gaussian distribution. We prove that if the texture of compound-Gaussian clutter is modeled by an inverse-gamma distribution, the optimum detector is the optimum Gaussian matched filter detector compared to a data-dependent threshold that varies linearly with a quadratic statistic of the data. We call this optimum detector a linear-threshold detector (LTD). Then, we show that the compound-Gaussian model presented here varies parametrically from the Gaussian clutter model to a clutter model whose tails are evidently heavier than any K-distribution model. Moreover, we show that the generalized likelihood ratio test (GLRT), which is a popular suboptimum detector because of its constant false-alarm rate (CFAR) property, is an optimum detector for our clutter model in the limit as the tails get extremely heavy. The GLRT-LTD is tested against simulated high-resolution sea clutter data to investigate the dependence of its performance on the various clutter parameters.

Coherent Radar Target Detection in Heavy-Tailed Compound-Gaussian Clutter

Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free. To facilitate joint chaos and fractal analysis of biosignals, we report an adaptive multiscale decomposition algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction schemes; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; (4) offers a new formulation of fractal and multifractal analysis that is better than the popular detrended fluctuation analysis when a biosignal contains a strong oscillatory component. The effectiveness of the approach is demonstrated by applying it to classify EEGs for the purpose of detecting epileptic seizures.Copyright © 2011 by ASME

https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1168&context=easpubs

Facilitating Joint Chaos and Fractal Analysis of Biosignals Through Nonlinear Adaptive Filtering

It is always a challenging problem for marine surface surveillance radar to detect sea-surface floating small targets. Conventional detectors using incoherent integration and adaptive clutter suppression have low detection probabilities for such targets with weak returns and unobservable Doppler shifts. In this paper, three features of a received vector at a resolution cell-the relative amplitude, relative Doppler peak height, and relative entropy of the Doppler amplitude spectrum-are exploited to give returns with targets from sea clutter. Real datasets show that each feature alone has some discriminability, and the three features jointly exhibit strong discriminability. Due to diversity of targets in practice, it is impossible to get features of returns with all kinds of targets. We recast detection of sea-surface floating small targets as a one-class anomaly detection problem in the 3D feature space. A fast convexhull learning algorithm is proposed to learn the decision region of the clutter pattern from feature vectors of clutter-only observations. As a result, a tri-feature-based detector is developed. The experiment results for the IPIX datasets show that the proposed detector at an observation time of several seconds attains better detection performance than several existing detectors.

Tri-feature-based detection of floating small targets in sea clutter

In recent years an abundance of technical papers and books have been written on several topics of radar signal processing. The detection of radar targets against ground and sea clutter is a problem of great interest in the radar community. The fusion of signals from different radar to improve detection performance is another relevant topic of research and application. These are two of several topics that have been extensively described in the technical literature. Needless to say that the consultation of technical references plays a key role in the daily work of researchers and engineers involved in the radar field. We collected almost 700 references in a single document to facilitate our work and the work of other colleagues of the radar community. The collection of references is by no means exhaustive; the period of screening mainly covers the last two decades.

Selected list of references on radar signal processing

X-band (9.5-10.0 GHz) backscatter at near grazing incidence (0.2 deg) from the sea off the coast of Kauai, Hawaii, was measured with a radar characterized by a high spatial resolution in range (0.3 m) and a high temporal resolution (2000 Hz pulse repetition frequency (PRF)). Extensive amounts (over 20 min per measurement) of vertically and horizontally polarized sea clutter data were taken with upwind (UP) and crosswind (CR) transmit geometries during the collection campaign. Specific but representative examples of the clutter were statistically and phenomenologically analyzed over time scales varying from long (200 s), to intermediate (5 s), to short (50 ms), and over range swaths varying from full (160 m), to partial (30 m), to a single range cell (0.3 m). All analyses and results presented here are noncoherent, involving only the clutter amplitudes. Each type of clutter exhibited the characteristic spiky behavior which has come to be expected from microwave sea backscatter observed at low grazing angles and high range resolutions, while showing, between themselves, marked transmit geometry and polarization dependent contrasts, with the horizontally polarized clutter, measured with an UP transmit geometry, being especially notable for its frequently occurring, significant high frequency spectral content. Within the same clutter type, differences were observed in the probability distributions of radar cross sections (RCS) of spatially and temporally extended spiking events.

Spiky sea clutter at high range resolutions and very low grazing angles

A radar pulse that impinges upon a radar resolution area of the sea surface produces backscattered returns which are called sea clutter. For low grazing angles and very fine radar cell resolution areas, the clutter intensity distribution departs significantly from the exponential distribution. In this case, the clutter is said to display spiky behavior and the distribution of the intensity develops a much longer tail relative to the exponential distribution. Statistical analysis of collected data near a grazing angle of 0.2° at X-band from the sea off the coast of Kauai, Hawaii are examined relative to the log-normal, Weibull and K distributions. Based on an analogy of sea clutter and other disciplines including computer networks and finance, we also apply the Pareto distribution to the collected data. We also compare the data to the WW and KK two-population mixture distributions. Maximum likelihood estimation of the parameters of the distributions are obtained from the measured data. In all cases, the two population mixture distributions and the Pareto distribution are more accurate than the three classical distributions. However the Pareto distribution has the advantage of being an analytically tractable two parameter distribution while having similar accuracy to the five parameter WW and KK at critical values.

The Pareto distribution for low grazing angle and high resolution X-band sea clutter

Sea clutter refers to the radar returns from a patch of ocean surface. Accurate modeling of sea clutter and robust detection of low observable targets within sea clutter are important problems in remote sensing and radar signal processing applications. Due to lack of fundamental understanding of the nature of sea clutter, however, no simple and effective methods for detecting targets within sea clutter have been proposed. To help solve this important problem, we apply three types of fractal scaling analyses, fluctuation analysis (FA), detrended fluctuation analysis (DFA), and the wavelet-based fractal scaling analysis to study sea clutter. Our analyses show that sea clutter data exhibit fractal behaviors in the time scale range of about 0.01 seconds to a few seconds. The physical significance of these time scales is discussed. We emphasize that time scales characterizing fractal scaling break are among the most important features for detecting patterns using fractal theory. By systematically studying 392 sea clutter time series measured under various sea and weather conditions, we find very effective methods for detecting targets within sea clutter. Based on the data available to us, the accuracy of these methods is close to 100%.

/pdf/target-detection-within-sea-clutter-a-comparative-study-by-2uqyzu11jh.pdf

Target detection within sea clutter: a comparative study by fractal scaling analyses

Because the wideband spiky sea clutter that is frequently observed at low grazing angles and high resolution plays a critical role in the performance of modern naval radars, it is necessary to analyze two important quantities: (1) the mean spike duration and (2) the mean interval between spikes. These analyses need to be conducted with representative examples of such wideband clutter taken from a suitable database. Microwave backscatter (X-band, 9.5-10.0 GHz) observed at near grazing incidence (0.2 degrees) from the sea off the coast of Kauia, Hawaii, was measured with a wideband radar characterized by a high spatial resolution in range (0.3 meters) and a high temporal resolution (2000 Hz pulse repetition frequency). Extensive amounts (over 20 minutes duration per measurement) of both vertically and horizontally polarized wideband sea clutter data were taken with upwind and crosswind transmit geometries during the data collection exercise. The analyses of the dependence of the mean spike duration and the mean interval between spikes upon three parameters: (1) the spike amplitude threshold, (2) the minimum spike width, and (3) the minimum interval between spikes, were carried out. This was done using all of the extensive data within a number of selected individual range cells for both vertically and horizontally polarized clutter, measured with an upwind transmit geometry.

Sea spike demographics at high range resolutions and very low grazing angles

X-band (9.5-10.0 GHz) backscatter at near grazing incidence (0.2 deg) from the sea off the coast of Kauai, Hawaii was measured with a radar characterized by a high spatial resolution in range (0.3 m) and a high temporal resolution (2000 Hz PRF). Extensive amounts (over 1200 s per measurement) of vertically and horizontally polarized sea clutter data were taken for upwind and crosswind transmit geometries. Each type of data was analyzed over time scales varying from long (200 s), to intermediate (5 s), to short (50 ms), and over range swaths varying from full (160 m), to intermediate (30 m), to short (an individual range cell, 0.3 m). The different types of data each exhibited the spiky behavior which has come to be expected from sea backscatter observed at low grazing angles and high range resolutions, while showing, between themselves, marked transmit geometry and polarization dependent contrasts, with the horizontally polarized, upwind sea clutter being especially notable for its frequently occurring, significant high frequency spectral content.

http://ieeexplore.ieee.org/iel4/5560/14888/00678036.pdf

Spiky sea clutter at low grazing angles and high range resolutions

The contribution of this paper is to propose, and compute the level crossing rate (LCR), average calm duration (ACD) and average surge duration (ASD) in the context of radar clutter and false alarm analysis. The derived formulas for the LCR, ACD and ASD are then compared to their measured values calculated from experimental radar sea clutter and are shown to be in good agreement. These quantities are useful for false alarm analysis and synthetic clutter validation. In the clutter region, they provide an estimate of the expected number of spikes per second, the mean spike duration and the mean interval between spikes.

Fred L. Posner

Papers

The Pareto distribution for low grazing angle and high resolution X-band sea clutter

Target detection within sea clutter: a comparative study by fractal scaling analyses

Sea spike demographics at high range resolutions and very low grazing angles

Spiky sea clutter at low grazing angles and high range resolutions

Application of the level crossing rate function to sea clutter