TARGET DETECTION WITHIN SEA CLUTTER: A COMPARATIVE STUDY BY FRACTAL SCALING ANALYSES

Fractals ◽  
2006 ◽  
Vol 14 (03) ◽  
pp. 187-204 ◽  
Author(s):  
JING HU ◽  
JIANBO GAO ◽  
FRED L. POSNER ◽  
YI ZHENG ◽  
WEN-WEN TUNG
Keyword(s):  
Time Scales ◽  
Fractal Theory ◽  
Weather Conditions ◽  
Radar Signal ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Sea Clutter ◽  
Fractal Scaling ◽  
Robust Detection ◽  
Scaling Analyses

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%.

scholarly journals Fractal scaling analysis of groundwater dynamics in confined aquifers

2017 ◽  
Vol 8 (4) ◽  
pp. 931-949 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

scholarly journals Fractal Scaling Analysis of Groundwater Dynamics in Confined Aquifers

2017 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydro-climatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations of confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality; and Multifractal detrended fluctuation analysis (MF-DFA) and Multiscale Multifractal Analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics which may be fitted by the Lévy stable distribution or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes, which can model both the long-memory behavior as well as the Brownian finite-memory behavior.

SCALING ANALYSIS OF THE A-PHASE DYNAMICS DURING SLEEP

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050050
Author(s):  
V. E. ARCE-GUEVARA ◽  
M. O. MENDEZ ◽  
J. S. MURGUÍA ◽  
A. ALBA ◽  
H. GONZÁLEZ-AGUILAR ◽  
...  
Keyword(s):  
Binary Sequence ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Sleep State ◽  
Phase Dynamics ◽  
A Value ◽  
Sleep Condition ◽  
Detrended Fluctuation

In this work, the scaling behavior of the sleep process is evaluated by using detrended fluctuation analysis based on wavelets. The analysis is carried out from arrivals of short and recurrent cortical events called A-phases, which in turn build up the Cyclic Alternating Pattern phenomenon, and are classified in three types: A1, A2 and A3. In this study, 61 sleep recordings corresponding to healthy, nocturnal frontal lobe epilepsy patients and sleep-state misperception subjects, were analyzed. From the A-phase annotations, the onsets were extracted and a binary sequence with one second resolution was generated. An item in the sequence has a value of one if an A-phase onset occurs in the corresponding window, and a value of zero otherwise. In addition, we consider other different temporal resolutions from 2[Formula: see text]s to 256[Formula: see text]s. Furthermore, the same analysis was carried out for sequences obtained from the different types of A-phases and their combinations. The results of the numerical analysis showed a relationship between the time resolutions and the scaling exponents; specifically, for higher time resolutions a white noise behavior is observed, whereas for lower time resolutions a behavior towards to [Formula: see text]-noise is exhibited. Statistical differences among groups were observed by applying various wavelet functions from the Daubechies family and choosing the appropriate sequence of A-phase onsets. This scaling analysis allows the characterization of the free-scale dynamic of the sleep process that is specific for each sleep condition. The scaling exponent could be useful as a diagnosis parameter in clinics when sleep macrostructure does not offer enough information.

scholarly journals Discriminating brain activity from task-related artifacts in functional MRI: Fractal scaling analysis simulation and application

NeuroImage ◽  
2008 ◽  
Vol 40 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Jae-Min Lee ◽  
Jing Hu ◽  
Jianbo Gao ◽  
Bruce Crosson ◽  
Kyung K. Peck ◽  
...  
Keyword(s):  
Functional Mri ◽  
Brain Activity ◽  
Scaling Analysis ◽  
Fractal Scaling

scholarly journals Late quaternary temperature variability described as abrupt transitions on a 1/<i>f</i> noise background

2015 ◽  
Vol 6 (2) ◽  
pp. 2323-2337
Author(s):  
M. Rypdal ◽  
K. Rypdal
Keyword(s):  
Time Scales ◽  
Late Quaternary ◽  
Scaling Law ◽  
Temperature Variability ◽  
Climate System ◽  
Scaling Analysis ◽  
Noise Background ◽  
Quaternary Climate ◽  
Last Glaciation ◽  
Climate Noise

Abstract. We show that in order to have a scaling description of the climate system that is not inherently non-stationary, the rapid shifts between stadial and interstadial conditions during the last glaciation cannot be included in the scaling law. The same is true for the shifts between the glacial and interglacial states in the quaternary climate. When these events are omitted from a scaling analysis we find that the climate noise is consistent with a 1/f law on time scales from months to 105 years.

MONOFRACTAL AND MULTIFRACTAL SCALING ANALYSIS OF pH TIME SERIES FROM DONGTING LAKE INLET AND OUTLET

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 309-317 ◽  
Author(s):  
ZHENG-WEN HUANG ◽  
CHUN-QIONG LIU ◽  
KAI SHI ◽  
BIN ZHANG
Keyword(s):  
Dongting Lake ◽  
Long Term Memory ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Lake Water Quality ◽  
Scale Free ◽  
Self Organized ◽  
Comparison Results ◽  
Water Ph ◽  
Multifractal Scaling

The water pH series from Dongting Lake Inlet and Outlet in China are analyzed by detrended fluctuation analysis (DFA), spectral analysis and multifractal methods. The results show that these pH series are characterized by long-term memory, 1/f noise and multifractal scaling, and these characteristics have obvious difference between the Lake Inlet and Outlet. The comparison results show that monofractal (DFA exponent) and multifractal (Δα, Δf, B) parameters can be quantitative dynamical indexes reflecting the capability of anti-acidification of Dongting Lake. Furthermore, we investigate the frequency-size distribution of pH series from Dongting Lake Inlet and Outlet. Our findings suggest that water pH is an example of a self-organized criticality (SOC) process. Based on concept of self-organized ctiticality, we analysis the cause that different scale-free power-law behavior between pH series from Dongting Lake Inlet and Outlet. This work can be helpful to improvement of modeling of lake water quality.

scholarly journals Signal processing algorithm of ship navigation radar based on azimuth distance monitoring

2019 ◽  
Vol 10 ◽  
pp. 12
Author(s):  
Yuxin Qin ◽  
Yu Chen
Keyword(s):  
Signal Processing ◽  
Processing Algorithm ◽  
Radar Signal ◽  
Radar Signal Processing ◽  
Good Precision ◽  
Clutter Suppression ◽  
Constant False Alarm Rate ◽  
Sea Clutter ◽  
Signal Processing Algorithm ◽  
Ship Navigation

The effect of ship navigation radar signal processing has a great impact on the overall performance of the radar system. In this paper, the signal processing algorithm is studied. Firstly, the principle of radar azimuth and distance monitoring is introduced, then the pulse accumulation algorithm and median filtering algorithm are analyzed, and finally a sea clutter suppression algorithm based on sensitivity time control (STC) and a rain and snow clutter suppression algorithm based on constant false alarm rate are designed to improve the target monitoring performance of radar. In the test of the algorithm, the radar signal processing algorithm designed in this study has good precision as monitoring error of the target's azimuth and distance is controlled within 1%; and it also has a better suppression effect of sea clutter and rain and snow clutter, which can suppress the clutter well, improve the target clarity, and ensure the safe navigation of the ship. The experiment proves the effectiveness of the proposed algorithm and provides some theoretical basis for the better processing of radar signals, which is beneficial to improve the environment perception ability of ships in harsh environments and promote the further development of the navigation industry.

scholarly journals Long-Range Behaviour and Correlation in DFA and DCCA Analysis of Cryptocurrencies

2019 ◽  
Vol 7 (3) ◽  
pp. 51 ◽  
Author(s):  
Natália Costa ◽  
César Silva ◽  
Paulo Ferreira
Keyword(s):  
Time Scales ◽  
Cross Correlation ◽  
Data Availability ◽  
Fluctuation Analysis ◽  
Financial Assets ◽  
Sliding Windows ◽  
Cross Correlation Analysis ◽  
Short Time ◽  
Detrended Fluctuation ◽  
Great Development

In recent years, increasing attention has been devoted to cryptocurrencies, owing to their great development and valorization. In this study, we propose to analyse four of the major cryptocurrencies, based on their market capitalization and data availability: Bitcoin, Ethereum, Ripple, and Litecoin. We apply detrended fluctuation analysis (the regular one and with a sliding windows approach) and detrended cross-correlation analysis and the respective correlation coefficient. We find that Bitcoin and Ripple seem to behave as efficient financial assets, while Ethereum and Litecoin present some evidence of persistence. When correlating Bitcoin with the other cryptocurrencies under analysis, we find that for short time scales, all the cryptocurrencies have statistically significant correlations with Bitcoin, although Ripple has the highest correlations. For higher time scales, Ripple is the only cryptocurrency with significant correlation.

Dynamic Singularity Spectrum Distribution of Sea Clutter

2014 ◽  
Vol 14 (01) ◽  
pp. 1550004 ◽  
Author(s):  
Gang Xiong ◽  
Wenxian Yu ◽  
Shuning Zhang
Keyword(s):  
Signal Processing ◽  
Multifractal Spectrum ◽  
Singularity Analysis ◽  
Radar Signal ◽  
Time Varying ◽  
Singularity Spectrum ◽  
Sea Clutter ◽  
Multifractal Theory ◽  
Spectrum Distribution ◽  
Target Detecting

The fractal and multifractal theory have provided new approaches for radar signal processing and target-detecting under the background of ocean. However, the related research mainly focuses on fractal dimension or multifractal spectrum (MFS) of sea clutter. In this paper, a new dynamic singularity analysis method of sea clutter using MFS distribution is developed, based on moving detrending analysis (DMA-MFSD). Theoretically, we introduce the time information by using cyclic auto-correlation of sea clutter. For transient correlation series, the instantaneous singularity spectrum based on multifractal detrending moving analysis (MF-DMA) algorithm is calculated, and the dynamic singularity spectrum distribution of sea clutter is acquired. In addition, we analyze the time-varying singularity exponent ranges and maximum position function in DMA-MFSD of sea clutter. For the real sea clutter data, we analyze the dynamic singularity spectrum distribution of real sea clutter in level III sea state, and conclude that the radar sea clutter has the non-stationary and time-varying scale characteristic and represents the time-varying singularity spectrum distribution based on the proposed DMA-MFSD method. The DMA-MFSD will also provide reference for nonlinear dynamics and multifractal signal processing.

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