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CFAR detection of weak target in clutter using chaos synchronization
Abstract
In this paper, a novel constant false alarm rate (CFAR) approach for detecting weak targets in sea clutter spectrum based on chaos synchronization is proposed. The weak target signal is detected when the synchronization between two identical chaotic systems is realized, even if the target spectrum lies inside the clutter spectrum. The threshold for the proposed CFAR detection is derived theoretically. The proposed chaos-synchronization-based CFAR technique is shown to be able to enhance the detectability of the target when the signal-to-clutter ratio and signal-to-noise ratio are low. Numerical experiments based on real radar sea clutter data confirm the effectiveness of the proposed chaos-synchronization-based CFAR detection method. The performance is superior to those of the standard autoregressive estimation-based and the cell-averaging CFAR detectors. Copyright © 2007 John Wiley & Sons, Ltd.
... Here, we also compare the proposed method with the traditional non-fractal CFAR-based detection methods, including the cellaveraging CFAR (CA-CFAR) [36] detection, the memory-based predictor (MBP) detection [37], and chaos-synchronisation-based CFAR (CS-CFAR) [36] in Table 2. From the table, it is observed that the detection probabilities of our method are higher than those of QMSPF, WL, CA-CFAR, MBP, and CS-CFAR detector at given false probability. In this paper, we propose a novel radar target detection method based on the CSPS distribution. ...
... Here, we also compare the proposed method with the traditional non-fractal CFAR-based detection methods, including the cellaveraging CFAR (CA-CFAR) [36] detection, the memory-based predictor (MBP) detection [37], and chaos-synchronisation-based CFAR (CS-CFAR) [36] in Table 2. From the table, it is observed that the detection probabilities of our method are higher than those of QMSPF, WL, CA-CFAR, MBP, and CS-CFAR detector at given false probability. In this paper, we propose a novel radar target detection method based on the CSPS distribution. ...
Recently, radar target detection based on fractal theory has received great attention. Especially in the sea clutter background, fractal modelling, fractal dimension, and multifractal spectrum are widely used in radar signal processing. Here, a novel target detection method based on cross-correlation singularity power spectrum (CSPS) is proposed. Firstly, the CSPS theory and algorithm is derived based on SPS; secondly, based on the SPS and CSPS analysis of radar sea clutter, radar target detection parameters are designed, and the detection flow and algorithm based on the CSPS method is presented in detail. The proposed methodology is tested on sea clutter, both with and without targets, from the Ice Multi-parameter Imaging X-Band radar data set. The simulation results indicate that the proposed method performs better than the conventional multifractal-based methods and traditional CFAR methods, and the detection probability of detecting low-observable targets within sea clutters is close to 100%.
... Recently, an increasing interest has been devoted to the study of complex networks, see [1][2][3][4][5][6], which can be regarded as a composition and interaction of several dynamical nodes. Among them, identical synchronization of coupled complex networks has attracted more attention, since synchronization can not only explain many natural phenomena [7], but also have many applications, such as neural networks, image processing, secure communication, etc., see [8][9][10][11][12][13][14]. ...
... NA C = UA C and NX = UX (13) then by the QUAD inequality (10), we havē ...
In this paper, new schemes to synchronize linearly or nonlinearly coupled chaotic systems with an adaptive coupling strength are proposed. Unlike other adaptive schemes, which synchronize coupled chaotic systems to a special trajectory ( or an equilibrium point) of the uncoupled node by adding negative feedbacks adaptively; here, adaptive schemes for the coupling strength are used to synchronize coupled chaotic systems without knowing the synchronization trajectory. Moreover, in many applications, the state variables are not observable; instead, some function s of the states can be observed. How to synchronize coupled systems with the observed data is of great significance. In this paper, synchronization of nonlinearly coupled chaotic systems with an adaptive coupling strength is also discussed. The validity of those s chemes are proved rigor- ously. Moreover, simulations show that by choosing some proper parameter �, the coupling strength obtained by adaptation could be much smaller. It means that chaos oscillators can be easily synchronized with a very weak coupling.
... Recently, an increasing interest has been devoted to the study of complex networks, see [1][2][3][4][5][6], which can be regarded as a composition and interaction of several dynamical nodes. Among them, identical synchronization of coupled complex networks has attracted more attention, since 632 X. LIU AND T. CHEN synchronization can not only explain many natural phenomena [7], but also have many applications, such as neural networks, image processing, secure communication, etc., see [8][9][10][11][12][13][14]. ...
... NA C = UA C and NX = UX (13) then by the QUAD inequality (10), we havē ...
In this paper, a new scheme to synchronize linearly or nonlinearly coupled identical circuit systems, which include neural networks and other systems, with an adaptive coupling strength is proposed. Unlike other adaptive schemes that synchronize coupled circuit systems to a specified trajectory (or an equilibrium point) of the uncoupled node by adding negative feedbacks adaptively, here the new adaptive scheme for the coupling strength is used to synchronize coupled systems without knowing the final synchronization trajectory. Moreover, the adaptive scheme is applicable when the coupling matrix is unknown or time-varying. The validity of the new adaptive scheme is also proved rigorously. Finally, several numerical simulations to synchronize coupled neural networks, Chua's circuits and Lorenz systems, are also given to show the effectiveness of the theory. Copyright © 2009 John Wiley & Sons, Ltd.
The cross correlation power spectrum of multiple signal sequences in the singularity domain is studied in this paper. With theoretical derivation and quantitative analysis, the cross correlation singularity power spectrum (CSPS) distribution theory is proposed. Developed from correlation function (CF), spectrum CF (SCF), singularity power spectrum (SPS), and multifractal cross correlation analysis, the CSPS can be applied for the correlation analysis of multiple fractal time series. In this paper, the CSPS is rigorously derived based on SPS and SCF, and is verified with classical multifractal time series. Furthermore, a target detection method based on the proposed CSPS method is also proposed. The proposed methodology is tested on sea clutters, both with and without target, from the Ice Multiparameter Imaging X-Band radar data set. The simulation results indicate that the target detection based on CSPS performs better than conventional multifractal spectrum methods, and can achieve almost 100% detection probability of detecting low-observable targets within sea clutters.
Based on the chaos forecasting model, a dissipative coupling detection method is proposed for detecting weak signal in chaotic background. The Radial Basis Function Neural Network (RBFNN) is applied to fit the chaos forecasting model. The synchronization between chaotic time series and chaos system is realized by combination of RBFNN and dissipative coupling. Then the synchronization error is used to detect the weak signal. The Rossler chaos system is taken as the object to test the feasibility of the proposed method and analyze its performance with weak signals of different frequencies. In order to avoid the mixed impact of noise and chaos time series to the performance of the method, the interference of noise intensity on weak signal detection is investigated in depth. Simulation results show that the proposed method can detect weak signal with different frequencies; under certain conditions, the method can detect weak periodic signal if the Signal-to-Clutter Ratio is bigger than -110 dB. The noise influence on the detection performance can be ignored if the Signal-to-Noise Ratio (SNR) ≥0 dB. On the basis of theoretical study, a new type chaotic evolution control experiment instrument MKS-CEC-III is applied to produce practical Coullet chaotic time series and add weak signals with different frequencies into time series respectively. This method is used to detect the weak signal from the mixed signal. It is demonstrated that the method can detect added frequency signal from chaotic background and it can also be applied to other chaotic systems.
This paper further investigates some novel methods for generating complex grid multi-wing hyperchaotic attractors from four-dimensional (4D) quadratic hyperchaotic systems, based on our previous works. First, a modified double-wing hyperchaotic Lü system by using non-uniform variable scaling transformation is obtained, and n-wing hyperchaotic system equipped with a duality-symmetric multi-segment quadratic function is also constructed. Then, by switching control in the z direction, mirror symmetry conversion and rotation transformation, three classes of n × m-wing hyperchaotic systems are respectively realized. Finally, two types of improved module-based circuits are designed for generating various grid multi-wing hyperchaotic attractors. One characteristic of the proposed approaches lies in their generality, which is also suitable for constructing 4D grid multi-wing hyperchaotic Lorenz and Chen systems. Both numerical simulation and circuit implementation have demonstrated the feasibility and effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.
In this paper, a chaos-based communication system in the presence of unknown transmission delay is studied. First, under master/slave configurations, two chaotic Chen systems as the slaves are synchronized with a master one via unidirectional coupling. Then at the transmitter, information of an image is embedded within a slave-one signal and the resultant signal along with another one which is used to determine the transmission delay is transmitted to the receiver. At the receiver, using the received signals and the slave-two counterpart signal, the image is recovered. The performance of the proposed method is experimentally illustrated. Copyright © 2009 John Wiley & Sons, Ltd.
In this paper, an adaptive controller for the synchronization of two generalized Lorenz hyperchaos systems (GLHSs) is designed by using the Lyapunov method. In the synchronization schema, the parameters of the drive system are unknown and different from those of the response system. By introducing update laws for both the control coefficients and the parameters of the response system, the adaptive controller proposed in this paper is brand new compared with the former relative works. The proposed adaptive controller is feasible for any possible parameters of GLHS. Numerical simulation is carried out to verify and illustrate the analytical result. Copyright © 2008 John Wiley & Sons, Ltd.
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
In this work, a methodology is established to design optimum chip pulse shapes which are absolutely
bandlimited, their energy mainly concentrated in the chip duration, and which minimize the variance
of the time-delay estimation error of an unbiased estimator. The low-complexity optimization method is
based on the prolate spheroidal wave functions. Thus, the variational problem at hand can be transformed
into a tractable parametric optimization problem. It is shown that the designed optimum chip pulse shapes
significantly improve the synchronization performance of direct sequence code-division multiple access
systems by minimizing the Cramer–Rao lower bound (CRLB). The time-delay estimation bias under the
presence of multipath is compared with the conventionally used bandlimited rectangular chip pulse shape.
We present a novel idea to recover synchronization using the genetic algorithm after a chaotic wave passes through an imperfect channel with constant attenuation and offset. The compensation block, which is added before the receiver, is used to compensate the distortion of the imperfect channel. A new concept, the synchronization mismatch is defined and used as the cost function in the genetic algorithm to design the compensation block. The validity of this approach is suggested by numerical simulations.
A circuit implementation of the chaotic Lorenz system is
described. The chaotic behavior of the circuit closely matches the
results predicted by numerical experiments. Using the concept of
synchronized chaotic systems (SCS's), two possible approaches to secure
communications are demonstrated with the Lorenz circuit implemented in
both the transmitter and receiver. In the first approach, a chaotic
masking signal is added at the transmitter to the message, and at the
receiver, the masking is regenerated and subtracted from the received
signal. The second approach utilizes modulation of the coefficients of
the chaotic system in the transmitter and corresponding detection of
synchronization error in the receiver to transmit binary-valued bit
streams. The use of SCS's for communications relies on the robustness of
the synchronization to perturbations in the drive signal. As a step
toward further understanding the inherent robustness, we establish an
analogy between synchronization in chaotic systems, nonlinear observers
for deterministic systems, and state estimation in probabilistic
systems. This analogy exists because SCS's can be viewed as performing
the role of a nonlinear state space observer. To calibrate the
robustness of the Lorenz SCS as a nonlinear state estimator, we compare
the performance of the Lorenz SCS to an extended Kalman filter for
providing state estimates when the measurement consists of a single
noisy transmitter component
Iterative methods to solve a linear equation system can be used to derive multistage interference cancellers (ICs) that converge to the decorrelating or the minimum mean-square error linear detectors. The link between linear multistage IC and iterative solution methods is well known; however, the parameters needed for fastest convergence are functions of the eigenvalues of the channel matrix. In this letter, we propose new methods for finding optimal parameters without eigendecomposition.
This book is downloadable from http://www.irisa.fr/sisthem/kniga/. Many monitoring problems can be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. The main goal of this book is to describe a unified framework for the design and the performance analysis of the algorithms for solving these change detection problems. Also the book contains the key mathematical background necessary for this purpose. Finally links with the analytical redundancy approach to fault detection in linear systems are established. We call abrupt change any change in the parameters of the system that occurs either instantaneously or at least very fast with respect to the sampling period of the measurements. Abrupt changes by no means refer to changes with large magnitude; on the contrary, in most applications the main problem is to detect small changes. Moreover, in some applications, the early warning of small - and not necessarily fast - changes is of crucial interest in order to avoid the economic or even catastrophic consequences that can result from an accumulation of such small changes. For example, small faults arising in the sensors of a navigation system can result, through the underlying integration, in serious errors in the estimated position of the plane. Another example is the early warning of small deviations from the normal operating conditions of an industrial process. The early detection of slight changes in the state of the process allows to plan in a more adequate manner the periods during which the process should be inspected and possibly repaired, and thus to reduce the exploitation costs.
The analog simulation of nonlinear dynamical systems is advantageous in some cases, i.e., when compared with the study using digital computers, and in particular when one wishes to investigate the role of noise in these systems. In the present work we introduce two di#erent methods of introducing a noise component in the most widely used chaotic circuit, namely, Chua's circuit, and apply these methods to study the e#ect of noise on identically driven chaotic circuits. I. Introduction The study of the behavior of nonlinear dynamical systems under the influence of noise is usually a di#cult task [1]. Normally one performs this type of studies through digital simulation. However, noise usually interacts with numerical methods in a complicated manner, often posing a di#cult challenge in the study of these stochastic di#erential equations [2], while the generation of high-quality random numbers in digital devices may prove di#cult [3]. One conclusion is that the results of these stud...
This Technical Note describes the Osborne Head database, collected at Osborne Head Gunnery Range, OHGR, in November 1993, with the McMaster University IPIX radar, under contract to DSS. Representative examples are worked out for the different operational modes of the radar (staring, scanning, alternate/single polarization, single/multi frequency). Strengths and weaknesses of the database are pointed out as well. The purpose of this Technical Note is to serve as a guide to the database, presenting enough information to allow the extraction of individual datasets from the raw data. These can subsequently be used for sea clutter, target model validation and/or testing of signal processing techniques, leading to enhanced target detection in sea clutter.
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
The research on the sufficient criterion for chaos synchronization of the master–slave Chua's circuits by linear state error feedback control has received much attention and some synchronization criteria for special control matrix were proposed. In this paper, the above synchronization issue is investigated in the situation of general linear state error feedback controller with propagation delay of control signals from the master Chua's circuit. First of all, a master–slave synchronization scheme for Chua's circuits with propagation delay is given and the relevant error system is derived. Using a quadratic Lyapunov function and frequency domain method, three new algebraic synchronization criteria for the synchronization scheme with general control matrix are proven. They are applied to derive the synchronization criteria for simple control matrices. Some examples are given to show the sharpness of these new criteria compared with the known criteria. Copyright © 2006 John Wiley & Sons, Ltd.
In this paper we present our work analysing electroencephalographic (EEG) signals for the detection of seizure precursors in epilepsy. Volterra systems and Cellular Nonlinear Networks are considered for a multidimensional signal analysis which is called the feature extraction problem throughout this contribution. Recent results obtained by applying a pattern detection algorithm and a non-linear prediction of brain electrical activity will be discussed in detail. The aim of this interdisciplinary project is the realization of an implantable seizure warning and preventing system. Copyright © 2006 John Wiley & Sons, Ltd.
In this paper, we present a fast and efficient technique for detecting and identifying the slippage and twisting motion of touching objects. This kind of action cannot be detected with tactile sensors sensing only the normal (perpendicular) component of the forces acting between surfaces. Our approach utilizes an integrated sensing–processing–actuating system comprising: (1) A 2 × 2 taxel (tactile pixel) array mounted on a two-fingered robot hand, (2) a 64 × 64 CNN-UM (Cellular Neural Network-Universal machine), and (3) a closed-loop controller. This arrangement, along with the proper analogic algorithm, allows detection and the control of the tactile event. It is essential to know and comprehend the forces between contact surfaces and the related 3D pressure fields is essential in many robotic applications discussed in the paper. Copyright © 2006 John Wiley & Sons, Ltd.
In this paper we show that, similar to the nervous system and the genetic system, the immune system provides a prototype for a ‘computing mechanism.’ We are presenting an immune response inspired algorithmic framework for spatial–temporal target detection applications using CNN technology (IEEE Trans. Circuits Syst. II 1993; 40(3):163–173; Foundations and Applications. Cambridge University Press: Cambridge, 2002). Unlike most analogic CNN algorithms (IEEE Trans. Circuits Syst. 1988; 35(10):1257–1290; Foundations and Applications. Cambridge University Press: Cambridge, 2002) here we will detect various targets by using a plethora of templates. These algorithms can be implemented successfully only by using a computer upon which thousands of elementary, fully parallel spatial–temporal actions can be implemented in real time. In our tests the results show a statistically complete success rate, and we are presenting a special example of recognizing dynamic objects. Results from tests in a 3D virtual world with different terrain textures are also reported to demonstrate that the system can detect unknown patterns and dynamical changes in image sequences. Applications of the system include in explorer systems for terrain surveillance. Copyright © 2006 John Wiley & Sons, Ltd.
The authors briefly review the use of a random process and a
dynamical system as mathematical models in the context of radar clutter.
Experimental results are summarized for the correlation dimension of sea
clutter, which provides an appropriate estimate for the embedding
dimension of the process. The authors use the embedding dimension of sea
clutter so estimated as a parameter in the design of a radial basis
function (RBF) network for model reconstruction; here again experimental
data are presented to support the theory
A scheme of chaotic synchronization based of transmission of information about the state of drive system to driven system wit use of symbolic dynamics formalism is presented. It is shown that the volume of transmitted information necessary to synchronize the driven system in such scheme approaches theoretical minimum.
Several time series of wind components and X-band Doppler radar signals, gathered concurrently over a approximately 0.01 km(2) area of the ocean surface, were examined for evidence of a low-dimensional dynamical attractor with the Grassburger-Procaccia algorithm. Only the vertically polarized radar reflectivity and the horizontal surface wind speed time series suggested the presence of such an attractor. The correlation dimension for these two observables appeared to be nearly the same. This suggested a working hypothesis that the dynamical behavior of both the vertically polarized radar reflectivity and the horizontal surface winds are controlled by a single low-dimensional dynamical system. The hypothesis was further examined by predicting winds from radar reflectivity, using a neural network deterministic model, and comparing the prediction performance with that of the SEASAT statistical algorithm for retrieving surface winds from radar backscatter. It was found that the deterministic model did, in fact, achieve a higher prediction correlation coefficient for a limited time period. (c) 1995 American Institute of Physics.
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.
Chaotic synchronization is generally extremely sensitive to the presence of noise and other interference in the channel. Is this sensitivity a fundamental property of chaotic synchronization or is it related to the choice of synchronization method and can it be suppressed by a modification of the method? If the answer is positive, then what are the relationships between the properties of a dynamical system and the level of noise at which the suppression of this sensitivity is still possible? What are particular methods to achieve synchronization stable to the presence of noise? In this paper we present the analysis of this issue from the standpoint of information theory. From this viewpoint the fundamental reason for this sensitivity is the fact that the chaotic signal contains information which requires a certain minimal threshold signal-to-noise ratio for transmission. Only in this case high-quality synchronization is transmitted (coded) optimally. Otherwise the threshold level can be much higher.
In this study, synchronization phenomena in chaotic oscillators
coupled by a transmission line are investigated. In particular
investigation using real circuits is done for the first time. We report
the very interesting results
The application of higher-order statistics (HOS) to the detection
of radar targets takes advantage of HOS characteristics that allow the
formulation of a test statistic that is unbiased by Gaussian noise and
insensitive to constant target velocity. To make use or these
characteristics using data from a coherent radar, the samples from the
radar's synchronous detector are formulated into special fourth-order
products and coherently averaged. A second version of the HOS detector
compensates for constant target acceleration. Comparisons are made
between the two HOS detectors, the pulsed Doppler detector and the
quadratic detector. The comparison shows a one to two dB improvement
using the HOS detectors with Gaussian noise. However, examples are
presented of an accelerating, synthetic target in actual, spiky sea
clutter that show a 2.5 to 11 dB of improvement
A new approach to synchronisation of Chua's circuit is presented.
It effectively combines the interior penalty method of optimisation and
chaotic synchronisation. Even under unfavourable, noisy conditions, the
approach shows attractive lower variance results compared with
conventional chaotic synchronisation in realising the synchronisation of
length-limited noisy chaotic signals
Previous research has claimed that sea clutter is a chaotic
process with a nonlinear predictor function. Indeed, results have been
reported which demonstrate that sea clutter is nonlinearly predictable,
and that this predictability can be exploited, using nonlinear predictor
networks, to improve the performance of maritime surveillance radars.
The aim of the paper is to investigate if nonlinear predictor networks
can be used to improve the performance of maritime surveillance radars,
using sea clutter data sets provided by the Defence Evaluation and
Research Agency (DERA). By presenting prediction results for radial
basis function network predictors, Volterra series filter predictors,
and linear predictors, it is shown that the clutter predictor functions
are well approximated by a linear function, and that nonlinear predictor
networks provide little or no improvement in performance. A novel and
effective training methodology is used for the radial basis function
network predictors
The performance of the likelihood ratio detector (LRD) for
moderately fluctuating targets (i.e. intermediate between Swerling II
and Swerling I models) is evaluated for the case of poor knowledge of
the target characteristics. In particular, the influence of incorrect
assumptions in the design phase about the signal-to-interference ratio
(SIR), the target correlation coefficient, the shape of the target
autocorrelation function, and the target mean Doppler frequency is
analysed by computing the detectability loss due to mismatching between
the design hypothesis and the real target characteristics. It is shown
that the LRD is extremely robust to an inaccurate choice of the design
SIR. The loss due to correlation mismatching depends not only on the
absolute value of the difference between the design value of the
correlation coefficient and the real value, but also on the sign of this
difference, with larger losses occurring when the design value is larger
than the real one. A sensible criterion is given for the choice of the
target correlation coefficient to be used in the design process. Also,
the performance degradation due to Doppler mismatching can be large and
calls therefore for the deployment of a bank of LRDs, each designed for
a different value of the target Doppler frequency. The minimum number of
LRDs needed to maintain acceptable performance under Doppler mismatching
is computed
An analysis of the detection of radar targets in multipath
environments is presented. Radar targets often undergo enhancements or
fades due to multipath where the direct-path energy combines with a
phase-shifted reflection to enhance or reduce the received energy. This
phenomenon is a function of frequency. Radars are often designed to
avoid the problems of fades by changing frequency or using an assortment
of frequencies in an M-out-of-N detector. To understand the detection
statistics and choose M and N, the probability density function (PDF) of
the noise plus the target times the multipath propagation factor must be
known. This PDF is derived for a nonfluctuating target and for a
Rayleigh target. The PDF is used to show the benefits of choosing the
best M for a multipath environment compared to using the M that would be
chosen in a free-space environment
The detection performance of a cell-averaging CFAR detector is
analysed for spatially correlated K-distributed clutter. In thermal
noise or uniform clutter, the performance of the cell-averaging CFAR can
be compared with that of the ideal fixed threshold, but with an
associated `CFAR loss', quantified by the increase in average
signal-to-clutter ratio required to achieve a given probability of
detection and probability of false alarm. In some types of clutter,
knowledge of the overall amplitude distribution alone is not sufficient
to assess the performance of a cell-averaging CFAR. In particular, sea
clutter may exhibit significant spatial correlation, often associated
with the sea swell. In such spatially varying clutter, the
cell-averaging CFAR may be able to follow the local fluctuations, giving
a considerable improvement in performance compared to the `ideal' fixed
threshold. This is quantified as a `CFAR gain' with the limit of such
improvement given by the performance of the `ideal CFAR' detector. The
CFAR gain or loss is illustrated in different clutter conditions for a
range of cell-averager configurations. It is shown that significant CFAR
gain, compared with the commonly accepted CFAR loss, can be achieved in
some circumstances
The detection of targets from a coherent radar scan is examined,
as well as how sophisticated signal processing techniques may be
incorporated into such tasks. Techniques of coherent
constant-false-alarm-rate (CFAR) detection are discussed for this
scanning-mode problem. In an attempt to better utilise the information
present in the scan plane for detection, the use of higher-dimensional
analysis techniques is discussed. The fundamental advantage is their
ability to provide spatial separation (in these higher dimensions) of
signal features, which it is hoped will enhance the detection
performance. A method, employing such techniques, is presented, and
contrasted with traditional CFAR approaches. Some examples are presented
using real data, collected with McMaster University's X-band coherent
radar
The main concern in this brief is how to design a better receiver structure and its synchronization error analysis. By exploiting a skew-symmetric type property existing in generalized Lorenz chaotic systems, we propose a novel receiver design for synchronizing the transmitter-receiver pair. Error analysis carried out by the Lyapunov direct method explicitly shows the relation among the magnitudes of the synchronization error, coupling noise, transmitter parameters, and signals. If no noise or message exists in the coupling channel, then exponential synchronization can be achieved for all state signals. As a guideline from the error analysis, a more suitable receiver can be successfully designed and implemented. Experiments are carried out on the circuit of the transmitter-receiver pair to show the performance of the synchronization and secure communication.
Optimal synchronization of two identical chaotic systems coupled
in a drive/response manner is considered in the paper. We derive a
relationship between the mean square synchronization error and the
coupling parameters in the presence of noise. By minimizing the mean
square synchronization error with respect to the coupling parameters, an
optimal synchronization, which minimizes the synchronization error
between the drive and response systems, can be achieved. It is shown
that the optimal coupling parameters depend on both the global and local
Lyapunov exponents of the chaotic drive system. However, they are
independent of the noise power. We apply this approach to design optimal
synchronization for various chaotic systems. The optimal design is then
applied to chaotic communication and it can recover the information
signal efficiently. Simulations show that our theoretical results are in
good agreement with the numerical analysis
We present a special chaos synchronization system based on coupled
time-delayed feedback optical systems. As far as we know, this paper
reports for the first time simulations of synchronization in such
optical circuits. The unsolved problem of the channel in communication
applications of chaos synchronization for electronic systems make the
optical systems very attractive. The quasi-infinite bandwidth, very low
attenuation and practically noiseless characteristic of single mode
fiber, used as information transmission medium, are the three main
advantages of our system. We show by simulations that synchronization is
effective, use a chaos shift keying modulation/demodulation scheme for
binary information transmission and present some estimation of the bit
rate in a such system
Recently, neural networks have been proposed for radar clutter
modeling because of the inherent nonlinearity of clutter signals. This
paper performs an analysis of the practicality of using a radial basis
function (RBF) neural network to model sea clutter and to detect small
target embedded in sea clutter. An experiment using an instrumental
quality radar was carried out on the eastcoast of Canada to create a
rich sea clutter and small surface target database. This database
contains both staring and scanning data under various environmental
conditions. Using data-sets with different characteristics, we
investigate the effects of quantization error, measurement noise,
generalization of the neural net over ranges and sampling rate on the
RBF clutter model. Despite these physical limitations, the RBF model was
shown to approach an optimal predictive performance. The RBF predictor
was also applied to detect various small targets in this database based
on the constant false alarm rate (CFAR) principle. This RBF-CFAR
detector was demonstrated to be able to detect small floating targets
even in rough sea conditions
It is demonstrated that the random nature of sea clutter may be
explained as a chaotic phenomenon. For different sets of real sea
clutter data, a correlation dimension analysis is used to show that sea
clutter can be embedded in a finite-dimensional space. The result of
correlation dimension analysis is used to construct a neural network
predictor for reconstructing the dynamics of sea clutter. The
deterministic model so obtained is shown to be capable of predicting the
evolution of sea clutter. The predictive analysis is also used to
analyze the dimension of sea clutter. Using the neural network as an
approximation of the underlying dynamics of sea clutter, a dynamic-based
detection technique is introduced and applied to the problem of
detecting growlers (small fragments of icebergs) in sea clutter. The
performance of this method is shown to be superior to that of a
conventional detector for the real data sets used here
Clutter is defined as any unwanted radar return. The presence of clutter in a range/Doppler cell complicates the detection of a target return signal in that cell. In order to quantify the effect of clutter on the probability of detection, we must first specify sets of models suitable for representing the clutter and target. The simplest and most common model for clutter is based on the gamma density. We include two additional models, the NCG and NCGG clutter models for low grazing angles. They are motivated by physical arguments, the latter of which can accommodate the well-known phenomenon of speckle. Using one of these models for clutter together with one of several models for targets, we determine, in a range/Doppler cell, expressions for probabilities of detection of a target in the presence of clutter. It is important to control the probability of false alarms. The presence of clutter in a cell necessitates an increase in the detection threshold setting in order to control false alarms, thus lowering the probability of detection. If the clutter level is unknown, then we need to take measurements of the clutter and use it to adjust the threshold. The more clutter samples we take, the better the estimate of the clutter level and the less is the resulting detection loss. Using the expressions for the probability of detection in clutter, we can quantify the detection loss for a pair of commonly used constant false-alarm rate (CFAR) techniques and investigate how the loss varies with different parameter values, especially with regard to the number of clutter samples taken to estimate the clutter level.
A commonly used density model for radar clutter is chi-square for
power, or, equivalently, Rayleigh for amplitude. However, for many
modern high resolution radar systems, this density underestimates the
tails of the measured clutter density. Log normal and Weibull
distributions have proved to be better suited for the clutter in these
high resolution radars. Generalizing the chi-square density by replacing
it with the noncentral chi-square density and allowing the mean power
level (the noncentrality parameter) to vary, we can both suitably shape
the clutter density to produce larger tails and model the fluctuation of
the average clutter power, commonly referred to as speckle. The
resulting form, although appearing cumbersome, readily allows for
efficient and accurate computations of the probability of detection in
clutter
In a recent paper, general expressions were derived for the density and cumulative probability functions of the amplitude of a linear matched-filter output given a nonfluctuating target in a clutter-limited environment. These expressions were based on the clutter amplitude density function. The results are extended to calculate the cumulative probability function of the output of a linear matched filter used to detect a chi-square fluctuating target in a clutter-limited environment. The resulting method is applied to a common radar clutter model, and experimental sonar data.
Optimal, in the maximum likelihood sense, constant false-alarm rate (CFAR) detection for Weibull clutter statistics, is investigated. The proposed OW (optimal Weibull) estimator is proved to be an asymptotically efficient estimator of the mean power of the Weibull clutter. Theoretical analysis of the OW-CFAR detector is provided, while detection performance analysis is carried out using the Monte Carlo simulation method. The operation of the median and morphological (MEMO)-CFAR detector in Weibull clutter statistics is also explained. It performs almost optimally in uniform clutter and, simultaneously, it is robust in multitarget situations. The performance of the proposed OW-CFAR detector in uniformal Weibull clutter is used as a yardstick in the analysis of the MEMO cell-averager (CA) and ordered statistic (OS) CFAR detectors. Nonfluctuating and fluctuating (Swerling II) targets are considered in detection analysis. The performance of the detectors is also examined at clutter edges.< >
A constant false alarm rate (CFAR) detection method which is based
on a combination of median and morphological filters (MEMO) is proposed.
The MEMO algorithm has robust performance with small CFAR loss, very
good behavior at clutter edges and high detection performance in the
case of closely spaced narrowband signals (targets). The proposed MEMO
method is favourably compared with cell averaging (CA) and ordered
statistics (OS) CFAR detectors. The Monte Carlo method is employed to
analyze the MEMO-CFAR detector
Some moving-target indicator (MTI) techniques are reviewed and
those based on the linear prediction theory are examined. A description
is given of the effects of the position of the reference sample in an
MTI processor on cancelling clutter in a radar system. The analysis of
this generalized linear prediction MTI is based on the evaluation of the
receiving operating characteristics (ROCs), assuming that the clutter
covariance matrix is known a priori as well as the matrix being
estimated on line. It is shown by analytical evaluations and Monte Carlo
simulations, that the performance is generally insensitive to the
position of the reference sample. An additional analysis is carried out
to compare the performance of the generalized linear prediction MTI with
the MTI based on the Hsiao approach. It is seen that with the formation
of the interference of two superimposed clutter sources the generalized
linear prediction MTI suffers, in some cases, several decibels of loss
Probability and Statistics: The Science of Uncertainty
- Evans Mj Js
Evans MJ, Rosenthal JS. Probability and Statistics: The Science of Uncertainty. Freeman: New York, 2003.
Technical Note 94-14 Defense Research Establishment Ottawa Ottawa Ont
- Drosopoulosa
Chaotic synchronization recovery through an imperfect channel
- Yangxm Wutx
On synchronization phenomena in chaotic systems coupled by transmission line
- Ushidaa Kawataj Nishioy