Order Statistics CFAR Research Articles

Distributed Fuzzy CFAR Detection for Weibull Clutter

In Distributed detection systems, restricting the output of the local decision to one bit certainly implies a substantial information loss. In this paper, we consider the fuzzy detection, which uses a function called membership function for mapping the observation space of each local detector to a value between 0 and 1, indicating the degree of assurance about presence or absence of a signal. In this case, we examine the problem of distributed Maximum Likelihood (ML) and Order Statistic (OS) constant false alarm rate (CFAR) detections using fuzzy fusion rules such as “Algebraic Product” (AP), “Algebraic Sum” (AS), “Union” (Un) and “Intersection” (IS) in the fusion centre. For the Weibull clutter, the expression of the membership function based on the ML or OS CFAR processors in the local detectors is also obtained. For comparison, we consider a binary distributed detector, which uses the Maximum Likelihood and Algebraic Product (MLAP) or Order Statistic and Algebraic Product (OSAP) CFAR processors as the local detectors. In homogenous and non homogenous situations, multiple targets or clutter edge, the performances of the fuzzy and binary distributed detectors are analyzed and compared. The simulation results indicate the superior and robust performance of the distributed systems using fuzzy detection in the homogenous and non homogenous situations.

Network Intrusion Detection Using CFAR Abrupt-Change Detectors

In this paper, the constant false alarm rate (CFAR) detectors are proposed for network intrusion detection. By using an autoregressive system to model the network traffic, predictor error is shown to closely follow a Gaussian distribution. CFAR detector approaches are then developed on the prediction error distribution. In the present study, we consider the optimal CFAR, the cell-averaging CFAR, and the order statistics CFAR. The use of these CFAR techniques can significantly improve the detection performance. In addition, we propose the use of fusion of these CFAR detectors by using Dempster-Shafer and Bayesian techniques. Computer simulations based on the DARPA traffic data show that the proposed approach achieves higher detection probabilities than the conventional detection method. Even under different types of attacks, the intrusion detection performances based on the proposed CFAR detectors shows consistent improvement.

Weighted order statistic and fuzzy rules CFAR detector for Weibull clutter

Order statistic (OS) CFAR processor is a powerful detector, but similar to many other CFAR detectors, suffers from clutter edge as well as interfering targets. To overcome these problems, two derivations of this detector have been developed. These are order statistic greatest of (OSGO) and order statistic smallest of (OSSO) CFAR processors. The cost, paid for this improvement, is a considerable decrease in detection probability for homogenous Weibull clutter. Furthermore, a substantial performance degradation of OSGO in interfering target (high target masking effect) and an excessive false alarm of OSSO in clutter edge, also, occur. This behavior is a result of non-soft rules used in these two detectors. This paper proposes a weighted order statistic and fuzzy rules-CFAR detector, which employs some soft rules based on fuzzy logic to cure the mentioned problems. Our simulation results demonstrate that considering realistic Weibull clutter, the proposed detector gives better detection probability than that of OSGO and OSSO detectors. Moreover, considering the problems of clutter edge and interfering target, the performance of the method is comparable to the best performance of the OSGO and OSSO detectors in different conditions.

Threshold optimization of decentralized CFAR detection in weibull clutter using genetic algorithms

The use of genetic algorithms (GAs) tool for the solution of distributed constant false alarm rate (CFAR) detection for Weibull clutter statistics is considered. An approximate expression of the probability of detection (PD) of the ordered statistics CFAR (OS-CFAR) detector in Weibull clutter is derived. Optimal threshold values of distributed maximum likelihood CFAR (ML-CFAR) detectors and distributed OS-CFAR detectors with a known shape parameter of the background statistics are obtained using GA tool. For the distributed ML-CFAR detection, we consider also the case when the shape parameter is unknown of the Weibull distribution. A performance assessment is carried out, and the results are compared and given as a function of the shape parameter and of system parameters.

APPLICATION OF DISTRIBUTED DETECTION METHOD FOR GROUND MOVING TARGETS IN SENSOR NETWORKS

This paper considers the problem of detecting ground moving targets in a wireless sensor network for military surveillance application. The sensor nodes are severely constrained in both power and computational performance, and the battle field environments are commonly very complicated. A modified order statistic constant false alarm rate (OS-CFAR) detection algorithm and its distributed detection algorithm were chosen to be implemented on sensor nodes. The algorithm includes background estimate and adaptive threshold. The experimental results with real acoustic and seismic data indicate that the OS-CFAR is robust and flexible and distributed algorithm can improve the detection performance somewhat.

Performance analysis of order-statistic CFAR detectors in time diversity systems for partially correlated chi-square targets and multiple target situations: A comparison

In radar systems, detection performance is always related to target models and background environments. In “time diversity systems”, the assumed Swerling complete correlation (slow fluctuation) and complete decorrelation (fast fluctuation) target models may not predict the actual system performance when the target returns are partially correlated. The probability of detection is shown to be sensitive to the degree of correlation among the received pulses. In this paper, we derive exact expressions for the probability of false alarm ( P fa ) and the probability of detection ( P d ) of a pulse-to-pulse partially correlated target with 2 K degrees of freedom in a pulse-to-pulse completely decorrelated thermal noise for the order statistics constant false alarm rate (OS-CFAR) detector and the censored mean level CFAR (CMLD-CFAR). The complete analysis is carried out for the “non-conventional time diversity system” (NCTDS) and multiple target situations. The obtained results are compared with the detection performance of the “conventional time diversity system” (CTDS).

Threshold optimization algorithm for weak signal in distributed-sensor fusion system

Distributed order statistics constant false alarm rate (OS-CFAR) detection techniques are important for nonstationary observation with varying weak narrowband random signals. However, it is very difficult to choose system parameters to obtain optimal threshold values at the fusion center because of the nonlinear property of distributed OS-CFAR detection system. This paper provides a novel solution based on an effective and flexible genetic algorithm. Using this approach, all system parameters are directly coded in decimal chromosomes and they can be optimized simultaneously. Furthermore, we also derive the more general model by implementing the K fusion rules. The simulation results show that applying the proposed approach one can achieve comparable performances with the reported methods and results.

Three types of distributed CFAR detection based on local test statistic

Three types of distributed constant false-alarm rate (CFAR) detection based on local test statistic (LTS) are developed under the condition that all the samples in different sensors are independent and identically distributed (IID). They are called R (ratio), S (substract) and P (plus) types. For a two-sensor network and local order statistics CFAR (OS-CFAR) algorithm, we derive their closed-form expressions for false alarm and detection probabilities of detecting a Swerling II target in Gaussian noise. The numerical results show that /spl rho/, the ratio between the noise power levels in two local sensors, has very strong effects on the performances of the S and P type schemes and the centralized detection. They can't hold to be CFAR when there isn't the precise prior knowledge of /spl rho/. Compared with the centralized detection, the distributed detection scheme is more robust for the effect of /spl rho/. Fortunately, the R type scheme is not affected by the /spl rho/ at all. It implies that the local CFAR processing can immunize the distributed detection against the /spl rho/.

Detection performance of CFAR detectors based on order statistics for partially correlated chi-square targets

The order statistics cell averaging (OSCA) constant false alarm rate (CFAR) and the order statistics greatest of (OSGO) CFAR detectors have the advantages of the order statistics (OS) CFAR detector, while the processing time of the OSCA and the OSGO CFAR detectors is less than that of the OS CFAR detector. This paper describes the exact formulas of the false alarm and the detection probabilities of CFAR detectors based on OS employing M-pulse noncoherent integration for partially correlated chi-square targets with two and four degrees of freedom.

Detection analysis of linearly combined order statistic CFAR algorithms in nonhomogeneous background environments

Automatic detection radars require some technique of adaptation against variations in the background clutter in order to control their false alarm rate. Recent interest has focused on order statistic based algorithms where they are quite robust against both interference and clutter edges. The primary purpose of this paper is to analyze the performance of a CFAR procedure that uses a linear combination of order statistics (LCOS) as a test statistic for its noise power level estimation. This processor is more general than the trimmed mean scheme. The LCOS-CFAR algorithm reduces to the cell-averaging (CA), order statistic (OS), censored cell averaging (CCA), censored mean level (CML) and trimmed mean (TM) CFAR algorithms for specific parameter values. The performance of the proposed detector is evaluated in the case where the reference sample set contains abrupt change in clutter power distribution amongst its elements and when the content of the sample set is contaminated with returns from the interferers. Besides providing a complete detection analysis for single pulse detection, this paper extends the single pulse analysis to the LCOS-CFAR processor with noncoherent integration of M-pulses when the background environments are nonhomogeneous. The primary and the secondary extraneous targets are assumed to be fluctuated in accordance with the Swerling II target model and closed-form expressions for the false alarm and detection probabilities are derived for the two cases.

Performance of cell-averaging and order-statistic CFAR detectors processing correlated sweeps for multiple interfering targets

The performances of the cell-averaging (CA) and order-statistic (OS) CFAR detectors processing M correlated sweeps are analysed for the case where one or more interfering target returns are present in the set of reference cells used in estimating the clutter-plus-noise level. Exact expressions are derived for the detection probabilities of these schemes under Rayleigh fluctuating target model. The OS-CFAR performance for that case gives an integral equation which is evaluated numerically. Performances when sweeps are independent can be obtained easily as a special case.

Data quantization effects in CFAR signal detection

In this paper, we investigate data quantization effects in constant false alarm rate (CFAR) signal detection. Exponential distribution for the input data and uniform quantization are assumed for the CFAR detector analysis. Such assumptions are valid in the case of radar for a Swerling I target in Gaussian clutter plus noise and a receiver with analog square-law detection followed by analog-to-digital (A/D) conversion. False alarm and detection probabilities of the cell averaging (CA) and order statistic (OS) CFAR detectors operating on quantized observations are analytically determined. In homogeneous backgrounds with 15 dB clutter power fluctuations, we show analytically that a 12-bit uniform quantizer is sufficient to achieve false alarm rate invariance. Detector performance characteristics in nonhomogeneous backgrounds, due to regions of clutter power transitions and multiple interfering targets, are also presented and detailed comparisons are given.

Detection analysis of a generalized order statistics CFAR detector for a correlated Rayleigh target

We analyze the performance of the generalized order statistics constant false alarm rate detector for a correlated Rayleigh target model. Detection probability is computed by contour integration. It is shown that the resulting detection performance depends on the degree of correlation. The more the correlation, the poorer the detection probability becomes.

Performance analysis of linearly combined order statistic CFAR detectors

Linearly combined order statistic (LCOS) constant false-alarm rate (CFAR) detectors are examined for efficient and robust threshold estimation applied to exponentially distributed background observations for improved detection. Two optimization philosophies have been employed to determine the weighting coefficients of the order statistics. The first method optimizes the coefficients to obtain efficient estimates of clutter referred to the censored maximum likelihood (CML) and best linear unbiased (BLU) CFAR detectors. The second optimization involves maximizing the probability of detection under Swerling II targets and is referred to as the most powerful linear (MPL) CFAR detector. The BLU-CFAR detector assumes no knowledge of the target distribution in contrast to the MPL-CFAR detector which requires partial knowledge of the target distribution. The design of these CFAR detectors and the probability of detection performance are mathematically analyzed for background observations having homogeneous and heterogeneous distributions wherein the trade-offs between robustness and detection performance are illustrated. >

Performance analysis of modified ordered-statistics CFAR processors in nonhomogeneous environments

Order-statistics (OS) is a constant false alarm rate (CFAR) technique which is relatively immune to the presence of interfering targets among the reference cells used to determine the average background level. Unfortunately, the large processing time required by this technique limits its practical use. Two modified versions of this processor, namely ordered-statistics greatest-of (OSGO) and ordered-statistics smallest-of (OSSO), are proposed. These versions require less processing time than OS technique. The purpose of this paper is to provide a complete detection analysis for these processors in nonhomogeneous background noise under chi-square target fluctuation model. Analytical results of performance are presented for OS-CFAR procedures in both multiple target environments with one or more interfering targets and in regions of clutter transitions. The OSGO detector has a better performance in homogeneous background and it accommodates interfering targets in the reference window. In addition, it controls the rate of false alarm in the presence of clutter edges.

Detection performance of the trimmed-mean CFAR processor with noncoherent integration

The ordered-statistic constant false alarm rate (OS-CFAR) detector has some advantages over the cell-averaging (CA) CFAR scheme, especially in cases where more than one target is present within the reference window or where this reference window is crossing clutter edges. The trimmed-mean (TM) CFAR processor is a more generalised OS-CFAR scheme which combines ordering and arithmetic averaging. The author analyses the detection performance of the TM-CFAR scheme when noncoherent integration is used under the chi-square target fluctuation model. For specific values of the trimming parameters, the performance of the TM-CFAR processor reduces to that of the CA-CFAR and OS-CFAR schemes. Results are depicted for the Swerling case II target model and for a homogeneous environment. As the number of noncoherently integrated pulses increases, lower threshold values and better performances are obtained for the three schemes considered.

Performance of two generalized order statistics CFAR detectors with automatic censoring technique in multiple target situations

This paper presents two generalized modified OS-CFAR detectors and an automatic censoring technique. For these two new OS-CFAR detectors, analytic expressions of the false alarm rate, the detection probabilities and the measure of ADT under the Swerling 2 assumption are obtained. Their detection performances are analyzed in homogeneous background and in the presence of strong interfering targets, and they are compared with several previously proposed CFARs.

A New Formula to Predict the Exact Detection Probability of a Generalized Order Statistics CFAR Detector for a Correlated Rayleigh Target

In this paper we present a new formula which can predict the exact detection probability of a generalized order statistics (GOS) constant false alarm rate (CFAR) detector for a partially correlated Rayleigh target model (0 < ρ < 1) in a closed form, where ρ is the correlation coefficient between returned pulses. By simply substituting a set of specific coefficient into the derived formula, one can obtain the detection probability of any kind of CFAR detector. Detectors may include the order statistics CFAR detector, the censored mean level detector, and the trimmed mean CFAR detector, but are not necessarily restricted to them. The numerical result for the first order Markov correlation model as applied to some of the detectors shows that as p increases from zero to one, higher signal-to-noise ratio is required to achieve the same detection probability.

Analysis of the Generalized Order Statistics Constant False Alarm Rate Detector

In this paper, we present an architecture of the constant false alarm rate (CFAR) detector called the generalized order statistics (GOS) CFAR detector, which covers various order statistics (OS) and cell-averaging (CA) CFAR detectors as special cases. For the proposed GOS CFAR detector, we obtain unified formulas for the false alarm and detection probabilities. By properly choosing coefficients of the GOS CFAR detector, one can utilize any combination of ordered samples to estimate the background noise level. Thus, if we use a reference window of size N, we can realize kinds of CFAR processors and obtain their performances from the unified formulas. Some examples are the CA, the OS, the censored mean level, and the trimmed mean CFAR detectors. As an application of the GOS CFAR detector to multiple target detection, we propose an algorithm called the adaptive mean level detector, which censors adaptively the interfering target returns in a reference window.

Ll-CFAR: a flexible and robust alternative

A new family of constant false alarm rate (CFAR) processors is introduced. An Ll-CFAR forms its noise power estimate by linearly filtering ranked samples from the reference set; the weights of this combination, however, depend not only on the rank, but also on the relative proximity of the sample to the cell under test. From the class of Ll-CFARs may be chosen members which effectively censor spurious targets; members which exhibit impressive control of false alarm in the presence of a clutter edge; and members which are robust against both such inhomogeneities. While the design of such schemes is involved, their implementation is not significantly more burdensome than that of plain ordered statistic CFAR (OS-CFAR). After a discussion of the stochastic training of Ll-CFAR, the performance is thoroughly assessed under the most commonly encountered instances of environmental conditions, and compared with those of classical CFAR techniques. >