Constant False Alarm Rate Loss Research Articles

G-Wishart Distribution in Multilook Polarimetric Whitening Filter and its Application

The polarimetric whitening filter (PWF) is widely used in constant false alarm rate (CFAR) ship detection in polarimetric synthetic aperture radar (PolSAR) imagery. The detection threshold plays a key role in the CFAR detection, which is generally determined by the statistical model of clutter. Many product models with different distributed textures are considered to fit the PWF output for an accurate threshold. Unfortunately, the product model with the general inverse Gaussian (<i>G</i>) texture, which can be named <i>G</i>-Wishart model according to the polarimetric covariance matrix, has not been well studied for its effective calculation. In this letter, the probability density function (PDF), the probability of false alarm (PFA), and the threshold in the CFAR algorithm based on the PWF are all obtained corresponding to the <i>G</i> distribution. The closed forms for the PDF and PFA are obtained with the Fox H function and its multivariate version, respectively. The threshold is derived by the bisection method when the false alarm rate (FAR) is constant. Finally, experimental results using both simulated and real data demonstrate that the different statistical models with the same log-cumulants can achieve almost the same CFAR loss.

A discriminant analysis-based automatic ordered statistics scheme for radar systems

The ordered statistics (OS) scheme is an effective constant false alarm rate (CFAR) technique deployed in many radar systems. It is widely deployed because of its simplicity and effectiveness under conditions of both homogeneous and non-homogeneous radar returns. However, the problem of inaccurate censoring typically degrades its performance since it is often difficult to accurately determine the actual number of interfering targets and clutter edges in the reference window per time. In this article, we address this problem based on the principle of discriminant analysis (DA) towards automatically and effectively estimating the kth rank ordered element of the OS scheme. Our scheme, termed the DA-OS scheme, works without requiring a priori knowledge about the statistical characteristics of the input radar returns. The results obtained via Monte Carlo simulation indicate that the DA-OS scheme achieves a small CFAR loss of about 0.392 dB relative to the cell averaging (CA) scheme under conditions of homogeneous radar returns at a probability of detection of 0.5. It outperforms other notable traditional schemes, including the CA, smallest-of CA, greatest-of CA, and the fixed OS schemes under conditions of non-homogeneous radar returns. Finally, it provides a number of desirable qualitative characteristics as against other existing censoring techniques.

Robust variability index CFAR for non‐homogeneous background

Radar signal detection using constant false alarm rate (CFAR) detectors encounters many non-ideal situations making it difficult to characterise the background. These include the presence of multiple targets, clutter edges and their combination in the reference window. Designing an efficient CFAR for these situations is a non-trivial problem. Algorithms based on ordered statistics (OS), outlier rejection using sorting and sample by sample hypothesis testing, variability index (VI), ordered data VI are proposed in the literature. These approaches require expensive sorting or prior information on the depth of censoring. In this study, the authors propose robust VI CFAR (RVI-CFAR) that obviates sorting. RVI-CFAR computes the threshold in multiple stages. The first stage uses VI-CFAR to determine an adaptive threshold. Outlier rejection in the computation of background, mean ratio (MR) and VI is carried out in subsequent stages. The updated MR and VI statistics are used to refine switching decisions at every stage of processing. RVI-CFAR exhibits low CFAR loss in homogeneous and multiple target scenarios, meanwhile achieving superior performance compared to other censored CFAR techniques. The proposed RVI-CFAR is evaluated and shown to be robust for all the cases of non-homogeneity compared to OS CFAR.

Modified reference window for two‐dimensional CFAR in radar target detection

The constant false alarm rate (CFAR) technology plays an important role in radar target detection. In cell averaging CFAR detectors, a reference window is usually adopted to estimate the average interference power in the range–Doppler matrix and to obtain the detection threshold, which should be set high enough to limit false alarm rate to a tolerably small rate. The conventional rectangular window, cross window, and column window are investigated in this study, which may suffer from a degraded detection performance due to involving some extraneous reference cells. Therefore, a modified reference window for two-dimensional CFAR is proposed to improve performance, depending on the distribution characteristics of radar targets in range and Doppler dimensions. The experimental results demonstrate its performance advantages on detection probability, CFAR loss, and figure of merit.

Detection Capability and CFAR Loss Under Fluctuating Targets of Different Swerling Model for Various Gamma Parameters in RADAR

Target detection of RADAR deals with different and manifold problems over few decades. The detection capability is one of the most significant factors in RADAR system. The main aim of detection is to increase probability of detection while decreasing rate of false alarm. The threshold of detection is modified as a function of the receiver noise level to keep a fixed rate of false alarm. Constant False Alarm Rate (CFAR) processors are used to maintain the amount of false alarm under supervision in a diverse background of interference. In Signal to Noise Ratio (SNR) level, a loss can be occurred due to CFAR processor. Gamma function is used to determine the probability of false alarm. It is assumed in adaptive CFAR that the interference distribution is familiar here. This type of CFAR also approximates the unknown parameters connected with various interference distributions. CFAR loss depends on gamma function. Incomplete gamma function plays an important role in maintaining threshold voltage as well as probability of detection. Changing the value of gamma function can improve the probability of detection for various Swerling Models which are proposed here. This paper has also proposed a technique to compare various losses due to CFAR in terms of different gamma function in presence of different number of pulses for four Swerling Models.

Clutter map CFAR detector based on maximal resolution cell

In order to improve the detection performance of clutter map constant false alarm rate (CFAR) detectors in multiple persisting targets situation, a clutter map CFAR (CM-CFAR) detector based on the maximal resolution cell (CM/MRC-CFAR) is proposed in this paper. In the CM/MRC-CFAR detector, at each scan, a comparison threshold is computed by multiplying the amplitude of the maximal resolution cell (MRC) in the map cell by a scaling factor. Then, the number of the left resolution cells, whose amplitudes are smaller than the comparison threshold, is counted and compared with a threshold integer. Based on the comparison result, proper resolution cells are selected to update the detection threshold. The detection probability of CM/MRC-CFAR in both homogeneous and multiple persisting targets situations is derived in a closed-form expression. The detection performance of CM/MRC-CFAR is evaluated in various environments and compared with other CM-CFAR detectors. CM/MRC-CFAR exhibits a very low CFAR loss in a homogeneous environment and achieves a robust detection performance in multiple persisting targets situations. Since no ranking is required except searching for the MRC, the computation load of CM/MRC-CFAR is low, and it is easy to implement the detector in radar systems in practice.

Constant false alarm rate detector based on the maximal reference cell

In order to improve the detection performance of constant false alarm rate (CFAR) detectors in multiple targets situations, a CFAR detector based on the maximal reference cell (MRC) named MRC-CFAR is proposed. In MRC-CFAR, a comparison threshold is generated by multiplying the amplitude of MRC by a scaling factor. The number of the reference cells left, whose amplitudes are smaller than the comparison threshold, is counted and compared with a threshold integer. Based on the comparison result, proper reference cells are selected for detection threshold computation. A closed-form analysis for MRC-CFAR in both homogeneous and non-homogeneous environments is presented. The performance of MRC-CFAR is evaluated and compared with other CFAR detectors. MRC-CFAR exhibits a very low CFAR loss in a homogeneous environment and performs robustly during clutter power transitions. In multiple targets situations, MRC-CFAR achieves a much better detection performance than switching CFAR (S-CFAR) and order-statistic CFAR (OS-CFAR). Experiment results from an X-band linear frequency modulated continuous wave radar system are given to demonstrate the efficiency of MRC-CFAR. Because ranking reference cells is not required for MRC-CFAR, the computation load of MRC-CFAR is low; it is easy to implement the detector in radar system in practice.

Automatic dual censoring cell-averaging CFAR detector in non-homogenous environments

Constant false alarm rate (CFAR) detectors are designed to regulate the false alarm rate against the noise and clutter background whose mean power is unknown and (or) varying. This is accomplished using local threshold estimate of the background observations. When background observations contain irrelevant samples, censoring is warranted to improve detection performance and to regulate the false alarm rate. In this paper, a new CFAR detector composed of an automatic dual censoring algorithm and cell-averaging CFAR detector is proposed. This new detector is named automatic dual censoring cell-averaging (ADCCA)-CFAR. The proposed detector does not require any prior knowledge about the background observation. It uses fuzzy membership function to determine and censor the unwanted samples in the reference window. The performance of the proposed detectors is evaluated and compared with those of the cell-averaging (CA), order statistic (OS) and automatic censoring cell-averaging based on ordered data variability (ACCA-OVD) CFAR detectors. The simulation results show that the ADCCA-CFAR detector not only provides low CFAR loss in homogenous background but also performs robustly in the presence of interfering targets and clutter edge situations.

Constant false-alarm rate algorithm based on test cell information

A new constant false-alarm rate (CFAR) detection algorithm, designated as switching CFAR (S-CFAR), is proposed and analysed. The S-CFAR algorithm selects CFAR reference samples using the magnitude of the sample in the cell under test, which is an information that has not been exploited in any other existing CFAR detectors. S-CFAR closed-form analysis is presented, and comparisons with other representative CFAR algorithms are given. An S-CFAR detector can be tuned such that it has a small CFAR loss when operating on a homogeneous background while achieving improved robustness in the presence of interfering targets and clutter power transition. The S-CFAR detector is also simple to design and implement since no sample ordering is required.

Target detection performance of CFAR systems used in an interference environment

When a flying object tracks a target, the location and velocity of the target are estimated based on a target detection process using radar. In general, the constant false alarm rate (CFAR) is used in the target detection process. However, if a high power interference wave is received in addition to the object signal, the target cannot be detected, so that tracking fails. This is caused by an uncontrolled increase in the threshold level at the time of target detection due to the interference component mixed in the reference cells. After the CFAR process, tracking of the target is possible by the use of a tracking filter as long as the existing target signal component is detected, even if the interference wave is evaluated as the target signal component. In this paper, an interference adaptive CFAR is discussed in which the CFAR process is carried out and the interference component mixed in the reference cell is detected and eliminated. The relationship between the threshold coefficient and the false alarm probability and a computation method for the CFAR loss are formulated in this paper. By means of the derived relationships, several case studies are carried out and the nature of the interference adaptive CFAR is discussed. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(10): 29–37, 1997

Target detection performance of CFAR systems used in an interference environment

When a flying object tracks a target, the location and velocity of the target are estimated based on a target detection process using radar. In general, the constant false alarm rate (CFAR) is used in the target detection process. However, if a high power interference wave is received in addition to the object signal, the target cannot be detected, so that tracking fails. This is caused by an uncontrolled increase in the threshold level at the time of target detection due to the interference component mixed in the reference cells. After the CFAR process, tracking of the target is possible by the use of a tracking filter as long as the existing target signal component is detected, even if the interference wave is evaluated as the target signal component. In this paper, an interference adaptive CFAR is discussed in which the CFAR process is carried out and the interference component mixed in the reference cell is detected and eliminated. The relationship between the threshold coefficient and the false alarm probability and a computation method for the CFAR loss are formulated in this paper. By means of the derived relationships, several case studies are carried out and the nature of the interference adaptive CFAR is discussed. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(10): 29–37, 1997

A new and robust CFAR detection algorithm

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance of MAX family of order-statistic CFAR detectors

The MAX family of constant-false-alarm-rate (CFAR) detectors is introduced as a generalization of the greatest of CFAR (GO-CFAR) or MX mean-level detector (MX-MLD). Members of the MAX family use local estimators based on order statistics and generate both a near-range and a far-range noise-level estimate. Local estimates are always combined through a maximum operation; this insures false-alarm control at clutter edges. At the same time, order-statistic-based estimators result in a high-resolution detector. A complete detection analysis is provided for SWII targets and a reference channel contaminated by large outliers. Results are presented for the MX censored MLD (MX-CMLD) operating in clutter. The MX order statistic detector (MX-OSD) based on only a single-order statistic per window, is analyzed, and curves showing the required threshold, CFAR loss, optimum censoring point, and signal-to-noise ratio (SNR) loss in the presence of outliers are given. Simulations are used to compare the dynamic responses of various MX-OSD detectors in a clutter and a multiple-target environment. >

Analysis of some modified ordered statistic CFAR: OSGO and OSSO CFAR

It is necessary for automatic detection radars to be adaptive to variations in background clutter in order to maintain a constant false alarm rate (CFAR). A CFAR based on an ordered statistic technique (OS CFAR) has some advantages over the cell-averaging technique (CA CFAR), especially in clutter edges or multiple target environments; unfortunately the large processing time required by this technique limits its use. The authors present two new OS CFARs that require only ahlf the processing time. One is an ordered statistic greatest of CFAR (OSGO), while the other is an ordered statistic smallest of CFAR (OSSO). The OSGO CFAR has the advantages of the OS CFAR with only a negligible increment to the CFAR loss. >

Ordered Statistic CFAR Processing for Two-Parameter Distributions with Variable Skewness

Rohling has developed a constant false alarm rate (CFAR) technique based on ordered statistics of the reference cells. An extension of his technique is presented that maintains a CFAR for two-parameter distributions, with both mean power and skewness variable. The new method is therefore more robust, but has higher CFAR loss than the single-parameter technique.

Analysis of the Arithmetic Mean CFAR Normalizer for Fluctuating Targets

The analysis of the arithmetic mean constant false-alarm rate (CFAR) normalizing processor for nonfluctuating targets entails consideration ion of the moderately complicated F-distribution. For Swerling 1 targets, the CFAR performance equations are quite simple. The mean signal-to-interference ratio (SIR), ϒ ─M, required as a function of probability of detection, P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> , false-alarm probabil ity, P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</sub> , and number of normalization cells, M, is given by ϒ─M = (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> / P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/M</sup> / (1-P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l/M</sup> ). A graph of the CFAR loss, the increased SIR relative to that required when the interference power is known (so that CFAR processing is not required), is given. The data indicate that the CFAR loss, in decibels, is halved when the number of normalization cells is doubled. This result is a special case of the more general gamma density fluctuation model. The more general case is derived and specialized to Swerling 1 and 3 target models.

Harbor surveillance radar detection performance

System requirements for harbor surveillance radars are reviewed. Experimental sea clutter data are presented and shown to be closely matched by a log-normal clutter model. Characteristics and parameters of the log-normal clutter model are described. Detection performance against a steady target in a log-normal clutter background, using logarithmic receivers, is provided. A log-normal target model is described. Detection curves for log-normal fluctuating targets in log-normal clutter are developed. A Constant False Alarm Rate (CFAR) processor that adaptively functions in log-normal clutter is described. CFAR detection performance is derived and presented in the form of CFAR loss curves.