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Studies of Target Detection Algorithms That Use Polarimetric Radar Data
Abstract
Algorithms are described which make use of polarimetric radar
information in the detection and discrimination of targets in a ground
clutter background. The optimal polarimetric detector (OPD) is derived.
This algorithm processes the complete polarization scattering matrix
(PSM) and provides the best possible detection performance from
polarimetric radar data. Also derived is the best linear polarimetric
detector, the polarimetric matched filter (PMF), and the structure of
this detector is related to simple polarimetric target types. New
polarimetric target and clutter models are described and used to predict
the performance of the OPD and the PME. The performance of these
algorithms is compared with that of simpler detectors that use only
amplitude information to detect targets. The ability to discriminate
between target types by exploring differences in polarimetric properties
is discussed
... In this paper, the comparative analysis of the proposed in the previous studies ( [1], [2], [7], [9]) polarimetric detection algorithms' performances are done in terms of the gain of detectability, with the goal to perform the validation of the developed and implemented polarimetric radar simulator, which generates the feature vectors using the covariance matrix-based statistical description of the radar-observed objects. ...
... In general, the detection of a target in the homogeneous clutter case can be formulated as a problem for testing two hypotheses: H 0 that in the analyzed signal only the clutter and noise are presented, and H 1 that the target echo is added to the clutter and noise mixture. The Optimal Polarimetric Detector (OPD) was designed to test these two hypotheses using a likelihood ratio test with consideration of known clutter's and target's statistics [9]. The formulation of this likelihood ratio creates the OPD algorithm [9]: ...
... The Optimal Polarimetric Detector (OPD) was designed to test these two hypotheses using a likelihood ratio test with consideration of known clutter's and target's statistics [9]. The formulation of this likelihood ratio creates the OPD algorithm [9]: ...
Starting from numerical simulation and comparative analysis of different polarimetric detector algorithms using the proposed Gain of Detectability measure, this paper has validated the feasibility and accuracy of polarimetric detectors in scenarios with homogeneous clutter. These algorithms’ application to real radar data with non-homogeneous clutter also shows that detection quality can be seriously improved using detectors that use a priori knowledge of the expected target and clutter polarimetric characteristics. A new application of the Polarimetric Whitening Filter and the Optimal Polarimetric Detector for the classification/mapping of targets and ground-based clutter has been proposed and demonstrated.
... T ARGET detection and urban area monitoring using polarimetric SAR (polSAR) are important areas of research, due to the all-weather capabilities of SAR and the additional information on ground scatterers brought by polarimetry. Several approaches to target detection have been investigated, for example, by comparing a pixel's value to its surroundings like in cell-averaging constant false alarm (CFAR) methods [1] when using scalar values like the received intensity, or in the polarimetric matching filter [2] when using the whole covariance matrix. Other methods, such as the polarimetric fork [3], compare each pixel to the expected return from a target, or decompose the signal in time-frequency analysis to find scatterers with anisotropic geometric structures [4] which highlight urban areas. ...
... Proof: We consider a p-component vector X ∼ N C (µ, Σ) partitioned into t subvectors of dimensions p 1 , . . . , p t with parameters partitioned similarly (1) X (2) . . . (1) µ (2) . . . ...
... , p t with parameters partitioned similarly (1) X (2) . . . (1) µ (2) . . . ...
In polarimetric synthetic aperture radar (SAR) images, speckle is removed by multilooking and the local covariance matrix is the main parameter of interest. In the covariance matrix from a backscatter with reflection symmetry, the terms
${\langle \boldsymbol{S}_{hh}\boldsymbol{S}_{hv}^*\rangle }$
,
${\langle \boldsymbol{S}_{vv}\boldsymbol{S}_{hv}^*\rangle }$
, and their complex conjugates are 0. The backscatter from natural covers, such as fields and forested areas, is typically reflection-symmetric, as these four elements have near-zero values. The backscatter from urban areas and man-made structures is substantially different, and the backscatter from buildings not aligned with the radar line of sight usually does not have reflection symmetry. A novel block-diagonality test statistic for reflection symmetry with a constant false alarm rate property is proposed. It is compared to an approximate test built on a change detection test statistic for Wishart-distributed covariance matrices. Their use on quad-polarimetric data in different situations shows their high potential for man-made structure detection. Applied after an orientation correction of the covariance matrices, these test statistics highlight with high-contrast buildings and urban areas. We also apply this test for ship detection at sea, and show that while the results are unconvincing at X-band, it can also be applied at longer wavelengths such as L-band.
... The polarimetric match filter has previously been used for contrast enhancement in target detection. The PMF was proposed by Novak [33]. ...
... The optimal polarimetric detector is based on the maximum likelihood ratio test under complex Gaussian statistics [33,35]. Considering both the target-to-clutter ratio and speckle reduction, the likelihood ratio test (LRT) can be derived as long as target and clutter distributions are known. ...
Satellite monitoring of icebergs in the Arctic region is paramount for the safety of shipping and maritime activities. The potential of PolSAR data in enhancing detection capabilities of icebergs under interchangeable and challenging conditions is explored in this work. We introduce RADARSAT-2 (RS2) quad-pol C-band data to detect icebergs in Kongsfjorden, Svalbard. The location contains two tidewater glaciers and is chosen because multiple processes are present in this region such as ice formation and its relationship with the glaciers, freshwater discharge. Six state-of-the-art detectors are tested for detection performance. These are the dual intensity polarisation ratio anomaly detector (iDPolRAD), polarimetric notch filter (PNF), polarimetric match filter (PMF), symmetry, polarimetric whitening filter (PWF), optimal polarimetric detector (OPD). Additionally, we also tested the parameters of the Cloude-Pottier decomposition. In this study, we make use of a ground-based radar for validation and comparison with satellite images. We show that in calm sea-state conditions, the OPD and PWF detectors give high Probability of Detection (PD) values of 0.7-0.8 when the Probability of False Alarm (PF) value is 0.01-0.05, compared to choppy sea conditions where the same detectors have degraded performance (PD = 0.5-0.7). Target to clutter ratio (TCR) values for each polarization channel is also extracted and compared to the icebergs’ dimensions. The ground-based radar shows higher values in TCR, compared to satellite images. These findings corroborate previous work and show that sea ice activity, surface roughness, incidence angle, weather and sea state conditions all affect the sensitivity of the detectors for this task.
... Later researchers have devoted great effort to utilizing the polarimetric information to enlarge the difference of ship wake and the background. Many optimal methods for polarimetric detection have been proposed, such as the Optimal Polarimetric Detector (OPD) [9,10], the Polarimetric Notch Filter (PNF) [11] and the Polarimetric Whitening Filter (PWF) [12]. P. Imbo et al. [13] described two methods for wake-shape detection in PolSAR imagery: the first one reduced the dimension of the scattering matrix using the PWF filter, which can improve the contrast between ships and sea clutter in the background; the second one utilized the covariance matrix in the Radon domain. ...
... where L is the nominal number of looks. The output after the PWF in PolSAR imagery is defined as follows [9,10]: ...
Ship wake detection using synthetic aperture radar (SAR) imagery provides a way to obtain small marine ship information, but it often becomes unavailable and unreliable during a high sea state. Polarimetric information provides a potential way to solve this problem, which can enhance the ship target as well as the ship wake features. However, three challenges still exist in ship wake detection in polarimetric SAR imagery: the unwanted influences of bright and singular points on ship wake detection, the lack of performance analysis of wake detection by new-type polarimetric enhancement methods, and the difficulty of using the assessment criteria for ship wake detection. In this paper, we try to solve the above problems. Firstly, fully polarized SAR imagery of both ship turbulent and Kelvin wake is simulated based on the two-scale composite model, and the Polarimetric Whitening Filter (PWF) and Polarimetric Detection Optimization Filter (PDOF) are applied to the simulated fully polarized SAR imagery to enhance the ship wake features. Secondly, since the bright and singular points resulting from the ship echoes and the polarimetric enhancement methods may lead to misdetections, a logarithm process and z-score normalization pre-processing has been applied to the images. Then, a new assessment criterion for wake detection performance has been formulated, and the probability of missing detections (PMDs) and the probability of false alarms (PFAs) have been defined for two different requirements. And a Radon transform-based ship wake detection method for both ship turbulence and Kelvin wake has been carried out in horizontal–horizontal (HH), vertical–vertical (VV), horizontal–vertical (HV), PWF and PDOF SAR imagery. Finally, an analysis of the wake detection performance has been carried out. The PWF and PDOF can improve the wake detection performance by an average of nearly 50 percent compared with the HH and VV.
... Compared with the conventional radar composed of unipolarized antennas, polarimetric radar composed of diversely polarized antennas holds potential advantages of the additional polarimetric information exploitation and target scattering matrix estimation [1][2][3]. Similar to polarimetric multiple-input multiple-output (MIMO) communication system [4][5][6][7], polarimetric MIMO radar system has been received much attention in recent years for the joint exploitation of spatial and polarimeric difference [8][9][10][11][12][13][14][15][16][17][18][19][20]. The representative publications include interference suppression [8], target detection [9][10][11][12], parameter estimation [13][14][15][16][17][18][19][20], etc. ...
... The CRB remarks corresponding to the estimated parameters can be calculated by 1 , ...
... Accordingly, targets exhibit a significantly different polarization behavior from the interference. The aforementioned fact is well recognized and utilized in polarimetric radar community [31,32]. ...
... Based on the description of the problem in Eq. (21), we provide the following preparatory considerations in order to pave the way to an effective solution to P. First of all, the problem P (i) relies on a nonconvex fractional objective function and (ii) enforces nonconvex constraints, both making it hard to tackle. Still, when the transmit waveform s is fixed, the problem of solving w can be equivalently written as (32) in next section, which is the well-known minimum variance distortionless response (MVDR) problem [35] w.r.t. the receive filter 2 w. On the contrary, if the receive filter w is fixed, P can be solved by the popular SDR with the aid of rank-one reconstruction techniques. ...
For an extended target with different polarimetric response, one way of improving the detection performance is to exploit waveform diversity on the dimension of polarization. In this paper, we focus on joint design of transmit signal and receive filter for polarimetric radars with local waveform constraints. Considering the signal-to-interference-plus-noise ratio (SINR) as the figure of merit to optimize, where the average Target-Impulse Response Matrix (TIRM) within a certain Target-Aspect-Angle (TAA) interval is employed as the target response, the waveform is decomposed and then designed for both horizontal and vertical polarization segments, subject to energy and similarity constraints. An iterative algorithm is proposed based on the majorization-minimization (MM) method to solve the formulated problem. The developed algorithm guarantees the convergence to a B-stationary point, where in each iteration, optimal horizontal and vertical transmit waveforms are respectively solved by using the feasible point pursuit and successive convex approximation (FPP-SCA) technique. Experiment results show the effectiveness of the proposed algorithm, the robustness of the output SINR against the TAA change, and the advantages of polarization diversity and local design.
... There is a well-established general consensus that polarimetric information can provide significant benefits in a wide range of applications including ship detection [1]- [9]. The Optimal polarimetric detector (OPD) derived from likelihood ratio test and the polarimetric whitening filter (PWF) derived from minimizing fluctuation are two classical methods [3]. Recently, the polarimetric notch filter (PNF) was proposed for ship detection by minimizing sea clutter power [4]. ...
... It can be found that although a few ship pixels have strong intensity, the refined detection cannot rely on only these pixels. As Novak noted in [3], target detection doesn't absolutely depend on TCR and CV and there exists other factors, such as clutter parameter estimation, scattering characteristics and dataset etc. The Pol-Correlation can effectively magnify specific structures of ships in PolSAR images, but it is not enough to retain details. ...
Polarimetric synthetic aperture radar (PolSAR) is an important tool for marine remote sensing. In the past two decades, subaperture decomposition is considered as an alternative method to extract ship targets, especially in complex conditions where the detection based on intensity performs not well. The introduction of polarization information can enhance the detection ability of radar. The combination of sublook techniques and polarization will lead to more precise target extraction. The first methods jointly using information of polarization and sublook is the polarimetric internal Hermitian product (Pol-IHP), which nowadays has been corrected as polarimetric Hermitian internal product (Pol-HIP). However, it is limited by the number of sublooks and recently developed as generalized multi-sublooks correlation (GMC). In this study, a novel sublook polarimetric covariance matrix (SPCM) is established, based on which a sublook-polarimetric whitening filter (Sub-PWF) is further proposed for ship detection. The SPCM represents a given pixel using a high-dimensional covariance matrix which utilizes the spectral correlation in imaging progress and the scattering characteristics of different polarization channels. The superiority of Sub-PWF based on SPCM is validated via the measured single look complex (SLC) PolSAR data from RadarSAT-2 (RS-2) and GaoFen-3 (GF-3). Results show this new method can improve the target to clutter ratio (TCR) and reduce the clutter fluctuation. The ROC curves in both small and large scenes proves that Sub-PWF can reach ideal detection performance.
... Traditional incoherent (not using the phase) detectors were used on each of the test images, including Difference, Normalised Difference, and Ratio Detectors in VV and VH polarisation channels. Newer coherent detectors (using the phase information) were also used and compared to the benchmark traditional detectors, including Optimisation of Power Difference, Optimisation of Power Ratio [46][47][48], and the Hotelling-Lawley trace [49] detectors. ...
... Optimisation of Power Difference: This algorithm also uses the PolSAR data in a covariance matrix format. It optimises the differences between two covariance matrices by finding the linear combination of polarimetric channels that provides the highest (or smallest) difference between the two polarimetric partial targets [46]. Again, this is performed using a diagonalisation and the distance is represented by the eigenvalues. ...
Plastics in the river environment are of major concern due to their potential pathways into the ocean, their persistence in the environment, and their impacts on human and marine health. It has been documented that plastic concentrations in riparian environments are higher following major rain events, where plastic can be moved through surface runoff. Considering the hazard that plastic waste poses to the environment, monitoring techniques are needed to aid in locating, monitoring, and remediating plastic waste within these systems. Dams are known to trap sediments and pollutants, such as metals and Polychlorinated Biphenyls (PCBs). While there is an established background on the monitoring of dams using the synoptic coverage provided by satellite imaging to observe water quality and volume, the detection of marine debris in riparian systems remains challenging, especially in cloudy conditions. Herein, we exploit the use of Synthetic Aperture Radar (SAR) to understand its capabilities for monitoring marine debris. This research focuses on detecting plastic islands within the Drina River system in Bosnia and Herzegovina and Serbia. Here, the results show that the monitoring of these plastic accumulations is feasible using Sentinel-1 SAR data. A quantitative analysis of detection performance is presented using traditional and state-of-the-art change detectors. The analysis of these detectors indicates that detectors that can utilise the coherent data from Single Look Complex (SLC) acquisitions are perform better when compared with those that only utilise incoherent data from Ground Range-Detected (GRD) acquisitions, with true positive detection ratings of ~95% with 0.1% false alarm rates seen in the best-performing detector. We also found that that the cross-pol VH channel provides better detection than those based on single-pol VV polarisation.
... Since the polarimetric scattering mechanism difference between ship and sea clutter is beneficial to ship detection, ship detection using polarimetric SAR (PolSAR) data has become a promising research area for maritime surveillance. Many ship detectors based on PolSAR data have been proposed [1][2][3][4][5][6][7][8][9][10][11][12]. According to whether spatial information is used, PolSAR ship detection methods can be divided into two categories. ...
... Liu et al. proposed a new form of the polarimetric notch filter (NPNF) based on the physical mechanism of targets and clutter which is further developed for partial targets [5]. The polarimetric matched filter (PMF) is another optimal polarimetric enhancement technique which improved the target detection performance by maximizing the target-to-clutter ratio (TCR) [12]. Liu et al. proposed a new optimal technique by combining the PMF and PNF to maximize the TCR and minimize the speckle noise, which was referred to as the polarimetric detection optimization filter (PDOF) [13]. ...
The detection of ships on the open sea is an important issue for both military and civilian fields. As an active microwave imaging sensor, synthetic aperture radar (SAR) is a useful device in marine supervision. To extract small and weak ships precisely in the marine areas, polarimetric synthetic aperture radar (PolSAR) data have been used more and more widely. We propose a new PolSAR ship detection method which is based on a keypoint detector, referred to as a PolSAR-SIFT keypoint detector, and a patch variation indicator in this paper. The PolSAR-SIFT keypoint detector proposed in this paper is inspired by the SAR-SIFT keypoint detector. We improve the gradient definition in the SAR-SIFT keypoint detector to adapt to the properties of PolSAR data by defining a new gradient based on the distance measurement of polarimetric covariance matrices. We present the application of PolSAR-SIFT keypoint detector to the detection of ship targets in PolSAR data by combining the PolSAR-SIFT keypoint detector with the patch variation indicator we proposed before. The keypoints extracted by the PolSAR-SIFT keypoint detector are usually located in regions with corner structures, which are likely to be ship regions. Then, the patch variation indicator is used to characterize the context information of the extracted keypoints, and the keypoints located on the sea area are filtered out by setting a constant false alarm rate threshold for the patch variation indicator. Finally, a patch centered on each filtered keypoint is selected. Then, the detection statistics in the patch are calculated. The detection statistics are binarized according to the local threshold set by the detection statistic value of the keypoint to complete the ship detection. Experiments on three data sets obtained from the RADARSAT-2 and AIRSAR quad-polarization data demonstrate that the proposed detector is effective for ship detection.
... Optimal polarimetric detection (OPD) is based on the likelihood ratio test and theoretically provides the best detection performance under the assumption that targets and clutter are both Wishart distributed [10]. The optimal polarimetric contrast enhancement (OPCE) method, which is mathematically equivalent to the polarimetric matched filter (PMF), maximizes the target-to-clutter ratio (TCR) using optimal antenna polarization states [11,12]. ...
... The objective of PDOF is to enlarge the TCR when reducing clutter fluctuation because both factors affect the detection performance [6]. The standard deviation of clutter fluctuation s/m should be minimized for speckle reduction [10,19]: ...
Polarimetric synthetic aperture radar (PolSAR) is widely used in remote sensing and has important applications in the detection of ships. Although many polarimetric detectors have been proposed, they are not well combined. Recently, a polarimetric detection optimization filter (PDOF) was proposed, which performs well in most environments. In this study, a novel subspace form of the PDOF [strict PDOF (SPDOF)] was further developed based on the Cauchy inequality and matrix decomposition theories, enhancing detection performance. Furthermore, a simple method to determine the optimal dimension of the subspace detector based on the trace ratio form was proposed by calculating the area under the receiver operating characteristic (ROC) curve, reaching the best detection performance among the subspaces of the detector. Moreover, to combine different subspace detectors, a modified linear discriminant analysis was proposed and developed for the diagonal loading detector (DLD) based on polarimetric subspaces. The experimental results demonstrate the superiority of these joint polarimetric subspace detectors. Most importantly, DLD solves for previous limitations due to the complex clutter background and achieves a performance comparable to that of the Wishart (Gaussian) distribution, particularly in the low target-to-clutter ratio (TCR) case.
... Within the aforementioned geometry, the received signal can be modeled as γM T , whereas M T is given by [44] ...
This paper addresses the Direction-of-Arrival (DOA) estimation problem using a narrowband polarimetric array sensing system. The considered receiving equipment is composed of two sub-arrays of sensors with orthogonal polarizations. By suitably modeling the received signal via a sparse representation (accounting for the multiple snapshots and the polarimetric array manifold structure), two iterative algorithms, namely Polarimetric Sparse Learning via Iterative Minimization (POL-SLIM) and Polarimetric Sparse Iterative Covariance-based Estimation (POL-SPICE), are devised to accomplish the estimation task. The proposed algorithms provide accurate DOA estimates while enjoying nice (rigorously proven) convergence properties. Numerical analysis shows the effectiveness of POL-SLIM and POL-SPICE to successfully locate signal sources in both passive sensing applications (with large numbers of collected snapshots) and radar spatial processing, also in comparison with single-polarization counterparts as well as theoretical benchmarks.
... Among the fields the PolSAR has been applied in, ship target detection is significant. Among the detectors have been proposed, the optimal polarimetric detector (OPD) based on the likelihood ratio test (LRT) proposed by Novak et al. performs well under the condition that the statical distributions of the clutter and target are known [2]. The polarimetric detection optimization filter (PDOF) can perform better than traditional detectors [3]. ...
Constant false alarm rate (CFAR) detector is a common method for ship detection in polarimetric synthetic aperture radar (PolSAR) image. CFAR detectors greatly depend on the clutter modeling which can be easily affected by the contamination caused by both lower- and higher-intensity outliers such as spilled oil, intensive targets and so on. Traditional CFAR detectors perform detection in a pixel-by-pixel manner which ignores the spatial information. Both the bias in clutter modeling and the absence of spatial information can degrade the ship target detection performance. In this study, a superpixel-level polarimetric bilateral truncated statistics (BTS) CFAR detector is proposed to promote the ship target detection performance in complex ocean scenarios. As the preprocessing of the PolSAR image, the superpixel segmentation is conducted based on the multilook polarimetric whitening filter (MPWF) result to select candidate ship target superpixels for bilateral truncation and background clutter modeling. The elliptical truncation is expanded to complex situation and the relationship between the second moments before and after truncation is derived. The maximum likelihood estimation (MLE) estimator of the equivalent number of looks (ENL) based on the bilateral truncation distribution is derived and compared with other parameter estimators. The influence of the truncation depth on estimator performance is analyzed, according to which the adaptive bilateral truncation method is determined. The Gaussian mixture model (GMM) and the Parzen window kernel method are compared with the model-based method and utilized for data fitting. The proposed method performs bilateral truncation based on the superpixel segmentation result to provide the pure clutter samples for the accurate parameter estimation and clutter distribution modeling, reducing time consumption and false alarm. The method is validated efficient on both simulated and measured data from RADARSAT-2.
... Based on different optimization rules, several excellent polarimetric features have been proposed, such as the optimal polarimetric detector (OPD) [35], polarimetric whitening filter (PWF) [36], polarimetric notch filter (PNF) [37], reflection symmetry detector (RS) [38] and so on. However, these detectors are model-driven by certain indices or features. ...
The utilization of polarimetric synthetic aperture radar (PolSAR) enables the preservation of more comprehensive target scattering characteristics compared to conventional SAR. Despite the significant advancements in deep learning (DL) technology for single polarimetric SAR ship detection, there remains a scarcity of DL research specifically focused on PolSAR ship detection. This paper proposed a Lightweight Theory-Driven Network (LT-Net) for combining domain knowledge and DL techniques, which is suitable to detect small targets and reduce the computational complexity. The LT-Net incorporates convolutional block attention module (CBAM), and employs differential downsampling during the process of high-dimensional feature extraction. The integration of domain knowledge lends each convolution step a distinct physical significance. Due to the limited availability of public datasets, this paper presents a public Fully-Polarized Ship Detection Dataset (FPSD) for the first time, which contains 853 Pauli pseudo-color maps (in JPG format) and multi-look complex data (in TIF format), with a total of 1714 ship targets from AIRSAR, UAVSAR, and RadarSAT-2. The FPSD encompasses a range of scenarios, with the majority of ship targets being small targets. Validation on FPSD shows that LT-Net exhibits significantly lower time complexity and space complexity compared to four popular target detection networks, Meanwhile, LT-Net achieves the best detection performance in the Pauli pseudo-color maps.
... Polarization information contains the phase relationships between various channels, and joint processing of multiple polarization channels can obtain richer and deeper target features [7], [8], [9]. Numerous studies have shown that polarization has great potential for improving radar's abilities in target detection [10], [11], resolution [12], [13], anti-interference [14], [15], and recognition [7], [16], [17]. In particular, [18] indicates that the radar's ability to obtain target information can be enhanced and range super-resolution can be achieved by adjusting polarization. ...
Compared to the steady-state part of the extended target echo, few scholars have paid enough attention to the echo establishment and disappearance part. They contain abundant target information, but have not been fully explored and utilized. Since the pulse duration of both parts is typically short, they can be considered as instantaneous processes. Polarization is an inherent property of electromagnetic waves, which can bring information gain to the analysis of the echo instantaneous part. The objective of this study is to utilize the instantaneous polarization response (IPR) of the echo to achieve super-resolution for two targets with different polarization scattering characteristics. It is analyzed that when two target echoes are “equal-amplitude and opposite-phase", echo decoupling can be achieved, which is the precondition for achieving range super-resolution. While making full use of the polarization information is instrumental in achieving the echo with “equal-amplitude and opposite-phase". A trihedral and a dihedral are selected to verify the effectiveness of the proposed method. Multiple sets of measured data show that the two target echoes do have the instantaneous part. When the signal-to-noise ratio (SNR) of the echo data is about 6-7dB, the range super-resolution and range estimation of the two targets are achieved by using the edge threshold detector.
... One type of pixel-level approach depends on a combination of multi-polarized scattering information embedded in the Sinclair matrix of the second-order covariance matrix, and includes the following: the SPAN detector [16], using total polarimetric power; the polarimetric whitening filter (PWF) detector [17,18], providing good speckle suppression; the polarimetric notch filter (PNF) detector [19] and its varied versions [15], Without prior knowledge of targets; the PWF [17,18], designed to suppress the speckle influence for target detection. In theory, the performance of PWF can be comparable to that of the optimal polarimetric detector (OPD) [20], which was derived from the likelihood ratio test for Wishart-distributed targets and clutter. A saliency detector, based on a similarity test and offering speckle-free PolSAR images, was proposed in [21]. ...
Ship detection based on synthetic aperture radar (SAR) imagery is one of the key applications for maritime security. Compared with single-channel SAR images, polarimetric SAR (PolSAR) data contains the fully-polarized information, which better facilitates better discriminating between targets, sea clutter, and interference. Therefore, many ship detection methods based on the polarimetric scattering mechanism have been studied. To deal with the false alarms caused by the existence of ghost targets, resulting from azimuth ambiguities and interference from side lobes, a modified polarimetric notch filter (PNF) is proposed for PolSAR ship detection. In the proposed method, the third eigenvalue obtained by the eigenvalue–eigenvector decomposition of the polarimetric covariance matrix is utilized to construct a new feature vector. Then, the target power can be computed to construct the modified PNF detector. On the one hand, the detection rate of ship targets can be enhanced by target-to-clutter contrast. On the other hand, false alarms resulting from azimuth ambiguities and side lobes can be reduced to an extent. Experimental results based on three C-band AIRSAR PolSAR datasets demonstrated the capability of the proposed PNF detector to improve detection performance while reducing false alarms. To be specific, the figure of merit (FoM) of the proposed method is the highest among comparative approaches with results of 80%, 100%, and 100% for the tested datasets, respectively.
... Subsequently, important contributions to polarization diversity techniques have been made on several aspects. Adaptive polarization filtering has been investigated in [13], [14], [15], [16]. The polarization dependency of scattering from target has been investigated theoretically in [17]. ...
In polarimetric radars, corresponding to the polarized antennas, exploiting waveform diversity along the polarization dimension becomes accessible. In this paper, we aim to maximize the signal-to-interference plus noise ratio (SINR) of a polari-metric radar by optimizing the transmit polarimetric waveform, the power allocation on its horizontal and vertical polarization segments, and the receiving filters jointly, subject to separate (while practical) unit-modulus and similarity constraints. To mitigate the SINR sensitivity on Target-Aspect-Angle (TAA), the average Target-Impulse-Response Matrix (TIRM) within a certain (TAA) interval is employed as the target response, which leads to an average SINR as the metric to be maximized. For the formulated nonconvex fractional programming problem, we propose an efficient algorithm under the framework of the alternating optimization method. Within, the alternating direction method of multiplier (ADMM) is deployed to solve the inner subproblems with closed form solutions obtained at each iteration. The analysis on computational cost and convergence of the proposed algorithm is also provided. Experiment results show the effectiveness of the proposed algorithm, the robustness of the output SINR against the TAA uncertainty, and the superior performance of polarimetric power adaption.
... Từ bộ phát hiện tối ưu được đề xuất bởi Novak năm 1989 [1], một số thuật toán phát hiện phân cực khác được phát triển [2][3][4]. Vấn đề này tiếp tục được giải quyết với đề xuất sử dụng độ phân cực DoP (Degree of Polarization) trong bài toán phát hiện [5]. ...
The paper proposes a new method to improve the performance of the target detection in the sea clutter using the standard deviation of degree of polarization DoP. The performance of the detection using parameter DoP and the standard deviation of DoP were examined with different types of targets in different models of clutter such as Rayleigh, Weibull and Laplace; and a special case of parameter DoP of target which is the same as that of the clutter was investigated as well. The results show that the effectiveness of the detection using the standard deviation of DoP is increased significantly and better than using only the parameter DoP.
... The PMSD has been proposed as an improvement with respect to the SD. By comparing several polarimetric fusion methods, Novak et al. [43] showed that the PMSD exhibits the highest detection performance without any a priori information about the polarization characteristics of the targets or clutter. Therefore, a fusion method based on the PMSD was implemented. ...
A dedicated signal and data processing chain is proposed for a fully polarimetric Doppler surveillance S-band radar to extract the polarimetric signatures of moving targets. To extract the target’s polarimetric features, detection, clustering, and tracking steps are realized for a multi-target environment in the range-Doppler domain. A dedicated data fusion method for all four polarimetric radar channel signals is implemented to take full advantage of the additional polarimetric information and improve the detection performance. While tracking each particular target, polarization information is collected and used to describe their polarization scattering characteristics. Using the polarimetric H/A/α decomposition technique, the polarimetric features of moving automotive targets are extracted and investigated. The developed processing chain has been applied to the signals scattered from vehicles moving in a highway. By employing both time averaging and spatial averaging of the statistical coherency matrix, the polarimetric signatures of both moving vehicles and static clutter have been presented in the two-dimensional H/α plane. It has been found that the spatial averaging approach results in polarimetric signatures of moving vehicles that give the opportunity to directly and without consideration of the motion of the targets compare the polarization features of moving targets and static clutter. Therefore, this method can be used to improve the performance of target detection or target classification.
... For instance, polarimetry is used in weather radar and polarimetric amplitude ratios are used in that case for classification and detection purposes. Synthetic Aperture Radar (SAR) [4][5] uses also polarimetry for instance for surface patch classification and target identification. Finally, polarimetry can improve detection in a maritime context [9]. ...
... To benchmark the processing, traditional detectors were used: Difference, Normalised Difference and Ratio Detectors in VV and VH polarisation channels. Additionally, we used newer detectors, Power Difference, Power Ratio [49][50][51] and the Hotelling-Lowley Trace [52,53] detectors. Once these were implemented, Receiver Operating Characteristic (ROC) curves were displayed to evaluate the performance of each detector. ...
Water hyacinth (Pontederia crassipes, also known as Eichhornia crassipes) is a highly invasive aquatic macrophyte species, indigenous to Amazonia, Brazil and tropical South America. It was introduced to India in 1896 and has now become an environmental and social challenge throughout the country in community ponds, freshwater lakes, irrigation channels, rivers and most other surface waterbodies. Considering its large speed of propagation on the water surface under conducive conditions and the adverse impact the infesting weed has, constant monitoring is needed to aid civic bodies, governments and policy makers involved in remedial measures. The synoptic coverage provided by satellite imaging and other remote sensing practices make it convenient to find a solution using this type of data. While there is an established background for the practice of remote sensing in the detection of aquatic plants, the use of Synthetic Aperture Radar (SAR) has yet to be fully exploited in the detection of water hyacinth. This research focusses on detecting water hyacinth within Vembanad Lake, Kuttanad, India. Here, results show that the monitoring of water hyacinth has proven to be possible using Sentinel-1 SAR data. A quantitative analysis of detection performance is presented using traditional and state-of-the-art change detectors. Analysis of these more powerful detectors showed true positive detection ratings of ~95% with 0.1% false alarm, showing significantly greater positive detection ratings when compared to the more traditional detectors. We are therefore confident that water hyacinth can be monitored using SAR data provided the extent of the infestation is significantly larger than the resolution cell (bigger than a quarter of a hectare).
... To evaluate the robustness of the proposed segmentation method, we tested the method under different parameters using Dataset 1. The main parameters of the proposed method include ν and Q according to Equation (4) and Algorithm 2. The regularization parameter ν was set to 0.05, 0.1, 0.2, 0.3, and 0.5. The splitting parameter Q was set to 2, 3, 4, 5, and 6. ...
Offshore oil platforms are difficult to detect due to the complex sea state, the sparseness of target distribution, and the similarity of targets with ships. In this paper, we propose an oil platform detection method in polarimetric synthetic aperture radar (PolSAR) images using level set segmentation of a limited initial region and a convolutional neural network (CNN). Firstly, to reduce the interference of sea clutter, the offshore strong scattering targets were initially detected by the generalized optimization of polarimetric contrast enhancement (GOPCE) detector. Secondly, to accurately locate the contour of targets and eliminate false alarms, the coarse results were refined using an improved level set segmentation method. An algorithm for splitting and merging the smallest enclosing circle (SMSEC) was proposed to cover the coarse results and obtain the initial level set function. Finally, the LeNet-5 CNN model was used to classify the oil platforms and ships. Experimental results using multiple sets of polarimetric SAR data acquired by RADARSAT-2 show that the performance of the proposed method, including the detection rate, the false alarm rate, and the Intersection over Union (IOU) index between the extracted ROI and the ground truth, is better than the performance of a method that combines a GOPCE detector and a support vector machine classifier.
Polarization diversity has been widely used in maritime radars to improve target detection performance. Full utilization of the polarimetric characteristics of sea clutter is the key to designing effective polarimetric detectors. For high-resolution maritime radars, the HH-HV dual-polarization is an affordable and effective mode to monitor small targets, owing to the simple configuration of single-polarimetric transmit and dual-polarimetric reception and lower clutter powers at the HH and HV polarizations. Enlightened by the analytical coherent detector in compound-Gaussian clutter with inverse Gamma texture, this paper investigates dual-polarimetric coherent detection in dual-polarimetric compound-Gaussian clutter with independent inverse Gamma distributed textures. The analytical dual-polarimetric near-optimum coherent detector is derived, which is a fusion of the generalized likelihood ratio test linear threshold detectors (GLRT-LTDs) at the two polarizations. For short, it is referred to as the P-GLRT-LTD. It is proven that the P-GLRT-LTD is of constant false alarm rate with respect to the Doppler steering vector, scale parameters of textures, and speckle covariance matrices. Moreover, the thresholds of the P-GLRT-LTD are given analytically. Experiments using simulated sea clutter data with the estimated scale and shape parameters from the two measured intelligent pixel processing radar (IPIX) datasets and two measured IPIX datasets with test targets are made to compare P-GLRT-LTD with other existing dual-polarimetric coherent detectors. The results show that the P-GLRT-LTD attains the same detection performance as the existing best-performance detector. The P-GLRT-LTD has a lower computational cost than the existing best-performing one.
In this paper, a comprehensive overview of radar detection methods for low-altitude targets in maritime environments is presented, focusing on the challenges posed by sea clutter and multipath scattering. The performance of the radar detection methods under sea clutter, multipath, and combined conditions is categorized and summarized, and future research directions are outlined to enhance radar detection performance for low-altitude targets in maritime environments.
This work proposed a novel constant false alarm rate detection method based on Gaussian mixture model (GMM). The main contribution contains two aspects. First, the Gabor wavelet is used to determine the GMM component number. Second, the expression of probability of false alarm is derived based on the GMM parameter.
A challenging issue in the field of marine remote sensing is the application of polarimetric synthetic aperture radar (PolSAR) to small ship detection in complicated environments. Several outstanding polarimetric detectors (such as the optimal polarimetric detector, polarimetric whitening filter, and polarimetric notch filter, etc.), have been effectively implemented in practical applications. A linear combination model based on quadratic optimization is summarized to establish a general framework for polarimetric detectors, transitioning the PolSAR ship target detection from a model driven approach to a hybrid (model/data)-driven approach. However, the dimension of the covariance matrix may be high, and the computation cost will be large. The higher dimension of the covariance matrix requires a bigger the data demand. As a result, when the sample size is small, the model performance will degrade. In this paper, to decrease the computational complexity and improve the robustness, we propose a novel method called the simultaneous diagonalization transform (SDT). The proposed method enables an almost simplest representation of information from the covariance matrix providing a rapid detection algorithm. The simulation experiments demonstrate that polarimetric detectors based on SDT consistently outperform those based on other methods in terms of accuracy, efficiency, and sample size requirements across various complex backgrounds. Furthermore, the effectiveness, robust, and fastness of the polarimetric detector based on SDT is validated using real data collected by RadarSAT-2, GaoFen-3, and Sentinel-1A.
The performance of the polarimetric notch filter (PNF) algorithm based on orthogonal projection technique has been widely recognized in the field of PolSAR ship detection. However, for detection problem in non-orthogonal target subspace and clutter subspace, using orthogonal projection technique results in detection performance loss. In this letter, we propose a new ship target detector based on oblique projection technique to deal with the condition that the target subspace and the clutter subspace are non-orthogonal. Since most sea clutter is inconspicuous in low-to-medium sea conditions, it is time-consuming to apply a fine target detector over the entire scene. Therefore, this letter proposes a keypoint detector based on the noncircularity and polarimetric scattering information to achieve fast localization of potential target regions. In general, we propose a novel two-step ship detection method for PolSAR data. The first step is to use the keypoint detector for potential target region localization, and the second step is to use the oblique projection detector to perform fine target detection on the potential target regions. Experiments on the synthetic and measured PolSAR data demonstrate that the proposed method is effective for ship detection.
The consideration of the polarization scattering characteristics of radar echo in the detection of small and dim targets in a sea clutter background leads to high detection probability and high recognition accuracy. In this study, a target detection method based on canonical polar decomposition (CPD) was developed. In particular, a polarization matrix [Formula: see text] was constructed for the radar echo of each range bin; the absolute value [Formula: see text] and phase [Formula: see text] of [Formula: see text] were extracted; the diagonal elements of the characteristic matrix [Formula: see text] were extracted and converted into the singular spectrum form; and the negative entropies [Formula: see text] and [Formula: see text] of the singular spectrum were calculated. We set [Formula: see text]; then, the negative entropy value [Formula: see text] of each range bin was obtained, and the range bin of the minimum value was identified, which was the target position. Thereafter, a seven-component scattering power decomposition (7SD) was performed on [Formula: see text]. The basic scattering structure of the target was analyzed, and a polar feature description word (PFDW) was formed to recognize the target characteristics. The effectiveness of the proposed method was verified by using the sea clutter dataset obtained with the IPIX radar. The comparison with the statistical model-based method is also made for indicating the advantage of the proposed method.
Polarimetric radar responses from moving automotive targets are studied aiming at target classification using the polarimetric H/A/α-decomposition technique. A signal- and data processing chain has been proposed for the detection and tracking of targets in a multi-target environment in the range-Doppler domain. Polarimetric information of the vehicles is collected during tracking and is analyzed by the H/A/α-decomposition technique. Employing both time averaging and spatial averaging of the statistical coherency matrix, the polarimetric signatures of both vehicles and static clutter have been presented in the two-dimensional H/α-plane. It has been found that the spatial averaging approach results in a polarimetric signature that can be very helpful to distinguish automotive vehicles from static clutter.
This letter presents the derivation of the generalized likelihood ratio test (GLRT)-based polarimetric detector in the non-Gaussian clutter. We model the non-Gaussian sea clutter as compound-Gaussian distribution with inverse-Gaussian texture (IG-CG), which has better goodness-of-fit for the high-resolution sea clutter. Based on the two-step GLRT criterion, we develop the test statistic of the proposed detector by assuming the texture component is known in the first step. In the second step, with the texture of the secondary data estimated as the power of the clutter, we insert the maximum
a posteriori
estimate (MAPE) of the texture of the primary data into the test statistic to achieve the fully adaptive detection. Furthermore, the model-based polarimetric detector, which exploits the independence between the co-polarized and the cross-polarized component, is derived. Finally, we conduct experiments with simulated clutter and real sea clutter to evaluate the performance of the proposed detector. The simulation results verify that the proposed detectors have better detection performance and the MAPE under different hypotheses leads to different levels of robustness to the mismatched signal.
Ship detection is an important task in civil or military applications and we can use polarimetric synthetic aperture radar (PolSAR). Many polarimetric detectors were proposed and achieved good performances in particular environments, such as optimal polarimetric detector (OPD), polarimetric whitening filter (PWF), polarimetric notch filter (PNF), polarimetric detection optimization filter (PDOF) and diagonal loading detector (DLD) etc. Up to know, the analytical links among different polarimetric detectors have not been found. In this work, the above polarimetric detectors are unified in mathematical forms and a general framework of polarimetric detectors based on quadratic optimization is presented. The mathematical forms are summarized as a trace of two matrices’ product. One is a detection transformation matrix and the other is the polarimetric covariance matrix of the pixel to be detected. We find that all these polarimetric detectors can be regarded as the optimization of such detection matrix, which is the key point of the general framework, and the difficulty turns to be a linear inseparable problem. Pocket Perceptron Linear Algorithm (PPLA) is used to solve the linear inseparable problem. In the case of low resolution, target detection is almost an indivisible problem, and multilayer perceptron (MLP) cannot provide better detection results than PPLA. In the case of high resolution, target detection becomes a nonlinear separable problem, and MLP is gradually superior to PPLA. Additionally, the optimal weights of the recent DLD are obtained to compare with other detectors in the general framework and the DLD is developed to a more general case (GDLD). The experiments validate the general framework of polarimetric detectors. Different detectors in the general framework are utilized and compared in both simulated and measured PolSAR data. The results show the optimal solution in the general framework can always reach the best performance, and the GDLD is the closest one to the optimal detector of the general framework.
The problem of adaptive radar detection with a polarimetric Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar is addressed in this paper. At the design stage, the target detection problem is formulated as a composite hypothesis test, with the unknowns given by the target angle, incremental range (target displacement with respect to the center of the occupied range cell), and scattering matrix, as well as the interference covariance matrix. The formulated detection problem is handled by resorting to sub-optimal design strategies based on the Generalized Likelihood Ratio (GLR) criterion. The resulting detectors demand, under the
$H_\mathrm{{1}}$
hypothesis, the solution of a box-constrained optimization problem for which several iterative techniques, i.e., the Linearized Array Manifold (LAM), the Gradient Projection Method (GPM), and the Coordinate Descent (CD) algorithms, are exploited. At the analysis stage, the performance of the proposed architectures, which ensure the bounded CFAR property, is evaluated via Monte Carlo simulations and compared with the benchmarks in both white and colored disturbance.
This paper investigates the dual-polarimetric target detection problem in non-Gaussian sea clutter. The compound Gaussian model with inverse Gamma texture is adopted to describe the real sea clutter of which characteristics are time-varying and heterogeneous. Three novel polarimetric detectors are proposed based on the two-step maximum
a posteriori
(MAP) generalized likelihood ratio test (GLRT), MAP Rao, and MAP Wald criteria. Specifically, we assume the polarimetric clutter covariance matrix (PCCM) and the inverse Gamma textures are known in the first step, and the test statistics of the proposed polarimetric detectors are derived. In the second step, we take advantage of the proposed polarimetric persymmetric property and MAP criterion to estimate the PCCM and inverse Gamma textures, respectively. The fully adaptive persymmetric polarimetric detectors are obtained by substituting the estimates into the test statistics of the proposed detectors. Then the proposed detectors are proved to have the constant false alarm rate (CFAR) properties with respect to the real PCCM. The performance assessments are evaluated by contrasting the proposed detectors with their counterparts on the simulated and measured sea clutter data. The numerical results verify the performance of the proposed persymmetric polarimetric detectors.
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 (
${\mathcal{ G}}$
) texture, which can be named
${\mathcal{ G}}$
-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
${\mathcal{ G}}$
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.
This paper shows a novel two-dimensional direction-of-arrival (2D DOA) estimation method which is based on the interpolation fitting (IF-based) algorithm for airborne conformal MIMO radar with unknown polarization in a multipath environment. Since the backscattered propagation paths from the same target include the direct path (DP) and indirect paths, we can separate the DP signal and indirect path signals from the range bins in signal detection. Therefore, target signals at different range bins can be adopted to measure the 2D DOA, respectively. Each conformal sensor is composed of one electric dipole distributed on the geometric surface of the airborne platform, which requires the 2D DOA estimation is carried out in the case of unknown polarization. Aiming at the problem of 2D DOA estimation with unknown polarization, the IF-MUSIC method is used to measure the 2D DOA through the 2D angle search vector preprocessed by a designed interpolation fitting matrix which can project the 2D angle and 2D polarization state subspace of conformal polarization sensitive array into the 2D angle subspace. To further improve the estimation accuracy, the fusion technology based on the variance minimization criterion is employed, which can obtain the optimal weight coefficients of different path signals. The proposed method needs one channel in each sensor and there is no mutual coupling effect inside the sensor. Finally, numerical experiments verify the high-precision 2D DOA estimation performance.
The subject of this chapter is the development of decision schemes that jointly process consecutive range bins to account for spillover. In a radar system, the spillover is a physical phenomenon and happens as the centroid of the received target pulse is somewhere between two consecutive range cells [1, 2], as shown in Fig. 4.1 which illustrates the frequently encountered scenario in practice where a target straddles between range cells n and \(n+1\) while the target location is not located exactly an integer multiple of the range cell size of the radar [3].
A mathematical model for non-Rayleigh microwave sea echo is developed which describes explicitly the dependence of statistical properties of the radar cross section on the area of sea surface illuminated by the radar. In addition to the first probability distribution of the scattered radiation, its temporal and spatial correlation functions are also considered. It is shown that, in general, these correlation functions decay on at least two scales, the second, non-Rayleigh, contributions being strongly dependent on the properties of a "single scatterer." Predictions of the model are found to be in qualitative agreement with existing experimental data. A new class of probability distributions, the " K -distributions," is introduced, which may prove useful for fitting such data.
A generalized signal processing problem is posed in which one seeks to detect the presence of a random signal in a background of additive colored noise. This detection is to be achieved by utilizing a linear decision functional which operates on a finite set of observed noise contaminated samples of the process of interest. When the magnitude of this functional exceeds a prescribed threshold, the presence of a target decision is rendered. It is shown that the determination of an optimum linear decision functional entails the solving of a generalized eigenvector-eigenvalue problem.
Results of a study of candidate target detection and selection techniques for use in millimeter airborne radar systems are presented. Improved target and ground clutter models are developed and the implications of these mathematical models on target detection and selection performance is discussed.
In meticulous detail, a succinct summary of basic electromagnetic wave polarization descriptors, of the various scatterer polarization transformation matrices, and its invariants of the associated optimal matrix polarizations, and of the scatterer descriptive operators is introduced. It is then shown how the five (5) independent matrix parameter for the relative phase mono-static scattering matrix describing an isolated, yet regionally distributed, target in a reciprocal propagation medium can be recovered from (1) amplitude-only, (2) mixed amplitude plus partial phase, (3) complete two-step amplitude-phase measurements. Basic properties of the radar scattering matrix for linear (H, V) and circular (R, L) polarization basis are described in terms of geometrical target features as functions of the specular point surface coordinate parameters, known as gaussian principal, main and related curvature functions. Based upon this succinct background introduction on radar polarimetry, the concepts are applied mainly for the coherent case to various classes of increasing order of sophistication, as defined in detail in the INTRODUCTION, to the problem of radar target handling for the non-cooperative, limited-data case. (Author)
In digital matched filtering, a discrete-point input function is Fourier transformed to produce a discrete-point Fourier transform. This transform is then multiplied by the matched filter, the product is retransformed, and the resulting pattern is examined. It is shown that the problem of deriving the matched filter can be recognized as a special case of linear discriminant analysis, which in turn is a special case of principal component analysis. What linear discriminant functions are, and in what sense they are optimum, is described.
The Mueller matrix and polarization covariance matrix are described for polarimetric radar systems. The clutter is modeled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model is applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. It is found that 8 out of 16 elements of the Mueller matrix are identically zero, corresponding to a covariance matrix with four zero elements. Theoretical predictions are matched with experimental data for vegetation fields.
A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow-covered fields is developed using the optimum polarimetric classifier. The covariance matrices for various terrain cover are computed from theoretical models of random medium by evaluating the scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Analytical and Monte Carlo simulated classification errors using the fully polarimetric feature vector are compared with classification based on single features which include the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.
The normalized polarimetric classifier (NPC) which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements. The probability density functions (PDFs) of polarimetric data are assumed to have a complex Gaussian distribution, and the marginal PDF of the normalized polarimetric data is derived by adopting the Euclidean norm as the normalization function. The general form of the distance measure for the NPC is also obtained. It is demonstrated that for polarimetric data with an arbitrary PDF, the distance measure of NPC will be independent of the normalization function selected even when the classifier is mistrained. A complex Gaussian distribution is assumed for the polarimetric data consisting of grass and tree regions. The probability of error for the NPC is compared with those of several other single-feature classifiers. The classification error of NPCs is shown to be independent of the normalization function.
The development of the SCR-270-271 series of radars is traced. These radar had their origin in the work that preceded and eventually culminated in the first US Army radar: Search Light Control Radar SCR-268. The principal technical characteristics of the 270-271 series are summarized and given in tabular form
An algorithm is presented for calculating recognition error when applying pattern vectors to an optimum Bayes' classifier. The pattern vectors are assumed to come from two classes whose populations have Gaussian statistics with unequal covariance matrices and arbitrary a priori probabilities. The quadratic discriminant function associated with a Bayes' classifier is used as a one-dimensional random variable from which the probability of error is calculated, once the distribution of the discriminant function is obtained.
A novel class of probability distributions resulting from a compound Poisson process is found to correlate well with amplitude distributions of radar clutter returns spatially sampled from composite terrain. This class of distributions, derived from assumptions of random scattering phase and Poisson spatial distribution of elementary scattering sources, is specified by several physical and statistical parameters in its complete generality. These parameters are: 1) the number of scatterer types; 2) the average radar scattering cross section and the cross-sectional distribution of each different scatterer type; 3) the occurrence probability or the average scatterer size and spatial density; 4) the radar resolution area; and 5) the average background radiation as well as the radar internal noise power. Excellent fits of the theoretical clutter distributions to the measurement data are obtained by assuming a Rayleigh amplitude distribution for the elementary scatterer return for high grazing angle cases and a more general K -distribution for low grazing angle cases.
A probabilistic model for nonstationary and/or nonhomogeneous clutter and target scattering is proposed and developed. The first-order probability density of the scattered power is treated as the expected value of a conditional density that is a function of random parameters. The family of gamma densities is a general solution for the density function of the intensity reflected by objects comprised of several scatterers and is selected as the conditional density. In the general case, the gamma density is a function of two parameters: the mean and the inverse of the normalized variance. Assuming various distributions for a random mean, expressions for the first-order density of the scattered power are derived and used to explain previous experimental and theoretical results. An example of detection performance for nonstationary target fluctuation based on the developed model is also presented.
On the Sensitivity of Bayes and Fisher Classifiers in Radar Target Detection
- L M Novak
L.M. Novak, "On the Sensitivity of Bayes and Fisher Classifiers in
Radar Target Detection," Proc. 18th Asilomar Conference on Circuits,
Systems, and Computers, Pacific Grove, CA, November 1984.
Detection of a Randomly Polarized Target
- R M Barnes
R.M. Barnes, "Detection of a Randomly Polarized Target," PhD Thesis,
Northeastern University, Department of Electrical Engineering (June
1984).
On the Performance of Linear and Quadratic Classifiers in Radar Target Detection
- M I T Cambridge
I
14. MACSYMA Reference Manual, Vol. 1, M.I.T., Cambridge, MA, 1983.
15. L.M. Novak and M.B. Sechtin, "On the Performance of Linear and
Quadratic Classifiers in Radar Target Detection," Proc. 20th Asilomar
Conference on Circuits, Systems, and Computers, Pacific Grove, CA,
November 1986.
On the Performance of Linear and Quadratic Classifiers in Radar Target Detection
- L M Novak
- M B Sechtin
L.M. Novak and M.B. Sechtin, "On the Performance of Linear and
Quadratic Classifiers in Radar Target Detection," Proc. 20th Asilomar
Conference on Circuits, Systems, and Computers, Pacific Grove, CA,
November 1986.
Theoretical Models for Polarimetric Radar Clutter
- R Shin
- L M Novak
- M Borgeaud
R. Shin, L.M. Novak, and M. Borgeaud, "Theoretical Models for Polarimetric Radar Clutter," Proc. 10th DARPA 14W/Tri-Service Symposium,
Adelphi, MD, 8-10 April 1986.