High-resolution Sea Clutter Research Articles

Compound-Gaussian Model with Nakagami-Distributed Textures for High-Resolution Sea Clutter at Medium/High Grazing Angles

In this paper, a compound-Gaussian model (CGM) with the Nakagami-distributed textures (CGNG) is proposed to model sea clutter at medium/high grazing angles. The corresponding amplitude distributions are referred to as the CGNG distributions. The analysis of measured data shows that the CGNG distributions can provide better goodness-of-the-fit to sea clutter at medium/high grazing angles than the four types of commonly used biparametric distributions. As a new type of amplitude distribution, its parameter estimation is important for modelling sea clutter. The estimators from the method of moments (MoM) and the [zlog(z)] estimator from the method of generalized moments are first given for the CGNG distributions. However, these estimators are sensitive to sporadic outliers of large amplitude in the data. As the second contribution of the paper, outlier-robust tri-percentile estimators of the CGNG distributions are proposed. Moreover, experimental results using simulated and measured sea clutter data are reported to show the suitability of the CGNG amplitude distributions and outlier-robustness of the proposed tri-percentile estimators.

An Empirical Model of Shape Parameter of Sea Clutter Based on X-Band Island-Based Radar Database

Sea clutter modelling and parameter estimation/prediction are important basis of system design, performance assessment, and target detection of maritime radars. Besides parameter estimation from measured data, parameter prediction from radar parameters, sea state, and the viewing geometry of the radar is an alternative way. In this letter, a dual-polarimetric full-recorded sea clutter database measured by an island-based X-band experimental radar on the Yellow sea of China is introduced. On this database, the model selection reveals that the compound-Gaussian model with inverse Gaussian (CGIG) texture is suited for HH high-resolution sea clutter data, the generalized Pareto (GP) intensity distributions are for HH moderate-resolution data, and the K amplitude distributions are for high and moderate-resolution VV polarized data. Further, three five-parametric empirical formulae are constructed to predict the shape parameter of the CGIG, GP, and K distributions of sea clutter from the area of spatial resolution cell, the grazing angle, the significant wave height, the average wave period, and the wave direction relative to the sight line of radar. The new empirical formulae attain more accurate prediction than existing empirical formula on the database.

Outlier-robust truncated maximum likelihood parameter estimators of generalized Pareto distributions

Compound-Gaussian model with inverse Gamma-distributed texture is widely used to characterize high-resolution sea clutter and is also referred to as the generalized Pareto (GP) distributions. In real oceanic environments, sea clutter data are often corrupted by a small number of outliers of very high intensity, which are probably from radar returns of ships or reefs. Thus, it is necessary to develop outlier-robust parameter estimators of the amplitude/intensity models of sea clutter for maritime radars. This paper proposes outlier-robust truncated maximum likelihood estimators of the GP distributions. To mitigate the influence of outliers on parameter estimation, the first k largest samples are deleted from the data to generate the right truncated data. The truncated likelihood function (TLF) of the two parameters is derived and the truncated maximum likelihood (TML) equations are given. An iterative algorithm is presented to fast attain the solution of the TML equations and outlier-robust TML estimators are developed, which are a generalization of the ML estimator in the case with outlier in data. The TML estimators are compared with outlier-sensitive estimators and existing outlier-robust estimators. Without outliers in data, the TML estimators have comparable performance with the best ML estimator. With outliers in data, the TML estimators attain higher precision than the existing outlier-robust estimators.

Small Target Detection in X-Band Sea Clutter Using the Visibility Graph

Small target detection in high-resolution sea clutter is one of the important problems in radar target detection. We propose a new detector that adopts the visibility graph (VG) algorithm and the graph convolution neural network (GCN). This detector extracts the graph feature of radar echo networks for target detection after converting the phase information of radar echo into complex networks. Different from the existing detector based on graph connectivity, the VG algorithm does not need radar data preprocessing and it can directly convert the radar data into complex networks by judging whether the series data are visible mutually. We extracted the graph feature that can effectively distinguish the background clutter and target echo by GCN instead of calculating the statistic of graphs manually. Experiments on the IPIX radar datasets show that the proposed method achieves superior performance than the existing detector based on graph connectivity, especially in a short observation time. When the observation time is 0.256 s, the average accuracy of #17, #54, and #320 datasets can reach 84.82%, 94.84%, and 90.59%, respectively.

Small Target Detection Based on Noncoherent Radial Velocity Spectrum of High-Resolution Sea Clutter

This paper proposes a multiscan joint non-coherent detection method of small targets in high-resolution sea clutter with spatial-temporally structural textures induced by large-scale swells and waves, which is composed of intrascan non-coherent integration at each spatial resolution cell followed by interscan integration on a radial velocity template. The main contributions of the paper are as follows. Firstly, a concept of non-coherent radial velocity spectrum (NCRVS) is proposed to model the non-homogeneity of multiscan integration of sea clutter with structural textures. In the NCRVS, the non-coherent intrascan integration and the interscan integration by passing the retrospective filter (RF) bank are fully combined. Secondly, the NCRVS of sea clutter has different statistics at individual radial velocity bins and the lognormal distributions are used to fit their statistics and an outlier-robust analytical bi-percentile estimator is constructed for parameter estimation. Thirdly, based on the lognormal-distributed NCRVS model, a double-channel multiscan joint detector (DC-MJD) is proposed, where the intrascan non-coherent integration channel is used to find floating or low radial velocity targets and the whitening plus intrascan non-coherent integration channel is used to find target with high radial velocity. Simulated data and measured X-band radar data are used to verify the DC-MJD detector. In comparison with the existing three multiscan detectors, the DC-MJD detector improves the detection probability by 96% in the measured data with a test target.

GLRT-Based Polarimetric Detection in Compound-Gaussian Sea Clutter With Inverse-Gaussian Texture

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> 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.

Outlier-robust tri-percentile parameter estimation of compound-Gaussian clutter with lognormal distributed texture

Compound-Gaussian model with lognormal distributed texture (CG-LNT) is one of effective amplitude distribution models to characterize high-resolution sea clutter and therefore it is important for high-resolution maritime radars to robustly estimate the parameters of the CG-LNT model from raw radar data, a mixture of sea clutter data and a small number of outliers. Existing estimators, such as moment-based and [zlog(z)]-based ones, are sensitive to outliers and fail to use in practical radars. In this paper, an outlier-robust tri-percentile estimator is proposed to realize the robust parameter estimation of the CG-LNT model of sea clutter. It is shown that the ratio of two percentiles is a monotonic function of the shape parameter and independent of the scale parameter, though without analytical expressions. In this way, the shape parameter is estimated from the ratio of the two sample percentiles by the look-up table method. Later, the scale parameter is estimated by the third sample percentile that is determined by the estimated shape parameter. Moreover, it is found that the positions of the three percentiles affect the performance and thus two empirical formulae are given to improve the estimate precision by numerical computation. Finally, the experimental results using simulated and real sea clutter data show that the proposed tri-percentile estimator implements robust and fast estimation of the parameters of the CG-LNT distribution.

Bi-Phase Compound-Gaussian Mixture Model of Sea Clutter and Scene-Segmentation-Based Target Detection

In high-resolution maritime surveillance radars, sea clutter exhibits highly spatial heterogeneity due to modulation of long waves with wavelengths longer than the width of one range cell. Compound-Gaussian model (CGM) fails to characterize the heterogeneous high-resolution sea clutter in both amplitude distribution and Doppler spectrum. In this article, a bi-phase compound-Gaussian mixture model (BP-CGMM) is proposed to characterize the heterogeneous sea clutter. In the BP-CGMM, spatial resolution cells are grouped into two disjoint sets, and the sea clutter in each set is represented by one CGM with inverse Gamma-distributed texture. The spectral heterogeneity indicates that sea clutter vectors at spatially adjacent resolution cells in one set share the same speckle covariance matrix, while that at two adjacent spatial cells separated in the two sets often have different speckle covariance matrices. The BP-CGMM is validated by a mass of measured high-resolution sea clutter data. Moreover, under the BP-CGMM, a detection method based on batch test is given to detect sea-surface small targets, which is composed of scene segmentation, by the aid of Bayesian threshold and morphological filtering, and adaptive generalized likelihood ratio test linear-threshold detector (GLRT-LTD) separately in each set. The detection method is verified by measured data with small targets under test. The experimental results show that it attains better detection performance than the adaptive GLRT-LTD under the CGM of sea clutter.

Modeling the Polarization Ratio in the Upper Microwave Band for Sea Clutter Analysis

The two-scale model (TSM) based on Bragg tilting is widely employed to model the normalized radar cross section (NRCS) from the sea surface in the microwave bands. It also leads to the compound distribution model when used to represent the distribution of intensity in high-resolution sea clutter. While the TSM satisfactorily describes the dynamical behavior of the polarized NRCS at moderate incidence angles for various sea states and radar frequencies, it fails to consistently describe the polarized sea clutter distribution in the upper microwave band. The hidden reason is an overestimation of the Bragg polarization ratio (PR) at larger local incidence angles. Following the concept of universal analytical scattering models and based on the experimental evidence of two independent X-band airborne data sets, we propose a simple correction to the facet NRCS which brings the PR in closer agreement to the observations and makes it analytically very close to the popular Thompson empirical model. This amended model preserves the simple structure of Bragg scattering; it admits one single extra parameter which makes a dynamical transition between the asymptotic Bragg and Kirchhoff regime depending on the sea state and the radar frequency. This allows to correctly describe the angular variations of the PR in the upper microwave regime (C-, X-, and Ku-bands) with minimal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information regarding the sea surface. Once this correction is incorporated in the TSM, a consistent modeling of the polarized sea clutter statistics can be obtained with the compound distribution model.

Bipercentile parameter estimators of bias reduction for generalised Pareto clutter model

The generalised Pareto distribution is an efficient model to characterise the high-resolution sea clutter. Robust and precise estimation of the model's parameters is a precondition of effective target detection in sea clutter. It is known that the explicit bipercentile (BiP) estimators are efficient in computation and robust to outliers. In this study, it is proved that the explicit BiP estimators are also consistent with respect to sample size. In practical applications, only limited samples are available and the bias of the BiP estimators degrades the estimation precision. The properties of the biases are analysed and BiP estimators of bias reduction are constructed by the look-up table method. The BiP estimators of bias reduction are verified by simulated data and measured sea clutter data.

Correlation feature-based detector for range distributed target in sea clutter

In this paper, a novel correlation feature-based detector is proposed to deal with the challenging problem of detecting a range-distributed target embedded in nonstationary sea clutter. It is well known that sea clutter consists of a speckle component modulated by texture. The nonstationary property of sea clutter is mainly reflected in texture, but its correlation characteristic is mainly dominated by the speckle. Therefore, this detector using the correlation feature of sea clutter can effectively eliminate the negative effect of the nonstationary property of sea clutter on the detection performance. In addition, in order to get rid of the limitation of the knowledge shortage of target scatterers, the modified entropy method is applied to adaptively estimate the number of target scatterers. The real range distributed target data and high-resolution sea clutter are used to evaluate the detector, and the experimental results show that it attains a better detection performance in comparison with several existing detectors. Comparing with the feature-based detector, the proposed detector can effectively reduce the computational complexity.

Detection of low-velocity and floating small targets in sea clutter via income-reference particle filters

In this paper, an adaptive composite generalized likelihood ratio test (GLRT) detector using the forward-backward income-reference particle filter (FB-IRPF) for signal estimation is proposed to detect low-velocity and floating small targets in high-resolution sea clutter. In integration duration of the order of seconds, target returns with nonlinear Doppler modulation and amplitude slow fluctuation are parameterized by a piecewise linear frequency modulated (PW-LFM) model equipped by a two-dimensional dynamic system of unknown statistics. Correspondingly, temporal nonstationary sea clutter time series is modelled into a piecewise spherical invariant random vector (PW-SIRV) sequences. By introducing the optimal test statistic at each piece as the user-defined cost and embedding it into the route of the forward-backward cost-reference particle filter (FB-CRPF), the FB-IRPF is developed to estimate the state sequence of a PW-LFM signal and to integrate its income at all the pieces. Using the integrated income as the test statistic, the adaptive composite GLRT is derived. It is compared with the fractal-based detector and tri-feature-based detector in a recognized sea clutter dataset for small target detection. The results show that the proposed detector attains better overall detection performance and is complementary with the tri-feature-based detector to some extent.

Iterative Maximum Likelihood and Outlier-robust Bipercentile Estimation of Parameters of Compound-Gaussian Clutter With Inverse Gaussian Texture

Compound-Gaussian model with the inverse Gaussian texture (IG–CG) is recognized to be one of the best models to characterize high-resolution sea clutter at low grazing angles. The model parameters are often estimated by the second- and fourth-order amplitude sample moments, which are of low precision and easily interfered by outliers of high power such as returns of ships and reefs and sea spikes. In this letter, an iterative maximum likelihood (ML) estimator and an outlier-robust bipercentile estimator are proposed and are compared with the moment-based estimator. The experimental results show that the iterative ML estimator is better in performance than the moment-based estimator when samples are without outliers and the bipercentile estimator behaves better when samples contain a small number of outliers.

Low‐order moment‐based estimation of shape parameter of CGIG clutter model

In this Letter, a low-order moment-based estimation of the parameters of compound-Gaussian clutter model with the inverse Gaussian texture (CGIG) is proposed. The CGIG clutter model proposed recently was known as an effective model to describe high-resolution sea clutter at low grazing angles. Its parameter estimation is often obtained by the explicit moment-based estimation using the second- and fourth-order moments, which is low precision in the case of small samples. Here, the first- and second-order moments are used to construct a higher precision estimator, where the look-up table method is employed to make up the lack of explicit expression of the shape parameter.

Floating small target detection in sea clutter via normalised Doppler power spectrum

This paper, proposes a detector based upon normalised Doppler power spectrum (NDPS) is proposed to find floating small targets in sea clutter. Doppler power spectra (DPS) of sea clutter are modelled by a positive stochastic process in Doppler bins. To measure the power fluctuation of sea clutter at each Doppler bin, the NDPS is constructed which equals the DPS of the received time series subtracting the mean function and divided by the standard deviation function of the stochastic process. In view of the Doppler spread when the target return power is integrated within a long observation time, a double detection scheme is developed. The NDPS at the cell under test (CUT) is first estimated from the DPS at the reference range cells and CUT. Then, the first-stage detection is conducted by the shape-parameter-dependent thresholds to yield the thresholded NDPS at individual Doppler bins. The second-stage detection is made by selective integration of the thresholded NDPS. The proposed detector is compared with the fractal-based and tri-feature-based detectors by using the real high-resolution sea clutter datasets. The experimental results show that the proposed detector attains better performance than the fractal-based detector and has comparable performance with the tri-feature-based detector but lower computational complexity.

Shape-parameter-dependent coherent radar target detection in K-distributed clutter

In this paper, shape-parameter-dependent matched filter (MF) detectors are proposed for moving target detection in K-distributed clutter, which are specified by a single parameter α [0, 1], the α-MF detectors for short. The α-MF detectors include the MF and normalized matched filter (NMF) detectors as special examples with α = 0 and 1. The parameter α can be chosen to match clutter characteristics. An empirical formula is given that the optimal parameter α equals the number of integrated pulses divided by it plus the shape parameter of K-distributed clutter. It is proved that the α-MF detectors are constant false alarm rate (CFAR) with respect to the scale parameter, clutter covariance matrix, and Doppler steering vector. The properties of adaptive α-MF (α-AMF) detectors are discussed. For K-distributed clutter, the optimal α-MF detectors are superior to the MF and NMF detectors and are comparable with the optimal K-distributed detectors (OKDs) of high computational cost. Finally, real high-resolution sea clutter data are available to verify the proposed detectors. The optimal α-AMF detectors under K-distributed clutter model are competitive in performance with the adaptive generalized likelihood ratio test linear threshold detectors (GLRT-LTDs) that are optimal for the compound-Gaussian clutter with the inverse Gamma texture.

Model for non-rayleigh clutter amplitudes using compound inverse gaussian distribution: an experimental analysis

A statistical model for high-resolution sea clutter, which we have called the compound inverse Gaussian (CIG) distribution, is proposed. The model is a mixture of the Rayleigh distribution and the inverse Gaussian (IG) distribution to model the speckle and the texture components, respectively. The CIG probability density function (pdf) is generalized to account for the additive thermal noise to achieve a good match to real data. The overall pdf is given in an integral form as a function of three parameters which are estimated from the recorded data based on the parametric curve-fitting estimation (PCFE) method of the complementary cumulative distributed function (CCDF). The Nelder-Mead (N-M) simplex algorithm is used to provide the best estimates of the pdf parameters. Using the IPIX backscatter database, the fitting of the CIG pdfs and the cumulative distributed functions (cdfs) are assessed and compared with the fitted Weibull, log-normal, Rician inverse Gaussian (RiIG), K plus noise, compound log-normal (CLN), and Pareto plus noise distributions. Experimental fitting results show that the sea-clutter amplitudes obey the proposed CIG model in most cases.

Suboptimal Coherent Radar Detection in a -Distributed Clutter Environment

The -Distribution is an important clutter model for high-resolution radar sea clutter returns obtained at X-band. The Neyman-Pearson optimal multilook detector has been derived recently, as well as the generalised likelihood ratio test suboptimal detector. Both these detectors are dependent on the modified Bessel-function of the second kind. This paper suggests a suitable suboptimal approach, using a well-known Bessel identity, eliminating the Bessel function dependence. This produces a computationally simpler detection scheme, whose performance is analysed using clutter parameters based upon real X-band radar returns.

Subband ANMF Detection of Moving Targets in Sea Clutter

For detecting moving targets in high-resolution sea clutter, an adaptive normalized matched filter (ANMF) detector is restricted in performance, because the nonstationarity of the clutter restricts spatial samples available for clutter covariance matrix estimation and integration duration. To overcome this limitation, this paper proposes a subband ANMF detector. It consists of a prepositive, discrete Fourier transform, modulated filter bank followed by a set of ANMF detectors in individual subbands. The prepositive filter bank is used to decompose high-rate received signals into low-rate subband signals. The subband decomposition realizes clutter suppression outside each subband and improves the short-time stationarity of sea clutter. Improved short-time stationarity and the low rate of the subband signals allow the subband ANMF detector to have longer integration duration than allowed by the traditional ANMF detector. The ANMF detector in each subband performs clutter suppression inside the subband and matched reception of target returns. The experimental results using real sea clutter data show that the subband ANMF detector attains much better detection performance than the traditional ANMF detector does.

Coherent Radar Target Detection in Heavy-Tailed Compound-Gaussian Clutter

This paper deals with the problem of detecting a radar target signal against correlated non-Gaussian clutter, which is modeled by the compound-Gaussian distribution. We prove that if the texture of compound-Gaussian clutter is modeled by an inverse-gamma distribution, the optimum detector is the optimum Gaussian matched filter detector compared to a data-dependent threshold that varies linearly with a quadratic statistic of the data. We call this optimum detector a linear-threshold detector (LTD). Then, we show that the compound-Gaussian model presented here varies parametrically from the Gaussian clutter model to a clutter model whose tails are evidently heavier than any K-distribution model. Moreover, we show that the generalized likelihood ratio test (GLRT), which is a popular suboptimum detector because of its constant false-alarm rate (CFAR) property, is an optimum detector for our clutter model in the limit as the tails get extremely heavy. The GLRT-LTD is tested against simulated high-resolution sea clutter data to investigate the dependence of its performance on the various clutter parameters.