#### Abstract

Detecting low observable targets within sea clutter at low grazing angle is one of the research hotspots in radar signal processing community. In this paper, we have proposed a novel method based on polarimetric decomposition theorem. The polar characteristics of sea clutter has been analyzed, with the parameters after the decomposition of target scattering matrix. The scattering entropy and the scattering angle are the key parameters to discriminate the target from the sea clutter. The technique is designed to suppress unwanted sea clutter at polarimetric domain. Datasets from real marine radar are used to illustrate the performance of the new approach.

#### 1. Introduction

Marine radars face the problems of sea clutter when detecting the surface ships, low-flying aircraft, icebergs, and other small surface objects. The sea clutter is highly dependent on the ocean state, radar grazing angle, wind velocity, and direction. Furthermore, sea echoes generally appear to have sea spikes, which will decrease the target detection performance, especially for the targets of low speed and low RCS [1]. What's worse, when the grazing angle of marine radar is lower than 3° and the lengths of targets to be detected are smaller than 30 m, such as growlers, buoys, and small boats, especially the height of these targets are also low, the detection problem will be very difficult [2].

The targets detection in sea clutter at the condition mentioned above is very important, because the primary purpose of marine radar is early warning targets, then to track or recognize them. Traditionally, sea clutter has been modeled as a stochastic process, and many models have been developed with employing different statistical distributions [3, 4]. Based on these models*，*one method is Constant False Alarm Rate (CFAR) algorithm [5], which can obtain satisfactory detection performance for surface targets with large RCS. But, this is not suitable for smaller targets at low grazing angle, even applying the K-distribution as the model, which has the good fitting with sea clutter, because of the frequent emergence of the sea spikes. To describe the sea clutter characteristics, chaotic process seems to be also an important approach [6]. However, the chaotic invariant measurements have been disputed by researchers interested in the field [7]. Making use of neural network trained, such as Radial Basis Function (RBF) network and Back Propagation (BP) network, to compare the difference between predicted value and the real data being tested is a very popular way to solve the detection problem focus on the sea surface with small targets recently [8]. Unfortunately, there are some faults of this approach. For example, since the real sea condition is always changing, the network cannot be once trained and for all sea states, and the computing is too huge to real-time processing. There are other solutions which are practiced with time-frequency analysis [9]. This kind of methods cannot work well for low speed small targets, because the characteristic difference between the sea clutter and targets smaller than the high speed ones. The measures adopting radon transform to detect the moving targets are also hot in this field [10]. But this way needs large quantities of data to shape one image including targets lines, which led to the performance decline of real-time process. And if the speed of target to be detected is low, it is very difficult to detect the target line, because the existence of diagonal effect and severe sea spikes. Tello regards vessels detection based on the Wavelet Transform in the paper [11]. But Telloo’s method is not adapted to solve the detection problem at low grazing angle.

Usually, the marine radars work at HH (horizontal transmit and horizontal receive) channel, because the average power of sea clutter at HH channel is smaller than that at VV (vertical transmit and vertical receive) channel, which is helpful for detecting targets. However, the not good thing is the more frequent appearance of sea spikes at HH channel than at VV channel at low grazing angle [12]. So, most methods tried to work out the problem at HH channel. With the popularization of full-polarization process in the PolSAR image process field, we find it also useful in this process, because the more information can be obtained from the full-polarization style than from the single-polarization style. Anderson and Morris made use of polarimetric decomposition analyzing the incidence angle and the azimuth angle dependence of the polarimetric characteristics of sea clutter at low grazing angle of marine radar [13, 14]. They pointed out that incidence angles above 85° are characteristic of random scattering, which there is no longer a single dominant scattering mechanism present. The characteristics values from the result of polarimetric decomposition can indicate that whether there is dominant scattering mechanism in the covariance matrix composed by scattering coefficient of radar echoes. In this paper, we analyzed the characteristics value difference between the range bins including and not including targets. Based on the difference, we proposed a detector, according to which we can judge whether the small targets hidden in some range bins. The detection performances of the proposed algorithms are evaluated based on the measured data collected by the McMaster IPIX radar at the east coast of Canada.

The remainder of the paper is organized as follows. In Section 2, a brief description of the radar dataset used in this study is provided. Section 3 presents a short review of the polarimetric decomposition theory. In Section 4, a novel target detection technique is proposed and the test results are given. Section 5 concludes the paper.

#### 2. Radar Data Analysis

In this paper, the dataset we applied was collected from the IPIX Radar which was established by McMaster University in Canada. This radar located on the shore facing to the Atlantic at the height of 30 m above the sea level. It is fully coherent and dual linear polarization, which can get full polarization matrix with two pulses. We choose the no. 280 and no. 54 files data from the database for analysis, which includes the range bins containing the echoes data of a small target. The target is a spherical block of styrofoam, wrapped with wire mesh. It has a diameter of one meter. Each file has fourteen bins, and the small target is located in the 8th range bin. The target may also be visible in the 7th, 9th and 10th range bin. The datasets were collected under the high and low two sea states with height of wave 1.4 m and 0.7 m, separately. The average target to clutter ratio varies in the range of 0–6 dB. Resolution of data is 30 m, sampled at 15 m. The radar work at X-band with 9.39 GHz and PRF is 1000 Hz. Some collected data of HH and VV channels are displayed in Figure 1.

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In Figure 1(a), the average data amplitude of HH channel is smaller than that of VV channel, as predicted by the composite surface theory and Bragg scattering [12]. In Figure 1(c), the average data amplitude of HH channel is larger than that of the VV channel and more frequent the sea spikes appeared at higher sea state, the reason of which can be explained by the much more emergence of the breaking wave, which may be giving the opportunity for a multipath reflection. For VV polarization, the Brewster effect may lead to strong cancellation of the return, whereas the HH polarization will exhibit a strong (possibly spiky) return [12]. The average data amplitude of every channel in Figure 1(b) is larger than that of corresponding channel in Figure 1(a), because of the existence of target. But this phenomenon cannot be seen in Figures 1(c) and 1(d), because of the high sea state. From analysis above, we know that the small targets detection at low grazing angle will be harder under a certain single-polarization channel in bad sea state. Figure 2 displays the Range-time image from the data. The bright spots mean the strong echoes. The dash-dot ellipse is the range bin including target, and other solid ellipse is the range bin not including the target, but which has strong echoes yet. Obviously, we can see that the small targets detection at low grazing angle will be harder under a certain single-polarization channel in bad sea state.

#### 3. The Review of Polarimetric Decomposition Theory

The scattering matrix is often used to describe the relationship between transmitted and back scattered fields. In this document, it has been always considered that , since reciprocity applies in a monostatic system configuration. The received signals were range-processed and combined to form an estimate for the 3-dimensional Pauli scattering vectors [15] for each bin: The polarimetric coherency matrices were then formed from the outer product of the Pauli scattering vector averaged over an bin:The information content of this matrix can be compactly assessed from its eigenvalue spectrum. is positive semidefinite and hence its eigenvalues are real and nonnegative, where Two secondary functions of the eigenvalues can be defined: the polarimetric scattering entropy and anisotropy where . If the entropy is low then the system may be considered weakly depolarizing and we can extract the dominant target scattering matrix component as the eigenvector corresponding to the largest eigenvalue and ignore the other eigenvector components. If the entropy is high, then the target is depolarizing and we can no longer consider it as having a single equivalent scattering matrix and we must consider the full eigenvalue spectrum.

When the anisotropy is fixed to a constant, such as 0.35, the relationship curve between entropy and dominant eigenvalue can be deduced [13]. In Figure 3(a), the rejected clutter power will increase from 75% to 92%, when the entropy value decreases from 0.65 to 0.3. When the anisotropy A verified from 0 to 1, the relationship between entropy and dominant eigenvalue can be seen in Figure 3(b). The Figures 3(c) and 3(d) are the actual raw data distributions at the domain decided by entropy and dominant eigenvalue. The Figure 3(c) is the distribution of the 1st range bin raw data, and the Figure 3(d) is the distribution of the 8th range bin raw data. The inner domain of ellipse is the maximum of the point distribution. From the Figure 3, we can see the difference between the pure sea clutter and with targets in it. In a word, the Figure 3 shows the prospect of achieving high levels of discrimination against sea clutter by filtering in the polarization domain.

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In general the three normalized eigenvectors, corresponded to the three eigenvalues, are written as columns of a unitary matrix in the parametric form The alpha parameter can be used to distinguish different types of surface, volume and double bounce scattering. It is convenient to define an average scattering mechanism from the weighted sum of eigenvector parameters defined as According to the some special and value, the - plane was defined by Cloude and Pottier [15]. The plane can be used to classify the targets, which have different scattering mechanism. The plane is displayed in Figure 4. The red solid curve is the border curve, at the left of which all the points, decided by and , are distributed. Z1~Z9 are the nine zones, which divided by the red dashed lines. They represent nine kinds of different scattering mechanism. In this paper, we need using the plane to analysis the main scattering mechanism of sea clutter, according to the distribution of the points, from which the polar characteristic of sea clutter would be seen. In the zone 9 occur low entropy surface scattering processes with alpha value less than 42.5°. An isolated dipole scatterer would appear in the zone 8. The zone 7 corresponds to low entropy double or “even” bounce scattering events, such as provided by isolated dielectric and metallic dihedral scatterers. The zone 6 reflects the increase in entropy due to changes in surface roughness and due to canopy propagation effects. The zone 5 has moderate entropy but with a dominant dipole-type scattering mechanism. The zone 4 accounts for dihedral scattering with moderate entropy. The zone 3 is not part of the feasible region in the plane. The zone 2 relates to high entropy volume scattering. We can distinguish double bounce mechanisms in a high entropy environment in the zone 1.

#### 4. A Novel Detection Technique

##### 4.1. The Polar Characteristic Analysis

The distribution of points in the - plane was then generated for the 1st and the 8th range bins of the two files. In Figure 5, the color bar is corresponding to the density of the point distribution. The high intensive of points, red colored, lie in the low entropy region for two files. In Figure 5(a), without target, the high density distribution occurs at Z8, which means the isolated dipole scatter is the dominant scattering mechanism. In Figure 5(b), with target, the high density distribution occurs at the Z9, which means the surface scatter is the dominant scattering mechanism, and the entropy of the peak is very close to zero, which can be explained that dielectric constant is raised by the sphere target at this range bin. In Figures 5(c) and 5(d), the situation is similar to Figure 5(a) and Figure 5(b). But the entropy of the peak, in Figures 5(c) and 5(d), is higher than the one, in Figures 5(a) and 5(d), respectively. The distribution of points in Figures 5(c) and 5(d), which have high density, is of less concentration than the ones in Figures 5(a) and 5(b), respectively, because of high sea state the no. 280 file data set possesses. We also find that there is still a single dominant scattering mechanism present at the high incidence angle above 85°, although others pointed that it is characteristic of random scattering [13]. The different result may be due to the radar resolution ability.

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From Figure 5, the polar characteristic of the sea clutter with sphere target is summarized. The entropy of the peak is lower than the one without target, and the more lower the sea state is, the lower the entropy of peak is. The dominant scattering mechanism belongs to surface scattering. From the summarization above, we deduce that if the target mainly has double bounce scattering events, the results will be different with that. We add the ideal target which has double bounce scattering events and plane or spherical target to the pure sea clutter (the 1st range bin of no. 280 file) by some SCR (signal-clutter rate). Figure 6 displays the simulation results when the SCR is equal to 6 dB. Obviously, in Figure 6(a), the target embed in the sea clutter is dihedral target, while, in Figure 6(b), the target is plane or spherical target. The reason why Figures 5(d) and 6(b) are different is that the echo of ideal target does not be polluted by sea clutter. Figure 5 just simulates the dominant scattering mechanisms of different targets in theory.

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##### 4.2. A Novel Detection Technique

From the analysis above, we design the steps for detecting the small target in sea clutter. Figure 7 shows the schematic diagram of the algorithm. The first step is preprocessing of the raw data, which purpose is reducing the sea spikes as far as possible. We precede the second step with polarimetric decomposition. According to the result, the - plane is drew. When the third step, we find the weighted points distribution from the distribution matrix of - plane. Then the Weighted Average and the Weighted Average are obtained from the weighted point distribution. The purpose of finding the and the is to finding the dominant scattering mechanism and the stochastic degree of the scattering mechanism embedded in the echoes tested. At last step, according to the conclusion from the Figure 5, we give the empiricism threshold of for judging the last result. The detailed steps of the new method are summarized as follows.(1)In order to reduce the influence of spiking events for detecting performance as far as possible, and in the meantime, to maintain the echoes of small target, which may be exist, we choose the valid data before Polarimetric Decomposition. The copolarization ratio is considered as a good parameter characterizing the diffuse background of sea clutter, spiking, and man made target echoes, which defined as The is the co-polarization ratio of each bin. The research indicates that the spikes possess higher co-polarization ratio than the diffuse background do [1]. The spiking events possess a power at HH that is equal to or even higher than their power at VV, Whereas the power at HH is, without spiking events, some 10 dB lower than the power at VV [1]. As for manmade target, the co-polarization radio is close to 0 dB [16]. Thus, we choose the data which possess the lower co-polarization radio between 0 dB and 10 dB according to experience, for example, 3 dB, as the valid data, which formulized followed by The is the assemble of all the valid Pauli scattering vectors , which meet the condition , Where . (2)The will be executed in the formula (2), (4), and (7) in Section 3, from which the , can be obtained. Every pair of and determine a point at - plane. Some points will overlap. We divide the - plane into 180 rows and 200 lines, which form a distribution matrix , the elements of which represent points numbers appear in corresponding place of the plane. The points, the number of which is maximum in the matrix , declare the dominant scattering mechanism, as shown in Figure 4.(3)This step is to find the weighted points, from the matrix , whose number is larger than partial of the peak number, such as where , , .

The is the distribution matrix of points numbers for weighted points. The is the element of the matrix . The purpose of finding the matrix is to find the dominant scattering mechanism of the radar echoes.(4)Then, we use the matrix to calculate the and According to the , we design the detector The is the thresholds, which formulized by where is the coefficient, according to empirical, set to 0.065. is average wave height of the sea condition. According to , we can judge which kind of scattering mechanism the target belongs to. According to the detector, the result can be obtained. In Figure 8, the ideal ROC curve at different SCR is displayed.

##### 4.3. Detection Result

We select a piece of raw data randomly, whose length is 1009 points (about one second sample). Then, the detection results of no. 280 file, after steps in Section 4, are displayed in Figures 9 and 10. Figures 9(a) and 9(c) plot the amplitude of the raw data for the 1st range bin and the 8th range bin, respectively. Figures 9(b) and 9(d) display the amplitude of the valid data for the two range bins.

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Figure 10 displays the difference results after step 3). For the 1st range bin, Figures 10(a) and 10(b) plot the raw data and the valid data results after step 3), respectively. For the 8th range bin, Figures 10(c) and 10(d) plot the raw data and the valid data results after step 3), respectively. Figures 10(e) and 10(f) are the results of simulation, which added ideal, dihedral target in the data of Figures 9(a) and 9(b). All the range bins of the data files are analyzed, whose figures did not display here all. But the last detection results, after step 4, are summarized in Table 1.

Table 1 lists the and value of every range bin using two dataset files, according to which the range bin including the target has been detected after the detector we proposed. It can be concluded that the performance on detecting the small targets, embed in sea clutter, even though under the high sea state, is good. Through one thousand times random data samples test, the right detection results count for 92% ± 3%. In Figure 11, the real ROC curve of the method proposed in this paper is displayed.

#### 5. Conclusion

In this paper, we apply the polarimetric decomposition theory to solve the small target detection problem in sea clutter after analyzing the polarization characteristic of sea clutter without and with target, using IPIX data, under low grazing angle. It indicates that, under the same sea state, the dominant scattering mechanism of sea clutter, with target, is surface scatter, but one, without target, is isolated dipole scatter. According to the characteristic mentioned in this paper the method based on polarimetric decomposition is proposed and the good detection result was given, which has been demonstrated as having good performance for detecting the small target in sea clutter. In this research, the small target is a spherical block of styrofoam, wrapped with wire mesh, whose scattering mechanism is spherical scatter. Because the spherical scatter matrix is the same as surface scatter matrix, which usually the calm sea has, we believe that if there are other targets, having different scattering mechanism, such as the small ship, which has the double bounce scattering events, provided by isolated dielectric and metallic dihedral scatters, embed in sea clutter, the novel approach can work much more better, according to the simulation results analyzed in this paper. In a word, the bigger the difference of scattering mechanism between the sea clutter and targets is, the better the detection performance the proposed method has. In the further research, we will study the intrinsic function between the thresholds and wind direction, wave height. In addition, we will study another polar parameters anisotropy, which may play a role as a detector when the sea state is very high.

#### Acknowledgments

The data used in this paper from IPIX radar which was established by McMaster University in Canada is thanked. Financial support, whose serial number is 9140C8004011008, from National Key Laboratory of ATR is highly appreciated.