Static High Target-Induced False Alarm Suppression in Circular Synthetic Aperture Radar Moving Target Detection Based on Trajectory Features

Abstract

The new mode of Circular Synthetic Aperture Radar (CSAR) has several advantages including multi-aspect and long-time observation, which can generate high-frame-rate image sequences to detect moving targets with a single-channel system. Nonetheless, due to CSAR being sensitive to 3D structures, static high targets are observed in scene display rotational motion within CSAR subaperture image sequences. Such motion can cause false alarms rising when utilizing image sequence-based moving target detection methods like logarithm background subtraction (LBS). To address this issue, this paper first thoroughly analyzes the moving target and static high target’s difference for the trajectory in an image sequence. Two new trajectory features of the rotation angle and moving distance are proposed to differentiate them. Based on the features, a new false alarm suppression method is proposed. The method first utilizes LBS to obtain coarse binary detection results comprising both moving and static high targets, then employs morphological filtering to eliminate noise. Next, DBSCAN and target tracking steps are employed to extract the trajectory features of the target and false alarm. Finally, false alarms are suppressed with trajectory-based feature discriminators to output detection results. The W-band CSAR open dataset is used to validate the proposed method’s effectiveness.

1. Introduction

Circular Synthetic Aperture Radar (CSAR) is a new SAR imaging mode capable of continuously observing areas of interest with a circular track [1,2]. Its long-time and multi-aspect capabilities are conducive to target detection and tracking, as well as estimating the velocity of moving targets [3,4]. Recently, such advantages for moving target detection have become a hot topic due to their potential to improve the detection performance [5,6,7].

Although the multi-channel system and corresponding methods are a common scheme in detecting moving targets (such as space–time adaptive processing) [8,9,10], it is important to develop single channel-based detection methods. The single-channel SAR still plays an important role in current SAR application. Several recent studies have shown that utilizing the advantages of CSAR can achieve a good performance in detecting moving targets, even with a single-channel system [11,12,13,14]. One topic of interest is the use of image sequences to detect moving targets in single-channel CSAR [15,16]. This kind of research can be categorized into two classes: detection with the moving target’s shadow [17,18,19] and detection with the target’s smear/displaced signature in the image sequence [20,21,22]. The former method relies on detecting the moving shadow to locate the target. However, this approach requires a high signal-to-noise ratio and only works in a higher frequency range like W-band SAR [23]. On the other hand, the latter method detects the target’s smear/displaced signature in image sequences, which has fewer constraints and is therefore more applicable. One of the typical image sequence-based methods is logarithm background subtraction (LBS) [24,25], which uses a median filter to obtain the static background image, and then extracts the moving target signature by subtracting it from the original images. Another typical example is low-rank-based methods like the Robust Principal Component Analysis (RPCA) and Go Decomposition (GoDec) [26,27,28]. These methods can separate the background and foreground images by utilizing their low-rank (background) and sparsity (foreground) nature in data.

Further investigation reveals that CSAR’s curved geometry makes static high targets such as buildings and towers have a rotational motion in subaperture image sequences. This happens due to the projections of these targets onto different positions relative to the corresponding azimuth viewing angle, ultimately leading to false alarms raising in the detection. Figure 1 shows the rotation of a highly stationary target in the image sequence. The four images are images of different azimuths in the image sequence at different times.

At present, there is no research on the suppression of a high-target false alarm in circular SAR (to the best of our knowledge), but according to the three-dimensional terrain extraction of circular SAR, there have been many studies on the use of circular SAR to conduct three-dimensional terrain [29,30]. In 2017, a team at Nanjing University of Posts and Telecommunications conducted a circular SAR DEM extraction of the scene and studied the extraction method [31]. In summary, the above research is only used to extract terrain or the target height. Although it is not combined with moving target research, its signal model has laid a foundation for moving target false alarm suppression. Since the existing moving target detection algorithm cannot solve the false alarm problem caused by the defocusing trajectory of the stationary elevation target, it is necessary to distinguish the moving target from the highly stationary target. The false alarm suppression algorithm for the false alarm problem caused by the stationary elevation target is studied to improve the detection accuracy and detection efficiency of the moving target in the observation scene using the CSAR subaperture image sequence. The high-precision CSAR moving target detection results are helpful for further research on target recognition and tracking applications.

A viable way to address this issue is to utilize the trajectory shape difference of the moving target and false alarm (static high target). Hence, this paper first thoroughly analyzes the moving target and static high target’s difference for the trajectory in an image sequence. Two new trajectory features of the rotation angle and moving distance are proposed to differentiate them. Based on the features, a new false alarm suppression method is proposed. The method first utilizes LBS to obtain coarse binary detection results comprising both moving and static high targets, then employs morphological filtering to eliminate noise. Next, DBSCAN and target tracking steps are employed to extract the trajectory features of the target and false alarm. Finally, false alarms are suppressed with trajectory-based feature discriminators to output detection results.

The rest of this paper is organized as follows. Section 2 is for the dataset. Section 3 is for the signal model. It analyzes the rotation motion of the static high target and makes a comparison with the moving target’s signature, which provide the basis for using the trajectory feature to suppress the false alarm. Section 4 is for the proposed false alarm suppression algorithm. Section 5 is for the real data experiment; a comparison experiment with other image sequence-based moving target detection methods is also described. Section 6 is the discussion and the last section is the conclusion.

2. Materials and Dataset

The proposed false alarm suppression algorithm was evaluated using open W-band CSAR data [23], and the parameters are provided in

Table 1. Parameters of W-band CSAR data.

Parameters	Description
Center Frequency	94 GHz
Flight Height	300 m
Resolution	15 cm × 12 cm
Frame Rate	20 Hz
Total Frames	607
Subaperture Overlap Rate	80%

. A specific area of interest in the data was selected for processing purposes, measuring 300 × 200 pixels and labeled with a red box, as illustrated in Figure 2. This region includes both a moving target, represented by a green circle, and a static high target, designated in a yellow circle. The outcomes of each step throughout the processing procedure are elaborated in detail in this section.

Figure 3 illustrates the rotation phenomenon of billboards; Figure 3a displays its optical image while Figure 3b presents its rotations in 4 sub-images. For instance, the detection results obtained using the logarithm background subtraction (LBS) method [24,25] are shown in Figure 4, where the green box indicates the moving target, and the red circle represents the billboard. Specifically, Figure 4a shows the original images and Figure 4b shows the corresponding detection result, which identifies that the billboard remains after applying the LBS method. Therefore, it is crucial to suppress the false alarms caused by static high targets to achieve a good detection performance.

3. Signal Model of Static High Target’s Rotation Motion

In this section, the signal model of the static high target’s rotation motion is described and analyzed with point target simulation. Specifically, the first subsection involves derivation of a formula for the rotation radius of an ideal static point target at a fixed height. In the second subsection, we present a theoretical analysis of the rotation radius formula, then investigate the differences between the trajectories of static high targets and moving targets. The comparison provides the basis for using a trajectory feature to suppress a false alarm.

3.1. Defocus Radius of Static High Target

Figure 5 details the geometric configuration of CSAR, where (a) represents the three-dimensional model and (b) provides a frontal view of the imaging plane $AP{P}^{\prime }{B}^{\prime }B$. An approximate circular path is traversed by the radar, which is used to fit the real application; A denotes the position of the radar in this setup, while P (x0, y0, $\Delta h$) signifies the coordinate location of the ideal point target.

As depicted in Figure 3b, the distance between the radar and the target is represented as R, while H signifies the vertical height distance to the target. In instances where the imaging plane is established at the same elevation as that of the target $\Delta h$, the object under observation is imaged at its actual position. The horizontal distance from the imaging plane to the target is considered as the ground range

$$R_g=\sqrt{R^2-H^2}$$

(1)

When the imaging plane selects the ground plane, the height difference is $\Delta h$. Then, the target is projected on a ground plane based on the iso-range principle. Its ground range is

In situations where the imaging plane is aligned with the ground plane; a height difference (represented as “$\Delta h$”) between the target and the imaging plane exists. In such instances, the target is projected onto the ground plane using the iso-range principle, representing the horizontal distance from the radar to the target on the earth’s surface. The corresponding quantity is effectively the ground range of the target

$$R{’}_g=\sqrt{R^2-{\left(H+\Delta h\right)}^2}$$

(2)

The ground range difference P′C represents the defocus radius, which is given as

$$\Delta R_g=R_g-R{’}_g=\frac{\Delta h\left(2H+\Delta h\right)}{\sqrt{R^2-H^2}+\sqrt{R^2-{\left(H+\Delta h\right)}^2}}$$

(3)

Equation (3) is the exact formula to calculate the range difference. To give the reader a simple physical meaning, here, we further use an approximation in deduction. In the case of a CSAR system, it is customary for the height of the radar to exceed the elevation of the target. As such, Formula (3) may be simplified and expressed as follows:

$$\Delta R_g\approx \frac{H\Delta h}{\sqrt{R^2-H^2}}=\Delta h\cdot \tan \left(\phi \right)$$

(4)

In Equation (4), it is found out that the distance between the target and its projection is only dependent on target elevation and the instantaneous incidence angle. It does not require the information of the radar’s three-dimensional position. This provides the basis for the analysis on designing and extracting the features for discrimination. Under an ideal circular case, for targets located at the scene center, the incidence angle remains constant, leading to a defocused circular signal within the full aperture image. In contrast, when the target is situated off-center, the resulting defocused signal is in an approximated circular shape. For both cases, we can see the rotation. In the next subsection, we delve into simulation-based investigations of this phenomenon and compare it with the trajectory observed in moving targets’ scenarios.

3.2. Trajectory Features of Moving Target and Static High Target

For this section, simulation was conducted to confirm the efficacy of the rotation radius formula. Since the simulation aimed to validate the signal model and phenomenon, here, we used X-band SAR parameters for simulation for convenience. Specifically,

Table 2. Parameters for simulation.

Parameters	Value
Aircraft height (m)	7251
Aircraft radius (m)	467
Target A height (m)	0
Target B height (m)	5
Incidence angle (°)	15
Subaperture degree (°)	2

illustrates the parameters, with the utilization of two target points located at 0 m and 5 m from the scene center. This study aimed to validate the accuracy of the aforementioned formula in an ideal circular track and constant-speed moving target environment.

The simulation results are presented in Figure 6, where Figure 6a depicts the subaperture image of a 45° azimuth angle, while Figure 6b presents a combination of all 24 subaperture images. In Figure 6a, it can be observed that target A is not offset, whereas target B is projected. By extracting the distance between targets A and B in Figure 6a, the rotation radius was estimated to be 77.85 m, which is illustrated as the red dashed line. The theoretical distance calculated with Equation (4) was 77.6 m. The minor discrepancy between these two values could be attributed to maximum selection during extraction, thereby validating the effectiveness of Equation (4). Figure 6b further corroborates the simulation analysis, depicting a focused target A at the scene center and a circular trajectory, indicating the phenomenon of rotation exhibited by target B.

Subsequently, a comparison was drawn between the trajectory features of a moving target and those of a stationary high target. As discussed in [32], the shape of a constantly moving target differs notably from the near-circle shape analyzed in Equation (4). To facilitate this comparison, we present the simulation results in Figure 6.

The simulation parameters mentioned in Table 1 were implemented, with the moving target placed within the range and azimuth dimensions and set to move at a constant speed of 0.2 m/s in simulation. Figure 7 shows the resulting trajectory feature comparison between the moving target and a stationary high target, with subaperture images covering an azimuth aperture interval of 15° from 0° to 360° presented in Figure 7a, which is the height target of non-origin and a complete image combination for the static high target shown in Figure 7b. The trajectory of the static high target, as evidenced by its circular path of rotation around the target location, contrasts significantly with the ‘W’- or ‘V’-shaped signatures generated by targets moving along the X-label and Y-label, which are depicted in Figure 7c,d, respectively. These observations provide the theoretical foundations necessary for distinguishing false alarms.

4. False Alarm Suppression Algorithm

The logarithm background subtraction was adopted to obtain the coarse detection result. As illustrated in Figure 2, the detection outcomes comprise of moving targets, false alarms, and residual clutters. To discriminate the moving target and suppress a false alarm, we developed a three-stage algorithm to address these challenges. Firstly, the use of morphological processing facilitated the removal of residual clutter. The second stage involved discrimination between false alarms and moving targets via the employment of a trajectory feature, which utilized clustering and tracking methods for feature extraction. Lastly, false alarm removal was achieved through the application of trajectory feature-based discrimination, with the resulting detection outcomes being reported as output.

A flowchart of the proposed approach is depicted in Figure 8, featuring the following steps: (1) inputting an image sequence of CSAR data; (2) processing with the logarithm background subtraction method; (3) morphological processing; (4) DBSCAN clustering implementation; (5) target tracking; (6) trajectory feature extraction; (7) discrimination based on trajectory features; and (8) false alarm removal and output processing results.

Next, the key step is introduced in detail.

4.1. Logarithm Background Subtraction

The logarithm background subtraction (LBS) method represents a single-channel CSAR moving target detection algorithm [24,25]. This algorithm extracts background (i.e., static scene) images from the sequence, followed by subsequent background subtraction procedures to facilitate detection of the moving target-containing foreground image. Due to this being the preprocessing step in this paper, details are not given here. For other image sequence-based detection methods like the low-rank method, they can be used as replacement. However, these methods also face the false alarm problem due to their sensitivity to the fast changes in an image sequence. During this first-stage detection, coarse detection comprises the signatures of residual clutter, static high targets, and moving targets.

The input CSAR image sequence has N images, which are denoted as $I_0(n),n=1\dots N$. The coarse detection result $I_1\left(n\right)$ is given as

$$I_1\left(n\right)=LBS\left[I_0\left(n\right)\right]$$

(5)

4.2. Morphological Processing

In the second step, morphological processing [30] was employed to eliminate residual clutter and alleviate target signal breakage issues due to subtraction. The resultant detection outcomes are binary images in Figure 9, rendering the utilization of dilation and erosion-based morphological processing approaches ideal for enhancing image quality. Furthermore, false alarms are labeled with a red circle, and moving targets are labeled using green boxes while yellow circles indicate residual clutter.

It is observed that residual clutter occupies a relatively small number of pixels, rendering them susceptible to elimination through erosion techniques. For those small sizes of the static high target such as antennas, they may be suppressed in this step. For a larger-size false alarm like a tower, the rest of the steps are necessary. The erosion process involves employing a template, typically a box, where the size of the template serves as the primary parameter. The success of the algorithm is heavily dependent on achieving an appropriate template size. If the template size is too small, residual clutter remnants may remain while an excessive size could result in loss of the target signal in $I_1(n)$. In practice, $B_e$ is the erosion template that is applied to binary images to obtain satisfactory results, whereas the outcome of this process is presented as the erosion results $I_2(n)$:

$$I_2(n)=\mathrm{erosion}\left\{I_1(n),B_e\right\}$$

(6)

Subsequent to the erosion process, a technique known as dilation is utilized in order to selectively repair broken sections of both target and false alarm signals, which are labelled with green boxes and red circles, respectively, in Figure 8. The effectiveness of the dilation method is highly dependent on selecting an appropriate template size as was previously observed with the erosion process. Here, the dilation template utilized in this procedure is referred to. The resulting output from this method is given, serving as a vital component for further processing and analyses, as $I_3\left(n\right)$:

$$I_3(n)=\mathrm{dilation}\left\{I_2(n),B_d\right\}$$

(7)

4.3. DBSCAN Clustering

Once the majority of residual clutter is successfully eliminated, the subsequent procedure involves clustering the moving target and false alarm signals. This process serves as a vital prerequisite for feature extraction. Through cluster analysis techniques [25], individual pixels can be grouped together, thereby rendering the shape, angle, center-of-mass, and other associated attributes easier to discern. Furthermore, the use of clustering methods can also offer potential solutions to issues relating to signal breakage, as broken segments may potentially be assigned membership to specific clusters.

The DBSCAN requires the consideration of two essential parameters, namely Eps and MinPts. Specifically, Eps is the radius of a given pixel’s neighborhood, whereas MinPts refers to the density threshold, the minimum required number of pixels that make up a cluster. By determining and setting these parameters at appropriate values, one can effectively cluster the pixels within the image. Ultimately, the output of DBSCAN results in the set of clustered data points $I_4\left(n\right)$:

$$I_4\left(n\right)=\mathrm{DBSCAN}\left[I_3\left(n\right)\right],\mathrm{n}=1,2,\dots \mathrm{N}$$

(8)

Although the targets and false alarm are clustered, the task of associating the same target in consecutive frames is not addressed. As such, an additional tracking step is necessary to ensure that this task is completed.

4.4. Target Tracking

The current section involves the implementation of a target tracking process for clusters with the aim of connecting the same target in the image sequence. It is important to note that the input image sequence makes use of overlapped subaperture images, meaning that the same target will inevitably overlap across adjacent images. The signal-to-noise ratio is greater in airborne conditions as compared to spaceborne scenarios. Hence, a straightforward approach such as utilizing Intersection Over Union (IoU) of the target in adjacent images can be employed for the purpose of tracking. The IoU ratio of the same target in two adjacent images is:

$$\mathrm{IoU}=\frac{B_{\mathrm{i}}(n)\cap B_{\mathrm{j}}(n+1)}{B_{\mathrm{i}}(n)\cup B_{\mathrm{j}}(n+1)},\mathrm{n}=1,2,\dots ,N$$

(9)

It can be expressed that $B_{\mathrm{i}}(n)$ and $B_j(n+1)$ represent the ‘i-th’ and ‘j-th’ clusters in the ‘n-th’ and ‘(n+1)th’ images, respectively. The numerator in the given formula represents the total number of pixels that overlap between these two clusters, while the denominator refers to the sum of all the pixels in both clusters. By applying this equation to all the clusters in adjacent images, their corresponding IoU value can be obtained. Additionally, if two clusters belong to the same target and have a relatively high IoU value, they can be categorized as being assigned to an index. In practice, a suitable threshold for connecting the same target across an entire image sequence can be established using the aforementioned equation, and by setting the appropriate associated IoU-value $C_0$ threshold via the formula previously mentioned.

$$\{\begin{array}{l}{I}_{\mathrm{area}}\ge C_0,\mathrm{same}\mathrm{target}\\ I_{\mathrm{area}}\le C_0,\mathrm{not}\mathrm{same}\mathrm{target}\end{array}$$

(10)

The presented approach treats all clusters within the initial frame as potential targets for tracking purposes. The IoU tracker is subsequently applied to associate clusters in adjacent frames and successfully link such targets across multiple frames. If a target’s signature enters the image from the boundary, it is treated as a new potential target for tracking purposes; conversely, if a target moves out of the image boundary, the tracking will stop.

The next step was to extract the trajectory features and distinguish the moving target from the false alarm.

4.5. Trajectory Feature Extraction

Following the target tracking procedure, identification and labeling of the false alarm and moving targets were performed. This stage relies on the utilization of rotation angles and moving distances for differentiation. The above-mentioned two trajectory features were established through the incorporation of four fundamental features, which necessitated their preliminary extraction.

4.5.1. Basic Features

Table 3. Four basic features’ description.

Basic Feature Name	Description
Equivalent ellipse	Minimum bounding ellipse with equal pixels
Centroid	Center of mass
Major axis length	The major axis of the ellipse
Orientation	The angle between ellipse’s major axis and X-axis

presents the four fundamental features, which are visually depicted in Figure 10. Specifically, Figure 10a is the equivalent ellipse denoted by a red ellipse. The centroid of the target is represented as a red star in Figure 10b, whereas Figure 10c showcases the major axis length through a red dotted line. Orientation feature β is presented in Figure 10d.

4.5.2. Trajectory Features

(1)

Rotation angle

Figure 11 displays the orientation feature of false alarms. The red arrow indicates the direction of rotation, while the yellow point corresponds to the centroid and the green point denotes the endpoint of the ellipse. The figure reveals that the false alarm exhibits near circular motion in the image sequence, where the circle represents the theoretical trajectory. Notably, the orientation angle around the endpoint has significant changes, whereas the endpoint remains stationary. Conversely, when the moving target is observed within the limited frames, its trajectory can be approximated as nearly linear motion. For instance, as presented in Figure 11b, the moving target moves toward the endpoint in a linear direction without rotation, resulting in minimal change in the red orientation angle.

In practical scenarios, the discrepancies in the target shape and size within image sequences can result in centroid errors that lead to inaccurate orientation angle estimation. Consequently, the utilization of the aforementioned orientation feature is not a viable approach. As a solution, the recalibration of the angle via basic features is necessary. Hence, the accumulation of the orientation angle was adopted for calculating the rotation angle. Given the nth and first orientation angles of the tracked ith cluster in an image sequence, labeled as ${\theta }_i\left(n\right)$ and ${\theta }_i\left(1\right)$, respectively, the corresponding rotation angle, denoted as ${\varphi }_i$, can be obtained through the following equation:

$${\varphi }_i\left(n\right)=\left|{\theta }_i\left(n\right)-{\theta }_i\left(1\right)\right|,i=1,2,3\dots \dots ,n=1,2,3\dots \dots N$$

(11)

The ${\varphi }_i\left(n\right)$ of the false alarm evidently changes along with the frame number, while the ${\varphi }_i\left(n\right)$ of the moving target is around zero.

(2)

Moving distance

Another crucial feature for discerning between two signal types is the distance traveled during the image sequence. Due to the restricted rotational motion within a relatively confined area, the false alarm exhibits limited displacement. In contrast, the moving target displays much longer travel distances, as demonstrated in the preceding section.

The moving distance feature is depicted in Figure 12, comprising illustrations of both false alarm and moving target cases in Figure 12a,b, respectively. This attribute is characterized by determining the standard deviation of the endpoint positions of the target across the image sequence. Specifically, as illustrated in Figure 12a, the endpoint of the ellipse follows a circular trajectory around the centroid with a radius of r. Consequently, the resulting moving distance, which corresponds to the standard deviation, is small. In contrast, as presented in Figure 12b, the moving target endpoint undergoes a considerably longer displacement due to the distinctive ‘W’-shaped pattern identified in the previous section.

The ith target’s position in the nth image is represented by $p_i\left(n\right)$. The two-dimensional mean value of the trajectory’s length is denoted as $p_m$, and it reflects the center coordinate of the trajectory. Furthermore, the moving distance or standard deviation, defined as $\sigma$, can be expressed as:

$$\{\begin{array}{c}\sigma =\sqrt{\frac{{\displaystyle \sum {\left[p_i(n)-p_m\right]}^2}}{N-1}},i=1,2,3\dots \dots ,n=1,2,3\dots \dots N\\ p_m=\frac{1}{N-1}{\displaystyle \sum p_i(n),}i=1,2,3\dots \dots ,n=1,2,3\dots \dots N\end{array}$$

(12)

After extracting trajectory features, the next step was to use these features to separate the moving target from the false alarm, so as to remove the false alarm.

4.6. Apply Trajectory Feature for Discrimination

The last step was using the rotation angle and moving distance to distinguish the false alarm and moving target, and suppress the false alarm.

In real data, two distinct signature types may have changes in the shape or size within the image sequence. These changes can be attributed to two causes. Firstly, azimuth viewing angle gradual changes may change the projection of the building. Secondly, the LBS and associated processing may either introduce or reduce the target occupied area, leading to morphological alterations. Consequently, it is essential to establish appropriate thresholds for discrimination.

Two threshold values were established for both features. The threshold for the rotation angle $\varphi$ is denoted as ${\varphi }_0$, and the moving distance $\sigma$ is denoted as ${\sigma }_0$. The corresponding formulas are given below.

$$\{\begin{array}{l}\varphi (n)>{\varphi }_0,\sigma <{\sigma }_0\mathrm{false}\mathrm{alarm}\\ \varphi (n)<{\varphi }_0,\sigma >{\sigma }_0\mathrm{moving}\mathrm{target}\end{array}$$

(13)

The thresholds applied in this study were established via experimental testing. The quantities analysis on how to determine them is one of the planned future works. Once the moving target and false alarm signals are distinguished between based on these criteria, the removal process can be conducted. As the signals are clustered and tracked, they are assigned a unique index to facilitate subsequent processing. Hence, static high target corresponding signals can be easily excluded from the final output detection results.

5. Experiment

5.1. Processing Results

5.1.1. LBS Result

The initial step involved obtaining an image sequence comprising 607 frames, which corresponded to the overlapped subaperture images. For illustrative purposes, frame number 171 was chosen as a representative example. Figure 13 displays the results of the LBS process on this frame.

Figure 13a displays the 171st frame. The extracted background image is displayed in Figure 13b and was obtained with a median filter in the image index dimension. As both the target and shadow signals manifested as significantly deviating from the pixel values of the static scene, the median filter proved effective in extracting the background image. It becomes apparent in Figure 13b that the target and shadow signals have disappeared, while the rotated billboard only covers a relatively small proportion of its base compared to Figure 13a. Subtraction of the original intensity image from the background extracted via LBS retains the signature of both the target and shadow along with the billboard, as illustrated in Figure 13c. Since the original LBS algorithm focused on detecting high-value targets rather than low-value shadows, the last step involved performing CFAR processing to generate coarse detection results, presented in Figure 13d. Upon examination of Figure 13d, one can observe that the static high target signal and moving target signals remain in the image, thus they were inputted into the subsequent steps for further processing.

5.1.2. Morphological Processing

Following CFAR detection, morphological processing was performed on the binary image. Firstly, erosion was employed to eliminate any remaining clutter present in the image. Subsequently, dilation was executed to repair fractured regions within the image. Figure 14a displays the 171st frame image in the absence of erosion/dilation procedures. Figure 14b illustrates the outcome of implementing both procedures on the same image. Evidently, application of these morphological operators effectively removes the clutter situated within the right-hand side image and repairs the minor abnormalities surrounding both the moving target and false alarm signals.

5.1.3. DBSCAN Clustering

The subsequent step undertook the application of a DBSCAN; it has two key parameters: Eps and MinPts. In this study, we set Eps to 0.07 and MinPts to 15 pixels based on prior testing experiences. The effectiveness of the DBSCAN was validated with the clustering result obtained from analyzing the 171st frame, represented in Figure 15. Specifically, the moving target and billboard are denoted by green boxes and red circles, respectively, as depicted in (a). Utilizing the DBSCAN, the extracted data are further presented in (b), with each signature accommodating allocation within unique clusters possessing distinct indices. From the results, the size and shape characteristics of false alarms remain unchanged before and after undergoing the clustering process, which corroborates the effectiveness of the clustering step.

5.1.4. Target Tracking

Subsequent to the clustering step, we established associations between identical targets situated within consecutive frames in the image sequence via tracking algorithms. Figure 16 displays the tracking results of a false alarm situated in frames 171 and 305. The false alarm is designated by a red rectangle, with its trajectory exhibited by the red line present in (b) that was drawn based upon the center of mass calculation. As demonstrated through these results, the false alarm can be tracked across multiple frames, utilizing a unique index for proper identification.

5.1.5. Trajectory Feature Extraction and Discrimination

In this section, we present the results related to trajectory features. Figure 17a showcases the rotation angle pertaining to the false alarm signal, superimposed with two adjacent frames (172 and 173). The equivalent ellipse extracted from these frames is represented by a red dotted line with the centroid indicated by a red star and the endpoint signified by a green dot. Subfigure (b) shows the feature observed in the rotation angle associated with the moving target. The extraction outcomes demonstrate the feature has detectable variance within the key trajectory features distinctive between the two signals, even across adjacent frames such as 172 and 173.

After extracting the aforementioned features on a frame-by-frame basis, we present the curves relating the rotation angle as a function of frame number for both the false alarm and moving target in Figure 18a,b, respectively. The results indicate a noticeable increase in the rotation angle exhibited by the false alarm with an increasing frame count. Notably, some frames demonstrate minor declines in the rotation angle attributable to centroid errors arising from irregular shapes during angle extraction, notwithstanding the underlying trend remaining consistent. Cumulatively, the false alarm experienced an approximate 60° rotation across a span of 134 frames.

Due to the data having a limited scene size coupled with the rapid motion of the moving target, the data presence within the scene was confined to a mere 10 frames. Hence, we utilized all 10 frames for further analysis purposes. In Figure 18b, the rotation angle for the moving target is changed a little. We established an initial threshold level for a cumulative rotation angle at 60°.

The following analysis pertains to the moving distance feature. As delineated in Figure 18, the extraction of endpoint frames for moving targets served as information for our subsequent calculations. Utilizing Equation (13), we calculated the standard deviation values associated with the moving distance features of both false alarm and moving target signals to be 3.8093 m and 23.2384 m, respectively, as depicted within

Table 4. Moving distance (standard deviation) of false alarm and moving target.

	False Alarm	Moving Target
Moving distance (m)	3.8093	23.2384

.

The threshold of the motion distance was set as 5 m; if the moving distance is lower than 5 m, it is judged as a false alarm. Therefore, the moving target and false alarm can be distinguished.

5.1.6. False Alarm Suppression

After distinguishing the moving target and false alarm signals based on their trajectory features, we proceeded with suppression of the false alarm via its unique tracking index. The effectiveness of this technique is exemplified within Figure 19, where (a) depicts the original CSAR image captured at the 171st frame, (b) showcases the results after background subtraction and morphological processing, comprising both moving target and static high target signals, and (c) illustrates the subsequent outcomes upon suppressing the false alarm signal. Of note, signature signals associated with the billboard are no longer present in the results, further validating the efficacy of our proposed methodology.

5.1.7. Method Comparison Experiment

For this section, we conducted the comparison experiment between the proposed method, original logarithm background subtraction (LBS) method, and GoDec method. As described in the previous section, current research has not focused on the static high target’s rotation motion-induced false alarm rate rising problem. As will be shown in this subsection, for such image sequence-based methods, the false alarm should be dealt with, which demonstrates the necessity of the proposed method. Here, we focus on the processing results of the GoDec method, then give the comparison of the final detection results of the proposed method, original LBS method, and GoDec algorithm.

The details of the GoDec method can be found in references [26,33]. We use the same parameters as in 5.2.1 for processing with the GoDec method, i.e., the same image sequence to filter the background and foreground. However, GoDec and LBS have one unique difference. For a given image sequence, the LBS can only have one background and all frames have to subtract it to obtain the foreground. The GoDec method uses all frame data to estimate every image’s low-rank part and sparse part with optimization. The low-rank part represents the stable part, i.e., the background, and the sparse part represents the fast-change part, i.e., the moving target and rotated static high target.

The GoDec result of the 171st, 221st, and 271st frames is given in Figure 20. The three columns from the left to right are the original image (the corresponding background and foreground). The three rows from the top to bottom are the 171st, 221st, and 271st frames, respectively. From the original images, we can see the evident rotation phenomenon and in the 171st frame, we can see the moving target. In the corresponding background in the second column, the image is quite like the original images while the noise is reduced and the moving target in the 171st frame is removed. And the billboard target has a slight change compared with the original image. In foreground images, we can see that most of the stable backgrounds are eliminated in three frames and the moving target is well persevered in the 171st frame. This is the basis for moving target detection. On the other hand, the billboard is also preserved, which proves the necessity of the false alarm removal still existing in the GoDec method. Then, we determined the final detection results of the three methods. The GoDec method and original LBS method conduct the CFAR detection step to output the binary detection result. The proposed method further distinguishes between the moving target and false alarm. The comparison results are given in Figure 21.

In Figure 21, the three columns from the left to right are the binary detection results of the GoDec method, the original LBS method, and the proposed method. We can clearly see that the moving target in the three frames is always detected. The GoDec method and proposed method have less residual clutter. This is because the GoDec method can reduce background and the proposed method has the morphological filter step to deal with it. The static high target, i.e., the billboard, is removed only in the proposed method, as labeled with a red circle. From the comparison experiments illustrated in the figure, it can be seen that the first two methods cannot remove the false alarm, and the proposed false alarm suppression algorithm in this paper can effectively remove it. It shows the better performance and necessity of the proposed method.

6. Conclusions

This paper proposed a new trajectory feature-based method to suppress the false alarm generated by a static high target in CSAR moving target detection. It first thoroughly analyzed the moving target and static high target’s difference for the trajectory in the image sequence. Two new trajectory features of the rotation angle and moving distance were proposed to differentiate them. Based on the features, a new false alarm suppression method was proposed. The method first utilizes LBS to obtain coarse binary detection results comprising both moving and static high targets, then employs morphological filtering to eliminate noise. Next, DBSCAN and target tracking steps are employed to extract the trajectory features of the target and false alarm. Finally, false alarms are suppressed with trajectory-based feature discriminators to output detection results. The W-band CSAR open dataset was used to validate the proposed method’s effectiveness.

Future works can include developing the moving target’s shadow detection method, conducting a W-band CSAR experiment for a threshold selection principle analysis, and thoroughly analyzing the performance of the proposed method.