An Attitude Estimation Method for Space Targets Based on the Selection of Multi-View ISAR Image Sequences

Highlights

What are the main findings?

• Proposes a novel imaging plane normal-based selection criterion for multi-view ISAR sequences, maximizing perspective coverage while minimizing data redundancy.
• Develops an efficient HRNet-PSO framework that enables accurate feature matching and attitude estimation from the sparse selected images.

What is the implication of the main finding?

• Significantly reduces the manual preprocessing burden for non-cooperative target attitude estimation without sacrificing accuracy.
• Provides a robust, algorithm-upgradable solution for enhancing current space surveillance and debris removal missions.

Abstract

Multi-view inverse synthetic aperture radar (ISAR) image sequences provide multi-dimensional observation information about space targets, enabling precise attitude estimation that is fundamental to both non-cooperative target monitoring and critical space operations including active debris removal and space collision avoidance. However, directly utilizing all images within an ISAR sequence for attitude estimation can result in a substantial data preprocessing workload and reduced algorithm efficiency. Given the inherent overlap and redundancy in the target information provided by these ISAR images, this paper proposes a novel space target attitude estimation method based on the selection of multi-view ISAR image sequences. The proposed method begins by establishing an ISAR imaging projection model, then characterizing the target information differences through variations in imaging plane normal, and proposing an image selection method based on the uniform sampling across elevation and azimuth angles of the imaging plane normal. On this basis, the method utilizes a high-resolution network (HRNet) to extract the feature points of typical components of the space target. This method enables simultaneous feature point extraction and matching association within ISAR images. The attitude estimation problem is subsequently modeled as an unconstrained optimization problem. Finally, the particle swarm optimization (PSO) algorithm is employed to solve this optimization problem, thereby achieving accurate attitude estimation of the space target. Experimental results demonstrate that the proposed methodology effectively filters image data, significantly reducing the number of images required while maintaining high attitude estimation accuracy. The method provides a more informative sequence than conventional selection strategies, and the tailored HRNet + PSO estimator resists performance degradation in sparse-data conditions, thereby ensuring robust overall performance.

1. Introduction

Inverse synthetic aperture radar (ISAR) is widely used in space target imaging and monitoring. ISAR image is the projection of a three-dimensional (3D) space target structure onto a two-dimensional (2D) imaging plane, reflecting the structural information of the space target [1,2,3,4]. A multi-view ISAR image sequence is the image dataset obtained from observations of the space target under different viewing angles, providing multi-angle observational information. Based on the multi-view ISAR image sequence, the attitude estimation of the space target can be realized [5,6,7]. The ISAR image-based space target attitude estimation technique offers unique advantages for non-cooperative target monitoring [8,9], particularly for malfunctioning spacecraft that have lost communication with ground stations. Moreover, this method can be extended to space debris attitude estimation—a capability essential for Active Debris Removal (ADR) missions and space collision avoidance operations [10].

Recently, many research teams have conducted studies on attitude estimation of space target based on ISAR image sequence [11,12,13]. Existing studies can be generally divided into two categories. The first category is attitude estimation based on the combination of a target’s 3D model and ISAR images, where attitude estimation is performed by matching the target features of ISAR images with those of the projection images of 3D model [14,15,16,17,18]. The second category is to estimate the attitude directly based on the ISAR image data, which applies to scenarios where the target’s 3D model is unknown [5,6,19,20,21]. This kind of methods usually utilize the typical structural features of the target in the ISAR image sequence and establish an attitude estimation optimization model through variations in these typical structures across multiple ISAR images. Then, a parameter search algorithm is used to solve the optimization model, and the attitude estimation result is obtained once the optimization model converges. Since prior information about the target’s 3D model is unavailable, such methods rely on sufficient ISAR images that can provide multi-perspective observational data on the space target. The solution of the attitude estimation optimization model is significantly affected by ISAR images, as the information provided by the ISAR image sequence is the key to successful attitude estimation.

The acquisition of a high-quality multi-view ISAR image sequence is a prerequisite for the aforementioned attitude estimation methods. Current research on ISAR image sequence processing can be broadly categorized into two streams. The first and predominant stream focuses on image quality assessment, aiming to select the clearest images from a sequence by evaluating metrics such as entropy, contrast, and focus [22,23,24]. This is crucial for mitigating the effects of noise and blur in real-world data. The second stream, more relevant to the core of this work, recognizes the fundamental importance of viewing angle diversity for tasks like 3D reconstruction and attitude estimation. Several studies have qualitatively emphasized that limited or uneven viewing angles can lead to poor reconstruction accuracy [25,26,27,28,29]. For instance, Ref. [27] demonstrated that 3D reconstruction results are inferior with partial angles compared to full-angle data. In practice, when dealing with long sequences, a common heuristic is to sub-sample images at equidistant intervals to roughly approximate uniform angular sampling [29]. However, these approaches remain qualitative or rely on simple, sub-optimal rules. There is a distinct lack of research on quantitative, optimization-driven methods for selecting an image subset that actively maximizes viewing angle coverage and uniformity to achieve the best performance for downstream tasks like attitude estimation.

Indeed, as underscored by the aforementioned literature, the larger the coverage range of radar imaging perspectives corresponding to the ISAR image sequence, the more comprehensive the target feature information provided, and the easier the convergence of the target attitude estimation algorithm, ultimately resulting in a higher accuracy of attitude estimation results [30,31,32,33,34,35]. Most existing attitude estimation methods directly employ all images in ISAR image sequence from a certain arc segment for attitude estimation [36,37]. Direct use of all images for attitude estimation ensures sufficient information and helps to obtain more accurate attitude estimation results. However, since ISAR images usually require image preprocessing, feature labeling and other work [5,38,39,40], using all images in an ISAR image sequence for attitude estimation faces multiple challenges: prolonged data preprocessing time, heavy workload for feature annotation and significant impact from manual labeling inaccuracies, which will lead to inefficient attitude estimation. In fact, ISAR images with similar viewing angles provide highly redundant information, thus ISAR image sequences typically contain overlapping and redundant target information. Target attitude estimation can be realized by selecting a certain number of ISAR images from the sequence. When selecting ISAR images, the combination of ISAR images from different perspectives provides different target feature information, and the target attitude estimation results with different precisions will be obtained. At present, the criterion and principle of ISAR image sequence selection are not clear. In order to ensure the accuracy of attitude estimation while reducing preprocessing and labeling workloads, rational selection of ISAR image sequence is particularly important, necessitating the research on ISAR image selection criteria and methods. In addition, accurate feature extraction from ISAR image proves crucial for attitude estimation precision. Manual feature labeling inevitably introduces human errors and efficiency limitations due to manual operations. While adaptive image association matching methods exist, they demand high continuity among ISAR image sequence. After ISAR image selection, reduced image count decreases inter-image relevance. Therefore, further research should focus on developing feature extraction and correlation matching methods specifically optimized for selected ISAR images.

In this paper, a multi-view ISAR image sequence selection method guided by the criterion of maximizing observation perspective coverage is proposed. This method characterizes the variation process of the observation perspectives by solving the normal vector of the ISAR imaging plane, and achieves maximum perspective coverage with the minimum number of images through optimal selection. Furthermore, an algorithm framework for multi-view ISAR image sequence selection and attitude estimation of the space target without model priors is constructed. Based on the range-Doppler imaging principle, the mapping relationship between the selected images and attitude parameters is analyzed. Through feature point extraction and optimization solution on the selected images, the 3D pointing estimation of the target structure is realized. Typical feature point extraction methods include high-resolution network (HRNet) [41], key points extraction network (KPEN) [42], and dense attention U-Network (DAU-Net) [43], etc. Considering its advantages of compact structure and training efficiency, HRNet is adopted in this paper for feature point extraction. It should be noted that other advanced networks such as KPEN and DAU-Net can also be applied within the proposed framework to further enhance performance. Finally, a constrained optimization model is established for the extracted feature points, where the orientation of typical components is optimized using the particle swarm optimization (PSO) algorithm to obtain the final attitude estimation results.

The remainder of this paper is organized as follows: Section 2 develops the Space target ISAR imaging projection model, while Section 3 presents the methodology for attitude estimation of space targets based on multi-view ISAR image sequence selection, including the image selection algorithm from the multi-view ISAR image sequence and the establishment and solution of the attitude estimation optimization model. In Section 4, experimental results utilizing the electromagnetic simulation data demonstrate the effectiveness of the proposed method. Section 5 draws the final conclusions.

2. Space Target ISAR Imaging Projection Model

Figure 1 shows the ISAR imaging geometry. The ground-based radar tracks the space target by transmitting the broadband signals and acquires the target’s echo signals with long integration time and wide angular variation. After imaging processing, a sequence of ISAR images of the target is obtained.

Figure 2 shows a schematic diagram of the data processing chain from raw echo data to sequential ISAR images. The wide-angle echo data of the space target obtained by ISAR must be processed in blocks firstly, and the whole echo is divided into $K$ overlapping sub-apertures. For uniform resolution preservation in range and azimuth dimensions, the azimuth accumulation angle of each sub-aperture is same. In Figure 2, “Start” and “End” represent the initial and terminal echoes of each sub-aperture, respectively. Through the processing, $K$ ISAR images (denoted as ${\mathrm{I}}_1,{\mathrm{I}}_2,\cdots ,{\mathrm{I}}_K$) are generated from the whole echoes.

Through the ISAR imaging process, the space target is projected onto a 2D imaging plane to form an ISAR image. By analyzing and processing the sequential ISAR images, the attitude and 3D structure of the space target can be reconstructed. The establishment of an accurate ISAR imaging projection model serves as the foundation for the attitude estimation.

Considering a scattering center located at $(x,y,z)$ in the 3D coordinate system of a space target. After ISAR imaging process [7], the space target is projected onto a 2D imaging plane, resulting in a corresponding 2D directional vector on the ISAR image:

$$\left[\begin{array}{c}r\\ d\end{array}\right]=M·\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$$

(1)

where $r$ and $d$ represent the range and azimuth coordinates of the target scattering center’s projection on the ISAR image, respectively. $M$ represents the projection matrix.

The projection matrix $M$ establishes the geometric relationship between the target’s 3D structure and its 2D ISAR image, which can be mathematically expressed as:

$$M=\left[\begin{array}{c}{i}^T\\ j^T\end{array}\right]$$

(2)

where $i$ represents the range projection vector and $j$ represents the azimuth projection vector.

According to ISAR imaging principles, the imaging plane orientation is determined by the target’s rotational motion relative to the radar. The range direction aligns with the radar line-of-sight (LOS) vector $i_{los}$. The range projection vector can be derived as:

$$i={\displaystyle \frac{1}{{\rho }_r}}{i}_{los}$$

(3)

where ${\rho }_r$ denotes the range resolution, determined by the transmitted signal bandwidth.

The relative motion between the target and the radar provides high azimuth resolution. For a three-axis stabilized target, the ISAR imaging plane’s azimuth direction can be determined solely by the LOS vector $i_{los}$ variation, without considering the target scatterers’ rotational motion relative to the coordinate system. Thus, by taking the derivative of the range projection, the azimuth projection vector is obtained:

$$j={\displaystyle \frac{1}{{\rho }_a}}{\displaystyle \frac{{\mathit{\Omega }}_{los}\times i_{los}}{‖{\mathit{\Omega }}_{los}\times i_{los}‖}}$$

(4)

where ${\mathit{\Omega }}_{los}$ represents the angular velocity of the radar LOS $i_{los}$, and ${\rho }_a$ represents the azimuth resolution determined by both the signal wavelength and the coherent integration angle.

Based on the space target ISAR imaging projection model shown in Equation (1), target attitude estimation can be performed using both the projection matrix information and features extracted from ISAR images.

3. Methodology

Building upon the space target ISAR imaging projection model presented in Section 2, the attitude estimation can be achieved by combining projection matrix information with features extracted from ISAR images. This section details the attitude estimation method of space target based on the selection of multi-view ISAR image sequence.

The methodology consists of two stages. The first stage involves the image selection from multi-view ISAR image sequence. Based on the imaging plane normal angles of the ISAR image sequence, the images are selected through a multi-view ISAR image selection method, yielding an optimized set of images. These selected images are then processed in the second stage. Within the established attitude estimation optimization framework, HRNet performs target feature point extraction from the selected images, while a PSO-based algorithm subsequently estimates the attitude angle parameters using these features. Figure 3 summarizes the complete workflow for space target attitude estimation, with detailed explanations of each stage provided in the following sections. Section 3.1 analyzes the principle of image selection and details the procedure of the proposed ISAR image selection method. Section 3.2 establishes the attitude estimation optimization model and presents the solution to the optimization model.

3.1. Selection of Multi-View ISAR Image Sequence

The multi-view ISAR image sequence is a collection of space target ISAR images acquired from multiple observation angles. For attitude estimation, increased angular diversity in the observation geometry enhances the target information content in ISAR images, which facilitates the convergence of the optimization process and improves the attitude estimation accuracy.

Although utilizing the whole images in multi-view ISAR sequence for attitude estimation ensures information sufficiency and improves the estimation accuracy, the preprocessing and feature labeling of numerous images significantly compromise the computational efficiency. In practice, ISAR images with similar viewing angles provide highly redundant information. To enhance the processing efficiency, a representative subset of images can be strategically selected from the sequence.

To achieve optimal image selection and reduce data redundancy, it is essential to first analyze the differences in target information content provided by the multi-view ISAR image sequence, followed by quantitative characterization of the variations induced by different viewing angles. Systematic image selection can then be implemented based on the measured disparities in viewing angles among multi-view images. When developing the image selection methodology, the proposed method reduces the preprocessing workload while fully utilizing the observational information of the target through two key criteria: (1) near-uniform angular distribution and (2) comprehensive viewing angle coverage.

Based on the preceding analysis, this section proposes an ISAR imaging plane normal variation-based selection method for multi-view ISAR image sequence. The proposed method consists of two main steps:

●

Calculation of the imaging plane normal angle for each ISAR image based on its imaging plane orientation to quantify observational information differences.

●

Selection of representative images through uniform angular sampling of the imaging plane normal variation profile.

3.1.1. Imaging Plane Normal Angle Calculation

The differences in target information representation across multi-view ISAR images primarily stem from variations in observation perspectives. During the radar tracking process of the space target, the azimuth and elevation angles within conventional RAE (Range-Azimuth-Elevation) measurements obtained by the radar are insufficient to accurately characterize the observational viewing angle of the target’s structure. Without an effective method for evaluating observational information disparities, neither the distribution of imaging perspectives can be analyzed nor reference criteria for image selection be established. Prior to image selection, these perspective variations must be quantitatively assessed through precise characterization of imaging viewpoints to enable the analysis of their distribution characteristics. Based on the imaging plane formed by the relative motion between the target and the radar LOS, combined with the angular parameters transformation in the target’s attitude-stabilized coordinate system, this section presents a precise characterization of the target structure’s observation viewing angle information.

As defined in Equations (1) and (2), each ISAR imaging plane is spanned by orthogonal basis vectors $i$ (range direction) and $j$ (azimuth direction). The imaging plane normal vector is computed as:

$$f=i\times j$$

(5)

For each ISAR image in the multi-view sequence, the imaging plane normal vector can be computed from its imaging plane using the given equation, and the changes in imaging plane of the multi-view ISAR image sequence can be obtained. Figure 4 shows such variations in a certain scenario. The target is positioned at the origin of a unit sphere aligned with its orbital reference frame. The direction from each red marked point to the sphere’s center is represented by an orange dashed line, corresponding to the imaging plane normal vector of individual ISAR images. The red curve composed of the red marked points reflects the changes in the imaging plane of the multi-view ISAR image sequence.

The variation in the imaging plane normal vector in multi-view ISAR sequence encodes 3D structural information of the space target. This variation enables quantitative analysis of information diversity across the image sequence, providing critical metrics for optimal image selection.

For reliable analysis, the normal vector variation must be evaluated in an attitude-stable reference frame. For three-axis stabilized space targets, the orbital coordinate system typically provides such stability. Consequently, it is necessary to establish the coordinate transformation between the target’s orbital reference frame and imaging plane normal vectors.

Based on the imaging timestamp and the radar tracking data, the target’s position $s$ and velocity $u$ in the J2000 inertial frame are derived through precise orbit determination [44]. As defined by the orbital coordinate system convention, the geocentric direction constitutes the Z-axis:

$$a_z=-{\displaystyle \frac{s}{\left|s\right|}}$$

(6)

The Y-axis of the target’s orbital coordinate system is normal to the orbital plane, defined by the direction of the specific angular momentum vector:

$$a_y={\displaystyle \frac{s\times u}{\left|s\times u\right|}}$$

(7)

The X-axis of the target’s orbital coordinate system lies within the orbital plane and completes the right-handed Cartesian coordinate system:

$$a_x={\displaystyle \frac{a_y\times a_z}{\left|a_y\times a_z\right|}}$$

(8)

The orientation of the ISAR imaging plane is characterized by two angular parameters relative to the target’s orbital coordinate system. The azimuth angle $\phi$ of the imaging plane normal is defined as the angle between the normal vector and the XOZ plane:

$$\phi =\arcsin \left({\displaystyle \frac{\left|{\mathit{a}}_y·\mathit{f}\right|}{\left|{\mathit{a}}_y\right|·\left|\mathit{f}\right|}}\right)$$

(9)

The elevation angle $\theta$ of the imaging plane normal is defined as the angle between the normal vector and the XOY plane:

$$\theta =\arcsin \left({\displaystyle \frac{\left|{\mathit{a}}_z·\mathit{f}\right|}{\left|{\mathit{a}}_z\right|·\left|\mathit{f}\right|}}\right)$$

(10)

The azimuth and elevation angles of the imaging plane normal accurately characterize the projection angles of the target’s 3D structure onto the imaging plane, providing the means to analyze observational information differences. Utilizing variations in those angles to describe viewpoint changes across ISAR images enables refined quantification of observational disparities. Therefore, these angular parameters can be used to evaluate the coverage completeness of viewing angle and establish a quantitative criterion for optimal image selection.

3.1.2. ISAR Image Selection

Figure 5 shows the ISAR image sequence and the relationship between the selected images. In the original sequence, the $k$-th ISAR image is characterized by its imaging epoch $t_k$, azimuth angle ${\theta }_k$, and elevation angle ${\phi }_k$. The ISAR image selection process involves choosing a subset of $n$ representative frames from the complete set of $K$ available images. The selection is formally defined by an index set $\left\{S_1,S_2,\cdots ,S_n\right\}$, where $S_n\in \left(\mathrm{1,2},3,\cdots ,K\right)$ denotes the original sequence index of each selected ISAR image.

The comprehensiveness of target information acquisition directly correlates with both the coverage range and distribution diversity of observation viewpoints [45]. This establishes two fundamental principles for ISAR image selection: (1) maximizing the angular coverage span and (2) optimizing the angular distribution uniformity. To achieve comprehensive viewing angle coverage, the selected images must include images acquired at the extremal values (both minimum and maximum) of azimuth and elevation angles along the imaging plane normal.

The sets of azimuth and elevation angles for the selected images’ imaging plane normal are denoted as $\overline{\phi }$ and $\overline{\theta }$ respectively. These angular sets must satisfy the following constraint equation:

$$\left\{\begin{array}{c}\max \left({\phi }_1,{\phi }_2,\cdots ,{\phi }_K\right)\in \overline{\phi },\min \left({\phi }_1,{\phi }_2,\cdots ,{\phi }_K\right)\in \overline{\phi }\\ \max \left({\theta }_1,{\theta }_2,\cdots ,{\theta }_K\right)\in \overline{\theta ,}\min \left({\theta }_1,{\theta }_2,\cdots ,{\theta }_K\right)\in \overline{\theta }\end{array}\right.$$

(11)

To ensure angular diversity in the ISAR image sequence, the selected images must additionally satisfy the uniform distribution criterion for the azimuth and elevation angles of the imaging plane normal. This requirement is formally expressed by the following constraint equation:

$$\left\{\begin{array}{c}{\phi }_{S_n}-{\phi }_{S_{n-1}}={\phi }_{S_{n-1}}-{\phi }_{S_{n-2}}\\ {\theta }_{S_n}-{\theta }_{S_{n-1}}={\theta }_{S_{n-1}}-{\theta }_{S_{n-2}}\end{array}\right.$$

(12)

Based on the aforementioned image selection principles, the selection of ISAR image sequence is carried out through the following procedure. Firstly, the azimuth and elevation angles of the imaging plane normal for all ISAR images are calculated, and then the ISAR images at both minimum and maximum azimuth/elevation angle values of the imaging plane normal are selected. Finally, additional ISAR images are selected at uniform angular intervals across the complete azimuth and elevation angle coverage domain of the imaging plane normal.

Considering the nonlinear and non-convex characteristics of the imaging plane normal variation, a grid partitioning strategy combined with Euclidean distance computation is developed to achieve optimized uniformity in the selection process. Specifically, the selection method implements uniform sampling in the 2D elevation and azimuth angle space through three key steps: (1) constructing an equally spaced grid with angular interval $∆\sigma$ by partitioning both elevation and azimuth angle ranges; (2) calculating the Euclidean distance $\overline{D_k}$ between the elevation and azimuth angles of each ISAR image and its nearest grid point; (3) selecting images satisfying $\overline{D_k}<{\displaystyle \frac{∆\sigma }{2}}$.

The interval angle size critically determines the selection density, exhibiting an inverse relationship with the number of selected images. Specifically, increased $∆\sigma$ value yields sparser image subsets, whereas decreased $∆\sigma$ produces more comprehensive selections.

The proposed multi-view ISAR image selection method fundamentally ensures that the selected images achieve a uniform distribution in both elevation and azimuth angles within the nonlinear 2D space, while simultaneously attaining comprehensive coverage.

Table 1. Steps of the multi-view ISAR image selection method.

The Multi-View ISAR Image Selection Method
1. Input: Interval angle $∆\sigma$;
2. Calculate the imaging plane $M_k$ of each image according to Equation (3) and Equation (4);
3. Calculate the imaging plane normal vector $f_k$ of each image according to Equation (5);
4. Calculate azimuth angle ${\phi }_k$ and elevation angle ${\theta }_k$ of the imaging plane normal of each image according to Equations (9) and (10);
5. According to the azimuth angle ${\phi }_k$ of the imaging plane normal of sequential ISAR images, select the ISAR image corresponding to the maximum $\mathrm{a}\mathrm{z}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{t}\mathrm{h} \mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e} \dot{\phi }=\mathrm{m}\mathrm{a}\mathrm{x}\left({\phi }_1,{\phi }_2,\cdots ,{\phi }_K\right)$ and minimum $\mathrm{a}\mathrm{z}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{t}\mathrm{h} \mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e} \ddot{\phi }=\min \left({\phi }_1,{\phi }_2,\cdots ,{\phi }_K\right)$;
6. According to the elevation angle ${\theta }_k$ of the imaging plane normal of sequential ISAR images, select the ISAR image corresponding to the maximum elevation angle $\dot{\theta }=\max \left({\theta }_1,{\theta }_2,\cdots ,{\theta }_K\right)$ and minimum $\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e} \ddot{\theta }=\min \left({\theta }_1,{\theta }_2,\cdots ,{\theta }_K\right)$;
7. According to the angle $\left({\phi }_k,{\theta }_k\right)$ of the imaging plane normal of sequential ISAR images and the interval angle $∆\sigma$, generate an equally spaced partition grid $\left({\phi }_a,{\theta }_a\right)$, where ${\phi }_a\in \left[\dot{\phi }:∆\sigma :\ddot{\phi }\right],{\theta }_a\in \left[\dot{\theta }:∆\sigma :\ddot{\theta }\right]$;
8. According to the angle $\left({\phi }_k,{\theta }_k\right)$ of sequential ISAR images and the equally spaced partition grid $\left({\phi }_a,{\theta }_a\right)$, find the point in the equally spaced grid $\left({\phi }_a,{\theta }_a\right)$ closest to the angle $\left({\phi }_k,{\theta }_k\right)$, and record the azimuth angle and elevation angle of this point as $\widetilde{{\phi }_k}$ and $\widetilde{{\theta }_k}$;
9. Calculate the Euclidean distance $\overline{D_k}={‖{\phi }_k-\widetilde{{\phi }_k}{,\theta }_k-\widetilde{{\theta }_k}‖}_2$ between imaging plane normal angle $\left({\phi }_k,{\theta }_k\right)$ and its nearest grid point $\left(\widetilde{{\phi }_k},\widetilde{{\theta }_k}\right)$, select the corresponding ISAR image when $\overline{D_k}<{\displaystyle \frac{∆\sigma }{2}}$;
10. Output: Selected ISAR images.

systematically summarizes the steps of the proposed method.

3.2. Establishment and Solution of Attitude Estimation Optimization Model

The projection result of the target model on the corresponding imaging plane can be obtained. Then, the target’s attitude can be determined by optimizing the attitude parameters until the error between the model projection feature and the image feature is minimal

Let $P$ represent the key points on the 3D model of space target, and construct the objective function of attitude estimation as follows:

$$\underset{\alpha ,\beta ,\gamma }{arg}\mathit{min}{\sum }_{h=1}^H{‖M_h\cdot R\left(\alpha ,\beta ,\gamma \right)\cdot P-{\overline{P}}_h‖}_2$$

(13)

where $\alpha$, $\beta$ and $\gamma$ are, respectively, euler angles of pitch, yaw and roll, which jointly determine the target attitude, $R\left(\alpha ,\beta ,\gamma \right)$ is the attitude rotation matrix obtained by euler angle [46], $M_h$ represents the imaging projection matrix corresponding to the $h$-th image in the image sequence after selection, ${\overline{P}}_h$ indicates the key feature of the target extracted from the $h$-th image. $H$ indicates the number of selected images.

Based on the selected images, target attitude estimation is performed by solving Equation (13), which involves both feature extraction and model optimization. To mitigate the performance degradation caused by the substantial reduction in image quantity after image selection, we propose an integrated HRNet-PSO framework that simultaneously enhances feature extraction accuracy and optimization convergence. The implementation process of feature extraction and attitude estimation are given as follows.

3.2.1. Feature Extraction of Space Target’s Typical Components Based on HRNet

Radar imaging is significantly influenced by the anisotropy of target electromagnetic scattering and its own structure occlusion [47]. As a result, the target structures in the obtained images are often sparse and incomplete. Moreover, the imaging results vary greatly under different viewing angles. This variability poses a substantial challenge to traditional feature extraction methods based on morphological processing, which struggle to robustly extract target structure features. To address this issue, this paper employs HRNet [41] for feature extraction of space target’s typical components. Upon completion of HRNet training, the optimally selected ISAR images are processed through the trained network to acquire feature extraction results. The feature extraction accuracy maintains consistency regardless of the reduced image quantity, demonstrating robust adaptability to attitude estimation scenarios involving diminished image sets from our image selection method.

This network connects the sub-networks of high resolution to those of low resolution in parallel, facilitating the exchange of information between different resolution features. By fusing multi-scale information while preserving high-resolution features, it can effectively improve the robustness of feature extraction of target structures. The specific network structure is illustrated in Figure 6.

The network employs a four-branch parallel structure with phased expansion, comprising four progressive stages: Stage 1, Stage 2, Stage 3, and Stage 4. Each stage gradually expands the low-resolution branches while retaining all the historical branches. Specifically, Stage 1 processes high-resolution features through a single-branch and performs two rounds of down-sampling, reducing the input image size to 1/4 of the original. In Stage 2, a new branch is introduced, which further down-samples the feature map to 1/8 of the original size, forming a dual-branch parallel structure. Stage 3 and Stage 4 further expand the architecture to a four-branch structure, reducing the feature map size to 1/32 of the original image. Each branch consists of two 3 × 3 convolution layers. Following each convolutional layer, a batch normalization layer and an activation function are connected. After each Stage structure, the number of channels is doubled, with the final number of branch channels reaching 512. Following the execution of each residual module, cross-branch fusion is performed. This cross-branch fusion includes both up-sampling fusion and down-sampling fusion, corresponding to the Up and Down modules in Figure 6, respectively. Up-sampling fusion employs bilinear interpolation and transposed convolution for low-resolution features, while down-sampling fusion usually utilizes 3 × 3 convolution. Both mechanisms effectively ensure the continuous interaction of multi-scale information.

Compared to traditional networks, which typically down-sample and then up-sample to restore resolution, resulting in the loss of spatial information, HRNet progressively incorporates low-resolution branches at different stages of the network, forming multiple parallel sub-networks. Each sub-network processes feature maps at different resolutions and achieve information exchange through cross-resolution connections. Moreover, HRNet repeats multi-scale fusion at multiple stages of the network, allowing high-resolution feature maps to gradually incorporate global semantic information while maintaining spatial precision.

This design enables high-resolution feature maps to integrate the global semantic information from low-resolution feature maps, while low-resolution feature maps can also incorporate local detail information from high-resolution feature maps. As a result, the richness and expressive power of the features are enhanced.

In the final stage, HRNet directly generates keypoint heatmaps from the high-resolution feature maps. Each keypoint corresponds to a heatmap, where the value of each pixel represents the probability or response score of that location being a keypoint. The high-resolution feature maps ensure the spatial accuracy of the heatmaps, thereby improving the precision of keypoint localization.

In this network, the weighted mean squared error (MSE) between extracted key point positions and ground-truth key point positions is used as the loss function, which is called the KpLoss [41]. It is computed as follows

$$L=\frac{1}{B}{\sum }_{b=1}^B{\sum }_{u=1}^U{ϵ}_{b,u}\cdot {\displaystyle \frac{1}{\tilde{H}\times \tilde{W}}}{\sum }_{\tilde{h}=1}^{\tilde{H}}{\sum }_{\tilde{w}=1}^{\tilde{W}}({\widehat{H}}_{b,u,\tilde{h},\tilde{w}}-{\overline{H}}_{b,u,\tilde{h},\tilde{w}}{)}^2$$

(14)

where $B$ represents the batch size, $U$ denotes the number of key points. $\tilde{H}$ and $\tilde{W}$ are the height and width of the heatmap. Consequently, $b$ and $u$ represent the index values of the current batch and key point, while $\tilde{h}$ and $\tilde{w}$ indicate the specific row and column of the heatmap, respectively. ${\widehat{H}}_{b,u,\tilde{h},\tilde{w}}$ and ${\overline{H}}_{b,u,\tilde{h},\tilde{w}}$ represent the values of the predicted heatmap and ground truth at position $(\tilde{h},\tilde{w})$ for the $b$-th batch for $u$-th key point. ${ϵ}_{b,u}$ is the weight coefficient assigned to the u-th key point. This loss function calculates the pixel-wise MSE between the predicted heatmap and the ground truth heatmap. A key point weighting mechanism is subsequently integrated to address issues related to occluded and invisible key points. Owe to its simple and efficient design, it has become the standard loss function for heatmap-regression-based key point detection tasks.

For network training, feature points on the target are selected to establish a key point model, and the corresponding labels for the image sequence are obtained through projection calculations. As shown in Figure 7, the selected points are all corner points of the target structure. Let $p_{u,h}$ represents the coordinates of the u-th feature point extracted from the image of frame $h$, the number of points is $U$, then

$${\overline{P}}_h=\left[p_{1,h},p_{2,h},\cdots ,p_{U,h}\right]$$

(15)

The trained network is employed to extract the key points from the h-th image. By inputting all images selected through the proposed image selection method into this network, we generate feature extraction results and obtain the feature set ${\overline{P}}_{ser}=\left\{{\overline{P}}_1,{\overline{P}}_2,\cdots ,{\overline{P}}_H\right\}$. The corresponding imaging projection matrix set is denoted as $M_{ser}=\left\{M_1,M_2,\cdots ,M_H\right\}$. Since the feature extraction process for each image is independent, the resulting features depend solely on the trained network’s parameters and remain unaffected by the quantity of selected images.

3.2.2. Typical Component Orientation Optimization Solution Based on PSO

To reduce the likelihood of the optimization process converging to a local optimum when using a limited number of selected images, the PSO algorithm was used to solve the objective function shown in Equation (13), thereby achieving optimal estimation of the attitude orientation based on the typical components of the space target. The implementation process of the algorithm is illustrated in Figure 8.

(1)

Parameter initialization: The initial state of each particle in the swarm is established, encompassing both position and velocity. The position of each particle corresponds to a set of attitude angle parameters. Specifically, for the n-th particle, the initial candidate attitude parameter vector is denoted as $A_n^0={\left[{\widehat{\alpha }}_n^0,{\widehat{\beta }}_n^0,{\widehat{\gamma }}_n^0\right]}^T$. Meanwhile, the initial velocity $v_n^0$ represents the optimization direction of the particle’s parameters.

(2)

Calculation of the cost function: In the l-th iteration, the candidate attitude parameter represented by the n-th particle is denoted as $A_n^l$. Based on Equation (13), the cost function is evaluated for the candidate attitude parameters of each particle. For the n-th particle, the attitude parameter corresponding to its historical optimal cost is denoted as $q_{best,n}^l$, while the attitude parameter corresponding to the global optimal cost across all particles is represented as $g_{best}^l$.

(3)

Iteration termination judgment: If $g_{best}^l$ no longer decreases, the iteration is terminated, and the parameters $\left\{\widehat{\alpha },\widehat{\beta },\widehat{\gamma }\right\}$ stored by $g_{best}^l$ are output. If $g_{best}^l<g_{best}^{l-1}$, proceed to step (4);

(4)

Parameter update: In the l-th iteration, the state of each particle is updated. Taking the n-th particle as an example, its state parameter update equation is as follows:

$$v_n^l=w{v}_n^{l-1}+c_1{m}_1\left(q_{best,n}^l-A_n^{l-1}\right)+c_2{m}_2\left(g_{best}^l-A_n^{l-1}\right)$$

(16)

$$A_n^l=A_n^{l-1}+A_n^{l-1}$$

(17)

where $m_1$ and $m_2$ are random numbers between (0, 1), $c_1$ and $c_2$ represent learning factors, and $w$ denotes the inertial weights. After the parameters are updated, the process returns to step (1) and continues until the iteration terminates.

Through the above solution process, the optimal attitude angle parameters of the space target can be effectively obtained.

4. Experiments

4.1. Experimental Scene Design

Due to the unavailability of public measured image data for space target, we validate the proposed method using the simulated radar data. The Tiangong-1 and Aqua are selected as the test target, with their 3D models shown in Figure 7. The attitudes of Tiangong-1 and Aqua are initialized at [−14°, −112°, 30°] and [145°, 32°, −84°], respectively, using the pitch-yaw-roll convention.

The orbital parameters of the space target are generated using two-line elements (TLE) obtained from Space-Track (https://www.space-track.org, accessed on 10 December 2024). The observation station is located in Beijing (39.9°N, 116.4°E, altitude 88 m). ISAR echo data is simulated through electromagnetic computation software implementing the physical optics (PO) method. Key system parameters are summarized in

Table 2. Key parameters of the ISAR imaging system.

Parameter	Specification
Image dimension	512 × 512
Bandwidth	3 GHZ
Frequency band	Ka-band
Pulse repetition rate	100 HZ

.

4.2. Validity Verification

This section aims to validate the effectiveness of the complete methodology proposed in this paper, which integrates the novel image selection method with the tailored attitude estimation approach.

Using the target’s TLE data, observation station coordinates, and pass time windows, we simulate both inbound and outbound trajectories relative to the radar, generating ISAR imaging data for three distinct observation arcs. For each arc, image selection is performed following the methodology outlined in Table 1, incorporating ISAR acquisition time, station position, and TLE-derived orbital parameters. The interval angle is fixed at 1° during the selection process.

Figure 9 illustrates the variations in imaging plane normal azimuth and elevation angles for the ISAR images selected by the proposed method across the three observation arcs. In Figure 9, the blue dashed lines represent the azimuth and elevation angle variations in all ISAR images within the sequence for each arc, whereas the red diamond markers indicate those of the selected images. As demonstrated in Figure 9, the selected ISAR images comprehensively cover the full variation ranges of both elevation and azimuth angles for all three arcs, with uniformly distributed sampling points across the angular domains.

Table 3. Comparison of ISAR image counts before and after selection.

Parameter	Arc 1	Arc 2	Arc 3
Original image count	204	108	189
Selected image count	15	13	10
Data reduction rate	92.6%	88.0%	94.7%

compares the total number of original images within the sequence versus the selected images for the three arcs. When the image selection interval angle is set to 1°, the proposed method achieves approximately a 90% reduction in the number of required images across all arcs. These results confirm that the proposed method significantly reduces the image dataset size while effectively preserving the diversity of observation angles.

To validate the effectiveness of the selected images in attitude estimation, we conducted experiments using simulated images of Tiangong-1 and Aqua. The HRNet was trained separately on the Tiangong-1 and Aqua datasets to address the feature extraction tasks for each target. For each dataset, a total of 3600 images were generated through electromagnetic simulation and imaging processing under random perspective, using the parameters detailed in Table 2. The labeled key point positions were determined via theoretical projection analysis of the resulting images. The generated images were divided into training, validation and testing datasets, with 2400, 600 and 600 images, respectively. Due to the structure diversity, 13 key points were annotated in each image of Tiangong-1, while 8 key points were annotated in each image of the Aqua satellite, as shown in Figure 7. For each dataset, the HRNet model was trained for 200 epochs, with a basic channel number of 32 and a batch size of 4. The initial learning rate was set to 0.001, and a multi-step learning rate decay strategy was employed for both Tiangong-1 and Aqua datasets. Specifically, the learning rate gradually decreased to 0.0001 from the 170th epoch to the 200th epoch, as shown in Figure 10a. The optimizer used was Adam with Weight Decay Correction, with an actual weight decay coefficient set to 0.0001.

The training loss variation curves of the HRNet for the Tiangong-1 and Aqua datasets are depicted in Figure 10b. It is evident that the training loss decreases rapidly during the initial training process, indicating that the network swiftly learns the underlying features. In the middle stage, the training loss continues to decrease at a slower rate and exhibits a smooth trend, suggesting that the information exchange between multi-resolution branches progressively optimizes the high-resolution features. In the final stage, the loss converges to a lower value, and the gap between the validation loss and the training loss narrows, indicating that the model has achieved a good balance between training performance and generalization ability. In addition to the parallel multi-resolution architecture of HRNet, we believe that the application scenario has also contributed to the rapid convergence of the training process. In our attitude estimation scenario, the network utilized in this study is specifically trained for a single, particular target. For example, a feature point extraction network designed for Tiangong-1 is trained exclusively on images of Tiangong-1 to accurately extract the feature points of the Tiangong-1 satellite. As a result, the network training process does not need to accommodate structural variations among different targets, which further ensures rapid convergence during training. Additionally, ISAR images often exhibit high contrast between the target and the background, enabling the network to swiftly identify key features in the early stages of training. Moreover, the strong spatial correlation among pixels in ISAR images is well-suited to HRNet’s multi-scale feature extraction capabilities, further facilitating efficient feature learning. The results of feature extraction and attitude estimation for Tiangong-1 and Aqua satellite are presented in the following subsections.

4.2.1. Tiangong-1

Typical components are extracted from selected ISAR images across all three arcs. Figure 11 displays the extracted features of the space target, with the first and second rows showing the initial and final selected images, respectively. Using these extracted features, target attitude estimation is performed following the methodology outlined in Figure 8.

The attitude estimation results and corresponding errors are presented in

Table 4. Attitude estimation results and errors of Tiangong-1.

Parmeter	Estimated Value	Truth Value	Error
Arc 1	(−14.9°, −108.1°, 36.2°)	(−14°, −112°, 30°)	6.5°
Arc 2	(−16.1°, −109.1°, 25.6°)		6.2°
Arc 3	(−13.6°, −111.0°, 34.4°)		4.3°

. Compared with the ground-truth attitude values, the estimation errors are below 7° for all three observation arcs, demonstrating the effectiveness of the proposed space target attitude estimation method. Figure 12 compares the target’s 3D models under both ground-truth and estimated attitudes. The near-perfect alignment between these models visually confirms the minimal attitude estimation errors.

4.2.2. Aqua

The experimental procedure is the same as in Section 4.2.1. Figure 13 shows the feature extraction results from the initial and final selected images in three arcs. Correspondingly, the attitude estimation results and errors are presented in

Table 5. Attitude estimation results and errors of Aqua.

Parmeter	Estimated Value	Truth Value	Error
Arc 1	(143.5°, 35.7°, −82.8°)	(145°, 32°, −84°)	4.8°
Arc 2	(144.5°, 31.1°, −78.0°)		5.6°
Arc 3	(150.1°, 30.1°, −83.4°)		5.4°

. As can be seen, the estimation errors are below 7° for all three observation arcs. Figure 14 presents a comparative visualization of the target’s 3D models under both ground-truth and estimated attitudes. The nearly identical alignment between these models serves as compelling visual evidence, further confirming the minimal residual errors in the attitude estimation process.

4.3. Comparative Analysis with Existing Methods

To further demonstrate the superiority of the proposed methodology, this section presents comprehensive comparisons with existing approaches. First, a comparative analysis of different image selection strategies is conducted to demonstrate the superiority of the proposed image selection method. Subsequently, the suitability of the attitude estimation method for the sparse images obtained after selection is verified.

4.3.1. Performance Comparison of Different Image Selection Methods

In engineering practice, images are typically selected at equal-frame intervals or equal-time intervals to reduce data volume [29], and target attitude estimation is subsequently performed using the selected images. To ensure a fair comparison and objectively evaluate the performance of the selection algorithms themselves, all following experiments in this subsection consistently employ the proposed HRNet + PSO method for the final attitude estimation. The superiority of the proposed image selection method is validated by comparing its final attitude estimation accuracy against that achieved using both equal-frame and equal-time image selection methods.

With reference to Figure 5, the set of selected images is defined as $\left\{S_1,S_2,\cdots ,S_n\right\}$ where each $S_n\in \left(\mathrm{1,2},3,\cdots ,K\right)$ denotes the frame index in the original K-image sequence. The equal-frame selection method maintains a constant difference between the frame numbers of adjacent selected images in the original sequence, expressed as $S_n-S_{n-1}=S_{n-1}-S_{n-2}$. Similarly, the equal-time selection method ensures a uniform time difference between consecutive selected images’ acquisition moments, satisfying ${t_S}_n-{t_S}_{n-1}={t_S}_{n-1}-{t_S}_{n-2}$.

Under experimental conditions consistent with Section 4.2, we compare the proposed method with two methods (equal-frame interval and equal-time interval) while maintaining identical selected images counts.

Figure 15 shows a comparison of the image selection results from the three methods in terms of image frame index and imaging time. Red markers indicate the frame index or imaging time of images selected by the proposed method, while blue and green markers denote those selected by the equal-frame and equal-time selection methods, respectively. As can be seen from Figure 15a, except for the equal-frame selection method, the frame index of the other two methods is non-equally spaced. Figure 15b demonstrates that, apart from the equal-time selection method, the imaging time of the other two methods is non-equally spaced.

Figure 16 shows the distributions of the azimuth and elevation angles of the imaging plane normal of ISAR images selected by the three methods, where the purple dashed line represents the complete angular variation profile of the original sequence. It can be observed that the ISAR images selected by the proposed method are more uniformly distributed across both elevation and azimuth angles compared to those selected by the other two methods. In terms of angular coverage completeness, the three methods show little difference, as they all include the maximum and minimum values in both azimuth and elevation angles.

Using the image sets selected by the three methods, target attitude estimation is performed following the pipeline in Figure 8, with consistent system configurations and simulated feature extraction errors. Zero-mean Gaussian noise with standard deviation $\sigma \in \left[0, 3\right]$ meters is added to extracted feature points. For each noise level, we conduct 100 Monte Carlo trials across three data groups, recording successful trials where attitude error < 20°. Figure 17 shows the success rates of each method versus feature extraction error, while Figure 18 presents the corresponding mean attitude estimation errors from successful trials.

Figure 17 compares the success times across the three methods under varying feature extraction error levels. The proposed method achieves higher success counts than other two methods, though all methods exhibit performance degradation with increasing image feature extraction errors. Figure 18 compares the mean attitude estimation errors across different methods. The results demonstrate that the proposed method achieves lower errors than the other two methods under varying levels of image feature extraction errors. All methods exhibit increased attitude estimation errors with larger image feature extraction errors.

To provide a more intuitive and direct demonstration as suggested, we have now added a specific trial case to the revised manuscript. This includes a new table listing the precise attitude estimation errors for all methods in this representative trial, alongside a new figure with 3D visualization results comparing the reconstructed models against the ground truth. This addition clearly shows that other methods yield significantly larger errors and poor model alignment, whereas our method achieves high accuracy and excellent visual overlap with the ground truth model.

For a more intuitive demonstration, we present the results from a representative trial at a noise level of σ = 1.5 m. The corresponding attitude estimation errors are quantitatively compared in

Table 6. Attitude estimation results and errors under different image selection methods.

Method	Estimated Value	Truth Value	Error
Equal-frame	(−17.9°, −117.6°, 37.9°)	(−14°, −112°, 30°)	11.5°
Equal-time	(−8.2°, −117.8°, 22.4°)		10.4°
Proposed	(−10.2°, −107.2°, 35.9°)		7.8°

. Furthermore, Figure 19 provides a qualitative visualization, comparing the 3D models reconstructed using the ground-truth attitudes against those from the estimated attitudes for three different methods. It can be observed that the estimated attitudes from the other methods result in significant errors and poor model alignment. In contrast, the model from our proposed method shows excellent visual overlap with the ground truth, demonstrating its superior accuracy.

The experimental results demonstrate that the proposed image selection method achieves significantly higher attitude estimation accuracy and robustness compared to conventional equal-frame and equal-time image selection methods. This reveals that different image sequence combinations—even with identical frame counts—provide varying levels of target information quality, directly impacting estimation precision.

As shown in Figure 15 and Figure 16, the three image selection methods exhibit differences in frame index, imaging time and imaging plane normal angular distribution. The proposed image selection method strategy demonstrates clear advantages for attitude estimation. Its superior sampling distribution uniformity constitutes the primary reason for the performance improvement over other methods.

Fundamentally, both the equal-time and equal-frame methods fail to achieve uniform coverage of the full elevation-azimuth variation ranges within the image sequence. This results in information loss and poor inter-image correlation, leading to suboptimal utilization of image data and degraded attitude estimation accuracy. Specifically, for the equal-time method, the non-stationary relative motion between the target and radar LOS causes nonlinear, non-uniform variations in the imaging plane. Consequently, the selected imaging plane normal vectors (parameterized by elevation and azimuth angles) exhibit non-uniform sampling distributions. This nonlinearity prevents uniform angular sampling of selected ISAR images. For the equal-frame method, while the selected ISAR images exhibit uniform distribution in the azimuth accumulation angle domain, the method cannot maintain linearity in the imaging plane’s elevation-azimuth variation. This nonlinear relationship causes the resulting imaging plane normal to deviate from a uniform sampling distribution, thereby precluding uniform angular coverage of selected ISAR images.

The image selection method proposed in this paper incorporates target orbit information, quantifies the difference in target information among ISAR images by analyzing the variation in imaging plane normal azimuth and elevation angles, and establishes image selection criteria based on imaging principles. By reducing information redundancy, the proposed method not only preserves image information across all observation angles but also achieves uniform coverage of the complete elevation and azimuth ranges. Consequently, the selected images exhibit strong inter-image correlation, and information from all observation perspectives is fully utilized. As a result, the attitude estimation accuracy is significantly improved compared to other methods.

The above experiments demonstrate that the main difference between existing image selection methods and our proposed method lies in the uniformity of sampling distribution, while their coverage ranges show relatively minor variations. Therefore, these experimental results can effectively validate our method’s compliance with the sampling uniformity criterion. Considering that our method also incorporates viewpoint coverage requirements during image selection, we now conduct simulation experiments to analyze its coverage performance.

The proposed method selects ISAR images covering azimuth angles of [−73°, −65°] and elevation angles of [−22°, −16.5°]. For comparative analysis of attitude estimation performance, two additional image selection sets (“Coverage-1”, “Coverage-2”) with progressively reduced angular coverage are generated based on our image selection method’s results. Specifically, Coverage-1 exhibits missing ranges of [−66.5°, −65°] in azimuth and [−22°, −21°] in elevation; Coverage-2 lacks [−71°, −67°] in azimuth and [−21°, −18°] in elevation. Figure 20 illustrates the imaging plane normal azimuth and elevation angle distributions for these different angular coverage sets. Comparative analysis reveals that the proposed method maintains significantly more comprehensive angular coverage, whereas the alternative sets demonstrate progressively severe coverage deficiencies. Regarding sampling distribution uniformity, all three results show comparable performance with relatively even distributions.

Attitude estimation is performed using the three different image selection sets, with identical system configurations and simulated feature extraction errors. Figure 21 presents the success rates under different feature extraction error levels, while Figure 22 compares their mean attitude estimation errors. The experimental results show that our proposed method achieves significantly higher attitude estimation accuracy and robustness across varying error conditions compared to the other image selection sets. Furthermore, the results demonstrate that reduced angular coverage leads to decreased robustness and precision in attitude estimation.

The image selection method proposed in this paper follows the principle of maximizing angular coverage to ensure comprehensiveness, preserving image information across all observation angles. In contrast, the other image selection sets suffer from coverage deficiencies that result in reduced available information. Consequently, our method achieves superior attitude estimation accuracy.

A representative trial at σ = 1.5 m is selected to intuitively compare the estimation performance. The quantitative errors, detailed in

Table 7. Attitude estimation results and errors under different angular coverage.

Method	Estimated Value	Truth Value	Error
Coverage-1	(−12.2°, −108.4°, 22.5°)	(−14°, −112°, 30°)	9.2°
Coverage-2	(−16.9°, −105.8°, 23.1°)		10.8°
Proposed	(−11.1°, −117.9°, 24.8°)		7.5°

, confirm the superior accuracy of our method. This is visually supported by Figure 23, which compares the resulting 3D models against the ground truth. The figure clearly shows that other angular coverages lead to poor model alignment due to attitude estimation errors, whereas our method achieves a high degree of visual overlap, demonstrating its high accuracy.

4.3.2. Suitability Validation of the Attitude Estimation Method

The preceding subsection validates the capability of our image selection method in generating an optimal sparse image set. This subsection aims to further demonstrate that the proposed HRNet + PSO method is particularly suited for attitude estimation under such sparse image sequences.

To analyze the performance differences among various attitude estimation algorithms under this condition, we conducted attitude estimation using both the proposed HRNet + PSO method and the projection area energy accumulation algorithm (PAEA) [21]. The simulation parameters remain identical to those in Section 4.2. For a comprehensive analysis, experiments are conducted using both the complete image set and the optimized sparse set selected by our method, enabling a direct comparison of estimation performance across these two scenarios. The experimental outcomes are presented in

Table 8. Attitude estimation results of different attitude estimation methods using complete images.

Target	Parmeter	PAEA		Proposed Method
		Result	Error	Result	Error
Tiangong-1	Arc 1	(−18.6°, −110.7°, 28.3°) Cost time: 216.3 s	5.2°	(−13.1°, −115.8°, 24.8°) Cost time: 79.5 s	5.7°
	Arc 2	(−11.3°, −110.2°, 26.7°) Cost time: 191.4 s	4.9°	(−17.3°, −108.5°, 28.6°) Cost time: 58.5 s	5.3°
	Arc 3	(−6.4°, −113.9°, 33.2°) Cost time: 244.9 s	4.7°	(−13.6°, −111.0°, 34.1°) Cost time: 75.2 s	4.0°
Aqua	Arc 1	(147.3°, 27.9°, −78.2°) Cost time: 225.8 s	5.4°	(141.0°, 32.5°, −81.7°) Cost time: 77.9 s	4.8°
	Arc 2	(148.6°, 34.1°, −85.8°) Cost time: 218.6 s	4.1°	(149.4°, 28.8°, −81.4°) Cost time: 59.1 s	5.2°
	Arc 3	(141.5°, 34.2°, −81.3°) Cost time: 253.8 s	5.6°	(148.7°, 30.7°, −85.2°) Cost time: 72.4 s	4.3°

and

Table 9. Attitude estimation results of different attitude estimation methods using selected images.

Target	Parmeter	PAEA		Proposed Method
		Result	Error	Result	Error
Tiangong-1	Arc 1	(−18.9°, −115.4°, 21.5°) Cost time: 15.1 s	9.5°	(−14.9°, −108.1°, 36.2°) Cost time: 19.9 s	6.5°
	Arc 2	(−13.1°, −119.1°, 25.9°) Cost time: 17.1 s	7.3°	(−16.1°, −109.1°, 25.6°) Cost time: 18.6 s	6.2°
	Arc 3	(−7.1°, −115.6°, 35.3°) Cost time: 16.6 s	9.7°	(−13.6°, −111.0°, 34.4°) Cost time: 17.4 s	4.3°
Aqua	Arc 1	(146.5°, 31.7°, −75.8°) Cost time: 18.7 s	8.2°	(143.5°, 35.7°, −82.8°) Cost time: 19.5 s	4.8°
	Arc 2	(144.9°, 44.3°, −92.5°) Cost time: 20.7 s	10.2°	(144.5°, 31.1°, −78.0°) Cost time: 18.9 s	5.6°
	Arc 3	(149.8°, 33.9°, −79.4°) Cost time: 12.5 s	7.6°	(150.1°, 30.1°, −83.4°) Cost time: 17.1 s	5.4°

, and the computational time for each experiment is recorded.

The experimental results show that the proposed method has better performance with few images. This is because the target in ISAR image is sparse and incomplete. The PAEA optimizes the sequence image energy covered by the target projection contour to achieve attitude estimation. However, due to the structural deficiencies in ISAR images, the optimization process of PAEA contains errors, especially when the number of images is small, the estimation error is significant. The proposed method leverages the powerful prediction ability of the deep network to accurately extract target features from structurally deficient images, ensuring the accuracy of attitude estimation results with a small number of images. Meanwhile, PAEA accumulates and optimizes the energy of the image sequence through correlation calculations, which is computationally intensive and severely time-consuming for attitude estimation. In contrast, the proposed method in this paper only optimizes the projection error of a few extracted key points, significantly improving the timeliness.

The comparative analyses in Section 4.3.1 and Section 4.3.2 collectively demonstrate the efficacy of the proposed methodology. The results from Section 4.3.1 confirm that, under an identical number of images, our selection method provides a more informative sequence, leading to superior estimation accuracy and robustness compared to conventional strategies. Furthermore, the findings in Section 4.3.2 validate that the HRNet + PSO method is uniquely suited to exploit this sparse yet optimal data, maintaining high performance where the other method degrades significantly with reduced image quantity. These results jointly affirm that the proposed image selection method forms the core of our contribution, while the tailored HRNet + PSO estimation method serves as a crucial enforcer, ensuring the overall robustness and accuracy of the proposed methodology.

5. Conclusions

In this paper, we propose a space target attitude estimation method based on the selection of multi-view ISAR image sequences. First, the ISAR imaging plane is calculated according to fundamental ISAR imaging principles, and the imaging projection model is constructed. Subsequently, the proposed method selects the ISAR images within the sequence by analyzing variations in viewing angles. An HRNet-based feature extraction method is employed to synchronize feature point extraction and matching across selected ISAR images. Finally, an attitude estimation optimization model is established and solved by PSO algorithm to determine the target’s attitude. By selecting ISAR images based on observation angle variations, the proposed method significantly reduces the number of ISAR images required for attitude estimation. The HRNet-based feature extraction method effectively resolves feature point correlation and matching challenges in the selected ISAR images, enabling accurate estimation with minimal data. Experimental results validate that the proposed image selection method, synergized with a tailored HRNet + PSO estimator, enables highly accurate and robust attitude estimation with significantly reduced data requirements. Specifically, the proposed image selection method exhibits excellent performance in reducing data volume, and provides a more informative sequence than conventional approaches at an identical reduction rate, while the tailored HRNet + PSO estimator maintains superior performance where other method degrades with sparse data. It should be noted that experimental validation was performed on simulated data due to difficulties in obtaining real measurements. Validation with real ISAR data remains an important objective for future research.