Non-cooperative spacecraft attitude estimation method and system based on laser radar

Abstract

The invention discloses a non-cooperative spacecraft attitude estimation method and system based on a laser radar, and the method comprises the steps: obtaining a scanning point, observed by the laser radar, of a non-cooperative spacecraft, carrying out the attitude initialization of the scanning point, obtaining a scanning point cloud, constructing a reference model of the non-cooperative spacecraft, and carrying out the attitude estimation of the non-cooperative spacecraft. The scanning point cloud is matched with the reference model to obtain a matching result, attitude tracking is performed on the matching result based on an iterative nearest point algorithm and a Kalman filter to complete attitude estimation of the non-cooperative spacecraft, and the problem of attitude tracking of the non-cooperative spacecraft of an airborne LiDAR system is solved. The limitation of an attitude initialization method based on template matching and point cloud registration is overcome, and the relative state of the non-cooperative spacecraft can be accurately estimated.

Description

Technical Field

[0001] The present invention belongs to the field of non-cooperative spacecraft navigation design, and in particular relates to a non-cooperative spacecraft attitude estimation method and system based on laser radar. Background Art

[0002] Many current and future spaceborne applications involve autonomous rendezvous and docking (AR&D) with dynamic, free-floating space targets, such as on-orbit satellite maintenance, capture of malfunctioning or out-of-control spacecraft, and robotic assembly of large space platforms. These operations require accurate and robust attitude estimation of space objects. However, estimating the relative attitude and position of non-cooperative spacecraft that lack active communication link systems or supplementary indicators (such as light-emitting diodes or corner reflectors) remains a formidable challenge.

[0003] To address the aforementioned challenges, recent mission concepts are investigating the use of onboard sensors for pose estimation on non-cooperative spacecraft (Lichter & Dubowsky (2004)). Passive sensors, such as monocular and stereo cameras, are commonly deployed on current spaceborne missions due to their low hardware complexity (Ventura (2016)). However, the imaging quality of passive sensors is susceptible to varying lighting conditions. In contrast, active sensors, such as light detection and ranging (LiDAR) and time-of-flight (ToF) cameras, generate electromagnetic radiation and receive echoes from target objects, making them more resilient in complex space environments. The scan points generated by LiDAR or ToF cameras provide a comprehensive representation of the target spacecraft's geometry, enabling pose estimation even in the absence of distinct features. However, most LiDAR-based methods rely on template matching for pose initialization, which presents certain limitations. Template matching requires a large database to improve the accuracy of pose initialization, but this reduces the computational speed of searching for relevant templates in the database. Therefore, there is an urgent need for accurate and robust approaches to pose estimation on non-cooperative spacecraft. Summary of the Invention

[0004] In view of this, the present invention provides a non-cooperative spacecraft attitude estimation method and system based on lidar, which can overcome the limitations of attitude initialization of template matching and point cloud registration and accurately estimate the relative attitude of non-cooperative spacecraft. It is specifically implemented by the following technical solutions.

[0005] In a first aspect, the present invention provides a non-cooperative spacecraft attitude estimation method based on laser radar, comprising the following steps: Obtaining scanning points of the non-cooperative spacecraft observed by the laser radar, and performing attitude initialization on the scanning points to obtain a scanning point cloud; Constructing a reference model of the non-cooperative spacecraft, and matching the scanned point cloud with the reference model to obtain a matching result, wherein the reference model takes the scanned point cloud as input, extracts global point features from the scanned point cloud, and regresses the relative pose of the non-cooperative spacecraft, using unit quaternions to represent the relative pose; The attitude tracking is performed on the matching result based on an iterative closest point algorithm and a Kalman filter to complete the attitude estimation of the non-cooperative spacecraft.

[0006] As a preferred embodiment of the above technical solution, obtaining the scanning point where the laser radar observes the non-target spacecraft includes: According to the Tait-Bryan angle From the target reference system in XYZ sequence To the lidar reference frame Derive the intrinsic rotation matrix , using unit quaternion Represents a 3D rotation matrix ,in, 、 is the scalar part and the vector part of the quaternion, The units are three spheres, and the LiDAR sensor is preset in the LiDAR reference system. Scan point observed , let u be the target reference system The target point corresponding to the scan point v is u from the target reference system Mapping to the LiDAR reference frame The expression is: (1) and (2) (3) in, Indicated by The skew-symmetric cross product matrix formed by the components of Represents the translation vector between the target point and the lidar sensor, using represents the Kronecker product.

[0007] As a preferred embodiment of the above technical solution, initializing the posture of the scanning points to obtain a scanning point cloud includes: Get the scanning point cloud at the kth moment and perform normalization processing; The normalized scan point cloud is input into the trained neural network to obtain the relative pose; The relative attitude is tracked using an iterative closest point algorithm, and the error state corresponding to the attitude tracking is corrected using a Kalman filter to obtain a real-time tracking result of the six-degree-of-freedom attitude of the non-cooperative spacecraft.

[0008] As a preferred embodiment of the above technical solution, the PPAM model is used for regression analysis. arrive Perform regression, where ,set up and Represents two random variables, given input and model parameters , the goal is to predict the corresponding , PPAM can be modeled as a local affine transformation, and the corresponding expression is: (4) Among them, the matrix and matrix Represents the parameters of the affine transformation; is an error vector used to explain high-dimensional observation noise and reconstruction error, and the corresponding latent variable It means if and only if from Mapping to the jth affine transformation ; like Following the diagonal covariance matrix The zero mean high speed distribution of and The joint probability distribution of can be decomposed into: (5) and (6) in, A vector representing the model parameters, constrained to be ,like The mixture of J Gaussian distributions is defined by equation (7): (7) By considering the observed variables X, Y and the latent variables The joint probability distribution of the model parameters Under the control of , the expectation maximization algorithm is used to maximize the expected complete data log-likelihood function , and obtain the model parameters, the corresponding expression is: (8) set up is a latent variable expectations, i.e. , if the model parameters are determined , the conditional density of regression can be derived according to formula (9): (9) (10) Output vector The default value is the expected value of formula (9): (11).

[0009] As a preferred embodiment of the above technical solution, constructing a reference model of the non-cooperative spacecraft includes: The centroid of the scan point cloud is converted to the origin, and the scan points are normalized according to the length of the main axis of the model. Each group of scan points is set to consist of n points, which is expressed as , using a shared multilayer perceptron as the nonlinear function, Embedded into high-dimensional space; The obtained output is subjected to maximum pooling to generate a high-dimensional global feature vector g; Each layer in the J different fully connected layer sets uses the weight matrix and bias vector to perform a linear transformation on the input vector. According to the local affine transformation of formula (4), the output of the jth fully connected layer is recorded as , the corresponding expression is: (12) in, and denote the weight and bias of the jth fully connected layer respectively; The neural network calculates the corresponding latent variables The expected value of replaces the , using shared MLP to transform the global feature vector and applying softmax function to Normalization is performed, where all shared MLPs use ReLU and batch normalization, and the estimated quaternion is the average of a set of J relative pose estimates in quaternion form with corresponding weights , the corresponding expression is: (13) Given The eigendecomposition of the matrix The elements on the diagonal are the eigenvalues ​​of the matrix M, the column vectors of the orthogonal matrix U are the eigenvectors of the matrix M, and the estimated quaternion is the eigenvector corresponding to the largest eigenvalue of the matrix M.

[0010] As a preferred alternative to the above technical solution, the mean square error loss is used to optimize the neural network: (14) (15) in, represents the conjugate of the ground truth quaternion label, Is the identity quaternion, ensuring the quaternion error when calculating network loss The scalar part is positive, and the last term of the loss function represents the network parameters Tikhonov regularization, the regularization parameter is determined by the hyperparameter control.

[0011] As a preferred embodiment of the above technical solution, performing attitude tracking on the matching results based on an iterative closest point algorithm and a Kalman filter to complete the non-cooperative spacecraft attitude estimation includes: The nominal vector is defined as: (16) Where q represents the relative attitude vector, w represents the relative acceleration, r represents the relative position, v represents the relative linear velocity, and the subscript k represents the time step; The extrapolation of attitude uses the previous estimate of velocity as the time interval The constant inside, calculate The expected value of the nominal state vector at starts from the previously adjusted value: (17) Where, the superscript f represents the prior estimate, and the superscript represents the posterior estimate, and the error state vector is: (18) The kinematics of the error state can be derived as: (19) , (20) Where I is the identity matrix, represents the error covariate, i represents the disturbance pulse vector, and is the predicted Jacobian matrix of the error state and the disturbance vector, and the random pulses applied to the error state of Gaussian white noise are given by 、 、 and express, The covariance of can be predicted by the following formula: (twenty one) in, is the covariance matrix of the disturbance pulse, The measurement relies on pose estimation using an iterative closest point algorithm.

[0012] As the preferred embodiment of the above technical solution, the observation model for: (twenty two) (twenty three) in, is the measurement Jacobian matrix relative to the error state vector, means that the mean is zero and the covariance is If the estimated attitude is corrected by the Kalman filter, the posterior estimates of the angular velocity and linear velocity are obtained by formula (24): (twenty four).

[0013] As a preferred embodiment of the above technical solution, the posture error Defined as the estimated quaternion The baseline distance between the ground truth q and the translation error Defined as translation The 2-norm of the difference between the ground truth r is used to evaluate the estimated attitude, and the corresponding expression is: (25) (26).

[0014] In a second aspect, the present invention further provides a non-cooperative spacecraft attitude estimation system based on laser radar, which is applied to the above-mentioned non-cooperative spacecraft attitude estimation method based on laser radar, comprising: A data acquisition module is used to obtain scanning points of non-cooperative spacecraft observed by the laser radar and perform attitude initialization on the scanning points to obtain a scanning point cloud; a model construction module, configured to construct a reference model of the non-cooperative spacecraft and match the scanned point cloud with the reference model to obtain a matching result, wherein the reference model takes the scanned point cloud as input, extracts global point features from the scanned point cloud, regresses the relative pose of the non-cooperative spacecraft, and uses unit quaternions to represent the relative pose; The attitude estimation module is used to perform attitude tracking on the matching results based on an iterative closest point algorithm and a Kalman filter to complete attitude estimation of the non-cooperative spacecraft.

[0015] The present invention provides a non-cooperative spacecraft attitude estimation method and system based on lidar. The method obtains scanning points of a non-cooperative spacecraft observed by a lidar, performs attitude initialization on the scanning points to obtain a scanning point cloud, constructs a reference model of the non-cooperative spacecraft, and matches the scanning point cloud with the reference model to obtain a matching result. The matching result is attitude tracked based on an iterative closest point algorithm and a Kalman filter to complete the non-cooperative spacecraft attitude estimation, solves the non-cooperative spacecraft attitude tracking problem of an airborne LiDAR system, overcomes the limitations of the attitude initialization method based on template matching and point cloud registration, and can accurately estimate the relative state of the non-cooperative spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0017] Figure 1 A flowchart of the non-cooperative spacecraft attitude estimation method based on laser radar provided by the present invention; Figure 2 A schematic diagram of a reference model provided by the present invention; Figure 3 Schematic diagram of the PPAM model provided by the present invention; Figure 4 A schematic diagram of the relative trajectory of the tracking spacecraft provided by the present invention in the target Hill reference frame; Figure 5 This is a structural block diagram of the non-cooperative spacecraft attitude estimation system based on lidar provided by the present invention. DETAILED DESCRIPTION

[0018] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0019] This paper proposes an innovative framework for non-cooperative spacecraft attitude tracking using sparse LiDAR points. First, a novel neural network is designed to initialize the target spacecraft's attitude. Inspired by probabilistic piecewise affine mapping, the neural network takes LiDAR points as input and regresses the relative attitude of the non-cooperative spacecraft using global features derived from these LiDAR points. To address the singularity of Euler angles, unit quaternions are used to represent the relative attitude. Subsequently, a customized Iterative Closest Point (ICP) algorithm and an Error State Kalman Filter (ESKF) are used for attitude tracking. The details are as follows: See Figure 1 The present invention provides a non-cooperative spacecraft attitude estimation method based on laser radar, comprising the following steps: S1: Obtain scanning points of non-cooperative spacecraft observed by the laser radar, and perform attitude initialization on the scanning points to obtain a scanning point cloud; S2: constructing a reference model of the non-cooperative spacecraft, and matching the scanned point cloud with the reference model to obtain a matching result, wherein the reference model takes the scanned point cloud as input, extracts global point features from the scanned point cloud, and regresses the relative posture of the non-cooperative spacecraft, using unit quaternions to represent the relative posture; S3: performing attitude tracking on the matching results based on an iterative closest point algorithm and a Kalman filter to complete the attitude estimation of the non-cooperative spacecraft.

[0020] In this embodiment, obtaining the scanning point where the laser radar observes the non-target spacecraft includes: According to the Tait-Bryan angle From the target reference system in XYZ sequence To the lidar reference frame Derive the intrinsic rotation matrix , using unit quaternion Represents a 3D rotation matrix ,in, 、 is the scalar part and the vector part of the quaternion, The units are three spheres, Preset LiDAR sensor in LiDAR reference frame Scan point observed , let u be the target reference system The target point corresponding to the scan point v is u from the target reference system Mapping to the LiDAR reference frame The expression is: (1) and (2) (3) in, Indicated by The skew-symmetric cross product matrix formed by the components of Represents the translation vector between the target point and the lidar sensor, using represents the Kronecker product.

[0021] It should be noted that initializing the posture of the scanning points to obtain the scanning point cloud includes: Get the scanning point cloud at the kth moment and perform normalization processing; The normalized scan point cloud is input into the trained neural network to obtain the relative pose; The relative attitude is tracked using an iterative closest point algorithm, and the error state corresponding to the attitude tracking is corrected using a Kalman filter to obtain a real-time tracking result of the six-degree-of-freedom attitude of the non-cooperative spacecraft.

[0022] The PPAM model was used for regression analysis. arrive Perform regression, where ,set up and Represents two random variables, given input and model parameters , the goal is to predict the corresponding , PPAM can be modeled as a local affine transformation, and the corresponding expression is: (4) Among them, the matrix and matrix Represents the parameters of the affine transformation; is an error vector used to explain high-dimensional observation noise and reconstruction error, and the corresponding latent variable It means if and only if from Mapping to the jth affine transformation ; like Following the diagonal covariance matrix The zero mean high speed distribution of and The joint probability distribution of can be decomposed into: (5) and (6) in, A vector representing the model parameters, constrained to be ,like The mixture of J Gaussian distributions is defined by equation (7): (7) By considering the observed variables X, Y and the latent variables The joint probability distribution of the model parameters Under the control of , the expectation maximization algorithm is used to maximize the expected complete data log-likelihood function , and obtain the model parameters, the corresponding expression is: (8) set up is a latent variable expectations, i.e. , if the model parameters are determined , the conditional density of regression can be derived according to formula (9): (9) (10) Output vector The default value is the expected value of formula (9): (11).

[0023] For the past few decades, visual navigation of orbiting spacecraft has primarily relied on the assistance of artificial markers or beacons mounted on target spacecraft. However, estimating the relative pose and position of non-cooperative spacecraft that do not deploy these devices remains a challenge. To address this challenge, various methods have been proposed for pose estimation of non-cooperative spacecraft using single images. Some researchers have leveraged the matching of geometric primitives from imaging, such as edges, circles, and curves, for spacecraft pose estimation. However, these methods are notoriously dependent on favorable lighting conditions. Airborne LiDAR points in spaceborne scenes can be very sparse, rendering existing algorithms based on feature descriptor matching ineffective. Given a good initial estimate, the Iterative Closest Point (ICP) algorithm has been proposed to align two sets of partially overlapping points without extracting point cloud descriptors. Therefore, the main challenge lies in pose initialization when using scans generated by airborne LiDAR. Inspired by the Gaussian Mixture Model registration algorithm, Deep Coherent Point Drift (DeepCPD) was introduced. This algorithm uses a learnable network to learn pose-invariant point-to-component correspondences to register two sets of partially overlapping points under arbitrary transformations.

[0024] It should be understood that by obtaining the scanning points of the non-cooperative spacecraft observed by the lidar, and performing attitude initialization on the scanning points to obtain a scanning point cloud, a reference model of the non-cooperative spacecraft is constructed, and the scanning point cloud is matched with the reference model to obtain a matching result, and the matching result is attitude tracked based on the iterative nearest point algorithm and the Kalman filter to complete the non-cooperative spacecraft attitude estimation, solve the non-cooperative spacecraft attitude tracking problem of the airborne LiDAR system, overcome the limitations of the attitude initialization method based on template matching and point cloud registration, and can accurately estimate the relative state of the non-cooperative spacecraft.

[0025] Optionally, constructing a reference model of the non-cooperative spacecraft includes: The centroid of the scan point cloud is converted to the origin, and the scan points are normalized according to the length of the main axis of the model. Each group of scan points is set to consist of n points, which is expressed as , using a shared multilayer perceptron as the nonlinear function, Embedded into high-dimensional space; The obtained output is subjected to maximum pooling to generate a high-dimensional global feature vector g; Each layer in the J different fully connected layer sets uses the weight matrix and bias vector to perform a linear transformation on the input vector. According to the local affine transformation of formula (4), the output of the jth fully connected layer is recorded as , the corresponding expression is: (12) in, and denote the weight and bias of the jth fully connected layer respectively; The neural network calculates the corresponding latent variables The expected value of replaces the , using shared MLP to transform the global feature vector and applying softmax function to Normalization is performed, where all shared MLPs use ReLU and batch normalization, and the estimated quaternion is the average of a set of J relative pose estimates in quaternion form with corresponding weights , the corresponding expression is: (13) Given The eigendecomposition of the matrix The elements on the diagonal are the eigenvalues ​​of the matrix M, the column vectors of the orthogonal matrix U are the eigenvectors of the matrix M, and the estimated quaternion is the eigenvector corresponding to the largest eigenvalue of the matrix M.

[0026] In this embodiment, the mean square error loss is used to optimize the neural network: (14) (15) in, represents the conjugate of the ground truth quaternion label, Is the identity quaternion, ensuring the quaternion error when calculating network loss The scalar part is positive, and the last term of the loss function represents the network parameters Tikhonov regularization, the regularization parameter is determined by the hyperparameter control.

[0027] Specifically, if Figure 2 As shown, the z-axis in the lidar reference frame points outward along the viewing axis, which means that when the relative pose is fixed, the shape of the scan points generated by the lidar sensor remains unchanged regardless of the relative position between the tracking spacecraft and the target spacecraft.

[0028] Optionally, performing attitude tracking on the matching result based on an iterative closest point algorithm and a Kalman filter to complete attitude estimation of the non-cooperative spacecraft includes: The nominal vector is defined as: (16) Where q represents the relative attitude vector, w represents the relative acceleration, r represents the relative position, v represents the relative linear velocity, and the subscript k represents the time step; The extrapolation of attitude uses the previous estimate of velocity as the time interval The constant inside, calculate The expected value of the nominal state vector at starts from the previously adjusted value: (17) Where, the superscript f represents the prior estimate, and the superscript represents the posterior estimate, and the error state vector is: (18) The kinematics of the error state can be derived as: (19) , (20) Where I is the identity matrix, represents the error covariate, i represents the disturbance pulse vector, and is the predicted Jacobian matrix of the error state and the disturbance vector, and the random pulses applied to the error state of Gaussian white noise are given by 、 、 and express, The covariance of can be predicted by the following formula: (twenty one) in, is the covariance matrix of the disturbance pulse, The measurement relies on pose estimation using an iterative closest point algorithm.

[0029] In this embodiment, the observation model for: (twenty two) (twenty three) in, is the measurement Jacobian matrix relative to the error state vector, means that the mean is zero and the covariance is If the estimated attitude is corrected by the Kalman filter, the posterior estimates of the angular velocity and linear velocity are obtained by formula (24): (twenty four).

[0030] As a preferred embodiment of the above technical solution, the posture error Defined as the estimated quaternion The baseline distance between the ground truth q and the translation error Defined as translation The 2-norm of the difference between the ground truth r is used to evaluate the estimated attitude, and the corresponding expression is: (25) (26).

[0031] It is important to note that, given the invariance of the scanned point cloud shape relative to the distance between the tracker and target spacecraft, and the fact that only the density of the point cloud changes, a neural network was proposed to directly regress the relative pose using the global features of the point cloud. The network incorporates a probabilistic piecewise affine mapping (PPAM), which proposes a piecewise linear model for low-dimensional to high-dimensional regression. Figure 3A graphical representation of a supervised PPAM is shown, where white represents latent variables and gray represents observations. The key point of this embodiment is to predict relative pose from global features of the point cloud, that is, to regress from high-dimensional to low-dimensional, rather than from low-dimensional to high-dimensional. After establishing the foundation of the probabilistic piecewise affine mapping algorithm, it is necessary to demonstrate the proposed neural network.

[0032] See Figure 5 The present invention further provides a non-cooperative spacecraft attitude estimation system based on laser radar, which is applied to the above-mentioned non-cooperative spacecraft attitude estimation method based on laser radar, comprising: A data acquisition module is used to obtain scanning points of non-cooperative spacecraft observed by the laser radar and perform attitude initialization on the scanning points to obtain a scanning point cloud; a model construction module, configured to construct a reference model of the non-cooperative spacecraft and match the scanned point cloud with the reference model to obtain a matching result, wherein the reference model takes the scanned point cloud as input, extracts global point features from the scanned point cloud, regresses the relative pose of the non-cooperative spacecraft, and uses unit quaternions to represent the relative pose; The attitude estimation module is used to perform attitude tracking on the matching results based on an iterative closest point algorithm and a Kalman filter to complete attitude estimation of the non-cooperative spacecraft.

[0033] In this example, the neural network was implemented in PyTorch 1.8.2. Adam with an initial learning rate of 5e-4 was used to tune the network parameters. During training, the learning rate was halved every 200 epochs. Training was performed on an Nvidia GTX 1070 GPU for 600 epochs with a batch size of 128. Three spacecraft CAD models (reference models) were selected as experimental subjects: the Lunar Reconnaissance Orbiter (LRO), the Space Shuttle Orbiter, and Aura. Table 1 shows the key parameters of the simulated lidar.

[0034] Table 1 Key parameters of simulated flash lidar

[0035] To create the training dataset, a rigid transformation was applied to the spcecraft CAD model along each axis, with 256 viewpoints (Tait-Bryan angles and ) is sampled uniformly on the attitude sphere via a Fibonacci grid, from Uniform sampling with an interval of 9°. LRO, Space Shuttle Orbiter, and Aura are located at 100 meters, 470 meters, and 120 meters away from the simulated lidar, respectively. At these distances, the field of view (FOV) of the simulated lidar covers the entire object, so occlusion is not considered in the experiment. For each pose of the given sample. The simulated Flash LiDAR first generates a set of scan points, and then uses farthest point sampling to downsample 128 points from each scan for batch processing to accelerate training. Three object-specific networks are trained for each spacecraft. For the validation and test datasets, random rotations are applied to each spacecraft CAD model, and the distance in the validation dataset is set to the training set.

[0036] The validation dataset allows the hyperparameters of the neural network to be modified during the training process. For the test dataset, LRO, Space Shuttle Orbiter, and Aura were placed approximately 110 meters, 530 meters, and 180 meters away from the simulated lidar, respectively. Each scan point cloud in the test dataset was subjected to a standard deviation of and The training, validation, and test datasets contain 18,432, 1,024, and 8,192 scan points per spacecraft, respectively. In the test dataset, the number of simulated scan points for LRO ranges from 94 to 311, for the Space Shuttle Orbiter from 47 to 320, and for Aura from 19 to 274.

[0037] Specifically, see Figure 4 ,Aura is selected as the experimental object to verify the performance of the posture tracking algorithm. The true relative angular velocity of each Tait-Bryan angle is set to The tracking program performed one simulation per second, while the tracking spacecraft gradually approached the target spacecraft at a speed of 0.05 m / s. The tracking process lasted for 1000 seconds, generating 1000 frames of scan points in the scene. The relative position between the tracking spacecraft and the target spacecraft varied from 130 to 180 meters. A total of 100 Monte Carlo simulations were performed during the attitude tracking experiment.

[0038] Given an appropriate initial pose prediction, ICP can improve the estimation results. Therefore, to evaluate the performance of the proposed method, special emphasis is placed on its pose recall, which is determined by calculating the percentage of initial pose estimates that are accurately aligned with the ground truth pose within a predefined tolerance. The number of Gaussian components J corresponds to the number of affine mappings and has a significant impact on the performance of the proposed method. Therefore, experiments are used to evaluate its impact on the pose initialization results. The initial value J is set from 1 to 32 to train three spacecraft. Among them, Approximately to the classic linear regression model, increasing J can improve the accuracy of the model, but it also increases the computational complexity. In addition, a large number of affine mappings can lead to overfitting of the neural network. When J exceeds 16, the performance of the proposed algorithm does not significantly improve. Therefore, in the following experiments, J is fixed to 16.

[0039] A comparative analysis was conducted between the proposed method and baselines for spacecraft pose estimation, including PCA-TM and DeepCPD. Experiments were conducted on a system equipped with an Intel Core i5-7300HQ CPU running at 2.50 GHz and 16 GB of memory. The value of J was set to 16. The results, shown in Table 2, clearly demonstrate the superior performance of the proposed method compared to the other baselines. Notably, PCA-TM yields favorable results for estimating the pose of slender spacecraft structures, such as the Aura satellite and the Space Shuttle Orbiter. However, these methods proved unsuitable for achieving successful pose estimation for spacecraft like the LRO because they rely heavily on determining the object's principal axes. In contrast, DeepCPD estimates pose by learning point-to-component correspondences from local features in the point cloud. Consequently, DeepCPD's performance is significantly affected by the point cloud density in the test dataset. Furthermore, DeepCPD performs poorly on the Aura satellite, which lacks distinguishable components. PCA-TM employs ICP refinement for the results. Table 2 shows the following: Table 2 Posture error and translation error of posture tracking

[0040] The CPU inference times for all methods are shown in Table 3. Our method stands out for its significant speed, as it does not rely on template matching or local feature extraction. Notably, PCA-TM incurs higher computational costs due to the creation of online templates. Single-precision floating-point values ​​are used for neural network parameters and input scan points to speed up processing. With a model size of 3.93 MB, the average inference time for the proposed pose initialization method is approximately 4 milliseconds. However, it is important to consider the significantly lower computational power of the onboard computer compared to our testbed. In terms of performance, the CPU in the testbed delivers 320 giga-operations per second (GOPS) of single-precision floating-point (FP32) performance. However, the space-grade Virtex-5QV FPGA only offers 51.93 GOPS of FP32 capability. Therefore, running the proposed method on the Virtex-5QV takes approximately 24 milliseconds. To accelerate execution, developing the program in C or C++ programming languages ​​is feasible.

[0041] Table 3 CPU inference time

[0042] The density of the scanned point cloud is affected by the relative position between the onboard lidar sensor and the target spacecraft. The proposed algorithm relies on the global features of the point cloud for pose regression, which is invariant to the density of the point cloud. Therefore, the algorithm is theoretically robust to distance variations. In order to evaluate this resilience, the success rate of the proposed method is evaluated at different ratios of distance to the length of the target spacecraft, taking into account the different sizes of each spacecraft. Results under distance variation A test dataset containing 1024 sets of scanned points was reconstructed for each spacecraft. Despite the influence of distance, the pose estimation can still be initialized with satisfactory performance. The Euler angle error of each axis is maintained at 1°, the translation error on each axis is maintained within 0.1m for most of the tracking time, and the estimated error of the relative angular velocity is less than , and the estimated error of the relative velocity is within 0.04m / s.

[0043] It is understood that the proposed framework is used to address the pose tracking problem of non-cooperative spacecraft using airborne LiDAR systems. The proposed framework includes pose initialization and tracking procedures. To overcome the limitations of pose initialization methods based on template matching and point cloud registration, inspired by the PPAM algorithm, this network directly maps global feature vectors to 3-DoF relative poses as a pose initialization method. To evaluate the effectiveness of the proposed initialization method, a series of comprehensive simulations involving three different spacecraft scenarios were conducted. These simulated complex space environments, accounting for factors such as the uncertainty of LiDAR range detection, the presence of outliers, and range variations. Results, including accuracy, success rate, and inference time, clearly demonstrate the superior performance of the proposed method compared to other methods. For pose tracking, a customized version of ICP with an ESKF was employed. Results obtained from the simulated scenarios demonstrate that the pose tracking procedure can accurately estimate the relative states of non-cooperative spacecraft.

[0044] In all examples shown and described herein, any specific values ​​should be interpreted as merely exemplary and not limiting, and thus other examples of the exemplary embodiments may have different values.

[0045] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0046] The above-described embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that variations and modifications are possible without departing from the scope of the present invention, and such variations and modifications are fully within the scope of protection of the present invention.

Claims

1. A non-cooperative spacecraft attitude estimation method based on laser radar, characterized in that: The following steps are involved: Obtaining scanning points of the non-cooperative spacecraft observed by the laser radar, and performing attitude initialization on the scanning points to obtain a scanning point cloud; Constructing a reference model of the non-cooperative spacecraft, and matching the scanned point cloud with the reference model to obtain a matching result, wherein the reference model includes taking the scanned point cloud as input, extracting global point features from the scanned point cloud to regress the relative attitude of the non-cooperative spacecraft, and using unit quaternions to represent the relative attitude; The matching result is subjected to attitude tracking based on an iterative closest point algorithm and a Kalman filter to complete attitude estimation of the non-cooperative spacecraft.

2. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 1 is characterized in that: Get the scanning points of non-target spacecraft observed by the lidar, including: According to Tait-Bryan angle From the target reference system according to the XYZ sequence To the LiDAR reference frame Derive the intrinsic rotation matrix , using unit quaternion Represents a 3D rotation matrix ,in, , are the scalar and vector parts of the quaternion, The units are three spheres, Preset LiDAR sensor in LiDAR reference frame Scan point observed , let u be the target reference system The target point corresponding to the scan point v is u from the target reference system Mapping to the LiDAR Reference Frame The expression is: （1） and (2) （3） in, Indicated by The skew-symmetric cross product matrix formed by the components of Represents the translation vector between the target point and the lidar sensor, using represents the Kronecker product.

3. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 2 is characterized in that: Initializing the scan points to obtain a scan point cloud includes: Get the scan point cloud at the kth moment and perform normalization processing; The normalized scan point cloud is input into the trained neural network to obtain the relative posture; The relative attitude is tracked by using an iterative closest point algorithm, and the error state corresponding to the attitude tracking is corrected by using a Kalman filter to obtain a real-time tracking result of the six-degree-of-freedom attitude of the non-cooperative spacecraft.

4. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 3 is characterized in that: The PPAM model was used for regression analysis. arrive Perform a regression where ,set up and Represents two random variables, given input and model parameters , the goal is to predict the corresponding , PPAM can be modeled as a local affine transformation, and the corresponding expression is: （4） Among them, the matrix and matrix Represents the parameters of the affine transformation; is an error vector used to explain high-dimensional observation noise and reconstruction error, and the corresponding latent variable It means if and only if from Mapped to the jth affine transformation ; like It follows that with a diagonal covariance matrix The zero mean high speed distribution of and The joint probability distribution of can be decomposed into: （5） and (6) in, A vector representing the model parameters, constrained by ,like The mixture definition of J Gaussian distributions follows from formula (7): （7） By considering the observed variables X, Y and the latent variables The joint probability distribution of the model parameters Under the control of , the expectation maximization algorithm is used to maximize the expected complete data log-likelihood function , and obtain the model parameters, the corresponding expression is: （8） set up is a latent variable expectations, that is , if the model parameters are determined , the conditional density of regression can be derived according to formula (9): （9） （10） Output vector The default value is the expected value of formula (9): （11）。 5. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 4 is characterized in that: Constructing a reference model of the non-cooperative spacecraft, including: The centroid of the scanned point cloud is converted to the origin, and the scanned points are normalized according to the length of the main axis of the model. Each group of scanned points is set to consist of n points, expressed as , using a shared multilayer perceptron as the nonlinear function, Embedded into high-dimensional space; The obtained output is subjected to maximum pooling to generate a high-dimensional global feature vector g; Each layer in the J different fully connected layer sets uses the weight matrix and bias vector to perform a linear transformation on the input vector. According to the local affine transformation of formula (4), the output of the jth fully connected layer is recorded as , the corresponding expression is: （12） in, and Represent the weight and bias of the jth fully connected layer respectively; Neural networks calculate the corresponding latent variables The expected value of replaces the , using the shared MLP to transform the global feature vector and applying the softmax function to Normalized, where all shared MLPs use ReLU and batch normalization, and the estimated quaternion is the average of a set of J relative pose estimates in quaternion form with corresponding weights , the corresponding expression is: （13） Given The eigendecomposition of The elements on the diagonal are the eigenvalues ​​of the matrix M, the column vectors of the orthogonal matrix U are the eigenvectors of the matrix M, and the estimated quaternion is the eigenvector corresponding to the largest eigenvalue of the matrix M.

6. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 5, characterized in that: Optimize the neural network using mean squared error loss: （14） （15） in, represents the conjugate of the ground truth quaternion label, is the identity quaternion, ensuring the quaternion error when calculating network loss The scalar part of the loss function is positive, and the last term of the loss function represents the network parameters Tikhonov regularization, the regularization parameter is determined by the hyperparameter control.

7. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 6 is characterized in that: Performing attitude tracking on the matching result based on an iterative closest point algorithm and a Kalman filter to complete attitude estimation of a non-cooperative spacecraft includes: The nominal vector is defined as: （16） Among them, q represents the relative attitude vector, w represents the relative acceleration, r represents the relative position, v represents the relative linear velocity, and the subscript k represents the time step; The extrapolation of attitude uses the previous estimate of velocity as the time interval The constant inside, calculate The expected value of the nominal state vector at starts from the previously adjusted value: （17） The superscript f indicates a priori estimate, and the superscript represents the posterior estimate, and the error state vector is: （18） The kinematics of the error state can be derived as: （19） ， （20） Where I is the identity matrix, represents the error covariate, i represents the disturbance pulse vector, and is the predicted Jacobian matrix for the error state and the disturbance vector, and the random pulses applied to the error state of Gaussian white noise are given by , , and express, The covariance of can be predicted by the following formula: （21） in, is the covariance matrix of the disturbance pulse, The measurement relies on pose estimation using an iterative closest point algorithm.

8. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 7, characterized in that: Also includes: Observation Model for: （22） （23） in, is the measurement Jacobian matrix relative to the error state vector, means that the mean is zero and the covariance is If the estimated attitude is corrected by the Kalman filter, the a posteriori estimates of the angular velocity and linear velocity are obtained by formula (24): （24）。 9. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 8, characterized in that: The attitude error The estimated quaternion is defined as The geodesic distance between the ground truth q and the translation error Defined as translation The 2-norm of the difference between the ground truth r is used to evaluate the estimated attitude, and the corresponding expression is: （25） （26）。 10. A non-cooperative spacecraft attitude estimation system based on laser radar, characterized in that: The non-cooperative spacecraft attitude estimation method based on laser radar as described in any one of claims 1 to 9 is characterized by comprising: A data acquisition module is used to acquire scanning points of non-cooperative spacecraft observed by the laser radar, and perform attitude initialization on the scanning points to obtain a scanning point cloud; a model building module, used to build a reference model of the non-cooperative spacecraft, and match the scanned point cloud with the reference model to obtain a matching result, wherein the reference model includes taking the scanned point cloud as input, extracting global point features from the scanned point cloud to regress the relative attitude of the non-cooperative spacecraft, and using unit quaternions to represent the relative attitude; The attitude estimation module is used to perform attitude tracking on the matching result based on an iterative closest point algorithm and a Kalman filter to complete attitude estimation of the non-cooperative spacecraft.

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