A method and system for attitude estimation of non-cooperative spacecraft based on lidar

Abstract

The present invention discloses a method and system for attitude estimation of a non-cooperative spacecraft based on lidar. 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 scanned point cloud, a reference model of the non-cooperative spacecraft is constructed, and the scanned point cloud is matched with the reference model to obtain a matching result. Attitude tracking is performed on the matching result based on the iterative closest point algorithm and the Kalman filter to complete the attitude estimation of the non-cooperative spacecraft, solving the problem of attitude tracking of the non-cooperative spacecraft by the airborne LiDAR system, overcoming the limitations of the attitude initialization method based on template matching and point cloud registration, and being able to accurately estimate the relative state of the non-cooperative spacecraft.

Description

Technical Field

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

[0002] Many current and future spaceborne applications involve autonomous rendezvous and docking (AR&D) with dynamically free - floating space targets, such as on - orbit satellite maintenance, capturing 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 lacking an active communication link system or supplementary indicators (such as light - emitting diodes or corner reflectors) remains a formidable challenge.

[0003] To address the above challenges, recent mission concepts are investigating the application of on - board sensors for non - cooperative spacecraft attitude estimation in Lichter & Dubowsky (2004). Passive sensors, such as monocular and stereo cameras, are commonly deployed in current spaceborne missions due to their low hardware complexity Ventura (2016). However, the imaging quality of passive sensors is susceptible to changes in lighting conditions. In contrast, active sensors, such as light detection and ranging sensors (LiDAR) and time - of - flight (ToF) cameras, emit 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 geometry, enabling attitude estimation even in the absence of distinct features. Nevertheless, most lidar - based methods rely on template matching for attitude initialization, which has certain limitations. Template matching requires a large database to improve the accuracy of attitude initialization, but this reduces the computational speed when searching for relevant templates in the database. Therefore, there is an urgent need to provide an accurate and robust method for non - cooperative spacecraft attitude estimation. Summary of the Invention

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

[0005] In a first aspect, the present invention provides a lidar - based non - cooperative spacecraft attitude estimation method, including the following steps:

[0006] Obtain the scan points of the non - cooperative spacecraft observed by the lidar, and perform attitude initialization on the scan points to obtain a scan point cloud;

[0007] Construct a reference model of the non-cooperative spacecraft, and match the scanned point cloud with the reference model to obtain a matching result, where the reference model includes taking the scanned point cloud as input, extracting global point features from the scanned point cloud, regressing the relative attitude of the non-cooperative spacecraft, and representing the relative attitude using unit quaternions;

[0008] Perform attitude tracking on the matching result based on the iterative closest point algorithm and the Kalman filter to complete the attitude estimation of the non-cooperative spacecraft.

[0009] As an optimization of the above technical solution, obtaining the scanned points of the non-target spacecraft observed by the lidar includes:

[0010] According to the Tait-Bryan angles In the X-Y-Z sequence from the target reference frame to the lidar reference frame Derive the intrinsic rotation matrix , and use the unit quaternion to represent the 3D rotation matrix , where , are the scalar part and the vector part of the quaternion, represents three spheres with a unit, and it is assumed that the preset lidar sensor observes the scanned point in the lidar reference frame . Let u be the target point corresponding to the scanned point v in the target reference frame . The expression for mapping u from the target reference frame to the lidar reference frame is:

[0011] (1)

[0012] and (2)

[0013] (3)

[0014] where represents the skew-symmetric cross product matrix formed by the components of , represents the translation vector between the target point and the lidar sensor, and is used to represent the Kronecker product.

[0015] As an optimization of the above technical solution, initializing the attitude of the scanned points to obtain a scanned point cloud includes:

[0016] Obtain the scanned point cloud at the k-th moment and perform normalization processing; ​

[0017] Input the normalized scanned point cloud into the trained neural network to obtain the relative pose;

[0018] Use the iterative closest point algorithm to perform pose tracking on the relative pose, and use the Kalman filter to correct the error state corresponding to the pose tracking to obtain the real-time tracking result of the six-degree-of-freedom pose of the non-cooperative spacecraft.

[0019] As an optimization of the above technical solution, the PPAM model is used for regression analysis. The PPAM model regresses from to where, Let and represent two random variables. Given the input and the model parameters , the goal is to predict the corresponding . The PPAM can be modeled as a local affine transformation, and the corresponding expression is:

[0020] (4)

[0021] where the matrix and the matrix represent the parameters of the affine transformation; is an error vector used to explain the high-dimensional observation noise and reconstruction error, and the corresponding latent variable indicates that when and only when maps from to the j-th affine transformation ;

[0022] If follows a zero-mean high-speed distribution with a diagonal covariance matrix , then the joint probability distribution of and can be decomposed as:

[0023] (5)

[0024] and (6)

[0025] where, represents the vector of model parameters, constrained to . If follows the mixture of J Gaussian distributions defined by formula (7):

[0026] (7)

[0027] By considering the observed variables X, Y and the latent variable The joint probability distribution, under the control of the model parameters Using the expectation-maximization algorithm to maximize the expected complete-data log-likelihood function And obtain the model parameters. The corresponding expression is:

[0028] (8)

[0029] Let Be the expectation of the latent variable That is, If the model parameters Are determined, the conditional density of the regression can be derived according to formula (9):

[0030] (9)

[0031] (10)

[0032] The output vector Is preset as the expected value of formula (9):

[0033] (11).

[0034] As an optimization of the above technical solution, a reference model of the non-cooperative spacecraft is constructed, including:

[0035] Convert the centroid of the scanned point cloud to the origin, normalize the scanned points according to the length of the model main axis, and set each group of scanned points consisting of n points, denoted as Use a shared multi-layer perceptron as a non-linear function to perform, and embed Into a high-dimensional space;

[0036] Generate a high-dimensional global feature vector g by performing max pooling on the obtained output;

[0037] In each of the J different sets of fully connected layers, perform a linear transformation on the input vector using the weight matrix and bias vector. According to the local affine transformation of formula (4), the output of the j-th fully connected layer is denoted as The corresponding expression is:

[0038] (12)

[0039] Where And Represent the weight and bias of the j-th fully connected layer respectively;

[0040] The neural network replaces In formula (9) when calculating the expected value of the corresponding latent variable , 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:

[0041] (13)

[0042] 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.

[0043] As a preferred embodiment of the above technical solution, the mean square error loss is used to optimize the neural network:

[0044] (14)

[0045] (15)

[0046] 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.

[0047] As a preferred embodiment of the above technical solution, the matching result is tracked based on an iterative closest point algorithm and a Kalman filter to complete the non-cooperative spacecraft attitude estimation, including:

[0048] The nominal vector is defined as:

[0049] (16)

[0050] 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;

[0051] 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:

[0052] (17)

[0053] Among them, the superscript f represents the prior estimate, and the superscript represents the posterior estimate. The error state vector is:

[0054] (18)

[0055] The kinematics of the error state can be derived as:

[0056] (19)

[0057] ,

[0058] (20)

[0059] Among them, I is the identity matrix, represents the error covariance, i represents the perturbation impulse vector, and are the predicted Jacobian matrices with respect to the error state and the perturbation vector. The random impulse applied to the error state of the Gaussian white noise is represented by , , and . The covariance of can be predicted by the following formula:

[0060] (21)

[0061] Among them, is the covariance matrix of the perturbation impulse. The measurement of relies on the attitude estimation of the iterative closest point algorithm.

[0062] As an optimization of the above technical solution, the observation model is:

[0063] (22)

[0064] (23)

[0065] Among them, is the measurement Jacobian matrix with respect to the error state vector, represents the observation error with a mean of zero and a covariance of . If the estimated attitude is corrected by the Kalman filter, the posterior estimates of the angular velocity and the linear velocity are obtained through formula (24):

[0066] (24).​​​​​

[0067] As an optimization of the above technical solution, the attitude error is defined as the geodesic distance between the estimated quaternion and the ground truth q, and the translation error is defined as the 2-norm of the difference between the translation and the ground truth r to evaluate the estimated attitude. The corresponding expressions are:

[0068] (25)

[0069] (26).

[0070] In a second aspect, the present invention also provides a non-cooperative spacecraft attitude estimation system for a lidar, which is applied to the above-mentioned non-cooperative spacecraft attitude estimation method based on lidar, and includes:

[0071] A data acquisition module, configured to acquire the scan points of the non-cooperative spacecraft observed by the lidar, and perform attitude initialization on the scan points to obtain a scan point cloud;

[0072] A model construction module, configured to construct a reference model of the non-cooperative spacecraft, and match the scan point cloud with the reference model to obtain a matching result, wherein the reference model includes using the scan point cloud as an input, extracting global point features from the scan point cloud, and regressing the relative attitude of the non-cooperative spacecraft, and representing the relative attitude using a unit quaternion;

[0073] An attitude estimation module, configured to perform attitude tracking on the matching result based on the iterative closest point algorithm and the Kalman filter to complete the non-cooperative spacecraft attitude estimation.

[0074] The present invention provides a non-cooperative spacecraft attitude estimation method and system based on lidar. By acquiring the scan points of the non-cooperative spacecraft observed by the lidar, performing attitude initialization on the scan points to obtain a scan point cloud, constructing a reference model of the non-cooperative spacecraft, matching the scan point cloud with the reference model to obtain a matching result, and performing attitude tracking on the matching result based on the iterative closest point algorithm and the Kalman filter to complete the non-cooperative spacecraft attitude estimation, the problem of non-cooperative spacecraft attitude tracking of the airborne LiDAR system is solved, the limitations of the attitude initialization method based on template matching and point cloud registration are overcome, and the relative state of the non-cooperative spacecraft can be accurately estimated. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the embodiments. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings.

[0076] Figure 1 Flowchart of the non-cooperative spacecraft attitude estimation method based on lidar provided by the present invention;

[0077] Figure 2 Schematic diagram of the reference model provided by the present invention;

[0078] Figure 3 Schematic diagram of the PPAM model provided by the present invention;

[0079] Figure 4 Schematic diagram of the relative trajectory of the tracking spacecraft in the target Hill reference frame provided by the present invention;

[0080] Figure 5 Block diagram of the structure of the non-cooperative spacecraft attitude estimation system based on lidar provided by the present invention. Detailed implementation manners

[0081] The following will describe the embodiments of the present invention in detail. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and should not be construed as limiting the present invention.

[0082] The present invention proposes an innovative framework for sparse LiDAR point non-cooperative spacecraft attitude tracking: First, a new neural network is designed to initialize the attitude of the target spacecraft; inspired by the probability piecewise affine mapping, the neural network takes lidar points as input and regresses the relative attitude of the non-cooperative spacecraft using the global features derived from the lidar points. To solve the singularity of the Euler angles, the relative attitude is represented using unit quaternions; subsequently, a customized iterative closest point (ICP) algorithm and an error state Kalman filter (ESKF) are used for attitude tracking. Specifically as follows:

[0083] Refer to Figure 1 , the present invention provides a non-cooperative spacecraft attitude estimation method based on lidar, including the following steps:

[0084] S1: Obtain the scan points of the non-cooperative spacecraft observed by the lidar, and perform attitude initialization on the scan points to obtain a scan point cloud;

[0085] S2: Construct a reference model of the non-cooperative spacecraft, and match the scanned point cloud with the reference model to obtain a matching result. The reference model includes using the scanned point cloud as input, extracting global point features from the scanned point cloud, and regressing the relative attitude of the non-cooperative spacecraft. The relative attitude is represented by a unit quaternion.

[0086] S3: Based on the iterative closest point algorithm and the Kalman filter, perform attitude tracking on the matching result to complete the attitude estimation of the non-cooperative spacecraft.

[0087] In this embodiment, obtaining the scanned points of the non-target spacecraft observed by the lidar includes:

[0088] According to the Tait-Bryan angles In the X-Y-Z sequence from the target reference frame to the lidar reference frame Derive the inherent rotation matrix , and use the unit quaternion to represent the 3D rotation matrix , where , are the scalar part and the vector part of the quaternion, represents a unit of three spheres,

[0089] Preset that the lidar sensor observes the scanned points in the lidar reference frame . Let u be the target point corresponding to the scanned point v in the target reference frame . The expression for mapping u from the target reference frame to the lidar reference frame is:

[0090] (1)

[0091] and (2)

[0092] (3)

[0093] where represents the skew-symmetric cross product matrix formed by the components of , represents the translation vector between the target point and the lidar sensor, and is used to represent the Kronecker product.

[0094] It should be noted that initializing the attitude of the scanned points to obtain the scanned point cloud includes:

[0095] Obtain the scanned point cloud at the k-th moment and perform normalization processing;​

[0096] Input the normalized scanned point cloud into the trained neural network to obtain the relative pose;

[0097] Use the iterative closest point algorithm to perform pose tracking on the relative pose, and use the Kalman filter to correct the error state corresponding to the pose tracking to obtain the real-time tracking result of the six-degree-of-freedom pose of the non-cooperative spacecraft.

[0098] Perform regression analysis using the PPAM model, and the PPAM model regresses from to where, , let and represent two random variables. Given the input and the model parameters , the goal is to predict the corresponding . The PPAM can be modeled as a local affine transformation, and the corresponding expression is:

[0099] (4)

[0100] where, the matrix and the matrix represent the parameters of the affine transformation; is an error vector used to explain the high-dimensional observation noise and reconstruction error, and the corresponding latent variable indicates that when and only when maps from to the j-th affine transformation ;

[0101] If follows a zero-mean high-speed distribution with a diagonal covariance matrix , then the joint probability distribution of and can be decomposed as:

[0102] (5)

[0103] and (6)

[0104] where, represents the vector of model parameters, constrained to . If follows the mixture of J Gaussian distributions defined by formula (7):

[0105] (7)

[0106] By considering the observed variables X, Y and the latent variable The joint probability distribution, under the control of the model parameters Using the expectation maximization algorithm to maximize the expected complete data log-likelihood function and obtain the model parameters, and the corresponding expression is:

[0107] (8)

[0108] Let be the expectation of the latent variable , that is . If the model parameters are determined, the conditional density of the regression can be derived according to formula (9):

[0109] (9)

[0110] (10)

[0111] The output vector is preset as the expected value of formula (9):

[0112] (11).

[0113] In the past few decades, the visual navigation of orbital spacecraft has mainly relied on the assistance of artificial markers or beacons installed on the target spacecraft. However, when dealing with non-cooperative spacecraft that do not deploy these devices, estimating their relative attitude and position remains a challenge. To address this challenge, various methods for attitude estimation of non-cooperative spacecraft using a single image have been proposed. Some researchers use geometric primitive matching of imaging, such as edges, circles, and curves, etc., for spacecraft attitude estimation. Notably, these methods rely heavily on favorable lighting conditions. And the on-board LiDAR points in the spaceborne scene may be very sparse, rendering existing algorithms based on feature descriptor matching ineffective. In the case of good initial estimation, the iterative closest point (ICP) algorithm has been proposed, which can align two sets of partially overlapping points without extracting point cloud descriptors. Therefore, the main challenge lies in attitude initialization when using the scan points generated by on-board LiDAR. Inspired by the Gaussian mixture model registration algorithm, Deep Coherent Point Drift (DeepCPD) is introduced, which learns attitude-invariant point-to-component correspondences through a learnable network to register two sets of partially overlapping points under arbitrary transformations.

[0114] It should be understood that by obtaining the scanning points of the non-cooperative spacecraft observed by the lidar, performing attitude initialization on the scanning points to obtain a point cloud, constructing a reference model of the non-cooperative spacecraft, and matching the point cloud with the reference model to obtain a matching result, attitude tracking is performed on the matching result based on the iterative closest point algorithm and the Kalman filter to complete the attitude estimation of the non-cooperative spacecraft, solving the problem of attitude tracking of non-cooperative spacecraft by the airborne LiDAR system, overcoming the limitations of the attitude initialization method based on template matching and point cloud registration, and accurately estimating the relative state of the non-cooperative spacecraft.

[0115] Optionally, constructing the reference model of the non-cooperative spacecraft includes:

[0116] Converting the centroid of the point cloud to the origin, normalizing the scanning points according to the length of the model's main axis, setting each group of scanning points consisting of n points, denoted as , using a shared multi-layer perceptron as a non-linear function to perform, and embedding into a high-dimensional space;

[0117] Generating a high-dimensional global feature vector g by performing max pooling on the obtained output;

[0118] In each layer of J different sets of fully connected layers, a linear transformation is performed on the input vector using the weight matrix and bias vector. According to the local affine transformation of formula (4), the output of the j-th fully connected layer is denoted as , and the corresponding expression is:

[0119] (12)

[0120] where and respectively represent the weight and bias of the j-th fully connected layer;

[0121] The neural network replaces in formula (9) when calculating the expected value of the corresponding latent variable , uses the shared MLP to transform the global feature vector, and normalizes by applying the softmax function. Among them, all shared MLPs adopt ReLU and batch normalization, and the estimated quaternion is in the form of a quaternion that is the average of a set of J relative attitude estimations with corresponding weights , and the corresponding expression is:

[0122] (13)

[0123] Given the eigen-decomposition of, the matrix The elements on the diagonal are the eigenvalues of matrix M, and the column vectors of the orthogonal matrix U are the eigenvectors of matrix M. The estimated quaternion is the eigenvector corresponding to the largest eigenvalue of matrix M.

[0124] In this embodiment, the mean squared error loss is used to optimize the neural network:

[0125] (14)

[0126] (15)

[0127] where denotes the conjugate of the ground truth quaternion label, is the identity quaternion, which ensures that the scalar part of the quaternion error is positive when calculating the network loss. The last term of the loss function represents the Tikhonov regularization of the network parameters and the regularization parameter is controlled by the hyperparameter .

[0128] Specifically, as Figure 2 shown, the z-axis in the lidar reference frame points outwards along the line of sight, which means that when the relative attitude 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.

[0129] Optionally, attitude tracking is performed on the matching result based on the iterative closest point algorithm and the Kalman filter to complete the non-cooperative spacecraft attitude estimation, including:

[0130] The nominal vector is defined as:

[0131] (16)

[0132] 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;

[0133] The extrapolation of the attitude utilizes the previous estimate of the velocity as a constant within the time interval to calculate the expected value of the nominal state vector at starting from the previously adjusted value:

[0134] (17)

[0135] where the superscript f represents the prior estimate and the superscript represents the posterior estimate. The error state vector is:

[0136] (18)

[0137] The kinematics of the error state can be derived as:

[0138] (19)

[0139] ,

[0140] (20)

[0141] where I is the identity matrix, denotes the error covariance, i represents the disturbance impulse vector, and are the predicted Jacobian matrices with respect to the error state and the disturbance vector. The random impulse of the error state imposed on the Gaussian white noise is represented by , , and . The covariance of can be predicted by the following formula:

[0142] (21)

[0143] where, is the covariance matrix of the disturbance impulse. The measurement of relies on the attitude estimation of the iterative closest point algorithm.

[0144] In this embodiment, the observation model is:

[0145] (22)

[0146] (23)

[0147] where, is the measurement Jacobian matrix with respect to the error state vector, denotes the observation error with a mean of zero and a covariance of . If the estimated attitude is corrected by the Kalman filter, the posterior estimates of the angular velocity and the linear velocity are obtained by formula (24):

[0148] (24).

[0149] As an optimization of the above technical solution, the attitude error is defined as the geodesic distance between the estimated quaternion and the ground truth q, and the translation error is defined as the 2-norm of the difference between the translation and the ground truth r to evaluate the estimated attitude. The corresponding expression is:

[0150] (25)

[0151] (26).

[0152] It should be noted that considering the invariance of the scanned point cloud shape with respect to the distance between the tracker and the target spacecraft, and only the density of the point cloud changes. Based on this feature, a method of directly regressing the relative attitude using the global features of the neural network of points is proposed. A Probabilistic Piecewise Affine Mapping (PPAM) is introduced into the network. PPAM proposes a piecewise linear model to solve the regression problem from low dimension to high dimension. Figure 3 The graphical display of the supervised PPAM is shown, where white represents the latent variable and gray represents the observed data. The key point of this embodiment is to predict the relative attitude from the global features of the point cloud, that is, regression from high dimension to low dimension, rather than from low dimension to high dimension. After establishing the basis of the probabilistic piecewise affine mapping algorithm, the proposed neural network needs to be shown.

[0153] Referring to Figure 5 , the present invention also provides a non-cooperative spacecraft attitude estimation system for lidar, which is applied to the above-mentioned non-cooperative spacecraft attitude estimation method based on lidar, and includes:

[0154] A data acquisition module, configured to acquire the scanned points of the non-cooperative spacecraft observed by the lidar, and perform attitude initialization on the scanned points to obtain a scanned point cloud;

[0155] 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 includes using the scanned point cloud as an input, and extracting global point features from the scanned point cloud to regress the relative attitude of the non-cooperative spacecraft, and representing the relative attitude using a unit quaternion;

[0156] An attitude estimation module, configured to perform attitude tracking on the matching result based on the Iterative Closest Point (ICP) algorithm and the Kalman filter to complete the non-cooperative spacecraft attitude estimation.

[0157] In this embodiment, the neural network is implemented in Pytorch 1.8.2. Adam with an initial learning rate of 5e-4 is used to adjust the parameters of the network. During the training process, the learning rate is halved every 200 epochs. The training is carried out on an Nvidia GTX 1070 GPU for a total of 600 epochs with a batch size of 128. Three spacecraft CAD models, namely reference models, including the Lunar Reconnaissance Orbiter (LRO), the Space Shuttle Orbiter, and Aura, are selected as experimental objects. Table 1 shows the key parameters of the simulated lidar.

[0158] Table 1 Key Parameters of the Simulated Flash LiDAR

[0159]

[0160] To create the training dataset, rigid transformations were applied to the spcecraft CAD model along each axis, and 256 viewpoints (Tait - Bryan angles and ) were uniformly sampled on the attitude sphere via a Fibonacci grid, sampled uniformly from at an interval of 9°. LRO, the Space Shuttle Orbiter, and Aura were located at positions 100 m, 470 m, and 120 m away from the simulated LiDAR respectively. At these distances, the field of view (FOV) of the simulated LiDAR covered the entire object, so occlusion was not considered in the experiment. For each sampled attitude, the simulated Flash LiDAR first generated a set of scan points, and then 128 points were downsampled from each scan using farthest point sampling for batch processing to accelerate training. Three object - specific networks were trained separately for each spacecraft. For the validation and test datasets, random rotations were applied to each spacecraft CAD model, and the distances in the validation dataset were set to those of the training set.

[0161] The validation dataset allowed the modification of the hyperparameters of the neural network during training. For the test dataset, LRO, the Space Shuttle Orbiter, and Aura were placed at positions approximately 110 m, 530 m, and 180 m away from the simulated LiDAR respectively. Each scanned point cloud in the test dataset was corrupted by Gaussian noise with standard deviation and outliers. The training, validation, and test datasets contained 18432, 1024, and 8192 sets of scan points for each spacecraft respectively. In the test dataset, the number of simulated scan points for LRO ranged from 94 to 311, for the Space Shuttle Orbiter ranged from 47 to 320, and for Aura ranged from 19 to 274.

[0162] Specifically, referring to Figure 4 , Aura was selected as the experimental object to verify the performance of the attitude tracking algorithm. The true relative angular velocity for each Tait - Bryan angle was set to , while the tracking spacecraft approached the target spacecraft at a speed of 0.05 m / s gradually, once per second for the tracking program. 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 ranged from 130 m to 180 m. In the attitude tracking experiment, a total of 100 Monte Carlo simulations were conducted.

[0163] Given appropriate initial pose predictions, ICP can improve the estimation results. Therefore, to evaluate the performance of the proposed method, special emphasis is placed on its pose recall rate, 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 conducted to evaluate its impact on the pose initialization results, setting the initial value of J from 1 to 32 to train three spacecraft. Among them, is similar to the classical linear regression model. Increasing J can improve the accuracy of the model but 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 improve significantly. Therefore, in the following experiments, J is fixed at 16.

[0164] A comparative analysis was carried out on the method proposed in the present invention and the spacecraft attitude estimation baselines, including PCA-TM and DeepCPD. The 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 that the method of the present invention has superior performance compared to other baselines. It is worth mentioning that when PCA-TM is adopted, favorable results are obtained for estimating the attitude of slender spacecraft structures such as the Aura satellite and the Space Shuttle orbiter. However, these methods have been proven unsuitable for achieving successful attitude estimation of spacecraft like LRO because they rely heavily on determining the main axis of the object. In contrast, DeepCPD estimates the attitude by learning the correspondence of point pairs through local features of the point cloud. Therefore, the performance of DeepCPD is severely affected by the point cloud density in the test dataset. In addition, DeepCPD performs poorly on the satellite Aura because Aura lacks distinguishable components. PCA-TM uses ICP for result refinement. Table 2 is as follows:

[0165] Table 2 Attitude error and translation error of attitude tracking

[0166]

[0167] The CPU inference times for all methods are shown in Table 3. Our method stands out for its remarkable speed as it does not rely on template matching or local feature extraction. It is worth noting that PCA-TM requires a higher computational cost due to the creation of online templates. Single-precision floating-point values are used as neural network parameters and input scan points to speed up the processing. With a model size of 3.93 MB, the average inference time of the proposed pose initialization method is approximately 4 milliseconds. However, it must be taken into account that the computational power of on-board computers is much lower compared to our test platform. In terms of performance, the CPU in the test platform provides a single-precision floating-point (FP32) performance of 320 giga-operations per second (GOPS). However, the space-grade FPGA Virtex-5QV only provides an FP32 capability of 51.93 GOPS. Therefore, it takes approximately 24 milliseconds to run the proposed method on the Virtex-5QV. To speed up the execution, it is feasible to develop the program using the C or C++ programming languages.

[0168] Table 3 CPU Inference Times

[0169]

[0170] The density of the scanned point cloud is affected by the relative position between the on-board 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 changes. To evaluate this resilience, considering the different sizes of each spacecraft, the success rate of the proposed method at different ratios of distance to the length of the target spacecraft was evaluated. The results under distance variation reconstructed a test dataset containing 1024 sets of scan points for each spacecraft. Despite the influence of distance, the pose estimation can still be initialized with satisfactory performance. The Euler angle error for each axis remains within 1°, and for most of the tracking time, the translational error on each axis remains within 0.1 m, and the estimated error of the relative angular velocity is less than , while the estimated error of the relative velocity is within 0.04 m / s.

[0171] It should be understood that it is used to solve the problem of attitude tracking of non-cooperative spacecraft in an airborne LiDAR system. The proposed framework includes attitude initialization and tracking procedures. To overcome the limitations of attitude initialization methods based on template matching and point cloud registration. Inspired by the PPAM algorithm. This network directly maps the global feature vector to a 3-DoF relative attitude as an attitude initialization method. To evaluate the effectiveness of the proposed initialization method, a series of comprehensive simulations were conducted involving three different spacecraft scenarios. These simulated a complex space environment, considering factors such as the uncertainty of lidar range detection, the presence of outliers, and the variation of distances. The results, including accuracy, success rate, and inference time, clearly show that the proposed method has superior performance compared to other methods. For attitude tracking, a customized version of ICP with ESKF was adopted. The results obtained from the simulated scenarios show that the attitude tracking procedure can accurately estimate the relative state of non-cooperative spacecraft.

[0172] In all examples shown and described herein, any specific value should be construed as merely exemplary and not as a limitation. Thus, other examples of the exemplary embodiments may have different values.

[0173] It should be noted that like reference numerals and letters denote like items in the following figures. Therefore, once an item is defined in one figure, it does not require further definition and explanation in subsequent figures.

[0174] The above-described embodiments merely represent several implementation manners of the present invention. Their descriptions are relatively specific and detailed, but should not be construed as limiting the scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope 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 matching 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; 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; 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; An iterative closest point algorithm is used to track the relative attitude, and a Kalman filter is used to correct an error state corresponding to the attitude tracking to obtain a real-time tracking result of the six-degree-of-freedom attitude of the non-cooperative spacecraft; 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.

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 3D rotation Matrix, where , 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 1, characterized in that: 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 Mapped to the jth affine transformation ; like It follows that with a diagonal covariance matrix The zero-mean Gaussian distribution is 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）。 4. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 1, 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.

5. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 4 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.

6. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 5, 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）。 7. The non-cooperative spacecraft attitude estimation method based on laser radar according to claim 6 is 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）。 8. 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 7 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 for building 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 matching 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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