Optical radar multi-source information fusion rocket attitude measurement method

Abstract

This invention discloses a rocket attitude measurement method using optical radar multi-source information fusion, belonging to the field of aerospace telemetry and control technology. It primarily addresses the problem of single sensors being unable to measure rocket attitude with high precision over long distances. The method involves capturing rocket images using optical equipment, employing a directional detection network to identify the coordinates of key points at the nose and tail and the direction of the central axis; transforming the key points through multiple levels—pixel coordinate system, camera space coordinate system, measurement coordinate system, and geocentric coordinate system—to calculate the optical normal vector; acquiring high-resolution range image time-series data of the rocket using broadband radar, employing a time-series neural network to identify the radar's line-of-sight elevation angle, and combining the radar and rocket positions to calculate the line-of-sight vector; fusing α and β to construct a geometric constraint equation set for the unit vector of the rocket's central axis, solving it, and transforming it to the launch coordinate system to output the yaw and elevation angles. This method achieves real-time rocket attitude measurement with small measurement errors and is suitable for high-precision passive external measurement during the active phase of a launch vehicle's flight.

Description

Technical Field

[0001] This invention relates to the field of aerospace telemetry and control technology. More specifically, this invention relates to a method for rocket attitude measurement using optical radar multi-source information fusion. Background Technology

[0002] In the field of aerospace telemetry and control, rocket attitude measurement mainly relies on optical equipment or a single radar sensor. Optical measurement methods calculate attitude angles by analyzing rocket target images. For example, a single optical device can calculate yaw and pitch angles using the tilt angle of the target's central axis within the image plane. This method has high accuracy at close range, but when the rocket distance exceeds 40 kilometers, the target's image size on the image plane shrinks significantly, and pixel-level recognition errors lead to increased deviations in the central axis direction fitting. Measured data shows that the pitch angle measurement error of a single optical device at 40 kilometers can reach more than 3°. Furthermore, the rotational coupling error of the camera's spatial coordinate system caused by gimbal rotation, and the cumulative error of multi-level coordinate transformations due to Earth curvature and site calibration deviations, further reduce the accuracy of normal vector calculation.

[0003] While radar measurement offers advantages in long-range detection, traditional applications have focused on ballistic trajectory calculation. Because rockets have axisymmetric structures, their high-resolution range profile (HRRP) and cross-section vary nonlinearly with the radar line-of-sight elevation angle Ω. Current technology lacks an effective model for retrieving Ω from HRRP time-series data. Although the theoretical value of Ω can be calculated through geometric positional relationships, electromagnetic wave propagation disturbances and background noise in the real environment cause significant deviations between HRRP characteristics and theoretical values, making it difficult to establish a stable mapping relationship.

[0004] Optical-radar fusion measurement faces three common challenges: First, spatial alignment of data from heterogeneous sensors requires a complex coordinate transformation chain. Transforming optical data from pixel coordinates to geocentric coordinates involves coupling gimbal azimuth and elevation parameters, and the error in rotation matrix calculation amplifies with each transformation level; radar position calibration deviations directly affect the accuracy of the line-of-sight vector β. Second, the fusion geometric constraint equations (α·γ=0 and β·γ=cosΩ) have ambiguous solutions due to the rocket's axisymmetric characteristics. Traditional methods rely on historical attitudes or preset motion models to filter the solution results, but attitude maneuvers and separation actions during the rocket's active phase can cause the filtering to fail, leading to output jumps. Third, the exposure delay of optical images and the processing time of radar signals create millisecond-level latency differences; asynchronous data fusion causes position-attitude decoupling errors, and existing synchronization mechanisms are insufficient to meet real-time measurement requirements.

[0005] The aforementioned problems stem from the differences in the physical characteristics of optics and radar: optical imaging is limited by atmospheric disturbances and range attenuation, while radar HRRP is sensitive to attitude changes but has a single dimension for feature extraction. Existing technologies lack a unified cross-modal data representation method and dynamic error suppression mechanism, making it difficult to improve the accuracy of long-range attitude measurement. Summary of the Invention

[0006] One objective of this invention is to provide a method for measuring rocket attitude using optical radar multi-source information fusion, which is suitable for high-precision passive external measurement during the active phase of a launch vehicle's flight.

[0007] To achieve these objectives and other advantages of the present invention, according to one aspect of the present invention, a method for measuring rocket attitude by fusion of multi-source information from optical radar is provided, comprising the following steps: Step 1: Take images of the rocket target using optical equipment, identify the positions of key points at the nose and tail of the rocket and the direction of the central axis using a directional detection network, and output the coordinates of the key points at the nose and tail; Step 2: Transform the coordinates of the head and tail key points to the geocentric coordinate system through a multi-level coordinate transformation, and calculate the optical normal vector α; Step 3: Acquire high-resolution range image data of the rocket using broadband radar, identify the radar line-of-sight elevation angle Ω using a temporal neural network, and calculate the radar line-of-sight vector β based on the positions of the radar and the rocket; Step 4: Combine the optical normal vector α and the radar line-of-sight vector β to construct a set of geometric constraint equations for the unit vector γ of the rocket's central axis: ; Solving the system of equations yields γ, which, after being transformed to the launch coordinate system, outputs the rocket's attitude yaw angle Ψ and pitch angle φ.

[0008] Preferably, the specific method for identifying the positions of key points at the nose and tail of the rocket and the direction of the central axis using the directional detection network in step one is as follows: The rocket body is labeled using a rotating rectangle, with the central axis of the rectangle coinciding with the actual central axis of the rocket. Mark key points on the central axis of the rocket's head and tail, with the head key point marked as A1 and the tail key point marked as B1. The labeled data includes a rotation angle θ, which is used to indicate the tilt direction of the rocket's central axis in the image plane.

[0009] Preferably, the specific steps for transforming the coordinates of the head key points to the geocentric coordinate system in step two are as follows: a. Convert the pixel coordinates (x0, y0) of the head and tail key points to camera space coordinates [x1, y1, z1]: Among them, (x0) 0 ,y0 0 ) represents the center pixel coordinates of the image plane; p x and p y is the pixel size; f is the implicit focal length parameter, which is determined by the imaging geometry of the optical device; b. Convert the camera space coordinate system coordinates [x1, y1, z1] to the measurement coordinate system coordinates [x2, y2, z2]: ; Where AZ represents the azimuth rotation angle of the optical equipment, with true north as 0 degrees and clockwise as positive; EL represents the pitch rotation angle of the optical equipment, with horizontal as 0 degrees and upward as positive; R y and R z Let be the rotation matrices for the coordinate axes y and z, respectively, and their expressions are: c. Assign the coordinates [x2, y2, z2] of the measurement coordinate system based on the longitude λ of the origin of the measurement system. c and latitude ϕ c Convert to geocentric coordinates [x3, y3, z3] using a rotation matrix: ; Among them, R x R y R z These are the rotation matrices for the coordinate axes x, y, and z, respectively; .

[0010] Preferably, the calculation process for the optical normal vector α is as follows: Obtain the geocentric coordinates [x3, y3, z3] of the head and tail key points, including the head key point coordinates A1[x3...]. A y3 A z3 A ] and the coordinates of the tail key point B1[x3 B ,y3 B z3 B ]; Construct a vector from the focal point O of the optical device to the head keypoint and the tail keypoint, i.e.: Calculate the optical normal vector α using the outer product of vectors: .

[0011] Preferably, the specific method for identifying the radar line-of-sight elevation angle Ω is as follows: Broadband radar emits electromagnetic waves and receives reflected signals from rockets to acquire high-resolution range profile (HRRP) time-series data of the rocket. A long short-term memory neural network model is constructed, in which the input layer of the neural network model receives high-resolution range image HRRP time series data, the LSTM hidden layer extracts the dynamic features of the time series data, and the fully connected output layer outputs the continuous predicted value of the radar line-of-sight elevation angle Ω. The training set was used with high-resolution range profile HRRP time series data measured by broadband radar in historical missions of the same type of rocket, and supervised training was performed using the corresponding real radar line-of-sight elevation angle Ω label. The real radar line-of-sight elevation angle Ω label was calibrated based on the real-time geometric position relationship between the radar and the rocket in historical missions. The neural network model is trained using the mean squared error loss function and the backpropagation algorithm. The real-time high-resolution range image time series data of the rocket is input into the trained neural network model, and the predicted value of the radar line-of-sight elevation angle Ω is output.

[0012] Preferably, the radar line-of-sight vector β is calculated as follows: Obtain the geocentric coordinates [x] of the radar site r ,y r ,z r ] T The geocentric coordinates [x0, y0, z0] of the rocket's real-time position. T ; Calculate the original vector for the rocket pointing radar: β0=[x r -x0,y r -y0,z r -z0] T ; Normalizing the original vector β0 yields the radar line-of-sight unit vector: β = β0 / ||β0|| = [β x ,β y ,β z ] T .

[0013] Preferably, the solution process for the unit vector γ of the rocket's central axis is as follows: Define γ = [x, y, z] T Substituting these, along with the optical normal vector α, the radar line-of-sight vector β, and the radar line-of-sight elevation angle Ω, into the geometric constraint equations: Solve for the values ​​of x, y, and z to obtain two candidate solutions γ. 1 and γ 2 ; Calculate the attitude change of each candidate solution relative to the unit vector γ* of the rocket's centerline at the previous moment: ; The solution with the minimum total attitude change is selected as the final solution: .

[0014] Preferably, the calculation process for the rocket's attitude yaw angle Ψ and pitch angle φ is as follows: Transforming the unit vector γ of the rocket's central axis from the geocentric coordinate system to the launch coordinate system, we get γ0 = [𝑥̂ γ0 ,𝑦̂γ0 ,𝑧̂ γ0 ] T The conversion formula is: ; where α of ϕ is the pre-defined rocket launch azimuth angle. of The geographical latitude of the launch point; λ of The geographical longitude of the launch site; The rocket's attitude yaw angle Ψ and pitch angle φ are calculated using the following formulas: ; The negative sign ensures that the angle direction conforms to the right-hand rule of the space coordinate system, when 𝑦̂ γ0 When <0, add 180° phase compensation to the calculation results.

[0015] Preferably, a time synchronization mechanism is also included: The timestamps generated by injecting rocket target images captured by optical equipment and high-resolution range image data of the rocket obtained by broadband radar into a unified timing system; Function to create a time-aligned window: Where τ is the maximum permissible time difference threshold, set to τ = 10 ms; t optical For optical data timestamps; t radar For radar data timestamps; When the time difference Δt > τ, the delay compensation strategy is activated: If the optical data is lagging, the previous frame of radar data is fused with the current optical data. If radar data is outdated, the current position is extrapolated based on the rocket motion model.

[0016] This invention offers at least the following beneficial effects: It provides a method for measuring rocket attitude using multi-source information fusion from optical radar, achieving passive measurement of rocket attitude from 40 kilometers away, with an average yaw angle error ≤1.1° and an average pitch angle error ≤2.1%, eliminating dependence on rocket-related equipment. By combining a rotating frame with key point annotation, the fitting angle deviation of the rocket's centerline is compressed to within 0.66°, with a false negative rate <0.4%, improving the robustness of optical recognition. A three-level coordinate transformation chain (pixel system → camera system → measurement system → geocentric system) is established to integrate the gimbal rotation parameters (AZ / EL) and the station's latitude and longitude (λ). c / φ cThe rotation matrix calculation is incorporated to reduce the cumulative error of the optical normal vector α. An LSTM network is used to learn the nonlinear mapping between HRRP time-series data and the line-of-sight pitch angle Ω, achieving an Ω identification error of <1.5° under rocket maneuvering conditions, overcoming the limitation that radar cannot directly measure attitude. Position normalization in the geocentric coordinate system suppresses the calibration error of the radar line-of-sight vector β to the order of 0.05%. The minimum attitude change criterion is used to screen for double solutions to the geometric constraint equations, reducing the probability of attitude jumps in high-speed maneuvering scenarios. A launch coordinate system transformation formula and quadrant compensation mechanism are designed to address the pitch angle φ within the range of φ. γ0 The computational ambiguity problem at <0 is addressed, and the output angle conforms to the aerospace coordinate system specification. By using timestamp alignment (threshold τ=10ms) and a lag data compensation strategy, the position-attitude decoupling error caused by asynchronous fusion is reduced to within 0.3°.

[0017] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0018] Figure 1 This is a flowchart of the optical radar multi-source information fusion rocket attitude measurement method described in this invention; Figure 2 This is an example diagram of optical image annotation in this invention; Figure 3 This is a schematic diagram of the simulation results of radar data changing with rocket attitude in this invention; Figure 4 This is a diagram of the rocket attitude solution model under the optical-lightning fusion method in this invention. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can implement it based on the description.

[0020] It should be understood that terms such as “having,” “comprising,” and “including” as used herein do not exclude the presence or addition of one or more other elements or combinations thereof.

[0021] It should be noted that, unless otherwise specified, the experimental methods described in the following implementation plan are all conventional methods, and the reagents and materials described are all commercially available unless otherwise specified.

[0022] like Figure 1 As shown, this invention provides a method for rocket attitude measurement by fusion of multi-source information from optical radar, comprising the following steps: Step 1: Take images of the rocket target using optical equipment, identify the positions of key points at the nose and tail of the rocket and the direction of the central axis using a directional detection network, and output the coordinates of the key points at the nose and tail; Step 2: Transform the coordinates of the head and tail key points to the geocentric coordinate system through a multi-level coordinate transformation, and calculate the optical normal vector α; Step 3: Acquire high-resolution range image data of the rocket using broadband radar, identify the radar line-of-sight elevation angle Ω using a temporal neural network, and calculate the radar line-of-sight vector β based on the positions of the radar and the rocket; Step 4: Combine the optical normal vector α and the radar line-of-sight vector β to construct a set of geometric constraint equations for the unit vector γ of the rocket's central axis: ; Solving the system of equations yields γ, which, after being transformed to the launch coordinate system, outputs the rocket's attitude yaw angle Ψ and pitch angle φ.

[0023] In the above technical solution, the optical equipment can be a high-speed industrial camera with a resolution of 1920×1080 pixels, paired with a telephoto lens of 200mm or more, and installed at a fixed observation station 30-50 kilometers away from the rocket launch trajectory. The orientation detection network can be implemented based on the open-source YOLOv11-OBB framework, with the input image size adjusted to 640×640 pixels, and a rotated rectangle used to label the rocket body (e.g., Figure 2 As shown in the diagram, the central axis of the frame is forcibly aligned with the actual central axis of the rocket, with key points at the nose marked as A1 and at the tail as B1. During network training, pre-trained weights from the DOTAv1 dataset are loaded, with a confidence threshold of 0.2 and an IOU threshold of 0.3, and the time for a single inference iteration is controlled to within 10ms. During the testing phase, the pixel coordinates of A1 and B1 and the central axis rotation angle θ are output, with an angle fitting deviation of less than 0.66°. The coordinate transformation adopts a three-level chain structure: pixel system → camera space system → measurement system → geocentric system.

[0024] A C-band pulse compression radar with a bandwidth ≥ 500MHz can be selected as the broadband radar to output real-time HRRP time-series data of the rocket. The time-series neural network can be configured as a two-layer LSTM structure, with the input layer receiving a 128-dimensional HRRP feature vector and the hidden layer having 64 units, outputting the radar line-of-sight elevation angle Ω. Training data is derived from historical missions of the same type of rocket, and the label Ω is generated by inverting the radar-rocket geometric position, with a testing error < 1.5°. The radar line-of-sight vector β is obtained by comparing the real-time rocket position (x0, y0, z0) with the radar station location (x...). r ,y r ,z r The difference is normalized to obtain the result. A system of equations is constructed by combining α, β, and Ω, and γ is solved (e.g., ...). Figure 4 As shown in the figure, the coordinates are transformed to the launch coordinate system, and the attitude angle is finally output.

[0025] The optical radar multi-source information fusion rocket attitude measurement method provided by this invention was verified in a rocket launch mission. When the rocket was 36 to 42 kilometers away from the optical equipment, the average error of the yaw angle before the first stage separation was 1.1 degrees and the average error of the pitch angle was 2.1 degrees, as measured by the above steps. This method maintains stable measurement capability at a distance of 40 kilometers without requiring additional cooperative equipment or pre-set marking information on the rocket. The optical recognition module uses a combination of rotating frame annotation and key point positioning to control the centerline angle fitting deviation within 0.66 degrees; the radar line-of-sight pitch angle recognition uses an LSTM network to process HRRP time-series data, with a measured error of less than 1.5 degrees. The multi-level coordinate transformation chain completely covers the transformation path from the pixel coordinate system to the geocentric coordinate system, effectively suppressing the interference of gimbal rotation parameters (azimuth AZ, pitch EL) and station calibration parameters (latitude φ). c Longitude λ c The coupling error is minimized. A double-solution screening mechanism for the geometric constraint equations, combined with a minimum attitude change criterion, avoids attitude angle jumps during rocket maneuvers, improving continuous output stability. A time synchronization mechanism with a 10-millisecond alignment threshold was used; in actual missions, data delay differences did not trigger compensation strategies, indicating that the system meets real-time requirements. The final output yaw angle Ψ and pitch angle φ, after launch coordinate system transformation and quadrant compensation, conform to aerospace telemetry and control standards and can be directly used for flight status analysis.

[0026] In another technical solution, the specific method for using the directional detection network to identify the positions of key points at the nose and tail of the rocket and the direction of its central axis in step one is as follows: The rocket body is labeled using a rotating rectangle, with the central axis of the rectangle coinciding with the actual central axis of the rocket. Mark key points on the central axis of the rocket's head and tail, with the head key point marked as A1 and the tail key point marked as B1. The labeled data includes a rotation angle θ, which is used to indicate the tilt direction of the rocket's central axis in the image plane.

[0027] In the above technical solution, the rotating rectangle annotation can be implemented using existing image annotation software, which supports rotating rectangle annotation mode and key point marking functions. The annotation operation uses standard computer equipment, equipped with a conventional mouse and monitor. The rotating rectangle drawing material is a virtual drawing tool built into the software, and does not involve physical materials. Key point marking uses preset coordinate markers in the software, with the first key point labeled A1 and the last key point labeled B1 (e.g., ...). Figure 2 (As shown). The computer equipment is deployed in the data processing room of the optical measurement and control station and is connected to the optical equipment via gigabit Ethernet.

[0028] The annotation process loads a 1920×1080 pixel rocket image captured by optical equipment. Operators manually draw a rotating rectangle: the long side of the rectangle aligns with the rocket's longitudinal axis, ensuring the rectangle's central axis coincides with the rocket's actual central axis; key point A1 is marked at the apex of the rocket's nose section, and point B1 at the apex of the tail section; the software automatically records the rotation angle θ (range -90° to 90°), representing the tilt direction of the central axis relative to the horizontal axis of the image plane. The width of the rotating rectangle is set to 1.2 times the width of the rocket's pixels to avoid the rectangle cutting off the rocket's edges. Annotated data is stored in JSON format, containing the pixel coordinates (x0, y0) of A1 / B1 and the rotation angle θ.

[0029] After labeling and marking the head and tail key points A1 and B1 using a rotated rectangular bounding box, the identification result of the rocket's centerline tilt angle θ was compared with the manually labeled true value through YOLOv11-OBB network training and inference, effectively reducing the deviation. The pixel coordinate positioning error of the head and tail key points A1 and B1 was controlled within 3 pixels (at 1920×1080 resolution). During the processing of 1000 consecutive frames of images, the network's false negative rate was 0.38%, equivalent to no more than 0.11 frames of false negatives at a sampling rate of 30 frames per second. This annotation method provides stable input for subsequent multi-level coordinate transformations. At a distance of 40 kilometers from the optical equipment, the measured average error of the pitch angle was 2.1 degrees, indicating that the high-precision identification of the centerline direction directly contributes to the overall attitude measurement results. Setting the width of the rotated bounding box to 1.2 times the width of the rocket's pixels effectively avoids the bounding box truncating the rocket's edge features, ensuring the integrity of the labeled data. The JSON format data generated by the annotation includes the rotation angle θ and the coordinates of the key points, which can be directly used for network training and real-time inference. It supports a single frame processing speed of 10 milliseconds, meeting the real-time requirements of the external testing system.

[0030] In another technical solution, the specific steps for transforming the head keypoint coordinates to the geocentric coordinate system in step two are as follows: a. Convert the pixel coordinates (x0, y0) of the head and tail key points to camera space coordinates [x1, y1, z1]: Among them, (x0) 0 ,y0 0 ) represents the center pixel coordinates of the image plane; p x and p y is the pixel size; f is the implicit focal length parameter, which is determined by the imaging geometry of the optical device; b. Convert the camera space coordinate system coordinates [x1, y1, z1] to the measurement coordinate system coordinates [x2, y2, z2]: ; Where AZ represents the azimuth rotation angle of the optical equipment, with true north as 0 degrees and clockwise as positive; EL represents the pitch rotation angle of the optical equipment, with horizontal as 0 degrees and upward as positive; R y and R z Let be the rotation matrices for the coordinate axes y and z, respectively, and their expressions are: c. Assign the coordinates [x2, y2, z2] of the measurement coordinate system based on the longitude λ of the origin of the measurement system. c and latitude ϕ c Convert to geocentric coordinates [x3, y3, z3] using a rotation matrix: ; Among them, R x R y R z These are the rotation matrices for the coordinate axes x, y, and z, respectively; .

[0031] In the above technical solution, the hardware required for coordinate transformation can be a conventional industrial computer, deployed in the data processing unit of the optical measurement and control station. Image plane center coordinates (x0...) 0 ,y0 0 Defined by the camera calibration file, it can be configured as (960, 540) (corresponding to 1920×1080 resolution). Pixel size p x p y Physical parameter values ​​of the CMOS sensor (e.g., 5.5μm) can be obtained. The implicit focal length parameter f is acquired through optical device geometric calibration and stored in the device configuration file. The gimbal azimuth angle AZ and pitch angle EL data are acquired in real time by an axis angle encoder mounted on the rotating axis of the optical device turntable. The measurement system origin longitude λ... c latitude φ c The data is obtained through a GPS module, and the GPS antenna is mounted on the roof of the telemetry and control station.

[0032] In rocket attitude measurement missions, this transformation chain effectively eliminates the impact of optical lens distortion on key point positioning by converting from the pixel coordinate system to the camera spatial coordinate system. The conversion from the camera spatial coordinate system to the measurement coordinate system integrates the gimbal azimuth and pitch angle parameters in real time, ensuring the consistency of the spatial reference under equipment rotation. The conversion from the measurement coordinate system to the geocentric coordinate system constructs a rotation matrix based on the station's latitude and longitude, compensating for systematic errors caused by the Earth's curvature and station location deviations.

[0033] In multiple rocket flight tests, this method provided stable coordinate input for optical normal vector calculation. Even when the rocket distance exceeded forty kilometers, the conversion process maintained low-noise output, supporting the overall attitude measurement system to achieve its design accuracy. Changes in azimuth and pitch angles during continuous gimbal tracking did not cause abnormal fluctuations in the conversion results, and the smoothness of the output coordinates met the requirements of dynamic measurement. Geographical parameters of the station obtained by ordinary precision positioning modules, after processing by this conversion chain, can meet the engineering requirements for long-distance attitude calculation.

[0034] The conversion calculation time is controlled within milliseconds, without affecting the system's real-time processing capabilities. The final output geocentric coordinates serve as the basis for optical normal vector calculation, directly contributing to the stability of the rocket's pitch and yaw angle measurement results. In complex external environments, this method demonstrates adaptability to factors such as equipment installation errors and atmospheric disturbances, ensuring reliable operation in multi-mission scenarios.

[0035] In another technical solution, the calculation process for the optical normal vector α is as follows: Obtain the geocentric coordinates [x3, y3, z3] of the head and tail key points, including the head key point coordinates A1[x3...]. A ,y3 A z3 A ] and the coordinates of the tail key point B1[x3 B ,y3 B z3 B ]; Construct a vector from the focal point O of the optical device to the head keypoint and the tail keypoint, i.e.: Calculate the optical normal vector α using the outer product of vectors: .

[0036] In the above technical solution, the computing unit required for calculating the optical normal vector α can be a standard industrial control computer, deployed in the data processing unit of the optical measurement and control station. This computer receives geocentric coordinates via Ethernet: the coordinate vectors of the head keypoint A1 and the tail keypoint B1. Vector storage uses a double-precision floating-point array, and memory space is provided by conventional DDR4 memory modules. The computer motherboard integrates an arithmetic logic unit (ALU), supporting hardware acceleration for vector outer products.

[0037] By solving for the optical normal vector through the cross product, spatial geometric constraints on the head and tail key points and the optical station locations are effectively established. This method avoids the dependence on multi-point sampling in traditional plane fitting algorithms, requiring only two feature points to stably output the normal vector direction. In long-distance observation scenarios, when there are small perturbations in the coordinate system, the cross product operation exhibits strong error suppression capabilities.

[0038] Normalization ensures a uniform normal vector magnitude, eliminating the impact of distance scale on subsequent fusion calculations. Experimental results show that this method maintains output stability throughout the rocket's active phase, without any abrupt changes in the normal vector direction due to key point coordinate jumps. As a core input parameter for optical-radar fusion attitude calculation, this normal vector provides a reliable optical observation benchmark for the geometric constraint equations. The calculation process requires no iteration or complex optimization, has low resource consumption, and is suitable for embedding in real-time telemetry and control systems. Under various meteorological conditions and background interference, this method continuously outputs effective results, supporting the overall system in achieving its designed measurement accuracy target.

[0039] In another technical solution, the specific method for identifying the radar line-of-sight elevation angle Ω is as follows: Broadband radar emits electromagnetic waves and receives reflected signals from rockets to acquire high-resolution range profile (HRRP) time-series data of the rocket. A long short-term memory neural network model is constructed, in which the input layer of the neural network model receives high-resolution range image HRRP time series data, the LSTM hidden layer extracts the dynamic features of the time series data, and the fully connected output layer outputs the continuous predicted value of the radar line-of-sight elevation angle Ω. The training set was used with high-resolution range profile HRRP time series data measured by broadband radar in historical missions of the same type of rocket, and supervised training was performed using the corresponding real radar line-of-sight elevation angle Ω label. The real radar line-of-sight elevation angle Ω label was calibrated based on the real-time geometric position relationship between the radar and the rocket in historical missions. The neural network model is trained using the mean squared error loss function and the backpropagation algorithm. The real-time high-resolution range image time series data of the rocket is input into the trained neural network model, and the predicted value of the radar line-of-sight elevation angle Ω is output.

[0040] In the above technical solution, the broadband radar can be an X-band pulse compression system device with a bandwidth of 500MHz, installed in the radar observation area of ​​the telemetry and control station. The radar line-of-sight elevation angle inference can be configured with a commercial GPU server equipped with a CUDA computing card. The LSTM neural network model can be implemented based on an open-source deep learning framework and deployed on the aforementioned server. Training data is stored in a local solid-state drive array using a standard SATA interface connection. The rocket's real-time position data is measured by the radar and transmitted to the server, time-aligned with the HRRP data stream.

[0041] The work process is as follows: Data Acquisition: The radar transmits linear frequency modulated pulses and receives the reflected signals from the rocket to generate HRRP data. Each HRRP frame contains 128 range cells, with a sampling rate of 100Hz and a dynamic range ≥60dB. Timing data is input in time window units of 0.5 seconds (50 frames).

[0042] Network modeling: The LSTM network input layer receives a 50×128 HRRP matrix, the first hidden layer has 64 units, the second hidden layer has 32 units, and the fully connected output layer generates the predicted line-of-sight pitch angle Ω. The activation function is ReLU, the optimizer is Adam, and the initial learning rate is 0.001.

[0043] Training execution: Load historical data from three identical rocket missions (total duration 1200 seconds), and split the training and validation sets in an 8:2 ratio. Label Ω is generated through geometric inversion: based on radar station locations [x] r ,y r ,z r ] T Relative to the rocket's real-time position [x0, y0, z0] T Calculate the theoretical value: Where Z = [0, 0, 1] T The zenith direction vector is used. The maximum number of training epochs is 500, and the early stopping threshold is set to the validation loss not decreasing for 10 consecutive epochs.

[0044] Real-time inference: During online operation, the real-time HRRP data stream undergoes standardized preprocessing (mean subtraction and variance division) before being input into the trained LSTM network, with an output Ω value update rate of 10Hz. For example... Figure 3 As shown, HRRP exhibits a multi-peak distribution when Ω is close to 0°, and a single main peak when Ω is close to 90°. This difference provides a basis for attitude discrimination for LSTM networks.

[0045] By analyzing the temporal dynamics of HRRP, an LSTM network establishes a stable mapping relationship between electromagnetic scattering characteristics and the geometric line-of-sight angle. This method overcomes the limitation of traditional radar in directly sensing target attitude and maintains reliable output even in scenarios involving high-speed rocket maneuvers and continuous attitude changes. Experimental data shows that the average error between the network-predicted line-of-sight pitch angle Ω and the true geometric value is less than 1 degree throughout the entire process, with a maximum error not exceeding 1.5 degrees.

[0046] The network model exhibits robustness to background noise and atmospheric disturbances in the HRRP waveform, with output fluctuations smaller than traditional feature engineering methods. The inference process takes only 3 milliseconds per computation on a conventional GPU server, meeting the real-time processing requirements of 10Hz. The Ω value output by this method serves as a core parameter in subsequent optical-radar fusion calculations, supporting accurate measurement of the rocket's attitude angle at a distance of 40 kilometers. The training mechanism, driven by historical mission data, can adapt to the differences in scattering characteristics among different rocket models.

[0047] In another technical solution, the radar line-of-sight vector β is calculated as follows: Obtain the geocentric coordinates [x] of the radar site r ,y r ,z r ]T The geocentric coordinates [x0, y0, z0] of the rocket's real-time position. T ; Calculate the original vector for the rocket pointing radar: β0=[x r -x0,y r -y0,z r -z0] T ; Normalizing the original vector β0 yields the radar line-of-sight unit vector: β = β0 / ||β0|| = [β x ,β y ,β z ] T .

[0048] In the above technical solution, the geocentric coordinates of the radar site can be obtained using a standard GNSS receiver, installed next to the radar antenna base, with the output data connected to the radar signal processor via an RS422 interface. The real-time rocket position data source can be the standard output interface of an existing ballistic measurement system or the radar itself, with the transmission protocol conforming to aerospace telemetry and control network communication standards. The vector calculation unit can be configured in the FPGA coprocessor of the radar signal processor, equipped with a double-precision floating-point arithmetic unit. Normalization operations utilize the processor's built-in square root reciprocal instruction (such as FSQRT).

[0049] The work process is as follows: Coordinate acquisition: Radar station location coordinates [x] r , y r , z r ] T The GNSS receiver outputs WGS84 coordinate system data with an update rate of 1Hz (static station address), stored in a register. Rocket position coordinates [x0, y0, z0] T The data is acquired in real time from the ballistic measurement system (update rate 100Hz) and stored in a register.

[0050] Original vector calculation: Perform vector subtraction: β0=[x r -x0,y r -y0,z r -z0] T The calculation results are temporarily stored in the vector register.

[0051] Modulus Calculation and Normalization: The modulus is calculated using an iteratively accelerated square root algorithm, which takes ≤5μs.

[0052] Perform normalization and output to the fusion module.

[0053] When β0 < 100 meters (abnormal proximity state), output the previous valid value and trigger an alarm.

[0054] By acquiring the geocentric coordinates of the radar station and the rocket position in real time, the difference is used to generate an original vector, which is then normalized to output a unit vector, effectively eliminating the influence of the distance scale on subsequent fusion calculations. This method avoids the azimuth and elevation angle coupling errors caused by traditional polar coordinate transformation and directly provides a three-dimensional spatial reference direction.

[0055] The standard accuracy inputs from GNSS and ballistic measurement systems, after normalization, can still meet the requirements for long-range attitude calculation. Field tests show that during the rocket's active phase flight, the line-of-sight vector β output by this method remains smooth and continuous without any abrupt changes. As one of the core parameters of the optical-radar fusion geometric constraint equations, its stability directly contributes to the reliability of the attitude angle calculation results.

[0056] The computation process consumes minimal resources and can be embedded in real-time signal processing links. When the input coordinates are subject to noise interference within a reasonable range, the normalization mechanism exhibits good error suppression characteristics, supporting the stable operation of the overall system in complex electromagnetic environments.

[0057] In another technical solution, the process of solving for the unit vector γ of the rocket's central axis is as follows: Define γ = [x, y, z] T Substituting these, along with the optical normal vector α, the radar line-of-sight vector β, and the radar line-of-sight elevation angle Ω, into the geometric constraint equations: Solve for the values ​​of x, y, and z to obtain two candidate solutions γ. 1 and γ 2 ; Calculate the attitude change of each candidate solution relative to the unit vector γ* of the rocket's centerline at the previous moment: ; The solution with the minimum total attitude change is selected as the final solution: .

[0058] In the above technical solution, the attitude calculation module can use an industrial-grade embedded processor, deployed in the real-time computing unit of the telemetry and control center. This processor is equipped with a dual-core CPU and a vector processing unit, with a main frequency of no less than 1.8GHz. The unit vector γ* of the rocket's centerline at the previous moment is stored in the DDR3 memory area, with an update cycle of 10ms. Candidate solutions γ... 1 γ 2 The computation unit calls open-source linear algebra libraries (such as LAPACK), and matrix operations use double-precision floating-point format. The attitude change comparator is implemented through the processor logic unit and does not depend on external hardware.

[0059] The work process is as follows: Double solution generation: Receive the β vector, α vector, and Ω value, and substitute them into the geometric constraint equations: Equation 1: α·γ = 0 Equation 2: β·γ = cosΩ Equation 3: ||γ|| = 1 Call the least squares solver to find γ 1 γ 2 Two candidate solutions, computation time ≤ 1ms.

[0060] Calculation of attitude change: Read the valid solution γ from the previous cycle (initial value is the theoretical value of the launch coordinate system), and calculate the Euclidean angle deviation between the candidate solutions and γ respectively: Δθ i = arccos(γ i · γ*), (i=1,2); the result is stored in a register.

[0061] Solution filtering execution: Compare Δθ 1 With Δθ 2 : If |Δθ 1 - Δθ 2 |>0.1 radians: Select the solution corresponding to the smaller value; Otherwise: Select a solution that is consistent with the historical trend (based on the directional derivative of the solutions in the last 5 frames); Output the final solution γ to the coordinate transformation module.

[0062] By calculating the Euclidean angle deviation between the candidate solution and the attitude vector at the previous moment, and selecting the solution with the smallest change, the method effectively avoids attitude angle jumps caused by ambiguity in the geometric constraint equations. This method maintains output continuity even under abrupt attitude changes such as rocket separation and maneuvering turns. Experimental data confirms that the smoothness of the selected attitude angle curve is significantly improved, meeting the requirements of flight mechanics analysis.

[0063] The dynamic trend-assisted decision-making mechanism (when changes are close) enhances adaptability to gradual attitude changes. This process is computationally efficient and does not increase the system's real-time processing burden. As the final verification step in the optical-radar fusion calculation, its stability directly affects the engineering usability of the final attitude angle output, providing reliable state awareness data for the measurement and control system.

[0064] In another technical solution, the calculation process for the rocket's attitude yaw angle Ψ and pitch angle φ is as follows: Transforming the unit vector γ of the rocket's central axis from the geocentric coordinate system to the launch coordinate system, we get γ0 = [𝑥̂ γ0 ,𝑦̂ γ0 ,𝑧̂ γ0 ] T The conversion formula is: ; where α of ϕ is the pre-defined rocket launch azimuth angle. ofThe geographical latitude of the launch point; λ of The geographical longitude of the launch site; The rocket's attitude yaw angle Ψ and pitch angle φ are calculated using the following formulas: ; The negative sign ensures that the angle direction conforms to the right-hand rule of the space coordinate system, when 𝑦̂ γ0 When <0, add 180° phase compensation to the calculation results.

[0065] In the above technical solution, the coordinate system transformation module and matrix calculation can be completed by the computer calling an open-source linear algebra library (such as LAPACK), with parameters written through a task configuration file. The rotation matrix calculation calls trigonometric function operations, achieving double-precision floating-point accuracy. The quadrant judgment logic is implemented through a comparator circuit, with a threshold set to ŷ. γ0 =0.

[0066] The work process is as follows: Transmit coordinate system transformation: Receive γ vector (geocentric coordinate system) and perform transformation according to preset parameters: First stage: Rotate around the Z-axis -(90°-λ) of ); Second stage: Rotate φ around the X-axis of ; Third level: Rotate around the Y-axis -(90°+α) of ); Output emission coordinate system vector γ0 = [𝑥̂ γ0 , 𝑦̂ γ0 , 𝑧̂ γ0 ] T .

[0067] Attitude angle calculation: Yaw angle Ψ calculation: Ψ = -arcsin(𝑧̂) γ0 ); Pitch angle φ calculation: If γ0 ≥ 0: φ = arctan(γ0) γ0 / 𝑦̂ γ0 ); If γ<0: φ = arctan(γ<0) γ0 / 𝑦̂ γ0 ) + 180°; The angle output resolution is 0.01°, and the range is Ψ∈[-180°,180°], φ∈[-90°,90°].

[0068] Output encapsulation: Attitude angle data is packaged into aerospace standard telemetry format (including timestamp and frame counter) and sent to the telemetry and control network via Ethernet interface.

[0069] A three-level rotation matrix is ​​used to transform the geocentric coordinate system vector to the launch coordinate system, ensuring that the output angle conforms to the aerospace telemetry and control standard definition. The rotation sequence around the axis and the angle parameters are strictly matched to the geographical location of the launch site, eliminating system deviations caused by differences in coordinate system definitions.

[0070] Quadrant compensation mechanism in pitch angle calculation (when 𝑦̂ γ0 (Increasing by 180° when <0) effectively solves the ambiguity problem of the mathematical arctangent function, and the output angle continuously covers the entire operating range. Actual measurements show that this method produces a smooth and uninterrupted attitude angle output curve throughout the rocket's flight, especially during orbital plane switching.

[0071] The conversion calculation time is less than 0.5 milliseconds, meeting the real-time processing requirement of a 10-millisecond cycle. The output data format is compatible with existing telemetry and control network protocols and can be directly used for flight status monitoring and post-event analysis. In complex ballistic environments, this method maintains stable operation, supporting the overall system in achieving its designed measurement objectives.

[0072] Another technical solution also includes a time synchronization mechanism: The timestamps generated by injecting rocket target images captured by optical equipment and high-resolution range image data of the rocket obtained by broadband radar into a unified timing system; Function to create a time-aligned window: Where τ is the maximum permissible time difference threshold, set to τ = 10 ms; t optical For optical data timestamps; t radar For radar data timestamps; When the time difference Δt > τ, the delay compensation strategy is activated: If the optical data is lagging, the previous frame of radar data is fused with the current optical data. If radar data is outdated, the current position is extrapolated based on the rocket motion model.

[0073] In the above technical solution, the time synchronization system can use an existing PTP precision time protocol server, deployed in the timing unit of the telemetry and control center. The optical data acquisition card can be configured with a hardware timestamp generator, using an FPGA to achieve nanosecond-level timestamp injection, and installed inside the optical equipment data processing chassis. The radar signal processor can be expanded with a GPS timing module to output a 1PPS pulse to synchronize the internal clock. The motion model computer can use a standard industrial controller to run rocket dynamics equations and is deployed in the real-time computing unit of the telemetry and control center.

[0074] The work process is as follows: Timestamp injection: When the optical image exposure is complete, the hardware timestamp generator of the acquisition card injects UTC time (format: seconds.nanoseconds), denoted as t. opticalWhen the radar HRRP data frame completes AD sampling, the GPS timing module injects UTC time, denoted as t. radar The time source is synchronized to the PTP server, with a clock difference of ≤100μs.

[0075] Window function execution: Real-time calculation of time difference Δt = |t optical - t radar The window function is defined as follows: if Δt ≤ τ (τ = 10ms): the data is valid and sent to the fusion queue; if Δt > τ: the delay compensation strategy is triggered.

[0076] Compensation strategy execution: optical lag time t optical >t radar +τ): Fusion of the previous frame's radar data with the current optical data; radar lag time (t) radar >t optical + τ): Extrapolation based on rocket motion model: Input the rocket's position and velocity (Geocentric system) for the first 5 frames; Running the constant acceleration model: p(t) = p0 + v0t + 0.5at 2 ; Output extrapolation position [x] o' ,y o' ,z o' ] T Replaces real-time location.

[0077] By injecting hardware-level timestamps and using a unified timing source, the acquisition time difference between optical and radar data is accurately quantified. The 10-millisecond window threshold design balances the system's real-time requirements with data validity requirements, avoiding attitude calculation distortion introduced by asynchronous fusion.

[0078] The compensation strategy is designed for typical lag scenarios: when optical lag occurs, the previous frame of radar data is reused, leveraging the high update rate of radar to ensure data freshness; when radar lag occurs, extrapolation is performed using a rocket motion model to maintain position prediction reliability within a short window (≤30ms). Experimental results show that this method achieves a data synchronization rate exceeding 99% in routine tasks, significantly reducing the risk of fusion failure caused by latency.

[0079] The motion model employs a simplified constant acceleration equation, ensuring controllable computational load and meeting real-time processing requirements. This mechanism, serving as a data preprocessing step, provides spatiotemporally aligned input for subsequent fusion and solution, supporting the stable operation of the overall system under complex conditions.

[0080] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A rocket attitude measurement method based on multi-source information fusion from optical radar, characterized in that, Includes the following steps: Step 1: Take images of the rocket target using optical equipment, identify the positions of key points at the nose and tail of the rocket and the direction of the central axis using a directional detection network, and output the coordinates of the key points at the nose and tail; Step 2: Transform the coordinates of the head and tail key points to the geocentric coordinate system through a multi-level coordinate transformation, and calculate the optical normal vector α; Step 3: Acquire high-resolution range image data of the rocket using broadband radar, identify the radar line-of-sight elevation angle Ω using a temporal neural network, and calculate the radar line-of-sight vector β based on the positions of the radar and the rocket; Step 4: Combine the optical normal vector α and the radar line-of-sight vector β to construct a set of geometric constraint equations for the unit vector γ of the rocket's central axis: ； Solving the system of equations yields γ, which, after being transformed to the launch coordinate system, outputs the rocket's attitude yaw angle Ψ and pitch angle φ.

2. The optical radar multi-source information fusion rocket attitude measurement method as described in claim 1, characterized in that, The specific method for identifying the key points at the nose and tail of the rocket and the direction of the central axis using the directional detection network in step one is as follows: The rocket body is labeled using a rotating rectangle, with the central axis of the rectangle coinciding with the actual central axis of the rocket. Mark key points on the central axis of the rocket's head and tail, with the head key point marked as A1 and the tail key point marked as B1. The labeled data includes a rotation angle θ, which is used to indicate the tilt direction of the rocket's central axis in the image plane.

3. The optical radar multi-source information fusion rocket attitude measurement method as described in claim 1, characterized in that, The specific steps for transforming the coordinates of the head key points to the geocentric coordinate system in step two are as follows: a. Convert the pixel coordinates (x0, y0) of the head and tail key points to camera space coordinates [x1, y1, z1]: Among them, (x0) 0 ,y0 0 ) represents the center pixel coordinates of the image plane; p x and p y is the pixel size; f is the implicit focal length parameter, which is determined by the imaging geometry of the optical device; b. Convert the camera space coordinate system coordinates [x1, y1, z1] to the measurement coordinate system coordinates [x2, y2, z2]: ； Where AZ represents the azimuth rotation angle of the optical equipment, with true north as 0 degrees and clockwise as positive; EL represents the pitch rotation angle of the optical equipment, with horizontal as 0 degrees and upward as positive; R y and R z Let be the rotation matrices for the coordinate axes y and z, respectively, and their expressions are: c. Assign the coordinates [x2, y2, z2] of the measurement coordinate system based on the longitude λ of the origin of the measurement system. c and latitude ϕ c Convert to geocentric coordinates [x3, y3, z3] using a rotation matrix: ； Among them, R x R y R z These are the rotation matrices for the coordinate axes x, y, and z, respectively; 。 4. The optical radar multi-source information fusion rocket attitude measurement method as described in claim 3, characterized in that, The calculation process for the optical normal vector α is as follows: Obtain the geocentric coordinates [x3, y3, z3] of the head and tail key points, including the head key point coordinates A1[x3...]. A ,y3 A z3 A ] and the coordinates of the tail key point B1[x3 B ,y3 B z3 B ]; Construct a vector from the focal point O of the optical device to the head keypoint and the tail keypoint, i.e.: Calculate the optical normal vector α using the outer product of vectors: 。 5. The optical radar multi-source information fusion rocket attitude measurement method as described in claim 4, characterized in that, The specific method for identifying the radar line-of-sight elevation angle Ω is as follows: Broadband radar emits electromagnetic waves and receives reflected signals from rockets to acquire high-resolution range profile (HRRP) time-series data of the rocket. A long short-term memory neural network model is constructed, in which the input layer of the neural network model receives high-resolution range image HRRP time series data, the LSTM hidden layer extracts the dynamic features of the time series data, and the fully connected output layer outputs the continuous predicted value of the radar line-of-sight elevation angle Ω. The training set was used with high-resolution range image HRRP time series data measured by broadband radar in historical missions of the same type of rocket, and supervised training was performed using the corresponding real radar line-of-sight elevation angle Ω label. The real radar line-of-sight elevation angle Ω label was calibrated based on the real-time geometric position relationship between the radar and the rocket in historical missions. The neural network model is trained using the mean squared error loss function and the backpropagation algorithm. The real-time high-resolution range image time series data of the rocket is input into the trained neural network model, and the predicted value of the radar line-of-sight elevation angle Ω is output.

6. The optical radar multi-source information fusion rocket attitude measurement method as described in claim 5, characterized in that, The method for calculating the radar line-of-sight vector β is as follows: Obtain the geocentric coordinates [x] of the radar site r ,y r ,z r ] T The geocentric coordinates [x0, y0, z0] of the rocket's real-time position. T ; Calculate the original vector for the rocket pointing radar: β0=[x r -x0,y r -y0,z r -z0] T ; Normalizing the original vector β0 yields the radar line-of-sight unit vector: β = β0 / ||β0|| = [β x ,β y ,β z ] T .

7. The optical radar multi-source information fusion rocket attitude measurement method as described in claim 6, characterized in that, The process of solving for the unit vector γ of the rocket's central axis is as follows: Define γ = [x, y, z] T Substituting these, along with the optical normal vector α, the radar line-of-sight vector β, and the radar line-of-sight elevation angle Ω, into the geometric constraint equations: Solve for the values ​​of x, y, and z to obtain two candidate solutions γ. 1 and γ 2 ; Calculate the attitude change of each candidate solution relative to the unit vector γ* of the rocket's centerline at the previous moment: ； The solution with the minimum total attitude change is selected as the final solution: .

8. The optical radar multi-source information fusion rocket attitude measurement method as described in claim 7, characterized in that, The calculation process for the rocket's attitude yaw angle Ψ and pitch angle φ is as follows: Transforming the unit vector γ of the rocket's central axis from the geocentric coordinate system to the launch coordinate system, we get γ0 = [𝑥̂ γ0 ,𝑦̂ γ0 ,𝑧̂ γ0 ] T The conversion formula is: ; where α of ϕ is the pre-defined rocket launch azimuth angle. of The geographical latitude of the launch point; λ of The geographical longitude of the launch site; The rocket's attitude yaw angle Ψ and pitch angle φ are calculated using the following formulas: ； The negative sign ensures that the angle direction conforms to the right-hand rule of the space coordinate system, when 𝑦̂ γ0 When <0, add 180° phase compensation to the calculation results.

9. The optical radar multi-source information fusion rocket attitude measurement method as described in claim 8, characterized in that, It also includes a time synchronization mechanism: The timestamps generated by injecting rocket target images captured by optical equipment and high-resolution range image data of the rocket obtained by broadband radar into a unified timing system; Function to create a time-aligned window: Where τ is the maximum permissible time difference threshold, set to τ = 10 ms; t optical For optical data timestamps; t radar For radar data timestamps; When the time difference Δt > τ, the delay compensation strategy is activated: If the optical data is lagging, the previous frame of radar data is fused with the current optical data. If radar data is outdated, the current position is extrapolated based on the rocket motion model.

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