A space-based space target trajectory segmentation fitting method based on infrared radiation characteristics

Abstract

The application discloses a space-based space target trajectory segmentation fitting method based on infrared radiation characteristics, and comprises the following steps: (1) acquiring initial positioning information of a space target in a ground-fixed coordinate system through double-star joint observation; (2) monitoring the infrared radiation intensity of the space target in real time through an infrared sensor, identifying the classification points of the space target in different flight stages according to the infrared radiation intensity and signal-to-noise ratio change, and completing target trajectory segmentation; (3) for different flight stages, the least square method is introduced through an adaptive factor, the trajectory optimization fitting of the space target in the space-based scene is completed, high-precision positioning and tracking are realized, and the motion characteristics of the target are acquired. By using the application, the overfitting or underfitting problems in the traditional method can be reduced, so that the precision and reliability of space-based space target detection and tracking are improved, and the application is suitable for a complex space target observation environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of target positioning and tracking, and in particular to a space-based space target trajectory segmentation fitting method based on infrared radiation characteristics. BACKGROUND

[0002] In space-based space target detection, infrared radiation characteristics are an important means of identifying and tracking targets. Infrared radiation can penetrate clouds and the atmosphere, and has high detection sensitivity for various space targets. By analyzing the infrared radiation characteristics of the target in different flight stages, the segmentation and accurate tracking of the target trajectory can be effectively realized. The aircraft will experience multiple stages during flight, and the infrared radiation characteristics of each stage are different. The infrared radiation is strong in the boost phase, the radiation intensity decreases significantly in the middle phase, and the radiation intensity increases again in the re-entry phase due to air friction. How to effectively segment and fit the target trajectory using these changes in radiation characteristics is an important problem in current space-based space target positioning and tracking.

[0003] Currently, commonly used trajectory fitting and optimization methods include Kalman filtering, least squares polynomial fitting, etc. For example, the Chinese patent document with publication number CN111324848A discloses a mobile laser radar measurement system vehicle trajectory data optimization method, which analyzes the motion state of the vehicle trajectory data based on Kalman filtering and establishes a vehicle motion model. The Chinese patent document with publication number CN114312840A discloses an automatic driving obstacle target trajectory fitting method, which uses the least squares method to fit the historical trajectory of the obstacle target and constructs the trajectory equation of a single obstacle target.

[0004] These methods have achieved certain success in trajectory fitting, but also have some shortcomings: (1) Kalman filtering assumes that the target motion is linear, and it is difficult to provide accurate trajectory fitting for complex nonlinear motion models and multi-stage motion targets; (2) the least squares polynomial fitting method fits the target trajectory by constructing a polynomial model, which is suitable for fitting smooth trajectories. Its advantage is that the calculation is simple and suitable for short-time trajectory fitting. However, this method cannot automatically identify the segmentation characteristics of the trajectory, and for a target trajectory containing multiple flight stages, the fitting accuracy is not high, and overfitting or underfitting problems are likely to occur. SUMMARY

[0005] The present application provides a space-based space target trajectory segmentation fitting method based on infrared radiation characteristics, which accurately identifies the flight stage of the target by monitoring the change in infrared radiation intensity of the target in real time, performs trajectory segmentation fitting, reduces the overfitting or underfitting problems in traditional methods, and thus improves the accuracy and reliability of space-based space target detection and tracking, and is suitable for complex space target observation environments.

[0006] A space-based space target trajectory segmentation fitting method based on infrared radiation characteristics, comprising the following steps:

[0007] (1) Through the joint observation of double satellites, the initial positioning information of the space target in the earth-fixed coordinate system is obtained;

[0008] (2) The infrared radiation intensity of the space target is monitored in real time through the infrared sensor, and the hierarchical points of the space target in different flight stages are identified according to the infrared radiation intensity and the signal-to-noise ratio change, so as to complete the target trajectory segmentation;

[0009] (3) For different flight stages, the least square method is introduced by introducing an adaptive factor, the trajectory optimization fitting of the space target in the space-based scene is completed, the high-precision positioning and tracking are realized, and the motion characteristics of the target are obtained.

[0010] The specific process of step (1) is as follows:

[0011] The observation satellites S1 and S2 obtain the position information of the space target M on the image plane, and convert the position information of the space target M on the image plane into the line-of-sight vector of the earth-fixed coordinate system

[0012] According to the vector addition principle, the position of the space target M is represented as

[0013]

[0014] In the formula, ||S i -M|| is the distance between the i-th observation satellite S i and the space target; the coordinates of the space target M in the earth-fixed coordinate system are (x t ,y t ,z t ); when the observation satellite is two, the components in each direction are expanded and arranged into a matrix form to obtain:

[0015]

[0016] Where (x s1 ,y s1 ,z s1 ), (x s2 ,y s2 ,z s2 ) are the positions of the observation satellites S1 and S2 in the earth-fixed coordinate system, respectively;

[0017] The result of the above formula is written as A·M=b, and the least square method is used to solve the position of the space target in the earth-fixed coordinate system as follows:

[0018] M=(A T A)-1 A T b

[0019] After the solution is completed, the initial positioning information of the space target in the earth-fixed coordinate system is obtained.

[0020] The position information of the space target M on the image plane is converted into the line-of-sight vector in the earth-fixed coordinate system through a geometric positioning model, and the formula is:

[0021]

[0022] In the formula, is the line-of-sight vector of the satellite pointing to the space target; R ref is the plane reflection matrix corresponding to the pointing mirror reflection angle θ; θ is the value of the pointing mirror reflection angle; is the conversion relationship between the geocentric inertial coordinate system and the geocentric terrestrial coordinate system, and t is the Julian time at the observation time; is the conversion matrix from the orbital coordinate system to the geocentric inertial coordinate system; is the calibrated installation matrix of the camera in the satellite body coordinate system; (i0, j0) is the coordinate of the principal point of the camera in the pixel coordinate system; Δi0, Δj0 is the principal point offset error of the camera; Δx, Δy is the distortion variable of the image point in the x and y directions; dx, dy is the size of the pixel in the x and y directions; f is the principal distance of the camera.

[0023] In step (2), the signal-to-noise ratio equation is:

[0024]

[0025] In the formula, D0 is the equivalent clear aperture of the camera; D * is the average value of the normalized spectral detectivity; τ0 is the spectral transmittance of the optical system; τ a is the atmospheric spectral transmittance; ΔJ is the difference between the target radiation intensity and the background radiation intensity; δ is the signal process factor; F is the aperture number of the camera; ω is the instantaneous field of view of the detector; Δf is the equivalent noise bandwidth of the detection system; R is the distance between the space target and the space-based platform.

[0026] In step (2), the classification points of the space target in different flight stages are identified according to the infrared radiation intensity and the signal-to-noise ratio change, which is specifically:

[0027] The change ΔSNR of the detection signal-to-noise ratio is detected, and the formula is:

[0028] ΔSNR = SNR Δt+i -SNR i

[0029] Wherein, i is the i th moment of effective observation, Δt is the time of setting the observation signal-to-noise ratio change, which is set as an integer multiple of the system observation period;

[0030] According to the infrared radiation intensity and the signal-to-noise ratio change, the flight process of the space target is divided into boost phase, midcourse phase and reentry phase.

[0031] The specific process of step (3) is as follows:

[0032] (3-1) Determine the fitting polynomial according to the given k observation data segments of different segments:

[0033]

[0034] Wherein, a i is the coefficient of the polynomial to be fitted, i=0,1,…,n;

[0035] (3-2) Determine the residual δ t , solve the similar coupling degree factor τ(t), the normalized coefficient η, and further calculate the adaptive weight factor λ t ;

[0036] (3-3) Convert the curve fitting problem into minimizing the sum of squares of residuals, and construct the objective function;

[0037] (3-4) Convert the curve fitting problem into solving the minimum point of the objective function, and calculate the undetermined parameter a i by using the least square method, that is, obtain the precise fitting trajectory of the target.

[0038] In step (3-2), the formula of the adaptive weight factor λ t is as follows:

[0039]

[0040] Wherein, t is the observation time; L is the length of the trajectory sequence; |δ| max is the maximum value of the residual sequence δ t ; is the adjacent trajectory sequence without the current data point; is the trajectory sequence containing the current data point; ρ(t) is the correlation coefficient of the residuals of the two trajectory sequences; τ(t) is the similarity degree between the adjacent sequences.

[0041] In step (3-3), the objective function is constructed as follows:

[0042]

[0043] Wherein, y t is the initial positioning value of the space target in the earth-fixed coordinate system in step (1).

[0044] Compared with the prior art, the present application has the following beneficial effects:

[0045] The present application can improve the accuracy and reliability of space-based space target positioning and tracking by monitoring the infrared radiation intensity of the target in real time, accurately identifying the flight phase of the target, and performing trajectory segmentation fitting. This method is based on a space-based platform and uses an infrared sensor to monitor the radiation characteristics of space targets in real time. By analyzing the infrared radiation characteristics of the target in different flight phases, the boost phase, the middle phase and the re-entry phase of the target are identified in real time. For different flight phases, adaptive segmented fitting methods are used to fit each segment of the trajectory, improving the overall fitting accuracy of the trajectory. This method can handle trajectory changes in multiple motion modes and is suitable for complex space target observation environments, achieving high-precision positioning and tracking, and thus obtaining the speed information of the target based on high-precision trajectory information. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 A space-based space target trajectory segmentation fitting method based on infrared radiation characteristics is provided for an embodiment of the present application.

[0047] Figure 2 A double-star positioning observation schematic diagram is provided for an embodiment of the present application. DETAILED DESCRIPTION

[0048] The present application will be described in further detail below in conjunction with the drawings and embodiments, it should be noted that the following embodiments are intended to facilitate the understanding of the present application and do not limit the present application in any way.

[0049] As shown in Figure 1 A space-based space target trajectory segmentation fitting method based on infrared radiation characteristics is provided. First, the initial observation position information of the space high-speed target in the earth-fixed system is obtained by a double-star positioning method. Second, the infrared sensor is used to monitor the radiation intensity information of the space target in real time, and the classification points between different flight phases are obtained by analyzing the infrared radiation intensity changes. Finally, combined with the motion characteristics of the target, the influence of wild value data is removed by introducing an adaptive factor least squares method, the trajectory optimization fitting of the space high-speed target in the space-based scene is completed, high-precision positioning and tracking are achieved, and the motion characteristics of the target are obtained.

[0050] Specifically, the following steps are included:

[0051] S01. Obtain the initial positioning information of the space target

[0052] The positioning of the space-based observation system for the space high-speed target is actually to convert the position information of the detected target on the two-dimensional image plane into the position information of the target in the three-dimensional space earth-fixed system.

[0053] AsFigure 2 As shown, These are the observation line-of-sight vectors of satellites S1 and S2 for space target M. First, this invention needs to convert the target's position on the image plane into a line-of-sight vector in the Earth-fixed system using a rigorous geometric positioning model:

[0054]

[0055] in, R is the line-of-sight vector pointing from the satellite to the target. ref (θ) is the planar reflection matrix corresponding to the reflection angle θ of the pointing mirror; θ is the reflection angle value of the pointing mirror; The transformation relationship between the geocentric inertial coordinate system and the geocentric Earth-fixed coordinate system is given by t, where t is the Julian time of the observation time. This is the transformation matrix from the orbital coordinate system to the geocentric inertial coordinate system; is the calibrated installation matrix of the camera in the satellite body coordinate system; (i0,j0) is the coordinate of the camera principal point in the pixel coordinate system; Δi0,Δj0 are the principal point offset errors; Δx,Δy are the distortions of the image point in the x and y directions; dx,dy are the dimensions of the pixel in the x and y directions; f is the camera principal distance.

[0056] Secondly, according to the principle of vector addition, the position of target M can be expressed as:

[0057]

[0058] Where M(x) t ,y t ,z t Let S be the location of the target within the Earth-fixed system, and ||S i -M|| represents the distance between the satellite and the target. When there are two satellites being observed, their components in each direction are expanded. Rearranging it into matrix form, we get:

[0059]

[0060] Among them, (x s1 ,y s1 ,z s1 ),(x s2 ,y s2 ,z s2 ( ) represent the positions of satellites S1 and S2 in the Earth-fixed system, respectively.

[0061] The result of the above equation can be simplified to A·M=b. The position of the target in the Earth-fixed system can be solved using the least squares method as follows:

[0062] M = (A T A)-1 A T b

[0063] At this point, the present application completes the solution to the target observation positioning position information.

[0064] S02. Trajectory segmentation according to radiation characteristics

[0065] During the flight of the target aircraft, each staging point can be effectively found according to the radiation characteristics. In a space-based early warning system, complex electromagnetic environments can produce noise interference, affecting the effective signal of the target and randomly causing missed alarms or false alarms. In order to evaluate the signal quality received by the sensor, the signal-to-noise ratio (SNR) can be used to measure the detection result. The signal-to-noise ratio equation of the detection system is:

[0066]

[0067] where D0 is the equivalent aperture of the optical system (i.e. the satellite camera); D * is the average value of the normalized spectral detection degree; τ0 is the spectral transmittance of the optical system; τ a is the atmospheric spectral transmittance; ΔJ is the difference between the target radiation intensity and the background radiation intensity; δ is the signal process factor; F is the F number of the optical system (i.e. the aperture number of the camera); ω is the instantaneous field of view of the detector; Δf is the equivalent noise bandwidth of the detection system; and R is the distance between the target and the space-based platform.

[0068] By continuously monitoring the infrared radiation intensity and the signal-to-noise ratio change of the aircraft, each staging point can be identified by the following steps, and the staging point can be determined by detecting the significant change ΔSNR in the signal-to-noise ratio:

[0069] ΔSNR = SNR Δt+i -SNR i

[0070] where i is the ith moment of effective observation, and Δt is the time set for the observation signal-to-noise ratio change, which is generally set as an integer multiple of the system observation period.

[0071] 1) In the boost phase, the tail flame radiation intensity increases from low to high, and the signal-to-noise ratio trend increases from low to high. At the end of the boost phase, the engine stops working, the infrared radiation intensity drops sharply, and the signal-to-noise ratio SNR also decreases, resulting in a significant decrease in ΔSNR;

[0072] 2) In the middle stage, the aircraft mainly flies by inertia, and the infrared radiation intensity is low and stable. At this time, the infrared radiation mainly comes from the residual heat of the aircraft surface due to heating in the previous period and the solar radiation in the space environment. At this time, the signal-to-noise ratio SNR is low, and the change of ΔSNR is small;

[0073] 3) Reentry phase, the aircraft re-enters the atmosphere, air friction causes the aircraft shell temperature to rise, the infrared radiation intensity increases, the signal-to-noise ratio SNR rises, and the ΔSNR will rise obviously.

[0074] So far, the present application completes the segmentation of the trajectory of the target by analyzing the infrared radiation characteristics of the target.S03. Introducing an adaptive factor to improve the least square trajectory fitting

[0075] The aircraft motion is mainly affected by the engine thrust, air resistance, gravity, Coriolis force and centripetal force during the flight process in the boost phase. Therefore, the dynamics model of the aircraft in the boost phase is:

[0076]

[0077] Where, p = [x, y, z] T and v = [v x x, v y y, v z z] T are the position and velocity of the aircraft; a t , a d , a g , a Cor , a cen are the engine thrust, air resistance, gravity, Coriolis force and centripetal force accelerations, respectively.

[0078] For the middle phase, the aircraft approximately flies in a vacuum, and the air resistance on the aircraft is almost zero. In the middle phase, the aircraft is only affected by gravity and perturbation forces. For the reentry phase, the aircraft is mainly affected by air resistance, gravity and perturbation forces. The aircraft has both longitudinal and lateral motion.

[0079] After completing steps S01 and S02, the positioning information and hierarchical point information of the target are obtained. Considering the motion characteristics of the target in different phases, the trajectory is first fitted, and the main steps of fitting are as follows:

[0080] 1) Determine the fitting polynomial according to the given k observation data segments in different phases:

[0081]

[0082] Where, a i (i = 0, 1, …, n) are the coefficients of the fitting polynomial.

[0083] 2) Determine the residual δ t , solve the similarity coupling degree factor τ(t), the normalization coefficient η, and calculate the adaptive weight factor λ t :

[0084]

[0085] where t is the observation time; L is the length of the trajectory sequence; |δ| max is the maximum value of the residual sequence δ t . is the adjacent trajectory sequence without the current data point; is the trajectory sequence containing the current data point; ρ(t) is the correlation coefficient of the residuals of the two trajectory sequences; τ(t) is the similarity between the adjacent sequences.

[0086] The higher the correlation coefficient is, the smoother the observation point sequence is. The correlation coefficient is low, which means that the current point is judged to be outlier data. When the residual of the observation point and the corresponding fitting curve is larger, the coupling degree of the observation point and the fitting trajectory is lower, and the weight factor is reduced, thereby reducing the reliability of the observation point; on the contrary, when the residual is small, λ t increases, thereby improving the reliability of the observation point. The outlier can be adaptively corrected through λ t .

[0087] 3) The curve fitting problem is converted into minimizing the sum of squares of residuals, and the objective function is:

[0088]

[0089] where y t is the initial positioning value of the space target in the earth-fixed coordinate system in step 1.

[0090] 4) The curve fitting problem is converted into solving the minimum value point of the objective function, and the least square method is used to calculate the undetermined parameter a i , and the precise fitting trajectory of the target is obtained.

[0091] Thus, the positioning of the space target and the high-precision segmented trajectory fitting under the space-based scene are completed.

[0092] The above-described embodiments have described the technical solutions and beneficial effects of the present application in detail. It should be understood that the above-described embodiments are only specific embodiments of the present application, and are not used to limit the present application. Any modification, supplement and equivalent replacement made within the principle range of the present application should be included in the protection range of the present application.

Claims

1. A space-based space object trajectory piecewise fitting method based on infrared radiation characteristics, characterized in that, Comprising the following steps: (1) Obtain the initial positioning information of the space target in the earth-fixed coordinate system through the joint observation of the double stars; (2) Real-time monitor the infrared radiation intensity of the space target through the infrared sensor, and identify the classification points of the space target in different flight stages according to the infrared radiation intensity and the signal-to-noise ratio change, and complete the target trajectory segmentation; (3) For different flight stages, complete the trajectory optimization fitting of the space target in the space-based scene through the least square method with the introduction of the adaptive factor, realize the high-precision positioning and tracking, and obtain the motion characteristics of the target; The specific process is as follows: (3-1) Determine the fitting polynomial according to the given k observation data segments of different segments: where a i are coefficients of the polynomial to be fitted, i = 0, 1,..., n; (3-2) Determine the residual error δ t , solve the similar coupling factor τ(t), the normalized coefficient η, and further calculate the adaptive weight factor λ t , the formula is as follows: where t is the observation time; L is the length of the trajectory sequence; |δ| max is the maximum value of the residual sequence δ t ; is the adjacent trajectory sequence without the current data point; is the trajectory sequence containing the current data point; p(t) is the correlation coefficient of the residuals of the two trajectory sequences; and τ(t) is the similarity between the adjacent sequences. (3-3) Convert the curve fitting problem into the minimum residual sum of squares, and construct the objective function; (3-4) The curve fitting problem is converted into solving the minimum point of the objective function, and the least square method is used to calculate the undetermined parameter a i , that is, the precise fitting trajectory of the target is obtained.

2. The method according to claim 1, wherein, The specific process of step (1) is as follows: The observation satellite S1, S2 obtains the position information of the space target M on the image plane, and converts the position information of the space target M on the image plane into a line-of-sight vector in the earth-fixed coordinate system According to the principle of vector addition, the position of the space target M is expressed as wherein ||S i is the distance between the i-th observation satellite S i and the space object M; the coordinates of the space object M in the earth-fixed coordinate system are (x t , y t , z t ) When the observation satellite is two, the components in each direction are expanded The arrangement is obtained in matrix form: where (x s1 ,y s1 ,z s1 ), (x s2 ,y s2 ,z s2 ) are the positions of the observation satellites S1, S2 in the earth-fixed coordinate system respectively; the result of the above formula is simply written as A·M = b, and the position of the space target in the earth-fixed coordinate system is solved by using the least square method as follows: M = (A T A) -1 A T b After solving, the initial positioning information of the space target in the earth-fixed coordinate system is obtained.

3. The method according to claim 2, wherein, The position information of the space target M on the image plane is converted into the line-of-sight vector in the earth-fixed coordinate system through the geometric positioning model, and the formula is: In the formula, is the line-of-sight vector of the satellite pointing to the spatial target; R ref (θ) is a plane reflection matrix corresponding to the pointing mirror reflection angle θ; θ is a pointing mirror reflection angle value; is the conversion relationship between the geocentric inertial coordinate system and the geocentric geodetic coordinate system, and t is the Julian time at the observation time; is the conversion matrix from the orbital coordinate system to the geocentric inertial coordinate system; is the calibrated installation matrix of the camera in the satellite body coordinate system; (i0, j0) is the coordinate of the camera principal point in the pixel coordinate system; Δi0, Δj0 are the principal point offset errors of the camera; dx, dy are the sizes of the pixels in the x and y directions; Δx, Δy are the distortion amounts of the image points in the x and y directions; and f is the principal distance of the camera.

4. The method according to claim 1, wherein, In step (2), the signal-to-noise ratio equation is: where D0 is the equivalent aperture of the camera; D * is the mean of the normalized spectral detectivity; τ0 is the spectral transmittance of the optical system; τ a is the atmospheric spectral transmittance; ΔJ is the difference between the target radiation intensity and the background radiation intensity; δ is the signal process factor; F is the F-number of the camera; ω is the instantaneous field of view of the detector; Δf is the equivalent noise bandwidth of the detection system; and R is the distance between the spatial target and the space-based platform.

5. The method according to claim 4, wherein, In step (2), the classification points of the space target in different flight stages are identified according to the infrared radiation intensity and the signal-to-noise ratio change, which is specifically: Detect the change of the signal-to-noise ratio, and the formula is: ΔSNR = SNR Δt+i -SNR i Wherein, i is the i th moment of effective observation, and Δt is the set time of observation signal-to-noise ratio change, which is set as an integer multiple of the system observation period; According to the infrared radiation intensity and the signal-to-noise ratio change, the flight process of the space target is divided into boost stage, middle stage and reentry stage.

6. The method of claim 1, wherein, In step (3-3), the objective function is constructed as follows: where y t is the initial positioning value of the spatial target in the earth-fixed coordinate system in step (1).

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