A multi-platform common-view orbit determination method for earth-moon space targets

Abstract

The embodiment of the application discloses a multi-platform common-view orbit determination method for a lunar-earth space target, relates to the technical field of space target orbit determination, and comprises the following steps: a plurality of observation platforms observe the same lunar-earth space target in the same observation period, obtain a motion data sequence of the observation platform in the observation period, and obtain observation data sequences obtained by observing the lunar-earth space target; the relative position relationship between the observation platform and the lunar-earth space target is determined, a first observation model for the lunar-earth space target is constructed, and the position and speed of the lunar-earth space target at each time in the corresponding observation period are calculated; a second observation model is constructed, and the orbit arc segment of the lunar-earth space target in the corresponding observation period is calculated. The application has small limitation on the type of the lunar-earth space target and can adapt to multiple types of orbits; after the initial orbit determination is successful, the original observation data can be combined to perform orbit refinement again, so that the initial orbit accuracy is improved.

Description

Technical Field

[0001] This application relates to the field of space target orbit determination technology, and in particular to a multi-platform common-view orbit determination method for Earth-Moon space targets. Background Technology

[0002] The cislunar space generally refers to the space influenced by the gravitational pull of the Earth and Moon systems, including near-Earth space, Earth-Moon transfer space, and lunar space. Cislunar space targets refer to objects located in near-Earth space, Earth-Moon transfer space, or lunar space, such as celestial bodies, spacecraft, and space debris. Recently, my country's lunar exploration and landing activities, and the promotion of cislunar space development, necessitate the formation of an independent and comprehensive cislunar space situational awareness system. This system aims to detect and discover cislunar space targets, control their orbital motion, and provide services such as space collision early warning. Its core is the construction of a space target orbital catalog database.

[0003] The core technologies for constructing a space target orbit catalog database are initial orbit determination (IOD) and track association. Initial orbit determination (IOD) is used to obtain the orbital parameters of the target to which the observed arc segment belongs when the prior orbital information is completely unknown. Track association (TA) is used to determine whether different arc segments belong to the same target, and then cluster a large number of arc segments according to their target to support the improvement of catalog data accuracy.

[0004] Currently, due to the complexity and chaos of the three-body dynamics in the Earth-Moon space, the types of target orbits in the Earth-Moon space are diverse, and the determination (prediction) of short-arc initial orbits is prone to divergence. For example, simulation data shows that in regions above near-Earth space, for a certain orbit of DRO or NRHO, even with an initial position difference of tens of kilometers and a relatively accurate initial velocity, the complexity of the three-body dynamics leads to increased uncertainty in orbital behavior. Even small initial errors can diverge over time, and after three days, the prediction error may reach hundreds or even thousands of kilometers, reducing the accuracy of the initial orbit prediction. This, in turn, leads to significant uncertainty in the orbital state of each arc segment, making arc segment correlation difficult and potentially leading to erroneous arc segment correlations, thus affecting the reliability of the entire orbit determination process.

[0005] Therefore, there is currently a lack of a reliable and efficient method for determining the orbit of a target in the Earth-Moon space. Summary of the Invention

[0006] This application provides a multi-platform common-view orbit determination method for lunar space targets, which addresses the shortcomings of the aforementioned related technologies. The technical solution is as follows:

[0007] In a first aspect, embodiments of this application provide a multi-platform common-view orbit determination method for Earth-Moon space targets, including:

[0008] Multiple observation platforms observe the same Earth-Moon space target during the same observation period, and obtain the motion data sequence of each observation platform during the observation period, and obtain the observation data sequence obtained by each observation platform from observing the Earth-Moon space target during the observation period;

[0009] Based on the motion data sequence and observation data sequence of each observation platform, the relative positional relationship between each observation platform and the Earth-Moon space target is determined. The first observation model of the Earth-Moon space target is constructed by combining the relative positional relationship, motion data sequence and observation data sequence.

[0010] Based on the first observation model, the position and velocity of the Earth-Moon space target at each moment within the corresponding observation period were calculated;

[0011] A second observation model is constructed based on the position and velocity at each time point, and the orbital arc of the Earth-Moon space target within the corresponding observation period is calculated based on the second observation model.

[0012] In one alternative embodiment of the first aspect, after acquiring the motion data sequence of each of the observation platforms during the observation period, the orbit determination method further includes:

[0013] The motion data sequence is transformed into the TOD coordinate system to obtain the transformed motion data sequence; wherein, the motion data sequence includes the motion data of the observation platform at various times, and the motion data includes the position and velocity of the observation platform;

[0014] After obtaining the observation data sequence obtained by each of the observation platforms from observing the Earth-Moon space target during the observation period, the method further includes preprocessing the observation data sequence:

[0015] Transform the optical angle information in the observation data sequence into the TOD coordinate system;

[0016] The optical angle information of the Earth-Moon space target observed by each observation platform is fitted with a binomial formula to obtain the right ascension and declination data of the Earth-Moon space target during the observation period.

[0017] Differentiating the right ascension and declination data respectively yields the right ascension rate of change data and the declination rate of change data;

[0018] The fitted observation data sequence was obtained based on right ascension data, declination data, right ascension rate of change data, and declination rate of change data;

[0019] Based on the transformed motion data sequence and the fitted observation data sequence, the step of determining the relative positional relationship between each observation platform and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform is performed.

[0020] In one alternative embodiment of the first aspect, determining the relative positional relationship between each of the observation platforms and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform includes:

[0021] Based on the motion data sequence of each observation platform, the motion data of each observation platform at the same moment is obtained. The position vector of the corresponding observation platform is determined according to the motion data. Based on the position vector of each observation platform, the unit position vector of the corresponding observation platform relative to the origin of the TOD coordinate system is calculated, and the formula is applied:

[0022] ;

[0023] Based on the observation data sequence of each observation platform, the observation data obtained by each observation platform at the same time is acquired. The observation vector of the corresponding observation platform towards the Earth-Moon space target in the line-of-sight direction is determined according to the observation data. Based on the observation vector of each observation platform, the unit observation vector of the corresponding observation platform towards the Earth-Moon space target in the line-of-sight direction is calculated, and the formula is applied:

[0024] ;

[0025] A first virtual plane is constructed based on each observation platform, the Earth-Moon space target, and the origin of the TOD coordinate system. The unit normal vector of the first virtual plane is calculated based on the unit position vector and unit observation vector of the corresponding observation platform, using the formula:

[0026] ;

[0027] A second virtual plane is constructed based on the unit normal vector of the first virtual plane corresponding to each observation platform and the unit observation vector of the corresponding observation platform. The unit normal vector of the second virtual plane is calculated using the following formula:

[0028] ;

[0029] The relative positional relationship between each observation platform and the Earth-Moon space target is determined based on the unit position vector, the unit observation vector, the unit normal vector of the first virtual plane, and the unit normal vector of the second virtual plane.

[0030] Where i represents the label of the observation platform, used to distinguish different observation platforms; For observation platform position vector Represents the magnitude of the position vector. For observation platform The unit observation vector of a lunar target in the line-of-sight direction. For observation platform The observation vector of the Earth-Moon space target in the line-of-sight direction. Let the magnitude of the observation vector be . For observation platform The observed right ascension values ​​at the corresponding times. For observation platform The observed declination values ​​for the corresponding time. For observation platform The unit normal vector of the corresponding first virtual plane. unit normal vector With unit observation vector The unit normal vector of Zhang Cheng's second virtual plane. For observation platform The unit position vector.

[0031] In one alternative embodiment of the first aspect, the construction of a first observation model for the Earth-Moon space target by combining relative positional relationships, motion data sequences, and observation data sequences includes:

[0032] Construct the position observation equation for the Earth-Moon space target, and apply the following formula:

[0033] ;

[0034] ;

[0035] ;

[0036] Differentiating both sides of the position observation equation with respect to time, we obtain the velocity observation equation. Applying the formula:

[0037] ;

[0038] Determine the parameters in the velocity observation equation and The steps include:

[0039] Calculate the rate of change of the unit observation vector of the observation platform relative to the Earth-Moon observation target, and the rate of change of the unit position vector of the observation platform, using the following formula:

[0040] ;

[0041] ;

[0042] Calculate the rate of change of the unit normal vector for each first virtual plane and the rate of change of the unit normal vector for each second virtual plane by applying the formula:

[0043] ;

[0044] The parameters in the velocity observation equation were calculated. and Apply the formula:

[0045] ;

[0046] ;

[0047] in, Let be the position vector of the Earth-Moon space target. Let be the velocity vector of the Earth-Moon space target. For observation platform The velocity vector, For observation platform Unit observation vector of the Earth-Moon observation target The rate of change, For observation platform unit position vector The rate of change, The unit normal vector for each first virtual plane The rate of change, The unit normal vector for each second virtual plane The rate of change, T represents the matrix transpose. For observation platform The rate of change of the position vector, , , , All of these are parameters in the velocity observation equation.

[0048] In one alternative to the first aspect, constructing the second observation model based on the position and velocity at each time point includes:

[0049] Based on the position and velocity of the Earth-Moon space target during the observation period, the state vector observation value is obtained, and the formula is applied:

[0050] ;

[0051] Based on the changes in the position and velocity of the Earth-Moon space target over time during the observation period, the motion equation of the Earth-Moon space target is established, and the formula is applied:

[0052] ;

[0053] ;

[0054] Using the observed state vector at the first moment of the observation period as the initial state vector observation, and using this initial state vector observation as the initial value of the predicted initial state vector of the motion equation, the function that transforms the observed state vector into the initial value of the predicted initial state vector is applied by the following formula:

[0055] ;

[0056] ;

[0057] The error equation is constructed based on the residual between the observed and predicted initial state vector values. The formula is then applied:

[0058] ;

[0059] At the moment corresponding to the initial state, obtain the predicted value of the initial state vector for the first iteration. Approximate the error equation at the predicted value of the initial state vector for the first iteration using a first-order Taylor expansion, and apply the formula:

[0060] ;

[0061] ;

[0062] The second observation model is obtained:

[0063] ;

[0064] Where z represents the observed state vector of the Earth-Moon space target. These are the initial state vector observations. Indicates the observation period The k-th observation in the corresponding observation time series, including location and speed The position and velocity of the Earth-Moon space target at each moment are represented as a state vector. , Motion state vector Rate of change over time t; Represents the residual matrix. The initial value of the predicted value of the initial state vector. A function representing the initial values ​​of the observed state vector z and the predicted initial state vector z. This represents the initial value of the predicted initial state vector for the first iteration. Indicates the partial derivative sign. For error parameters, This represents the correction amount of the predicted state vector obtained from the corresponding iterative calculation. The symbols used to replace those in the above formulas, Let be the state transition matrix.

[0065] In one alternative embodiment of the first aspect, the calculation of the orbital arc segment of the Earth-Moon space target within the corresponding observation period based on the second observation model includes:

[0066] The correction amount for the predicted initial state vector is calculated using the following formula:

[0067] ;

[0068] The initial state vector prediction value for the (j-1)th iteration is optimized based on the correction value obtained from the j-th iteration to obtain a new initial state vector prediction value, using the formula:

[0069] ;

[0070] For the correction amount in the j-th iteration, determine whether the constraint conditions are met:

[0071] ;

[0072] If the correction amount in the j-th iteration does not meet the constraint conditions, increment j by 1, and proceed to the step of calculating the correction amount of the predicted value of the initial state vector. Perform the (j+1)-th iteration calculation until the calculated correction amount meets the constraint conditions.

[0073] If the correction in the j-th iteration satisfies the constraints, output the predicted value of the initial state vector obtained by the optimization in the j-th iteration.

[0074] Based on the predicted value of the initial state vector obtained by optimization and combined with the kinematic equation of the Earth-Moon space target, the optimized state vector of the Earth-Moon space target at each moment during the observation period is calculated, and the orbital arc of the Earth-Moon space target during the observation period is obtained based on the optimized state vector.

[0075] in, The preset iteration limit, The correction amount is calculated in the j-th iteration. The predicted value of the initial state vector obtained in the (j-1)th iteration. The new initial state vector prediction value is calculated and optimized for the j-th iteration.

[0076] In one alternative embodiment of the first aspect, the orbit determination method further includes:

[0077] Obtain multiple track segments;

[0078] Obtain the root mean square residual for each orbital arc segment; the root mean square residual is calculated based on the difference between the observed value of the state vector and the predicted value of the state vector at each observation time within the observation period corresponding to the orbital arc segment.

[0079] Compare the root mean square residuals of every two orbital segments. If the difference between the root mean square residuals is less than a preset difference threshold, determine that the two orbital segments with a difference less than the preset difference threshold belong to the same Earth-Moon space target.

[0080] Secondly, embodiments of this application also provide a multi-platform common-view orbit determination device for Earth-Moon space targets, comprising:

[0081] The data acquisition module is used to acquire the motion data sequence of each observation platform during the observation period, and also to acquire the observation data sequence obtained by each observation platform from observing the Earth-Moon space target during the observation period; wherein, multiple observation platforms observe the same Earth-Moon space target during the same observation period;

[0082] The first calculation module is used to determine the relative positional relationship between each observation platform and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform, and to construct a first observation model of the Earth-Moon space target by combining the relative positional relationship, motion data sequence and observation data sequence.

[0083] The first calculation module is used to calculate the position and velocity of the Earth-Moon space target at each moment within the corresponding observation period based on the first observation model;

[0084] The second calculation module is used to construct a second observation model based on the position and velocity at each time point, and is also used to calculate the orbital arc of the Earth-Moon space target within the corresponding observation period based on the second observation model.

[0085] Thirdly, embodiments of this application also provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method provided by the first aspect or any implementation thereof of the embodiments of this application.

[0086] Fourthly, this application also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method provided by the first aspect of the embodiments of this application or any implementation thereof.

[0087] The beneficial effects of the technical solutions provided in some embodiments of this application include at least the following:

[0088] This application provides a multi-platform common-view orbit determination method for Earth-Moon space targets. This method has few limitations on the types of Earth-Moon space targets and can adapt to various orbit types. After successful initial orbit determination, the orbit can be refined again using the original observation data to improve initial orbit accuracy. During the multi-arc orbit refinement process, the orbit arcs can be correlated simultaneously based on the accuracy of the orbit refinement, enabling rapid and accurate determination of whether orbit arcs belong to the same space target. Moreover, the observation equipment can be deployed on some commonly used orbits in the space-based environment, and the initial orbit accuracy can be improved by increasing the observation duration. This method can solve the technical challenges of diverse target types, difficulty in initial orbit determination, insufficient initial orbit accuracy, and intricate arc correlation in Earth-Moon space. Attached Figure Description

[0089] To more clearly illustrate the technical solutions in this application or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0090] Figure 1 This is a flowchart illustrating a method for determining the common orbit of a multi-platform target in the Earth-Moon space, as provided in an embodiment of this application.

[0091] Figure 2 This is a schematic diagram of the relative positional relationship of a multi-platform common-view orbit determination method for Earth-Moon space targets provided in an embodiment of this application;

[0092] Figure 3 This is a schematic diagram of the structure of a multi-platform common-view orbit determination device for Earth-Moon space targets provided in an embodiment of this application;

[0093] Figure 4 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0094] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0095] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or modules is not limited to the steps or modules listed, but may optionally include steps or modules not listed, or may optionally include other steps or modules inherent to such process, method, product, or apparatus.

[0096] It should be noted that the terms "first" and "second" used in this application are merely to distinguish similar objects and do not represent a specific ordering of the objects. It is understood that "first" and "second" can be interchanged in a specific order or sequence where permitted. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in an order other than those described or illustrated herein.

[0097] The present application will now be described in detail with reference to specific embodiments.

[0098] Next, combine Figure 1 This application introduces a multi-platform common-view orbit determination method for Earth-Moon space targets, provided by embodiments of this application. For details, please refer to... Figure 1 , Figure 1 This illustration shows a flowchart of a multi-platform common-view orbit determination method for Earth-Moon space targets, provided in an embodiment of this application. Figure 1 As shown, the method includes the following steps:

[0099] S101, acquire the motion data sequence of each of the observation platforms during the observation period, and acquire the observation data sequence obtained by each of the observation platforms from observing the Earth-Moon space target during the observation period; wherein, multiple observation platforms observe the same Earth-Moon space target during the same observation period.

[0100] S102, determine the relative positional relationship between each observation platform and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform, and construct a first observation model for the Earth-Moon space target by combining the relative positional relationship, motion data sequence and observation data sequence;

[0101] S103, calculate the position and velocity of the space target at each moment in the corresponding observation period based on the first observation model;

[0102] S104, construct a second observation model based on the position and velocity at each time point, and calculate the orbital arc of the Earth-Moon space target within the corresponding observation period based on the second observation model.

[0103] In some embodiments, in S101, the observation platform can be a space-based observation platform or a ground-based observation platform. Specifically, it can be an observation platform equipped with optical monitoring equipment, such as a satellite or other observation subject operating in a typical orbit equipped with monitoring equipment for observing targets in the Earth-Moon space, or an observation station set up on the ground. The multiple observation platforms include two or more observation platforms. They can include only space-based platforms, only ground-based platforms, or a combination of space-based and ground-based platforms. This application embodiment does not limit this.

[0104] Specifically, the motion data sequence of the observation platform can be directly obtained through the platform's management. This motion data sequence includes the platform's position and velocity information within the corresponding observation period. For space-based platforms, the motion data sequence can be described using three-dimensional coordinate information (position and velocity) in an inertial coordinate system or the six roots of an elliptical orbit. For ground-based platforms, the motion data sequence can be described using three-dimensional coordinate information (position and velocity) in an inertial coordinate system or position information (longitude, latitude, elevation, etc.) relative to the Earth's surface in a non-inertial coordinate system (Earth-fixed system). This application does not limit the specific format.

[0105] Specifically, in S101, the observation platform can observe the same Earth-Moon space target according to the performance of the corresponding optical monitoring equipment, such as working time, working mode, and field of view of the observation equipment, and at a certain observation sampling frequency.

[0106] Specifically, the observation data sequence observed by the observation platform in S101 is the optical angle information of the observed space target at each observation time during the observation period. The data observed by the space-based platform can be recorded in the form of right ascension (RA) and declination (Dec), while the data observed by the ground-based observation platform can be recorded in the form of pitch angle and elevation angle.

[0107] In some embodiments, after S101, the observed observation data sequence can be preprocessed to convert the optical angle information in the observation data sequence to the TOD (True of Date, TOD) coordinate system. Similarly, the motion data sequence of the observation platform is also converted to the TOD coordinate system. The TOD (True of Date, TOD) coordinate system is a well-known instantaneous true celestial coordinate system in the art, commonly used in aerospace, astronomy, and earth sciences. Its coordinate axis directions are based on the true celestial reference base of the observation time ("Date"), rather than a fixed epoch (such as J2000.0).

[0108] Subsequently, a binomial fitting was performed on the optical angle information of the Earth-Moon space target observed by each observation platform to obtain the right ascension and declination data of the Earth-Moon space target during the observation period. These data are expressed as the fitted right ascension and declination expressions, respectively. The derivatives of the right ascension and declination expressions were then calculated to obtain the expressions for the rate of change of right ascension and the rate of change of declination.

[0109] Taking declination as an example, during the observation period The observation value is obtained by observing the Earth-Moon space target at the s-th time. Using ordinary least squares to fit the observations with a binomial formula, the fitted right ascension expression is obtained as follows:

[0110] ;

[0111] Differentiating the expression for right ascension, we obtain the expression for the rate of change of right ascension:

[0112] ;

[0113] Where a, b, and c are all parameters of the binomial fitting. Binomial fitting is equivalent to fitting the motion curve of the observed target within the corresponding time period based on the angle information observed at each time. The values ​​of the binomial fitting parameters a, b, and c determine the specific curve shape, which depends on the specific motion of the observed target and can be calculated from the observation data sequence.

[0114] The expressions for the rates of change of right ascension and declination can also be expressed in the following forms:

[0115] ;

[0116] ;

[0117] in, This represents the right ascension observed by the observation platform at the s-th observation time. This represents the declination value observed by the observation platform at time s. This represents the rate of change of right ascension at time s. Represents the rate of change of declination at time s, and the observation period. Including N observation times, Indicates the observation period The s-th time within the observation period, where s represents the observation time interval. The number of observation times depends on the observation sampling frequency of the observation platform, and this application embodiment does not limit this.

[0118] Further, step S102 is executed to determine the relative positional relationship between each observation platform and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform, specifically determining the relative positional relationship between each observation platform and the observed Earth-Moon space target at the same time.

[0119] According to the description in S101, the motion data sequence of the observation platform consists of the position and velocity of the observation platform at various times. First, based on the motion data at any time in the motion data sequence of the observation platform, the position vector and velocity vector of each corresponding platform in the TOD coordinate system are established. For the observation platform... The corresponding position vector can be represented as The velocity vector can be expressed as The observation platform can be calculated based on the position vector and its magnitude. Unit position vector in the direction of the origin of the TOD coordinate system Apply the formula:

[0120] ;

[0121] Where i represents the label of the observation platform, used to distinguish different observation platforms; This represents the magnitude of the position vector.

[0122] Furthermore, based on the observation data sequence obtained from each observation platform's observation of the Earth-Moon space target, an observation vector of the corresponding observation platform in the light-of-sight (LOS) direction of the Earth-Moon space target is established. The unit observation vector of the observation platform in the LOS direction of the Earth-Moon space target can be calculated based on the observation vector and its magnitude, using the formula:

[0123] ;

[0124] in, For observation platform The unit observation vector of a lunar target in the line-of-sight direction. For observation platform The observation vector of an Earth-Moon space target along the light of sight (LOS). Let the magnitude of the observation vector be . For observation platform The observed right ascension values ​​at the corresponding times. For observation platform The observed declination values ​​for the corresponding time.

[0125] Furthermore, a first virtual plane is determined for each observation platform. This first virtual plane is constructed based on the origin (i.e., the geocenter) of each observation platform, the Earth-Moon space target, and the TOD coordinate system, and is based on the unit observation vector of the corresponding observation platform. and unit position vector Calculate the unit normal vector of the first virtual plane using the formula:

[0126] ;

[0127] in, For observation platform The first virtual plane OB is constructed by combining the Earth-Moon space target and the origin (i.e., the Earth's center) of the TOD coordinate system. The unit normal vector, For observation platform The unit position vector.

[0128] Furthermore, the second virtual plane corresponding to each observation platform is determined, specifically the first virtual plane OB. unit normal vector The unit observation vector of the corresponding observation platform A second virtual plane is constructed, and its unit normal vector is calculated. The formula is then applied:

[0129] ;

[0130] in, unit normal vector With unit observation vector The unit normal vector of Zhang Cheng's second virtual plane.

[0131] The relative positional relationship between each observation platform and the Earth-Moon space target is determined based on the unit position vector, the unit observation vector, the unit normal vector of the first virtual plane, and the unit normal vector of the second virtual plane.

[0132] For example, taking two observation platforms as an example, the obtained vectors are determined as follows: Figure 2 As shown, the center of the TOD coordinate system is the Earth's center O, the observed spatial target is object, denoted as point B, observation platform 1 is denoted as point P1, and observation platform 2 is denoted as point P2. Figure 2 middle, The position vector of the observed spatial target. Let be the position vector of observation platform 1. Let be the position vector of observation platform 2.

[0133] like Figure 2For example, the unit position vector of observation platform 1 relative to the origin O of the TOD coordinate system is: The unit position vector of observation platform 2 relative to the origin O of the TOD coordinate system is: The unit observation vector of observation platform 1 for the Earth-Moon space target B in the line-of-sight direction is: The unit observation vector of observation platform 2 for the Earth-Moon space target B in the line-of-sight direction is: .

[0134] like Figure 2 For example, the first virtual plane formed by platform P1, the geocenter O, and the observed target B is OBP1. Similarly, the first virtual plane formed by platform P2, the geocenter O, and the observed target B is OBP2. The unit vector of the normal vector of the first virtual plane OBP1 is... The unit vector of the normal vector of the first virtual plane OBP2 is .

[0135] like Figure 2 Example, and Zhang Cheng became the second virtual plane corresponding to platform P1, and the unit normal vector of the second virtual plane is... , and Zhang Cheng became the second virtual plane corresponding to platform P2, and the unit normal vector of the second virtual plane is... .

[0136] Furthermore, based on the vector information determined above, step S102 is executed to construct the first observation model for the Earth-Moon space target, specifically including position observation equations and velocity observation equations, including the following steps:

[0137] Specifically, the position vector of the Earth-Moon space target It can be represented as velocity vector It can be represented as Apply the formula:

[0138] ;

[0139] ;

[0140] Where x, y, and z correspond to the position coordinates of the Earth-Moon space target, respectively. These correspond to the velocity components of the Earth-Moon space target, respectively.

[0141] The observation platforms are determined based on their relative positions to the Earth-Moon space targets. observation vector unit normal vector to the first virtual plane Vertical, that is Determine the observation platform observation vector unit normal vector to the second virtual plane Vertical, that is We obtain the following equation:

[0142] ;

[0143] The position observation equation constructed by combining the above vectors is expressed as follows:

[0144] ;

[0145] Wherein, parameters A and b are represented by the following formula:

[0146] ;

[0147] ;

[0148] Differentiating both sides of the position observation equation with respect to time, we obtain the velocity observation equation as follows:

[0149] ;

[0150] To determine the parameters in the velocity observation equations and The steps include:

[0151] Computational observation platform Unit observation vector of the Earth-Moon observation target variability and observation platform unit position vector variability Apply the formula:

[0152] ;

[0153] ;

[0154] Calculate the unit normal vector of each first virtual plane. variability and the unit normal vector of each second virtual plane variability Apply the formula:

[0155] ;

[0156] Therefore, parameters and This can be expressed as the following formula:

[0157] ;

[0158] ;

[0159] in, Let be the position vector of the Earth-Moon space target. Let be the velocity vector of the Earth-Moon space target. For observation platform The velocity vector, For observation platform Unit observation vector of the Earth-Moon observation target The rate of change, For observation platform unit position vector The rate of change, The unit normal vector for each first virtual plane The rate of change, The unit normal vector for each second virtual plane The rate of change, T represents the matrix transpose. For observation platform The rate of change of the position vector, , , , All of these are parameters in the velocity observation equation.

[0160] Through the above calculation process, the position and velocity observation equations of the observed Earth-Moon space targets are obtained.

[0161] Further, by performing step S103, the position observation equation and velocity observation equation are solved using the ordinary least squares method to obtain the position and velocity of the Earth-Moon space target at each time.

[0162] Formulas used in the calculation process:

[0163] ;

[0164] ;

[0165] This allows us to calculate the position and velocity of the Earth-Moon space target at various points in time during the observation period.

[0166] Furthermore, the steps in S104, which involve constructing the second observation model, include:

[0167] S1041, based on the position and velocity of the Earth-Moon space target calculated in S103 during the observation period, obtains the state vector observation value, denoted as:

[0168] ;

[0169] in, Indicates the observation period The k-th observation in the corresponding observation time series, including location and speed .

[0170] In some embodiments, k is generally related to the observation period. The number of observations s within a given period is equal. Furthermore, after obtaining the observations, all observations can be preprocessed to remove obvious outliers (such as isolated points). If preprocessed, the value of k may be less than or equal to the observation period. The number of observations s within the range.

[0171] S1042, Constructing the motion equations of the Earth-Moon space target, including the following steps:

[0172] Specifically, the motion equations of the Earth-Moon space target are derived based on the changes in the position and velocity of the Earth-Moon space target over time during the observation period, with the position and velocity at each moment specifically represented as a state vector. , the motion state vector The derivative with respect to time t is expressed as a motion state vector. rate of change with time t That is, the rate of change of state vector, and the equation of motion is specifically expressed as the following formula:

[0173] ;

[0174] ;

[0175] Where x is the state vector consisting of the position and velocity of the Earth-Moon space target during the observation period. Let x be the state change rate vector of the position and velocity of the Earth-Moon space target over the observation period, expressed as a function of time. It can describe the change in the motion state of a lunar target over time during the observation period.

[0176] Understandably, for each observation time, the equation of motion can be used to calculate the predicted state vector value for that time.

[0177] S1043, select the observed state vector at the first moment in the observation period as the initial state vector observation value, denoted as... The initial state vector observations are used as the initial values ​​for the initial state vector predictions of the motion equations, thus transforming the state vector observations z into the initial values ​​for the initial state vector predictions. The function, applying the formula:

[0178] ;

[0179] ;

[0180] Further, in S1044, a second observation model is established. Specifically, the second observation model is an error equation constructed based on the residual between the observed values ​​and predicted values ​​of the initial state vector. This includes the following steps:

[0181] Based on the least squares estimation algorithm, the predicted value of the initial state vector is optimized. The optimized predicted value of the initial state vector should minimize the value of the least squares objective loss function. The formula is as follows:

[0182] ;

[0183] The error equation can be expressed as:

[0184] ;

[0185] At the time corresponding to the initial state At that time, let the predicted value of the initial state vector in the first iteration be... The error equation is in The first-order Taylor expansion approximation is as follows:

[0186] ;

[0187] in, The least squares objective loss function is... The function used to solve for the minimum value. Represents the residual matrix. The initial values ​​represent the observed state vector z and the predicted initial state vector z. The function, This represents the initial value of the predicted initial state vector for the first iteration. Indicates the partial derivative sign. This is the error parameter.

[0188] The second observation model should be adjusted using the following formula:

[0189] ;

[0190] The adjusted second observation model is represented as follows:

[0191] ;

[0192] in, This represents the correction amount of the predicted state vector obtained from the corresponding iterative calculation. The symbols used to replace those in the above formulas, Let be the state transition matrix.

[0193] Furthermore, S104 also includes solving the second observation model using an iterative least squares algorithm, including the following steps:

[0194] The first iteration includes:

[0195] The correction amount of the initial value of the predicted initial state vector is calculated based on the adjusted second observation model. Apply the formula:

[0196] ;

[0197] Initial value of the predicted value of the initial state vector based on the correction. For the first optimization, apply the following formula:

[0198] ;

[0199] After completing the first iteration, based on the results of the first iteration Continue with the next iteration.

[0200] The specific steps included in the j-th iteration calculation are as follows:

[0201] S201, calculate the correction amount of the initial state vector prediction value. Apply the formula:

[0202] ;

[0203] S202, Based on the correction amount calculated in the j-th iteration, optimize the initial state vector prediction value in the (j-1)-th iteration to obtain a new initial state vector prediction value. Apply the formula:

[0204] ;

[0205] For the correction amount in the j-th iteration Execute S203 to determine whether the constraints are met:

[0206] ;

[0207] in, The preset iteration limit depends on the set orbit determination accuracy, and this application embodiment does not limit it.

[0208] If the correction amount in the j-th iteration does not meet the constraints, proceed with step S204:

[0209] S204, increment j by 1, go to step S201, and perform the (j+1)th iteration calculation until the calculated correction satisfies the constraint conditions.

[0210] If the correction in the j-th iteration satisfies the constraints, proceed with step S205:

[0211] S205, Output the predicted value of the initial state vector obtained from the j-th iteration optimization. .

[0212] After iterative calculations in steps S201-S205, the optimized initial state vector prediction value is obtained. Combined with the kinematic equations of the Earth-Moon space target, the optimized state vector of the Earth-Moon space target at each moment during the observation period can be calculated. Then, the orbital arc of the Earth-Moon space target during the observation period can be obtained based on the optimized state vector.

[0213] The initial orbit determination was completed through the above steps S101-S103. Step S104 refined the initially determined orbit to obtain the precise orbital arc segment within the observation period.

[0214] In some embodiments, steps S101-S104 can be repeated multiple times to obtain multiple precise track segments. Further association of the segments is required, including the following steps:

[0215] Obtain multiple track segments;

[0216] Obtain the root mean square residual for each orbital arc segment; the root mean square residual is calculated based on the difference between the observed value of the state vector and the predicted value of the state vector at each observation time within the observation period corresponding to the orbital arc segment.

[0217] Compare the root mean square residuals of every two orbital segments. If the difference between the root mean square residuals is less than a preset difference threshold, determine that the two orbital segments with a difference less than the preset difference threshold belong to the same Earth-Moon space target.

[0218] In some embodiments, multiple orbital arcs belonging to the same Earth-Moon space target can be identified, and these orbital arcs belonging to the same Earth-Moon space target can be clustered to update the space target orbit cataloging library corresponding to the Earth-Moon space target, thereby improving the accuracy of the cataloging data.

[0219] In a specific embodiment, a suitable space target and observation platform in the Earth-Moon orbit can be selected. For example, two space-based platforms can be selected, as shown in Table 1. Observation platform 1 is set in the DRO(a) orbit, observation platform 2 is set in the NRHO(a) orbit, and the observed Earth-Moon space target is set in the DRO(c) orbit.

[0220] The simulation parameters include: the three-dimensional position errors of the observation platform. The angular measurement error of the optical equipment on the observation platform is The spatial target position is error-free.

[0221] It should be noted that, due to the special nature of the three orbits, lunar targets within the observation period are visible to the observation platform throughout the entire period. The process of calculating the visibility of the targets by the space-based platform is ignored here, and the observation values ​​of the targets by the platform (such as right ascension and declination) are obtained directly.

[0222] Table 1. Parameters of the platform and target orbits

[0223]

[0224] Furthermore, the feasibility of determining the initial orbit based on the common view of the dual platforms was verified. Three sets of single-point instantaneous positioning experiments were constructed according to sampling frequencies of / (1 min), / (10 min), and / (60 min). For each simulation experiment, three points were sampled with the observation time as the intermediate time to calculate the temporal rate of change of the angle at the observation time. The positioning deviation of the target based on the common view of the dual platforms satisfies the deviation formula:

[0225] ;

[0226] The first term of the equation The second term represents the positional deviation between the two observation platforms. Indicates observation platform The pointing error of the line of sight, the third item Indicates observation platform The length error in the line of sight direction, and the errors corresponding to the second and third terms are caused by the angle measurement error of the observation equipment and the geometric distance between the platform and the target.

[0227] The simulation results are shown in Table 2. The orbital position deviations calculated by the three different sampling rates are similar and conform to the deviation formula for dual-platform common-view positioning.

[0228] Table 2. Influence of different sampling rates on the orbit determination accuracy of the dual-platform system.

[0229]

[0230] A sampling rate of ( / 10 min) was selected to simulate the platform speed with noise at different ratios. The experimental results are shown in Table 3. It can be found that the speed error of the platform itself will affect the speed accuracy in the dual-platform common-view orbit determination results, but the orbit determination speed deviation is basically of the same order of magnitude as the platform speed deviation.

[0231] Table 3. Influence of different platform speed accuracies on orbit determination speed accuracy

[0232]

[0233] Furthermore, multi-segment arc correlation and joint trajectory refinement were performed. Although the target was visible to the platform throughout the observation period, the continuous observation duration designed in the simulation was much shorter than the visibility duration in order to simulate harsh observation conditions.

[0234] Under simulation conditions with a sampling rate of 10 min and a velocity-to-velocity error ratio of 2%, the observation time and interval for each arc segment observed by the dual platforms are set to be equal. The observation interval between adjacent pairs of the four arc segments of the target DRO(c) by the dual platforms is 2 days, so the four arc segments cover about half a cycle.

[0235] The simulation included two types of short arcs: 1 hour and 4 hours, with a single arc observation duration of 1 hour. A 1-hour arc yielded 5 valid data points, while a 4-hour arc yielded 23 valid data points.

[0236] The initial orbit refinement result can be obtained based on a single arc (Arc1). Then, two single arcs (Arc1 and Arc2) can be combined for trial correlation. If the accuracy within the orbit determination is comparable to that of the single arc, it means that the two arc segments belong to the same target, that is, the orbit correlation and joint refinement are successful at the same time. Otherwise, it means that the correlation and refinement fail at the same time.

[0237] Furthermore, multiple successfully linked arc segments can continue to participate in subsequent identical operations to gradually improve the initial orbit accuracy.

[0238] The simulation results are shown in Table 4. From the table, we can see that: (1) The accuracy of the alignment within the four arc segments is consistent, and the correlation is successful. After the 4-hour single arc and the four arc segments are successfully refined, the external alignment positioning error of the track is 5.5 km, the 3-day forecast error is 9.1 km, and the 7-day forecast error is 13.3 km; (2) In general, the longer the observation time of a single arc segment, the higher the orbit determination accuracy. The more arc segments there are, the higher the orbit determination accuracy and the higher the forecast accuracy.

[0239] Table 4. Results of multi-arc correlation and orbit refinement for dual-platform co-view DRO(c)

[0240]

[0241] Continued:

[0242]

[0243] The following are apparatus embodiments of this application, which can be used to execute the method embodiments of this application. For details not disclosed in the apparatus embodiments of this application, please refer to the method embodiments of this application.

[0244] Please see below. Figure 3This is a schematic diagram of a multi-platform common-view orbit determination device for lunar space targets, provided as an exemplary embodiment of this application. This device can be implemented as all or part of a terminal through software, hardware, or a combination of both, or it can be integrated as an independent module on a server. The multi-platform common-view orbit determination device for lunar space targets in this embodiment can be applied to a terminal or the cloud. The device 30 includes a data acquisition module 301, a first calculation module 302, and a second calculation module 303, wherein:

[0245] The data acquisition module 301 is used to acquire the motion data sequence of each observation platform during the observation period, and also to acquire the observation data sequence obtained by each observation platform from observing the Earth-Moon space target during the observation period; wherein multiple observation platforms observe the same Earth-Moon space target during the same observation period.

[0246] The first calculation module 302 is used to determine the relative positional relationship between each observation platform and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform, and to construct a first observation model of the Earth-Moon space target by combining the relative positional relationship, motion data sequence and observation data sequence.

[0247] The first calculation module 302 is used to calculate the position and velocity of the Earth-Moon space target at each moment within the corresponding observation period based on the first observation model;

[0248] The second calculation module 303 is used to construct a second observation model based on the position and velocity at each time point, and is also used to calculate the orbital arc of the Earth-Moon space target within the corresponding observation period based on the second observation model.

[0249] It should be noted that the apparatus 30 provided in the above embodiments, when executing the multi-platform common-view orbit determination method for Earth-Moon space targets, is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus provided in the above embodiments and the multi-platform common-view orbit determination method embodiments for Earth-Moon space targets belong to the same concept, and its implementation process is detailed in the method embodiments, which will not be repeated here.

[0250] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of any of the methods described above.

[0251] Please see Figure 4 This is a structural block diagram of an electronic device provided in an embodiment of this application.

[0252] like Figure 4 As shown, the electronic device 400 includes a processor 401 and a memory 402.

[0253] In this embodiment, the processor 401 is the control center of the computer system, and can be a processor of a physical machine or a processor of a virtual machine. The processor 401 may include one or more processing cores, such as a 4-core processor or an 8-core processor. The processor 401 can be implemented using at least one hardware form selected from DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array).

[0254] Processor 401 may also include a main processor and a coprocessor. The main processor is a processor used to process data in the wake-up state, also known as a CPU (Central Processing Unit). The coprocessor is a low-power processor used to process data in the standby state.

[0255] Memory 402 may include one or more computer-readable storage media, which may be non-transitory. Memory 402 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In some embodiments of this application, the non-transitory computer-readable storage media in memory 402 is used to store at least one instruction, which is executed by processor 401 to implement the method in the embodiments of this application.

[0256] In some embodiments, the electronic device 400 further includes a peripheral device interface 403 and at least one peripheral device 404. The processor 401, memory 402, and peripheral device interface 403 can be connected via a bus or signal line. Each peripheral device 404 can be connected to the peripheral device interface 403 via a bus, signal line, or circuit board. Specifically, the peripheral device 404 includes: a display screen, a camera, and audio circuitry. The peripheral device interface 403 can be used to connect at least one I / O (Input / Output) related peripheral device to the processor 401 and memory 402.

[0257] In some embodiments of this application, the processor 401, memory 402, and peripheral device interface 403 are integrated on the same chip or circuit board; in other embodiments of this application, any one or two of the processor 401, memory 402, and peripheral device interface 403 can be implemented on separate chips or circuit boards. This application does not specifically limit the implementation in this regard.

[0258] The block diagram of the electronic device shown in the embodiments of this application does not constitute a limitation on the electronic device 400. The electronic device 400 may include more or fewer components than shown, or combine certain components, or use different component arrangements.

[0259] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the methods in any of the foregoing embodiments. The computer-readable storage medium may include, but is not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives, as well as magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic cards or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0260] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the related technology, can be embodied in the form of software products. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0261] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for determining the common orbit of a multi-platform target in the Earth-Moon space, characterized in that, include: Multiple observation platforms observe the same Earth-Moon space target during the same observation period, and obtain the motion data sequence of each observation platform during the observation period, and obtain the observation data sequence obtained by each observation platform from observing the Earth-Moon space target during the observation period; Based on the motion data sequence and observation data sequence of each observation platform, the relative positional relationship between each observation platform and the Earth-Moon space target is determined. Combining the relative positional relationship, motion data sequence, and observation data sequence, a first observation model for the Earth-Moon space target is constructed. The first observation model includes a position observation equation and a velocity observation equation. The position and velocity observation equations are solved using ordinary least squares to calculate the position and velocity of the Earth-Moon space target at each moment within the corresponding observation period; the state vector observation values ​​are obtained based on the position and velocity of the Earth-Moon space target within the observation period. A second observation model is constructed based on the position and velocity at each time point, and the orbital arc of the Earth-Moon space target within the corresponding observation period is calculated based on the second observation model; wherein, the second observation model is an error equation constructed based on the residual between the observed value and the predicted value of the initial state vector.

2. The method for determining the common orbit of a multi-platform space target for Earth-Moon space as described in claim 1, characterized in that, After acquiring the motion data sequence of each observation platform during the observation period, the orbit determination method further includes: The motion data sequence is transformed into the TOD coordinate system to obtain the transformed motion data sequence; wherein, the motion data sequence includes the motion data of the observation platform at various times, and the motion data includes the position and velocity of the observation platform; After obtaining the observation data sequence obtained by each of the observation platforms from observing the Earth-Moon space target during the observation period, the method further includes preprocessing the observation data sequence: Transform the optical angle information in the observation data sequence into the TOD coordinate system; The optical angle information of the Earth-Moon space target observed by each observation platform is fitted with a binomial formula to obtain the right ascension and declination data of the Earth-Moon space target during the observation period. Differentiating the right ascension and declination data respectively yields the right ascension rate of change data and the declination rate of change data; The fitted observation data sequence was obtained based on right ascension data, declination data, right ascension rate of change data, and declination rate of change data; Based on the transformed motion data sequence and the fitted observation data sequence, the step of determining the relative positional relationship between each observation platform and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform is performed.

3. The method for determining the common orbit of a multi-platform space target for Earth-Moon space as described in claim 2, characterized in that, Determining the relative positional relationship between each observation platform and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform includes: Based on the motion data sequence of each observation platform, the motion data of each observation platform at the same moment is obtained. The position vector of the corresponding observation platform is determined according to the motion data. Based on the position vector of each observation platform, the unit position vector of the corresponding observation platform relative to the origin of the TOD coordinate system is calculated, and the formula is applied: ； Based on the observation data sequence of each observation platform, the observation data obtained by each observation platform at the same time is acquired. The observation vector of the corresponding observation platform towards the Earth-Moon space target in the line-of-sight direction is determined according to the observation data. Based on the observation vector of each observation platform, the unit observation vector of the corresponding observation platform towards the Earth-Moon space target in the line-of-sight direction is calculated, and the formula is applied: ； A first virtual plane is constructed based on each observation platform, the Earth-Moon space target, and the origin of the TOD coordinate system. The unit normal vector of the first virtual plane is calculated based on the unit position vector and unit observation vector of the corresponding observation platform, using the formula: ； A second virtual plane is constructed based on the unit normal vector of the first virtual plane corresponding to each observation platform and the unit observation vector of the corresponding observation platform. The unit normal vector of the second virtual plane is calculated using the following formula: ； The relative positional relationship between each observation platform and the Earth-Moon space target is determined based on the unit position vector, the unit observation vector, the unit normal vector of the first virtual plane, and the unit normal vector of the second virtual plane. Where i represents the label of the observation platform, used to distinguish different observation platforms; For observation platform position vector The magnitude of the position vector. For observation platform The unit observation vector of a lunar target in the line-of-sight direction. For observation platform The observation vector of the Earth-Moon space target in the line-of-sight direction. Let the magnitude of the observation vector be . For observation platform The observed right ascension values ​​at the corresponding times. For observation platform The observed declination values ​​for the corresponding time. For observation platform The unit normal vector of the corresponding first virtual plane, unit normal vector With unit observation vector The unit normal vector of Zhang Cheng's second virtual plane. For observation platform The unit position vector.

4. The method for determining the common orbit of a multi-platform space target for Earth-Moon space as described in claim 3, characterized in that, The first observation model for the Earth-Moon space target, constructed by combining relative positional relationships, motion data sequences, and observation data sequences, includes: Construct the position observation equation for the Earth-Moon space target, and apply the following formula: ； ； ; Differentiating both sides of the position observation equation with respect to time, we obtain the velocity observation equation. Applying the formula: ； Determine the parameters in the velocity observation equation and The steps include: Calculate the rate of change of the unit observation vector of the observation platform relative to the Earth-Moon observation target, and the rate of change of the unit position vector of the observation platform, using the following formula: ; ； Calculate the rate of change of the unit normal vector for each first virtual plane and the rate of change of the unit normal vector for each second virtual plane by applying the formula: ; The parameters in the velocity observation equation were calculated. and Apply the formula: ； ; in, Let be the position vector of the Earth-Moon space target. Let be the velocity vector of the Earth-Moon space target. For observation platform The velocity vector, For observation platform Unit observation vector of the Earth-Moon observation target The rate of change, For observation platform unit position vector The rate of change, The unit normal vector for each first virtual plane The rate of change, The unit normal vector for each second virtual plane The rate of change, T represents the matrix transpose. For observation platform The rate of change of the position vector, , , , These are all parameters in the velocity observation equation. The rate of change of right ascension, This represents the rate of change of declination.

5. The method for determining the common orbit of a multi-platform space target for lunar targets according to claim 4, characterized in that, The construction of the second observation model based on the position and velocity at each time point includes: Based on the position and velocity of the Earth-Moon space target during the observation period, the state vector observation value is obtained, and the formula is applied: ； Based on the changes in the position and velocity of the Earth-Moon space target over time during the observation period, the motion equation of the Earth-Moon space target is established, and the formula is applied: ; ; Using the observed state vector at the first moment of the observation period as the initial state vector observation, and using this initial state vector observation as the initial value of the predicted initial state vector of the motion equation, the function that transforms the observed state vector into the initial value of the predicted initial state vector is applied by the following formula: ; ； The error equation is constructed based on the residual between the observed and predicted initial state vector values. The formula is then applied: ； At the moment corresponding to the initial state, obtain the predicted value of the initial state vector for the first iteration. Approximate the error equation at the predicted value of the initial state vector for the first iteration using a first-order Taylor expansion, and apply the formula: ； ； The second observation model is obtained: ； Where z represents the observed state vector of the Earth-Moon space target. These are the initial state vector observations. Indicates the observation period The k-th observation in the corresponding observation time series, including location and speed The position and velocity of the Earth-Moon space target at each moment are represented as a state vector. , Motion state vector Rate of change over time t; Represents the residual matrix. The initial value of the predicted value of the initial state vector. A function representing the initial values ​​of the observed state vector z and the predicted initial state vector z. This represents the initial value of the predicted initial state vector for the first iteration. Indicates the partial derivative sign. For error parameters, This represents the correction amount of the predicted state vector obtained from the corresponding iterative calculation. The symbols used to replace those in the above formulas, Let be the state transition matrix.

6. The method for determining the common orbit of a multi-platform space target for lunar targets according to claim 5, characterized in that, The calculation of the orbital arc segment of the Earth-Moon space target within the corresponding observation period based on the second observation model includes: The correction amount for the predicted initial state vector is calculated using the following formula: ； The initial state vector prediction value for the (j-1)th iteration is optimized based on the correction value obtained from the j-th iteration to obtain a new initial state vector prediction value, using the formula: ; For the correction amount in the j-th iteration, determine whether the constraint conditions are met: ; If the correction amount in the j-th iteration does not meet the constraint conditions, increment j by 1, and proceed to the step of calculating the correction amount of the predicted value of the initial state vector. Perform the (j+1)-th iteration calculation until the calculated correction amount meets the constraint conditions. If the correction in the j-th iteration satisfies the constraints, output the predicted value of the initial state vector obtained by the optimization in the j-th iteration. Based on the optimized initial state vector prediction value and the kinematic equation of the Earth-Moon space target, the optimized state vector of the Earth-Moon space target at each moment during the observation period is calculated, and the orbital arc of the Earth-Moon space target during the observation period is obtained based on the optimized state vector. in, The preset iteration limit, The correction amount is calculated in the j-th iteration. The predicted value of the initial state vector obtained in the (j-1)th iteration. The new initial state vector prediction value is calculated and optimized for the j-th iteration.

7. A method for determining the common orbit of a multi-platform space target for Earth-Moon space targets according to any one of claims 1-6, characterized in that, The orbit determination method also includes: Obtain multiple track segments; Obtain the root mean square residual for each orbital arc segment; the root mean square residual is calculated based on the difference between the observed value of the state vector and the predicted value of the state vector at each observation time within the observation period corresponding to the orbital arc segment. Compare the root mean square residuals of every two orbital segments. If the difference between the root mean square residuals is less than a preset difference threshold, determine that the two orbital segments with a difference less than the preset difference threshold belong to the same Earth-Moon space target.

8. An apparatus for determining the common orbit of a multi-platform space target based on any one of claims 1-7, characterized in that, include: The data acquisition module is used to acquire the motion data sequence of each observation platform during the observation period, and also to acquire the observation data sequence obtained by each observation platform from observing the Earth-Moon space target during the observation period; wherein, multiple observation platforms observe the same Earth-Moon space target during the same observation period; The first calculation module is used to determine the relative positional relationship between each observation platform and the Earth-Moon space target based on the motion data sequence and observation data sequence of each observation platform, and to construct a first observation model of the Earth-Moon space target by combining the relative positional relationship, motion data sequence and observation data sequence. The first calculation module is used to calculate the position and velocity of the Earth-Moon space target at each moment within the corresponding observation period based on the first observation model; The second calculation module is used to construct a second observation model based on the position and velocity at each time point, and is also used to calculate the orbital arc of the Earth-Moon space target within the corresponding observation period based on the second observation model.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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