A method for associating and high-precision fusion orbiting of heterogeneous measurement data between star clusters

Abstract

The application discloses a kind of star group between heterogeneous measurement data association and high-precision fusion orbit determination method, belong to space relative navigation technical field.The method includes grouping to the member star in star group, constructs the measurement set of the angle measurement and ranging of all member stars in time t, then calculates the position assumption set of member star, calculates the distance assumption value between member stars under each association assumption, constructs association degree evaluation index by distance assumption value and actual distance measurement, constructs cost matrix according to association degree evaluation index, and then obtains optimal association result, obtains the ranging and angle measurement data corresponding to all member stars at current time relative orbit determination, including using optimal estimation method to carry out state estimation, and including determining system state, constructing system measurement equation and system equation;Finally, the above steps are repeatedly executed for each measurement time, until filter convergence, obtain the high-precision orbit determination result of member star.

Description

Technical Field

[0001] This invention relates to the field of space relative navigation technology, specifically to a method for correlation and high-precision fusion orbit determination of heterogeneous measurement data between star clusters. Background Technology

[0002] The prerequisite for a satellite formation to complete its mission is maintaining its configuration, which in turn requires precise relative orbit determination among its members. For satellite formations, limited sensor capabilities allow only angle or range measurement information to be acquired, and due to the large number of satellites in the constellation, multi-target observation is typically performed. While electronic tags can be used for communication ranging, long-range optical angle measurement cannot identify the individual tags of multiple targets within the field of view. Therefore, only by correlating and matching multiple sets of angle and range measurement information simultaneously acquired within the constellation can high-precision relative orbit determination among its members be achieved.

[0003] Currently, existing data association methods mainly focus on the association and matching of homogeneous data, such as the collaborative association of angle measurement data from multi-satellite and multi-target observations, and the temporal association of angle measurement data from a single satellite at different times for the same target. Existing technologies cannot effectively fuse heterogeneous measurement information (labeled ranging and unlabeled angle measurement) that coexist in a constellation, which directly limits the ability to perform high-precision relative orbit determination using multi-source data. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method for correlation and high-precision fusion orbit determination of heterogeneous measurement data between star clusters.

[0005] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0006] A method for correlation and high-precision fusion of heterogeneous measurement data between star clusters is proposed. This method correlates the line-of-sight angle measurement and distance measurement between the origin star and member stars to obtain measurement input for high-precision orbit determination of member stars, thereby achieving high-precision relative navigation of member stars. The method includes:

[0007] (1) Group the member stars in the star cluster, construct the angle measurement set and distance measurement set of all member stars within time t, calculate the position hypothesis set of member stars based on the distance measurement set and the angle measurement set, and then calculate the distance hypothesis value between member stars under each correlation hypothesis based on the position hypothesis set. Construct a correlation evaluation index through the distance hypothesis value and the actual distance measurement, construct a cost matrix based on the correlation evaluation index, and then calculate the optimal correlation result through the cost matrix.

[0008] (2) Based on the distance and angle measurement data of all member stars obtained in step (1) at the current time, relative orbit determination is performed, including state estimation using the optimal estimation method, and including determining the system state, constructing system measurement equations and system equations;

[0009] (3) Repeat steps (1)-(3) for each measurement time until the filtering converges, and obtain the high-precision orbit determination result of the member star.

[0010] Furthermore, the origin star refers to a satellite in a constellation that has established a relative navigation system, and the other satellites in the constellation are member stars. The origin star obtains the line-of-sight angle measurement of the other member stars through optical detection, but cannot determine the member star corresponding to the line-of-sight angle. The origin star and member stars, as well as member stars and member stars can perform distance measurement and communication.

[0011] Furthermore, step (1) specifically includes:

[0012] The set of distance measurements between the origin star and the selected m member stars from time 0 to time t is represented as follows: The set of angle measurements for all n member stars is represented as: The subscripts i and j correspond to the measurement group numbers for distance measurement and angle measurement, respectively;

[0013] The positional assumptions of the member stars are calculated by converting the line-of-sight angle into a unit line-of-sight vector, then multiplying it by the distance to obtain the position. The resulting set of positional assumptions is represented as follows: , , subscript ij Indicates the distance measurement of the i-th group Measurement of the line of sight angle of the j-th group Location assumptions obtained through association matching;

[0014] For the i-th group of distance measurements The associated matching angle measurements yield n sets of distance hypotheses, which are represented as follows:

[0015] ;

[0016] in, This represents the distance between the origin star and the member stars at time t. , These are the azimuth and elevation angles of the member star relative to the origin star, respectively.

[0017] Furthermore, the distance assumptions between member stars based on each association hypothesis. The calculation method is:

[0018] definition For the firsti All n positional hypotheses obtained from group distance measurements correspond to member stars The actual measured distance between the member stars is expressed as:

[0019] ;

[0020] in, Subscript indicates member star And members of the star The ranging value; based on the member stars And members of the star The distance and position are assumed to be obtainable The group distance hypothesis is expressed as:

[0021] ,

[0022] in Indicates the corresponding Get the first place One location assumption used as a distance calculation assumption:

[0023] ;

[0024] ;

[0025] The correlation evaluation index is defined as the norm sum of the differences between the actual distance and the assumed distance, expressed as:

[0026] ,

[0027] f To represent the correlation evaluation index, a cost matrix C is constructed as an array consisting of all possible correlation evaluation indexes:

[0028] ,

[0029] Its superscript This indicates the corresponding association hypothesis, that is, the hypothesis about the member star. The distance measurement and the first The measured angles are correlated.

[0030] Furthermore, in step (2), the relative orbit determination target is to determine the relative position and velocity of the satellites. Therefore, the system state is defined as the relative position and relative velocity of the m member satellites relative to the origin satellite, and the system state is expressed as:

[0031] ,

[0032] in The elements are the projections of the relative positions and velocities of the member stars with respect to the origin star onto the three axes of the origin star's orbital coordinate system, and the superscript T indicates the transpose of the matrix.

[0033] Angle measurement data The ranging data is d Convert angle and distance measurement data into position vectors:

[0034] ,

[0035] Using the position vector as the system measurement input, the system measurement equations are constructed as follows:

[0036] ,

[0037] in, This represents the measurement equation corresponding to angle measurement. This represents the measurement equation corresponding to the distance measurement.

[0038] For relative navigation, this method uses the CW equations for the system equations, enabling high-precision relative navigation even when the absolute state of the origin star is inaccurate. The system equation expression is as follows:

[0039]

[0040] in, The system matrix represents the overall system. The state transition matrix represents the relative motion of a spacecraft. Let be the angular velocity of the star at the origin, using , , , , , The corresponding values ​​represent the spacecraft's position and velocity in the three-axis components of the orbital coordinate system.

[0041] Beneficial effects: This invention enables the correlation and matching of angle and distance measurement information from multiple stars through a hybrid undermeasured data association method among star clusters. Secondly, by combining the CW equations and angle and distance measurement information with an unscented Kalman filter algorithm, this invention achieves high-precision relative orbit determination without requiring absolute orbit information. Finally, this invention enables rapid relative navigation among star clusters through data association and initial orbit determination methods. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of distance measurement between star clusters;

[0043] Figure 2 A schematic diagram of angle measurement between star clusters;

[0044] Figure 3A statistical chart of the relative navigation three-axis position and velocity errors of member star 1;

[0045] Figure 4 A statistical chart of the relative navigation three-axis position and velocity errors of member satellite 2;

[0046] Figure 5 A statistical chart of the relative navigation three-axis position and velocity errors of member star 3. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] This invention provides a method for correlation and high-precision fusion orbit determination of heterogeneous measurement data between star clusters. When angle and ranging information between star clusters can be obtained but cannot be correlated to the same target, the method correlates the angle and ranging information of satellites using only the ranging information between star clusters, and uses the angle and ranging information to perform rapid initial high-precision orbit determination.

[0049] We first assume a constellation of n satellites, with the relative navigation system established on one of these satellites, denoted as the origin satellite. The remaining satellites are called member satellites. The origin satellite can measure the line-of-sight angle of the other member satellites through optical detection, but it cannot determine the member satellite corresponding to the line-of-sight angle. Distance measurement and communication can occur between the origin satellite and member satellites, as well as between member satellites themselves. The core of this invention lies in solving the data association problem using a "geometric configuration verification" approach. That is, instead of directly identifying optical targets, it uses precise inter-satellite distance measurement information as a "benchmark." By calculating and comparing the constellation's geometric configuration formed by all possible "distance-angle measurement" association combinations, it identifies the unique combination that best matches the actual distance measurement, thereby deducing the correct data association relationship. Furthermore, this method associates the line-of-sight angle measurement of the origin satellite to the member satellites with the distance measurement to obtain measurement input for high-precision orbit determination of the member satellites, thereby achieving high-precision relative navigation of the member satellites. The implementation steps include:

[0050] (1) Group the member stars in the constellation and correlate the angle measurement and distance measurement data of each group of member stars in the following way:

[0051] A set of angular and range measurements for all member stars within time t is constructed. By accumulating time-series data, measurement noise and correlation ambiguity at single moments are overcome. Based on the range and angular measurement sets, a set of positional hypotheses for the member stars is calculated, generating all possible "range-angle" matching schemes and forming a complete correlation hypothesis space. Then, based on the set of positional hypotheses, the distance assumptions between member stars under each correlation hypothesis are calculated, transforming the abstract positional correlation problem into a geometric distance problem that can be directly verified by real inter-star distance measurement data. A correlation evaluation index is constructed using the distance assumptions and actual distance measurements, establishing a quantitative standard to accurately assess the degree of agreement between each correlation hypothesis and the actual measurement data. A cost matrix is ​​constructed based on the correlation evaluation index, and the optimal correlation result is then calculated using the cost matrix.

[0052] (2) Based on the distance and angle measurement data of all member stars obtained in step (1) at the current time, high-quality fused measurement data with correct identity labels are obtained. Based on this, high-precision relative orbit determination calculation can be performed, including state estimation using the optimal estimation method, determining the system state, and constructing the system measurement equations and system equations;

[0053] (3) Repeat steps (1)-(3) for each measurement time until the filtering converges, and obtain the high-precision orbit determination result of the member star.

[0054] like Figure 1 , Figure 2 The diagram shows the angle and distance measurements of a group of three satellites and the originating star in this constellation. The originating star provides a set of measurements containing the relative line-of-sight angles of all member stars, but the elements lack labels for the corresponding measurement objects. It also provides a set of measurements containing the relative distances between stars in the constellation, which includes labels for the corresponding measurement objects. Therefore, if both types of measurement information are needed simultaneously, measurements of the same target must be correlated. The specific steps of this data correlation method under mixed undermeasurement conditions are as follows:

[0055] Step 1, from the initial time 0 to... t The set of distance measurements between the origin star and the selected three member stars is denoted as . The set of line-of-sight angle measurements for all n member stars is: For the angle measurement data at time t , and These are the azimuth and elevation angles of the member star relative to the origin star at time t, respectively.

[0056] This step utilizes historical data from multiple time points to enhance the robustness and reliability of the associated decisions, providing a data foundation for subsequent processing.

[0057] Step 2: Obtain position information based on angle and distance measurement information, for the third group of distance measurements. There are n sets of angle measurements that may be associated with and matched, so n sets of distance hypotheses can be obtained accordingly.

[0058] ,

[0059]

[0060] in, Subscript ij Indicates the first i Group distance measurement With the j Group line of sight angle measurement The location assumptions obtained through association matching are used to generate all possible association schemes, transforming implicit data relationships into explicit, computable geometric location spaces, thus creating conditions for subsequent quantitative verification.

[0061] Step 3, Define For all n positional assumptions obtained from the third group of distance measurements, where Distance can be measured between member stars to obtain the actual measured distance. , represented as For member stars And members of the star The distance and location can be obtained. Group distance assumption:

[0062] ;

[0063] in Indicates the corresponding Get the first place The positional assumptions used as the distance calculation assumptions are as follows:

[0064]

[0065] .

[0066] This step unifies heterogeneous data that are difficult to compare directly into distance comparison, and then obtains a comparison value of the correlation accuracy through the geometric constraints of inter-satellite ranging.

[0067] Step 4: Set the correlation evaluation index as the norm sum of the differences between the actual distance and the assumed distance, i.e.

[0068] ,

[0069] The calculated distance under correct association is almost identical to the actual measurement, and the evaluation index value is small; while incorrect association will lead to huge index values.

[0070] Step 5, construct the cost matrix C An array consisting of all possible correlation evaluation indicators, i.e.

[0071] ,

[0072] Its superscript This indicates the corresponding association hypothesis, that is, the hypothesis about the member star. The distance measurement and the first The measured angles are correlated.

[0073] This step maps the data association problem to a mathematical optimization problem, using the corresponding positions of elements in C to more intuitively represent the association relationships.

[0074] Step 6: Sort the elements in the cost matrix from smallest to largest. The smallest element corresponds to the smallest association cost, and the association corresponding to its superscript is the most likely correct association, which is output as the association result.

[0075] This step uses a sorting algorithm to obtain the position of the minimum element in the cost matrix, and the correct association can be obtained based on the corresponding superscript number.

[0076] Step 7, therefore the system state is defined as the relative positions and relative velocities of the m member stars relative to the origin star, i.e. , , where the elements are the relative positions and velocities of the member stars with respect to the origin star, and their corresponding projections onto the three axes of the origin star's orbital coordinate system.

[0077] Furthermore, the position vector is used as the system measurement input to construct the system measurement equations. For relative navigation, the CW equations are adopted, which enable high-precision relative navigation even when the absolute state of the origin star is not completely accurate. The system equation expression is as follows:

[0078] ;

[0079] in, n ω is the angular velocity of the star at the origin.

[0080] The angle and distance measurement information is converted into position information as the new measurement input. The conversion method is as follows:

[0081] ;

[0082] in and All data are angular measurements. dThis is the ranging data. The position field of the initial value of the filtered state is set to the position information at the initial time.

[0083] Step 8: Use unscented Kalman filtering for state estimation.

[0084] Finally, the above steps are repeated for each measurement moment until the filtering converges, and the high-precision orbit determination results of the member stars are obtained.

[0085] The feasibility of this invention is illustrated below with examples.

[0086] The following calculation conditions and technical parameters are set:

[0087] 1) The simulated satellite parameters are set as shown in Table 1 below.

[0088] 2) The observation duration is 3600s, and the measurement period is 2s.

[0089] 3) The standard deviation of the distance measurement error is 10m, and the standard deviation of the angle measurement error is 0.05°.

[0090] 4) The filter parameters are set as shown in Table 2 below.

[0091] Table 1. Satellite initial time parameters

[0092]

[0093] Table 2. Filtering Parameter Table

[0094]

[0095] The heterogeneous measurement data correlation and high-precision fusion orbit determination technology between star clusters based on the present invention was simulated and verified using the above-mentioned calculation conditions and technical parameters. The simulation time was 3600s, and the measurement cycle was 2s. Table 3 shows the correlation accuracy under different measurement errors obtained from 1000 target tests. Figures 3-5 The image shows the initial orbit determination position and velocity error diagrams of three satellites obtained from 100 target tests. Table 3 shows that the data association method proposed in this invention can achieve an association accuracy rate of over 99% under different measurement errors. Figures 3-5 According to the 3σ principle, the probability of the error falling within the ±3σ boundary is 99.7%. The ±3σ boundaries at three time points after filtering convergence are recorded in Table 4 (including Table 4 continued). The relative position errors of the three member stars after filtering convergence are all below 3m, and the relative velocity errors are below 0.002m / s. This breakthrough overcomes the problem of high-precision correlation and fusion of heterogeneous measurement data between star clusters under under-measurement conditions, which is impossible with existing methods.

[0096] Table 3. Data Association Accuracy

[0097]

[0098] Table 4. Relative Navigation Error Table

[0099]

[0100] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for correlation and high-precision fusion of heterogeneous measurement data between star clusters for orbit determination, characterized in that, This method correlates the line-of-sight angle measurement and distance measurement between the origin star and the member stars to obtain measurement inputs for high-precision orbit determination of the member stars, thereby achieving relative navigation of the member stars, including: The member stars in the constellation are grouped, and a set of line-of-sight angle measurements and a set of distance measurements for all member stars within time t are constructed. Based on the set of line-of-sight angle measurements and the set of distance measurements, a set of positional assumptions for the member stars is calculated. Then, based on the set of positional assumptions, the distance assumption values ​​between member stars under each association assumption are calculated. An association degree evaluation index is constructed by using the distance assumption values ​​and the actual distance measurements. A cost matrix is ​​constructed based on the association degree evaluation index, and then the optimal association result is obtained by calculating the cost matrix. Relative orbit determination is performed based on the distance and angle measurement data of all member stars at the current moment, including state estimation using the optimal estimation method, and also includes determining the system state, constructing the system measurement equations and system equations; Repeat the above steps for each measurement moment until the filtering converges and the high-precision orbit determination results of the member stars are obtained. In this method, the distance assumptions between member stars are based on each association hypothesis. The calculation method is: definition For the first i All n positional hypotheses obtained from group distance measurements correspond to member stars The actual measured distance between the member stars is expressed as: ； in, Subscript indicates member star And members of the star The ranging value; based on the member stars And members of the star The distance and position are assumed to be obtainable The group distance hypothesis is expressed as: ， in Indicates the corresponding Get the first place The location assumptions used as the basis for distance calculations are expressed as follows: ； ； The correlation evaluation index is defined as the norm sum of the differences between the actual distance and the assumed distance, expressed as: ， f To represent the correlation evaluation index, a cost matrix C is constructed, which is an array consisting of all possible correlation evaluation indexes: ， Its superscript This indicates the corresponding association hypothesis, that is, the hypothesis about the member star. The distance measurement and the first Correlate the measured angles; In this method, the relative orbit determination objective is to determine the relative position and velocity of the satellites. Therefore, this method defines the system state as the relative position and relative velocity of the m member satellites relative to the origin satellite. The system state is expressed as: ， in The elements are the relative positions and velocities of the member stars with respect to the origin star, projected onto the three axes of the origin star's orbital coordinate system, respectively. The superscript indicates that the elements are the projections of these relative positions and velocities onto the origin star's orbital coordinate system. T Represents the transpose of a matrix; Angle measurement data The ranging data is d Convert angle and distance measurement data into position vectors: ， Using the position vector as the system measurement input, the system measurement equations are constructed as follows: ， in, This represents the measurement equation corresponding to angle measurement. This represents the measurement equation corresponding to the distance measurement.

2. The method for correlation and high-precision fusion of heterogeneous measurement data among star clusters according to claim 1, characterized in that, The origin star refers to the satellite in a constellation that has established a relative navigation system, while the other satellites in the constellation are member stars; The origin star acquires line-of-sight angle measurements of other member stars through optical detection, but cannot determine the member star corresponding to the line-of-sight angle. The origin star and member stars, as well as member stars, can perform distance measurement and communication.

3. The method for correlation and high-precision fusion of heterogeneous measurement data among star clusters according to claim 1, characterized in that, The set of distance measurements between the origin star and the selected m member stars from time 0 to time t is represented as follows: The set of angle measurements for all n member stars is represented as: The subscripts i and j correspond to the measurement group numbers for distance measurement and angle measurement, respectively; The positional assumptions of the member stars are calculated by converting the line-of-sight angle into a unit line-of-sight vector, then multiplying it by the distance to obtain the position. The resulting set of positional assumptions is represented as follows: subscript ij Indicates the distance measurement of the i-th group Measurement of the line of sight angle of the j-th group Location assumptions obtained through association matching; For the i-th group of distance measurements The associated and matched angle measurements yield n sets of distance hypotheses. This can be represented as: ； in, This represents the distance between the origin star and the member stars at time t. , These are the azimuth and elevation angles of the member star relative to the origin star, respectively.

4. The method for correlation and high-precision fusion of heterogeneous measurement data among star clusters according to claim 1, characterized in that, For relative navigation, this method uses the CW equations for the system equations, enabling high-precision relative navigation even when the absolute state of the origin star is inaccurate. The system equation expression is as follows: in, The system matrix represents the overall system. The state transition matrix represents the relative motion of a spacecraft. Let be the angular velocity of the star at the origin, using , , , , , The corresponding values ​​represent the spacecraft's position and velocity in the three-axis components of the orbital coordinate system.

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