A Multi-Target Orbit Tracking Method for Spaceborne Autonomous Passive Measurement

Abstract

This invention discloses a spaceborne autonomous passive measurement method for multi-target orbit tracking, applied to two observation satellites. The method includes: Step 1, establishing a dynamic model of the observed spacecraft and a sensor line-of-sight angle measurement model, and constructing a random finite set to describe the dynamic changes and uncertainties of multiple targets; Step 2, constructing a cost matrix based on the minimum distance between different sensor line-of-sight vectors, and solving the correlation results of angle measurement data through two rounds of filtering; Step 3, constructing multiple sets of expanded-dimensional measurements based on the data correlation results and solving the measurement correlation probability of each set of expanded-dimensional measurements; Step 4, introducing the corresponding measurement correlation probability into the GM-PHD filter to correct the posterior Gaussian weights, designing a centralized parallel fusion multi-target tracking method that considers the measurement correlation probability, achieving accurate tracking of multiple targets through dual-satellite information fusion, and solving the problem of poor tracking accuracy caused by the high miscorrelation rate of angle measurement data in the generation of expanded-dimensional measurements in centralized parallel fusion under the background of multi-target tracking.

Description

Technical Field

[0001] This invention relates to the field of space non-cooperative target situational awareness technology, specifically a multi-target orbit tracking method for spaceborne autonomous passive measurement. Background Technology

[0002] With the rapid development of aerospace technology, orbital space is becoming increasingly crowded, with a large number of space debris and satellites operating in low Earth orbit, making orbital safety issues increasingly prominent. To avoid collisions between on-orbit satellites and non-cooperative space targets such as space debris, developing space situational awareness technologies, including initial orbit determination, target tracking, maneuver detection, and intent recognition, has become an inevitable choice. Multi-target tracking tasks refer to continuously estimating the number of targets within the spacecraft's sensor field of view and the state variables of each target at different times. In addition to common radar observation modes, space-based passive sensors are widely used in tracking the orbits of non-cooperative targets in space due to their advantages such as strong concealment, large observation range, and small size. However, target tracking by a single passive sensor platform is limited by factors such as orbital configuration, lack of measurement dimensional information, and target density, resulting in poor tracking performance in some complex orbital situations. Therefore, multi-target tracking modes using multi-sensor networking and collaboration have gradually become a hot topic in research and application.

[0003] Traditional multi-target tracking methods mainly rely on techniques such as data association and Kalman filtering. However, these methods often perform poorly when the number of targets varies over time and sensor data has high uncertainty. To address these issues, finite set statistics theory has been introduced into the field of multi-target tracking. Multi-target tracking methods based on stochastic finite sets have significant advantages in handling association uncertainty, detection uncertainty, and sensor clutter. Based on stochastic finite set theory, the probability hypothesis density (PHD) filter for the first-order statistical moments of the transfer system state has been proposed. However, the multiple integrals corresponding to the multidimensional state variables of the PHD filter are often difficult to compute. A common approach is to use a Gaussian mixture GM-PHD closed-loop solution.

[0004] Extending to multi-sensor multi-target tracking technology, data fusion can be categorized into centralized, distributed, and hybrid systems based on different data fusion structures. The main difference lies in whether the fusion processing focuses on measurements or posterior estimated state variables. Distributed multi-target tracking technology aims to perform single-platform tracking first, followed by fusion processing of posterior estimation results, primarily employing arithmetic mean fusion and geometric mean fusion. Centralized information fusion systems, on the other hand, send the raw measurement information acquired by each sensor to a central processor for spatiotemporal registration, data association, and tracking. This fusion method exhibits minimal information loss and high data fusion accuracy, achieving optimal fusion. However, when faced with undermeasurement issues from passive sensors such as optical cameras, the primary challenge becomes how to correlate measurement information from different sensors. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a space-based passive dual-satellite collaborative centralized parallel fusion multi-target tracking method that considers the measurement association probability. This method solves the problem of poor tracking accuracy caused by the high misassociation rate of angle measurement data in the extended dimension measurement generation of centralized parallel fusion under the background of multi-target tracking.

[0006] A multi-target orbit tracking method based on spaceborne autonomous passive measurement includes the following steps:

[0007] Step 1: Construct a random finite set based on the dynamic model of the observed spacecraft and the sensor line-of-sight measurement model;

[0008] Step 2: Construct a cost matrix based on the minimum distance between line-of-sight vectors from different sensors, and solve the correlation results of angle measurement data through two rounds of filtering;

[0009] Step 3: Referring to the data association results above, construct multiple sets of expanded dimension measurements and solve the measurement association probability of each set of expanded dimension measurements;

[0010] Step 4: The corresponding measurement correlation probability is introduced into the weight of the corrected Gaussian term in the GM-PHD filter, and a centralized parallel fusion multi-target tracking method considering the measurement correlation probability is designed.

[0011] Step 5: Apply the above algorithm to the two observation satellites to achieve information fusion between the two satellites and accurate tracking of multiple targets.

[0012] Preferably, step 1 specifically comprises: Step 1.1, establishing a spacecraft dynamics model and a spaceborne optical camera line-of-sight measurement model under the perturbation of the non-spherical shape of the Earth and the gravitational pull of the Moon in a geocentric inertial frame; Step 1.2, modeling the multi-target tracking problem using a stochastic finite set approach to describe the dynamic changes and uncertainties of the targets. Based on the theoretical framework of stochastic finite sets, the states and measurements of the multiple targets can be represented as finite sets X, respectively. k and Z k

[0013]

[0014]

[0015] in,

[0016] The state variable of the i-th target at time k is obtained from the absolute dynamics model; This represents the j-th measurement from the target obtained at time k, derived from the sensor line-of-sight angle measurement model; finite set X k Z k The elements in the space belong to the space. and and N are finite subsets of sets x and z, respectively; k and M k These represent the number of targets and measurements at the current moment, respectively.

[0017] As a preferred option, step 2 specifically involves: Step 2.1, constructing a minimum distance model between line-of-sight vectors from different sensors to evaluate the possibility that two line-of-sight vectors originate from the same target; Step 2.2, constructing a measurement association cost matrix L using the minimum distance model, using the values ​​of the elements in the cost matrix as the correlation evaluation index for measurement association between different sensors, and determining the measurement association results through two rounds of screening.

[0018] As a preferred option, the first round of selection in step 2.2 is as follows: in the first round of mandatory selection, the element with the smallest substitution value in each row is selected as the result of the mandatory selection. This is to ensure that at least one measurement in each row is selected, and to prevent the situation where all elements in a row are not selected after the second round of optimal selection.

[0019] As a preferred option, the second round of selection method in step 2.2 is as follows: in the second round of optimization screening stage, the elements of the cost matrix L after forced selection are arranged in ascending order of minimum distance value, and the first j elements with the smallest minimum distance value are selected.

[0020] As a preferred option, step 3 specifically involves: step 3.1, combining the results of the two rounds of screening into the final association result, and constructing multiple sets of expanded dimension measurements; step 3.2, solving the measurement association probability of each set of expanded dimension measurements.

[0021] As a preferred option, step 3.1 specifically involves merging the forced selection results of the first round and the optimal selection results of the second round to obtain the final angle measurement data association result at time k, and executing the two-round association procedure once at each time step throughout the entire simulation time.

[0022] Dimensional expansion measurement can be written as: in and The measurements acquired by sensor 1 and sensor 2 are respectively. and The observation equations for sensor 1 and sensor 2 are respectively. and The observation noise of sensors 1 and 2 are respectively. and For the elements measured by sensor 1, and The elements measured by sensor 2.

[0023] As a preferred embodiment, step 3.2 specifically involves: denoting the expanded dimension measurement set after association as... Let the measurement association probability corresponding to the dimension-expanded measurement in the set be . Suppose the associative combination of a certain row is L row =[l2 l5], the measurement correlation probability corresponding to this row. Solve for the obedience formula

[0024] As a preferred option, step 4 specifically involves: incorporating the corresponding measurement correlation probability into the weight of the corrected Gaussian term in the GM-PHD filter, and designing a centralized parallel fusion multi-target tracking method that considers the measurement correlation probability.

[0025] As a preferred option, the method for introducing the measurement association probability correction Gaussian term weight in step 4 is as follows: the correction of the posterior Gaussian weight conforms to the formula in These are the weights corresponding to the posterior Gaussian terms of the measurement z and the Gaussian hypothesis h. To measure the correlation probability of z, P D This represents the detection probability of the sensor. These are the weights corresponding to the prior Gaussian terms. To measure z, To measure the z-clutter intensity function, and These are the Kalman filter parameters.

[0026] Beneficial effects:

[0027] (1) This invention solves the problem of poor tracking accuracy caused by high miscorrelation rate of angle measurement data in the generation of extended dimension measurement in centralized parallel fusion under the background of multi-target tracking, and proposes a centralized parallel fusion multi-target tracking method that considers the measurement association probability.

[0028] (2) This invention can correctly associate measurements from different sensors through algorithm improvement, and finally achieve stable tracking of two stars in cooperation without changing the existing passive sensor equipment.

[0029] (3) This invention solves the correlation results of angle measurement data through two rounds of screening, which can ensure that each row of angle measurement data has correlation data, and can also perform two rounds of selection according to the actual computing power of the hardware, thereby improving the stability and applicability of the algorithm.

[0030] (4) This invention corrects the weight of Gaussian terms by introducing measurement correlation probability, so that some Gaussian terms can be quickly pruned by the post-processing algorithm, thus ensuring the running speed and performance of the algorithm.

[0031] (5) This invention uses dual-star collaboration to perform multi-target tracking, which solves the problem of missing measurement information and weak observability of a single passive sensor, and improves the tracking accuracy of the target. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the angle measurement data association process according to an embodiment of the present invention;

[0033] Figure 2 This is a target number estimation diagram according to an embodiment of the present invention;

[0034] Figure 3 This is a target GOSPA evaluation chart according to an embodiment of the present invention;

[0035] Figure 4 This is a comparison chart of target GOSPA evaluations according to an embodiment of the present invention;

[0036] Figure 5 This is a non-full-time target state estimation error diagram according to an embodiment of the present invention;

[0037] Figure 6 This is a non-full-time target state estimation error diagram according to an embodiment of the present invention. Detailed Implementation

[0038] 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.

[0039] This invention discloses a spaceborne autonomous passive measurement method for multi-target orbit tracking. To address the problem of poor tracking accuracy caused by the high miscorrelation rate of angle measurement data in the generation of expanded-dimensional measurements using centralized parallel fusion, a space-based passive dual-satellite collaborative centralized parallel fusion multi-target tracking method considering the measurement correlation probability is proposed.

[0040] Combination Figure 1 A multi-target orbit tracking method based on spaceborne autonomous passive measurement includes the following steps:

[0041] Step 1: Construct a random finite set based on the dynamic model of the observed spacecraft and the sensor line-of-sight measurement model.

[0042] Step 1.1: Establish a spacecraft dynamics model and a spacecraft line-of-sight angle measurement model for the onboard optical camera under the perturbation of the non-spherical shape of the Earth and the gravitational pull of the Moon in a geocentric inertial frame.

[0043] Specifically, a spacecraft dynamics model is established in a geocentric inertial frame. The origin of the geocentric inertial frame is located at the Earth's center of mass, the x-axis points to the vernal equinox, the z-axis points to the Earth's north celestial pole, and the y-axis forms a right-handed frame with the xz-axis. Ignoring the influence of solar radiation pressure, an absolute dynamics model incorporating Earth's non-spherical perturbation and lunar gravitational perturbation is constructed as follows:

[0044]

[0045] in, It is the non-spherical perturbation acceleration of the Earth, a m This is the gravitational acceleration due to the Moon, r = [x, y, z] T Let μ be the position vector of the spacecraft. e is the Earth's gravitational constant.

[0046] The following model for measuring the line-of-sight angle of a spaceborne optical camera is constructed, assuming that the state variables of the target in the inertial frame at time k are: The state quantities of the observed star in an inertial frame Therefore, the equation for angle measurement using a passive sensor can be written as:

[0047]

[0048] Among them, z k Let α be the measurement from the target obtained at time k. k and e k For z k The elements in For measuring noise.

[0049] line-of-sight vector i los The definition is as follows:

[0050]

[0051] Define the coordinate transformation matrix Φ as the transformation from the geocentric inertial frame to the LVLH coordinate system. el Therefore, the unit line-of-sight vector in the LVLH coordinate system can be expressed as:

[0052]

[0053] α k and e k The azimuth and elevation angles are respectively represented by the following formulas:

[0054]

[0055]

[0056] in, It follows a zero mean and has a covariance matrix of R. αe The Gaussian distribution.

[0057] Step 1.2: The multi-target tracking problem is modeled using a random finite set approach to describe the dynamic changes and uncertainties of the targets. Based on the theoretical framework of random finite sets, the states and measurements of the multiple targets can be represented as finite sets respectively.

[0058] Specifically, based on the RFS theoretical framework, the states and measurements of multiple targets at time k can be represented as finite sets:

[0059]

[0060] in, Let represent the state variable of the i-th target at time k. Let j be the j-th measurement at time k, and let the elements in the finite set belong to the space. and and Let N be a finite subset of sets x and z respectively. k and M k These represent the number of targets and measurements at the current moment, respectively.

[0061] Step 2: Construct a cost matrix based on the minimum distance between line-of-sight vectors from different sensors, and solve the correlation results of angle measurement data through two rounds of screening.

[0062] Step 2.1: Calculate the minimum distance between line-of-sight vectors from different sensors as the cost value to construct a cost matrix. Use the values ​​of the elements in the cost matrix as the correlation evaluation index of measurement association between different sensors to evaluate the possibility that two line-of-sight vectors come from the same target.

[0063] Step 2.2 involves two rounds of screening of the elements of the cost matrix to determine the measurement correlation results.

[0064] Specifically, assuming the spacecraft target is a point target, meaning each target generates only one line-of-sight vector during single-satellite observation. Ideally, the line-of-sight vectors of two observing satellites observing the same target should intersect. However, due to factors such as angle measurement errors, camera installation errors, and image distortion errors, line-of-sight vectors from the same target may not necessarily intersect. Nevertheless, the minimum distance between any two line-of-sight vectors from different observing satellites can be calculated. The minimum distance corresponding to the line-of-sight vector from the same target should be a smaller value, while the minimum distance corresponding to the line-of-sight vector from different targets should be a larger value.

[0065] Considering clutter and missed detections in the sensor system, assume that the set of measurements observed by sensor 1 at time k is as follows: The set of measurements observed by sensor 2 is Without any measurement preprocessing method, all measurements from sensor 1 have an equal probability of being fused with measurements from sensor 2, resulting in mn measurements at time k after fusion and dimension expansion. This surge in the number of expanded measurements fails to meet the real-time requirements of subsequent multi-target tracking methods. Furthermore, this expanded measurement method retains a large number of correlations between spurious measurements or between spurious and real measurements, severely impacting target tracking accuracy or causing target tracking divergence. Therefore, this paper uses minimum distance as an indicator to evaluate the correlation between measurements originating from the same target, constructs a measurement dimension expansion fitting method that meets real-time tracking requirements, and introduces the measurement correlation probability into the PHD tracking method to adjust the weights of the corresponding Gaussian components.

[0066] Solve for the measurement set of sensor 1 at time k. Each element in the set and the measurement set of sensor 2 at time k Let l be the minimum distance between each element in the set. ij Construct the cost matrix L.

[0067]

[0068] The values ​​of the elements in the cost matrix are used as the correlation evaluation index for measurement association between different sensors. The entire association process is divided into two rounds.

[0069] A schematic diagram of the correlation of angular measurement data of two stars is shown below. Figure 1 As shown, in the first round of forced selection, the element with the smallest substitution value in each row is selected as the result of the forced selection (a total of m elements are retained). This is to ensure that at least one measurement in each row is selected, and to prevent the situation where all elements in a row are not selected after the second round of optimal selection.

[0070] In the second round of optimization screening, the elements of the cost matrix L after forced selection are sorted in ascending order of minimum distance value, and the first j elements with the smallest minimum distance value are selected.

[0071] In the second round of optimization screening, some rows may not have any elements selected, while others may have multiple elements selected, which is acceptable. This is because for the cost matrix L, smaller matrix element values ​​represent a greater probability of association of angle measurement data. Some rows are easy to select with correct association results, while others have significant uncertainty and ambiguity in the association of angle measurement data due to factors such as the configuration between the observed satellite and the target. Therefore, for such rows, more association pairs should be selected to prevent filtering divergence during the tracking process.

[0072] Step 3: Referring to the data association results above, construct multiple sets of expanded dimension measurements and solve the measurement association probability of each set of expanded dimension measurements.

[0073] Step 3.1: Combine the results of the two rounds of screening above into the final association results and construct multiple sets of expanded dimension measurements.

[0074] Specifically, the forced selection results (m elements) of the first round and the optimal selection results (j elements) of the second round are combined to obtain the final angle measurement data association results (m+j in total) at time k. The above two rounds of screening procedures are executed once at each time step of the entire simulation time.

[0075] Association results as follows Figure 1 As shown, the value of each element in the matrix is ​​the minimum distance, corresponding to the measurement association probability (obtained through the normalization weight method in step 3.2). The position of each element corresponds to the association combination. The row where the element is located corresponds to the sequence number in the measurement set of sensor 1, and the column where the element is located represents the sequence number in the measurement set of sensor 2.

[0076] The expanded dimension measurement set after association at time k is denoted as The measurement association probability corresponding to the expanded dimension measurement in the set is denoted as The dimension expansion measure in the set is represented separately as:

[0077]

[0078] in, and The measurements acquired by sensor 1 and sensor 2 are respectively. and The observation equations for sensor 1 and sensor 2 are respectively. and The observation noise of sensors 1 and 2 are respectively. and For the elements measured by sensor 1, and The elements measured by sensor 2.

[0079] It is noted that some rows in the correlation results contain multiple correlation pairs, while each sensor observes at most one measurement per target. Therefore, each row has at most one true correlation pair. Thus, based on the correlation results of angle measurement data, the concept of measurement correlation probability is proposed. Each row contains multiple correlation pairs with corresponding specific correlation probabilities, which are calculated by normalizing the minimum distance corresponding to the correlation pair. Finally, m+j correlation pairs and their corresponding measurement correlation probabilities are obtained. The selection of j can be based on the hardware computing power and real-time requirements of practical applications.

[0080] Step 3.2: Solve for the measurement correlation probability of each group of expanded dimensions measurements.

[0081] like Figure 1 As shown, the value of each point in the matrix (minimum distance value) corresponds to the measurement association probability, the position of each point corresponds to the association combination, and the probability of each point is obtained by normalizing the weights.

[0082] Elements in the same row are grouped together, and weights are assigned using normalized cost values ​​to obtain the measured association probability for each element. This embodiment uses the first row as an example, where the association combination for the first row is L. row =[l2 l5], the measurement correlation probability corresponding to this row. The solution follows the formula:

[0083]

[0084] The mathematical notation 1. / L indicates taking the reciprocal of each element in matrix L. l2 = 8, l5 = 12, and the weights are obtained by normalization. That is, the measurements corresponding to the positions of the elements in l2. The measurement correlation probability is 0.6, and the measurement corresponding to the position of element l5 is... The probability of the measurement association is 0.4.

[0085] Step 4: The corresponding measurement correlation probability is introduced into the weight of the corrected Gaussian term in the GM-PHD filter, and a centralized parallel fusion multi-target tracking method considering the measurement correlation probability is designed.

[0086] "Considering the measurement association probability" refers to correcting the posterior Gaussian weights by measuring the association probability; "centralized parallel fusion" refers to the process of calculating and expanding the dimension of the measurement association results.

[0087] Specifically, in the Gaussian mixture-based GM-PHD closed-loop solution, it is assumed that the intensity of the newly formed target follows a Gaussian mixture distribution, considering the nonlinearity of orbital dynamics and measurement equations. The posterior intensity distribution at time k-1 can be written as:

[0088]

[0089] in, This represents the number of posterior Gaussian component terms at time k-1. This represents the weight of the h-th Gaussian component. and Let h represent the mean and variance of the h-th Gaussian component at time k-1, and let h be the posterior intensity distribution at time k-1. Mixing of Gaussian components.

[0090] The prior intensity distribution at time k is:

[0091]

[0092] in, λ represents the survival strength from time k-1 to time k. b,k (x) represents the birth intensity at time k. It is the number of Gaussian components. The corresponding weights for Gaussian classification, and These represent the mean and variance of the corresponding Gaussian components.

[0093] The posterior update strength at time k is:

[0094]

[0095] Among them, P D D represents the detection probability of the sensor. k|k-1 (x) represents the prior strength from time k-1 to time k. These are the weights corresponding to the posterior Gaussian terms of the measurement z and the Gaussian hypothesis h. and These represent the mean and variance of the corresponding Gaussian components.

[0096] The modified posterior Gaussian weight conforms to the formula:

[0097]

[0098] in, It is a measurement The weights corresponding to the posterior Gaussian terms of the Gaussian hypothesis h. For measurement The probability of association, P D This represents the detection probability of the sensor. The weights are the a priori Gaussian terms. For measurement Clutter intensity function and These are the Kalman filter parameters.

[0099] Step 5: Apply the above algorithm to the two observation satellites to achieve information fusion between the two satellites and accurate tracking of multiple targets.

[0100] The feasibility of this invention is illustrated by the following examples.

[0101] The following calculation conditions and technical parameters are set:

[0102] 1) Select 2 observation satellites and 10 target satellites in GEO orbit, for a total of 12 satellites. The distance between two observation satellites is approximately 150 km, the distance between target satellites is approximately 100 km, and the difference in the semi-major axis of the orbits of the target satellites and observation satellites is 1000 km;

[0103] 2) Set the total simulation time to 1000s. Considering the possible birth and death of the targets or their entry and exit from the sensor's field of view, set the birth time of target 5 to 200 seconds after the initial time, the birth time of target 9 to 600 seconds after the initial time, the birth time of target 10 to 300 seconds after the initial time, the death time of target 4 to 800 seconds after the initial time, and the death time of target 5 to 500 seconds after the initial time.

[0104] 3) The angular measurement accuracy of the observed stars is 1×10⁻⁶. -4 The true orbit values ​​of the target and the observed star at different times are obtained by integrating the dynamic model. The dynamic model for the target's filtered estimation adopts a model that removes the lunar gravitational perturbation. Due to the nonlinearity in the tracking system, the UKF filtering method is used.

[0105] Based on the dual-star collaborative centralized multi-target tracking method of the present invention and the above-mentioned calculation conditions and technical parameters, simulation experiments were conducted using MATLAB software.

[0106] The algorithm estimates the number of targets at different times as follows: Figure 2 As shown, its estimation results match the true values ​​over the time period, and its performance is stable in terms of target base (number) estimation. It can adapt well to the birth and death of targets caused by targets entering or leaving the sensor's field of view.

[0107] Within the tracking system, the target's GOSPA evaluation results are as follows: Figure 3 As shown, the kinematics term describes the magnitude of the target state estimation error under the association result, and this term is a linear superposition of multiple targets. The target state estimation error is large at the beginning, and converges to a smaller value as the filtering result recursively changes over time. Note that it shows a small surge followed by a decrease at 200s, 300s, and 600s. This is because new targets appear at these times, and the initial filtering stage of new targets is unstable, with a large state estimation error, which is reflected in the graph as a surge in the overall kinematics term. The Missed and False terms represent the penalty compensation for missed detections and false detections of the tracking system, respectively. Since the algorithm can estimate the target base (number) well, both of these terms are 0, and there is no penalty compensation for missed detections and false detections. The first subgraph, GOSPA, is a superposition of the kinematics, Missed, and False terms. The GOSPA graph evaluates the performance of the tracking algorithm.

[0108] Compared with the traditional single-observation platform GM-PHD tracking algorithm, the proposed algorithm has better GOSPA evaluation capabilities. Figure 4As shown, except for the algorithm used, all other tracking parameters, including angle measurement accuracy, clutter intensity, detection probability, and initial error, are the same, as are the parameters of the GOSPA evaluation system. It is evident that the proposed method significantly outperforms the single-platform GM-PHD algorithm in both target state estimation accuracy and target number estimation.

[0109] The detailed state estimation error of the target is as follows Figure 5 and Figure 6 As shown, for targets that are always within the sensor's field of view (such as...) Figure 5 As shown), the tracking results converged to a small value after initial filtering fluctuations. At a relative distance of 1000km, the three-axis position error converged to within 100m, and the three-axis velocity error converged to within 10m / s. For targets that appeared or left the sensor's field of view midway (such as...), Figure 6 As shown in the diagram, abrupt changes occurred at certain points in the error graph. This is partly due to the large initial orbit determination error immediately after the target enters the sensor's field of view, leading to a large initial error transmitted to the tracking system. Another reason is the large Gaussian spot corresponding to the target's error covariance in the initial stage, indicating significant uncertainty. However, after stable tracking, both the position and velocity errors converged to smaller values, demonstrating good tracking performance.

[0110] Therefore, the method of this invention can correctly correlate angle measurement data from different sensors and achieve centralized collaborative tracking. Compared with the traditional single-platform passive PHD tracking method, the method of this invention solves the problem of ambiguity or divergence in multi-target tracking caused by the lack of measurement information in the traditional method. Experiments have shown that the proposed method has superior performance.

[0111] 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 multi-target orbit tracking method for spaceborne autonomous passive measurement, characterized in that, include: Step 1: Establish the dynamic model of the observed spacecraft and the sensor line-of-sight measurement model, and construct a random finite set to describe the dynamic changes and uncertainties of multiple targets; Step 2: Construct a cost matrix using the minimum distance between the line-of-sight vectors of different sensors as the cost. The smaller the cost value, the greater the probability of correlation of angle measurement data. After multiple rounds of screening, the cost matrix is ​​retained. Several elements with low medium-value; Step 3: Merge the elements selected in each round to obtain the data association results, and construct the expanded dimension measurement set based on the association results. And solve for the measurement association probability corresponding to each expanded dimension measurement in the set. Specifically, Let a set of association results be The measurement correlation probability corresponding to this row is The minimum distance corresponding to normalization , Solve for the measurement correlation probability of this set of extended-dimensional measurements. : ; Step 4, Design considering measurement correlation probability The centralized parallel fusion multi-target tracking method incorporates the corresponding measurement correlation probability into the GM-PHD filter to correct the posterior Gaussian weights. , represented as: ,in It is a measurement The weights corresponding to the posterior Gaussian terms of the Gaussian hypothesis h. For measurement The probability of association, This represents the detection probability of the sensor. These are the weights corresponding to the prior Gaussian terms. For measurement Clutter intensity function , , and These are the Kalman filter parameters; Step 5: Apply steps 1-4 to the two observation satellites to achieve information fusion between the two satellites and accurate tracking of multiple targets.

2. The method according to claim 1, characterized in that, In step 1, based on the RFS theoretical framework, the states and measurements of multiple targets at time k are represented as finite sets: ， ， in, The state variable of the i-th target at time k is obtained from the absolute dynamics model; This represents the j-th measurement from the target obtained at time k, derived from the sensor line-of-sight angle measurement model; a finite set. , The elements in the space belong to the space. and , and It is a finite subset; and These represent the number of targets and measurements at the current moment, respectively.

3. The method according to claim 1 or 2, characterized in that, In step 2, the cost matrix is ​​constructed as follows: calculate the measurement set of sensor 1 at time k. Each element in the set and the measurement set of sensor 2 at time k The minimum distance between each element in the matrix is ​​used as the cost value to construct the cost matrix. : ， matrix middle This represents the minimum distance between the i-th measurement in the sensor 1 measurement set and the j-th measurement in the sensor 2 measurement set, used to evaluate the probability that the two line-of-sight vectors originate from the same target.

4. The method according to claim 3, characterized in that, The values ​​of the elements in the cost matrix are used as the correlation evaluation index for measurement associations between different sensors. The measurement association results are determined through two rounds of screening. In the two-round association method, the first round is a mandatory selection, which selects the cost matrix. Each row contains m elements with the lowest value; the second round is an optimization screening, which involves selecting the cost matrix after forced selection. Among the elements, arrange them in order of their value, and select the j elements with the smallest values.

5. The method according to claim 4, characterized in that, Step 3 includes: throughout the entire simulation cycle, a two-round screening is performed at each time step. The m+j elements after the two rounds of screening are merged to obtain the final association result and construct an expanded dimension measurement set. The measurement association probability corresponding to each measurement is calculated. Specifically, the value of each element in the association result is the cost value. Elements in the same row are grouped together, and the weights are allocated by normalizing the cost values ​​of each element to obtain the measurement association probability corresponding to each element.

6. The method according to claim 5, characterized in that, In step 3, the expanded dimension measurement set at time k is represented as follows: The measurement association probability corresponding to the expanded dimension measurement in the set is ; Dimensional expansion measurement in a set is represented as: , in and The measurements acquired by sensor 1 and sensor 2 are respectively. and The observation equations for sensor 1 and sensor 2 are respectively. and The observation noise of sensors 1 and 2 are respectively. and For the elements measured by sensor 1, and The elements measured by sensor 2.

Images