Multi-target orbit tracking method for satellite-borne autonomous passive measurement

Abstract

The invention discloses a multi-target orbit tracking method for satellite-borne autonomous passive measurement, which is applied to two observation satellites and comprises the following steps of: 1, establishing a dynamic model of a shot spacecraft and a sensor line-of-sight angle measurement model, and constructing a random finite set to describe the dynamic change and uncertainty of multiple targets; 2, constructing a cost matrix according to the minimum distance between sight vectors of different sensors, and solving an angle measurement data association result through two rounds of screening; step 3, according to a data association result, constructing multiple groups of dimension expansion measurements and solving a measurement association probability of each group of dimension expansion measurements; and step 4, introducing the corresponding measurement association probability into GM-PHD filtering to correct a posterior Gaussian weight, designing a centralized parallel fusion multi-target tracking method considering the measurement association probability, and realizing double-satellite information fusion and multi-target accurate tracking. The problem of poor tracking precision caused by high error correlation rate of angle measurement data in dimension expansion measurement generation of centralized parallel fusion under a multi-target tracking background is solved.

Description

Technical Field

[0001] The invention relates to the technical field of space non-cooperative target situation awareness, and in particular to a multi-target orbit tracking method using satellite-borne autonomous passive measurement. Background Art

[0002] With the vigorous development of aerospace technology, orbital space is becoming increasingly crowded, and a large number of space debris and satellites are operating in low-Earth orbit, and orbital safety issues are becoming increasingly prominent. In order to avoid collisions between satellites in orbit and non-cooperative space targets such as space debris, the development of space situational awareness technologies including initial orbit determination, target tracking, maneuver detection, and intention recognition has become an inevitable option. The multi-target tracking task refers to the continuous estimation of the number of targets in the field of view of the spacecraft sensor at different times and the state of each target. In addition to the common radar observation mode, space-based passive sensors are widely used in the orbital tracking of non-cooperative space targets due to their advantages such as strong concealment, large observation range, and small size. However, the target tracking of a single passive sensor platform is limited by factors such as orbital configuration, lack of measurement dimension information, and target density, and the tracking performance is poor in the face of some complex orbital conditions. Therefore, the multi-target tracking mode of multi-sensor networking and coordination has gradually become a hot topic for research and application.

[0003] Traditional multi-target tracking methods mainly rely on technologies such as data association and Kalman filtering, but these methods often perform poorly when the number of targets varies and the uncertainty of sensor data is high. In order to solve these problems, the theory of finite set statistics has been introduced into the field of multi-target tracking. Multi-target tracking methods based on random finite sets have great advantages in dealing with association uncertainty, detection uncertainty and sensor clutter. On the basis of random finite set theory, the probability hypothesis density (PHD) filter that transmits the first-order statistical moment of the system state is proposed. Faced with the multiple integrals corresponding to the multi-dimensional state quantities of the PHD filter, it is often difficult to calculate. The GM-PHD closed-loop solution form of Gaussian mixture is a common processing method.

[0004] Extended to multi-sensor multi-target tracking technology, it can be divided into centralized, distributed and hybrid types according to different data fusion structure systems. The main difference lies in whether the fusion processing is performed on the measurement or the fusion processing is performed on the a posteriori estimated state quantity. Distributed multi-target tracking technology aims to first perform single-platform tracking and then fuse the a posteriori estimated results. There are two main types: arithmetic average fusion and geometric average fusion. The centralized information fusion system sends the original measurement information obtained by each sensor to the central processor for time-space alignment, data association, tracking and other processing. This fusion method has small information loss and high data fusion accuracy, and can achieve fusion in the optimal sense. However, in the face of the lack of measurement of passive sensors such as optical cameras, how to associate the measurement information of different sensors becomes the primary problem to be solved. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a space-based passive dual-satellite collaborative centralized parallel fusion multi-target tracking method taking into account the measurement correlation probability, which solves the problem of poor tracking accuracy caused by the high miscorrelation rate of angular measurement data in the expanded-dimensional measurement generation of centralized parallel fusion in the context of multi-target tracking.

[0006] A multi-target orbit tracking method for spaceborne autonomous passive measurement comprises the following steps:

[0007] Step 1, construct a random finite set based on the dynamic model of the captured spacecraft and the sensor line of sight angle measurement model;

[0008] Step 2: construct a cost matrix based on the minimum distance between the sight vectors of different sensors, and solve the angle measurement data association result through two rounds of screening;

[0009] Step 3, referring to the above data association results, construct multiple groups of extended dimension measurements and solve the measurement association probability of each group of extended dimension measurements;

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

[0011] Step 5: Apply the above algorithm to two observation satellites to achieve dual-satellite information fusion and precise tracking of multiple targets.

[0012] As a preferred embodiment, step 1 is specifically as follows: step 1.1, establishing a spacecraft dynamics model and a satellite optical camera sight angle measurement model for a spacecraft subjected to the non-spherical shape of the earth and the gravitational perturbation of the moon in the geocentric inertial system; step 1.2, using a random finite set method to model the multi-target tracking problem to describe the dynamic changes and uncertainties of the targets. Based on the random finite set theoretical framework, the states and measurements of the multi-targets can be represented as finite sets X k and Z k

[0013]

[0014]

[0015] in,

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

[0017] Preferably, step 2 is specifically as follows: step 2.1, constructing a minimum distance model between line of sight vectors of different sensors to evaluate the possibility that two line of sight vectors come from the same target; step 2.2, constructing a measurement association cost matrix L through the minimum distance model, using the values ​​of the elements in the cost matrix as correlation evaluation indicators of the measurement associations between different sensors, and determining the measurement association results through two rounds of screening.

[0018] Preferably, the first round selection method in step 2.2 is: in the first round of mandatory selection, the element with the smallest replacement value is selected in each row as the result of mandatory selection. This is to ensure that at least one measurement is selected for each row, and to prevent the situation where all elements of a row are not selected after two rounds of optimal selection.

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

[0020] Preferably, step 3 is specifically as follows: step 3.1, combining the above two rounds of screening results into the final correlation results, and constructing multiple groups of expanded-dimensional measurements; step 3.2, solving the measurement correlation probability of each group of expanded-dimensional measurements.

[0021] Preferably, step 3.1 is specifically as follows: combining the mandatory selection results of the first round and the optimized 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 in each time step of the entire simulation time.

[0022] The dimension-expanding measurement can be written as: in and are the measurements obtained by sensor 1 and sensor 2 respectively, and are the observation equations of sensor 1 and sensor 2 respectively, and are the observation noise of sensors 1 and 2, respectively, and is the element being measured by sensor 1, and is the element being measured by sensor 2.

[0023] As a preferred embodiment, step 3.2 is specifically as follows: the expanded dimension measurement set after association is recorded as The measurement association probability corresponding to the expanded dimension measurement in the set is Assume that the associated combination of a row is L row =[l2 l5], the measured association probability corresponding to this row Solve the compliance

[0024] Preferably, step 4 is as follows: introducing the corresponding measurement association probability into the GM-PHD filter to modify the weight of the Gaussian term, and designing a centralized parallel fusion multi-target tracking method considering the measurement association probability.

[0025] As a preferred method, the method of introducing the measurement association probability to correct the Gaussian term weight in step 4 is: the modified posterior Gaussian weight conforms to the formula in is the weight corresponding to the posterior Gaussian term of the measurement z and Gaussian hypothesis h, is the associated probability of measuring z, P D is the detection probability of the sensor, is the weight corresponding to the prior Gaussian term, is the measurement z, is the function for measuring the z clutter intensity, and are the Kalman filter parameters.

[0026] Beneficial effects:

[0027] (1) The present invention solves the problem of poor tracking accuracy caused by high misassociation rate of angle measurement data in the generation of extended-dimensional measurements by centralized parallel fusion in the context of multi-target tracking, and proposes a centralized parallel fusion multi-target tracking method that considers the measurement association probability;

[0028] (2) The present invention can correctly correlate measurements from different sensors through algorithm improvements, ultimately achieving dual-satellite coordinated stable tracking without changing existing passive sensor equipment;

[0029] (3) The present invention solves the angle measurement data association result through two rounds of screening, which can ensure that each row of angle measurement data has associated data, and can 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) The present invention introduces the measurement association probability to correct the weight of the Gaussian term, so that some Gaussian terms can be quickly pruned away by the post-processing algorithm, thereby ensuring the running speed and performance of the algorithm;

[0031] (5) The present invention tracks multiple targets through dual-satellite collaboration, thereby solving the problem of missing measurement information and weak observability of a single passive sensor and improving the tracking accuracy of the target. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0034] Figure 3 It is a target GOSPA evaluation diagram of one embodiment of the present invention;

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

[0036] Figure 5 A non-full-time target state estimation error diagram of an embodiment of the present invention;

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

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] The present invention discloses a multi-target orbit tracking method for satellite-borne autonomous passive measurement. Aiming at the problem that the mis-association rate of angular measurement data in the generation of centralized parallel fusion extended-dimensional measurement leads to poor tracking accuracy, a space-based passive dual-satellite collaborative centralized parallel fusion multi-target tracking method considering the measurement association probability is proposed.

[0040] Combination Figure 1 , a multi-target orbit tracking method for spaceborne autonomous passive measurement, comprising the following steps:

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

[0042] Step 1.1, establish the spacecraft dynamic model and the onboard optical camera line of sight angle measurement model under the geocentric inertial system and the non-spherical shape of the earth and the gravitational perturbations of the moon.

[0043] Specifically, the spacecraft dynamics model is established in the geocentric inertial system. The origin of the coordinate system is located at the center of mass of the earth, the x-axis points to the vernal equinox, the z-axis points to the north celestial pole of the earth, and the y-axis and the xz-axis form a right-handed system. Ignoring the influence of solar light pressure, the absolute dynamics model including the non-spherical perturbation of the earth and the gravitational perturbation of the moon is constructed as follows:

[0044]

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

[0046] The following satellite optical camera sight angle measurement model is constructed, assuming that the state of the target in the inertial system at time k is: The state quantity of the observed star in the inertial system Then the passive sensor only measures the angle and the observation equation can be written as:

[0047]

[0048] Among them, z k is the measurement from the target at time k, α k and e k For z k The elements in To measure noise.

[0049] Line of sight vectori los The definition of is as follows:

[0050]

[0051] Define the coordinate transformation matrix from the geocentric inertial system to the LVLH coordinate system as Φ el , then the unit sight vector in the LVLH coordinate system can be expressed as:

[0052]

[0053] α k and e k denote the measured azimuth and altitude respectively and are defined by the following formula:

[0054]

[0055]

[0056] in, It obeys 0 mean and the covariance matrix is ​​R αe Gaussian distribution.

[0057] Step 1.2, use the random finite set method to model the multi-target tracking problem to describe the dynamic changes and uncertainties of the targets. Based on the random finite set theory framework, the states and measurements of 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, represents the state of the i-th target at time k, represents the jth measurement at time k, and the elements in the finite set belong to the space and and are finite subsets of sets x and z respectively, N k and M k Respectively represent the number of targets and measurements at the current moment.

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

[0062] Step 2.1, calculate the minimum distance between the sight vectors of different sensors as the cost value to construct a cost matrix, and use the value of the elements in the cost matrix as the correlation evaluation index of the measurement association between different sensors to evaluate the possibility that the two sight vectors come from the same target;

[0063] Step 2.2, two rounds of screening are performed on the elements of the cost matrix to determine the measurement correlation results.

[0064] Specifically, it is assumed that the spacecraft target is a point target, that is, each target only generates one sight vector when observed by a single star. Ideally, when two observation stars observe the same target, their sight vectors should intersect. Affected by angle measurement errors, camera installation errors, and image distortion errors, the sight vectors from the same target may not intersect. However, the minimum distance corresponding to any two sight vectors between different observation stars can be calculated. The minimum distance corresponding to the sight vectors from the same target should be a smaller value, while the minimum distance corresponding to the sight vectors from different targets should be a larger value.

[0065] Considering the clutter and missed detection of the sensor system, assume that the set of measurements observed by sensor 1 at time k is The set of measurements observed by sensor 2 is If no measurement preprocessing method is used, the measurements in sensor 1 have the same probability of being fused with the measurements in sensor 2, and the number of measurements at time k after fusion and dimension expansion is mn. Such a surge in the number of dimension expansion measurements cannot meet the real-time requirements of subsequent multi-target tracking methods, and this type of dimension expansion measurement retains a large number of correlation results between false measurements or between false measurements and true measurements, which seriously affects the target tracking accuracy or causes target tracking divergence. Therefore, this paper uses the minimum distance as an indicator to evaluate the correlation correlation of measurements from the same target, constructs a measurement dimension expansion fitting method that meets the real-time tracking requirements, and introduces the measurement correlation probability into the PHD tracking method to adjust the weight of the corresponding Gaussian component.

[0066] Solve for the measurement set of sensor 1 at time k Each element in and the measurement set of sensor 2 at time k The minimum distance between each element in the measurement set of sensor 1 and the minimum distance between the jth measurement in the measurement set of sensor 2 is l ij , construct the cost matrix L.

[0067]

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

[0069] The schematic diagram of the correlation of the double-satellite angle measurement data is as follows: Figure 1 As shown, in the first round of mandatory selection, the element with the smallest replacement value is selected in each row as the result of mandatory selection (a total of m elements are retained). This is to ensure that at least one measurement is selected in each row to prevent the situation where all elements of a row are not selected after the second round of optimization selection.

[0070] In the second round of optimization screening, the elements of the cost matrix L after mandatory selection are arranged in ascending order of the 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 some rows may have multiple elements selected, which is acceptable. Because for the cost matrix L, the smaller the matrix element value, the greater the possibility of angle measurement data association. Some rows are easy to select the correct association results, while some rows have great uncertainty and ambiguity in the association of angle measurement data due to configuration problems between the observation satellite and the target. Therefore, for such rows, several pairs of association combinations should be selected to prevent filter divergence during the tracking process.

[0072] Step 3, referring to the above data association results, construct multiple groups of expanded dimension measurements and solve the measurement association probability of each group of expanded dimension measurements.

[0073] Step 3.1, combine the above two rounds of screening results into the final correlation results and construct multiple sets of expanded dimension measurements.

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

[0075] The associated results are 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 by the normalized 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 measurement sequence number in the measurement set of sensor 1, and the column where the element is located represents the measurement sequence number in the measurement set of sensor 2.

[0076] The expanded dimension measurement set after association at time k is recorded as The measurement association probability corresponding to the expanded dimension measurement in the set is recorded as The expanded dimension measures in the set are expressed individually as:

[0077]

[0078] in, and are the measurements obtained by sensor 1 and sensor 2 respectively, and are the observation equations of sensor 1 and sensor 2 respectively, and are the observation noise of sensors 1 and 2, respectively, and is the element being measured by sensor 1, and is the element being measured by sensor 2.

[0079] Note that some of the association results have multiple pairs of association combinations selected in the row, and each sensor produces at most one measurement for each target, so there is at most one pair of true association combinations in each row. Therefore, based on the angle measurement data association results, the concept of measurement association probability is proposed. Multiple association combinations in each row have corresponding specific association probabilities, which are obtained by normalizing the minimum distance corresponding to the association combination. Finally, m+j association combinations and their corresponding measurement association probabilities are obtained. The selection of j can be selected based on the hardware computing power and real-time requirements in actual applications.

[0080] Step 3.2, solve the measurement association probability of each group of expanded-dimensional measurements.

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

[0082] The elements in the same row are taken as a group, and weights are assigned by normalizing the cost value to obtain the measurement association probability corresponding to each element. This embodiment takes the first row as an example, and the association combination of the first row is L row =[l2 l5], the measured association probability corresponding to this row The solution obeys the following formula:

[0083]

[0084] Mathematical notation 1. / L means taking the inverse of the elements of matrix L. l2 = 8, l5 = 12, and the weights are obtained by normalization. That is, the measurement corresponding to the position of the l2 element The measurement association probability is 0.6, and the measurement corresponding to the l5 element position The measured association probability is 0.4.

[0085] In step 4, the corresponding measurement association probability is introduced into the weight of the modified Gaussian term in the GM-PHD filter, and a centralized parallel fusion multi-target tracking method considering the measurement association probability is designed.

[0086] “Considering the measured association probability” means correcting the posterior Gaussian weight by measuring the association probability; “centralized parallel fusion” refers to the process of calculating and expanding the measurement association results.

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

[0088]

[0089] in, represents the number of posterior Gaussian components at time k-1, represents the weight of the h-th Gaussian component, and represents the mean and variance of the hth Gaussian component at time k-1, and the posterior intensity distribution at time k-1 is A mixture of Gaussian components.

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

[0091]

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

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

[0094]

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

[0096] The modified posterior Gaussian weights conform to the formula:

[0097]

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

[0099] Step 5: Apply the above algorithm to two observation satellites to achieve dual-satellite information fusion and precise tracking of multiple targets.

[0100] The feasibility of the present invention is illustrated with reference to the following examples.

[0101] Set the following calculation conditions and technical parameters:

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

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

[0104] 3) The angular measurement accuracy of the observed stars is 1×10 -4 rad, the orbital true values ​​of the target and the observed star at different times are obtained by integrating the dynamic model. The filtered estimated dynamic model of the target adopts a model with the lunar gravitational perturbation removed. The UKF filtering method is used in the tracking system due to nonlinearity.

[0105] Based on the dual-satellite coordinated centralized multi-target tracking method of the present invention and the above-set calculation conditions and technical parameters, a simulation experiment was carried out using MATLAB software.

[0106] The algorithm estimates the number of targets at different times as follows: Figure 2 As shown, the estimation result is consistent with the true value within the time length, has stable performance in target cardinality (number) estimation, and can better adapt to the birth and death of targets caused by targets entering or leaving the sensor's field of view.

[0107] In the tracking system, the GOSPA evaluation results of the target are as follows: Figure 3 As shown in the figure, the kinematics term describes the size of the target's state estimation error under the association result. This term is the linear superposition of multiple targets. The target's state estimation error is large at the beginning, and the recursive filtering result converges to a smaller value over time. It is noted that it has a small surge and then a downward trend at 200s, 300s and 600s. This is because new targets appear at these moments. The initial filtering stage of the new targets is unstable, and the state estimation error is large, which is reflected in the figure and causes a surge in the overall kinematics term. The Missed term and the False term represent the penalty compensation for missed detection and false detection of the tracking system, respectively. Since the algorithm can better estimate the target cardinality (number), the values ​​of these two items are both 0, and there is no penalty compensation for missed detection and false detection. The first sub-graph GOSPA term is the superposition of the kinematics term, the Missed term and the False term. 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 a better GOSPA evaluation Figure 4As shown in the figure. Except for the algorithm used, the other tracking parameters including angle measurement accuracy, clutter intensity, detection probability, and initial error are set to be the same, and the GOSPA evaluation system parameters are also the same. It can be seen that the proposed method is significantly better than the single-platform GM-PHD algorithm in terms of 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 in the figure, the tracking results converge to a smaller value after the initial filtering fluctuation. At a relative distance of 1000km, the three-axis position error can be converged to within 100m, and the three-axis velocity error can be converged to within 10m / s. Figure 6 As shown in the figure, sudden changes occur at some moments in the error graph. On the one hand, the initial orbit determination error is large after the target just enters the sensor field of view, which leads to a large initial error in the tracking system. On the other hand, the Gaussian spot corresponding to the error covariance in the initial stage of the target is large and the uncertainty is strong. However, after stable tracking, both the position error and the velocity error converge to smaller values, and the system shows a good tracking effect.

[0110] Therefore, the method of the present invention can correctly associate the angle measurement data of different sensors and realize centralized collaborative tracking. Compared with the traditional single-platform passive PHD tracking method, the method of the present invention solves the problem of fuzzy or divergent multi-target tracking caused by the lack of measurement information in the traditional method. Experiments have proved that the proposed method has superior performance.

[0111] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A multi-target orbit tracking method for satellite-borne autonomous passive measurement, characterized in that: include: Step 1: Establish the dynamic model of the captured spacecraft and the sensor line-of-sight angle measurement model and construct a random finite set to describe the dynamic changes and uncertainties of multiple targets; Step 2: The minimum distance between the sight vectors of different sensors is used as the cost value to construct the cost matrix L. The smaller the cost value, the greater the probability of the angle measurement data being associated. After multiple rounds of screening, several elements with small cost values ​​in the cost matrix L are retained; Step 3: Merge the elements selected in each round to obtain data association results, and build an expanded dimension measurement set based on the association results. And solve the measurement association probability corresponding to each expanded dimension measurement in the set Step 4: Design considerations to measure association probability The centralized parallel fusion multi-target tracking method introduces the corresponding measurement association probability into the GM-PHD filter to correct the posterior Gaussian weight Step 5: Apply steps 1-4 to two observation satellites to achieve dual-satellite information fusion and precise 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, represents the state quantity of the i-th target at time k, obtained by the absolute dynamics model; represents the jth measurement from the target at time k, obtained by the sensor line of sight angle measurement model; the finite set X k , Z k The elements in belong to the space and and is a finite subset; N k and M k Respectively represent the number of targets and measurements at the current moment.

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 and the measurement set of sensor 2 at time k The minimum distance between each element in is used as the cost value to construct the cost matrix L: In the matrix L ij represents the minimum distance between the i-th measurement in the measurement set of sensor 1 and the j-th measurement in the measurement set of sensor 2, which is used to evaluate the probability that the two line of sight vectors come 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 correlation evaluation indicators of the measurement associations between different sensors, and the measurement association results are determined through two rounds of screening. In the two-round association method, the first round is a mandatory selection, and m elements with the smallest cost value in each row of the cost matrix L are selected; the second round is an optimization screening, and the elements of the cost matrix L after mandatory selection are arranged in order according to the size of the cost value, and the first j elements with the smallest values ​​are selected.

5. The method according to claim 4, characterized in that Step 3 includes: in the entire simulation cycle, two rounds of screening are performed in each time step, the m+j elements after the two rounds of screening are merged to obtain the final correlation result and build an expanded dimension measurement set, and the measurement correlation probability corresponding to each measurement is calculated. Specifically, the numerical value of each element in the correlation result is the cost value, and the elements in the same row are taken as a group. The cost values ​​of each element are normalized and weighted 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 expressed as The measurement association probability corresponding to the expanded dimension measurement in the set is The dimensionality expansion measurement in the set is expressed as: in and are the measurements obtained by sensor 1 and sensor 2 respectively, and are the observation equations of sensor 1 and sensor 2 respectively, and are the observation noise of sensors 1 and 2, respectively, and is the element being measured by sensor 1, and is the element being measured by sensor 2.

7. The method according to claim 5, characterized in that In step 3, let a set of association results be L row =[l a l b ], the measured association probability corresponding to this row is By normalizing the corresponding minimum distance l a , l b Solve the measurement association probability of this set of expanded-dimensional measurements 8. The method according to claim 1, characterized in that In step 4, the modified posterior Gaussian weights conform to the formula: in It is measurement The weights corresponding to the posterior Gaussian terms of the Gaussian hypothesis h, For measurement The association probability, P D is the detection probability of the sensor, is the weight corresponding to the prior Gaussian term, For measurement Clutter intensity function, and are the Kalman filter parameters.

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