Passive multi-sensor multi-target angular trajectory association method

Abstract

The invention provides a passive multi-sensor multi-target angular trajectory association method, and relates to the technical field of optical target detection, and the method specifically comprises the steps: obtaining angular trajectories obtained by observing all targets through two observation platforms, and obtaining an angular trajectory association relationship set; according to each association matching relationship in the angular trajectory association relationship set, obtaining a target three-dimensional position estimation result; obtaining a target spatial position according to the target three-dimensional position estimation result; obtaining a first observed quantity according to the target spatial position; obtaining a second observed quantity, and carrying out topological structure matching according to the first observed quantity and the second observed quantity to obtain topological structure matching error statistics; obtaining inclination angle difference statistics, and obtaining association cost statistics of each association matching relation according to the topological structure matching error statistics and the inclination angle difference statistics; and obtaining an angle trajectory association result according to the association cost statistics and a preset judgment threshold. According to the invention, the accuracy of angle trajectory association in a dense target scene can be improved.

Description

Technical Field

[0001] This application relates to the field of optical target detection technology, and in particular to a passive multi-sensor multi-target angular trajectory correlation method. Background Technology

[0002] In optical detection systems, passive single sensors can only acquire target orientation information, constituting incomplete observation. Multi-sensor collaborative detection is necessary to determine the target's three-dimensional state. Before calculating the target's three-dimensional state, it is crucial to determine the homology of the target's two-dimensional angular trajectories output by multiple sensors. This involves associating angular trajectories belonging to the same target. Incorrect association results will generate "ghost" targets. The quality of angular trajectory association directly determines the subsequent target state estimation performance; therefore, research on multi-platform, multi-target angular trajectory association algorithms is of paramount importance.

[0003] In existing passive multi-sensor multi-target angular trajectory association schemes, spatial consistency assumptions are often used to test the hypothesis of angular trajectory association. Inclination difference is a commonly used spatial consistency constraint. The angular trajectory statistical test association algorithm based on inclination difference essentially utilizes this spatial geometric constraint. However, relying solely on spatial geometric constraints, in dense target scenarios, is prone to erroneous associations due to measurement errors and the influence of observation angle, resulting in poor association performance.

[0004] Therefore, how to improve the accuracy of corner trajectory correlation in dense target scenarios is an urgent problem to be solved in this field. Summary of the Invention

[0005] To address the aforementioned technical issues, this application provides a passive multi-sensor multi-target angular trajectory association method, which can improve the accuracy of angular trajectory association in dense target scenarios.

[0006] The technical solution provided in this application is as follows: A passive multi-sensor multi-target angular trajectory association method includes: Obtain the angular trajectories obtained by the first and second observation platforms from observing all targets, and based on the angular trajectories, traverse all possible angular trajectory associations to obtain a set of angular trajectory association relationships; Based on each association matching relationship in the set of angular trajectory association relationships, cross-localization is performed to obtain the target's three-dimensional position estimation result under each association matching relationship; Based on the target's three-dimensional position estimation result, the distance between the target and the first observation platform is obtained. The target's three-dimensional position estimation result is then projected along the line of sight of the first observation platform to obtain the target's spatial position. The target spatial location is projected onto the observation space of the second observation platform to obtain the first observation measurement; obtaining a second observation amount of a target in an observation space of a second observation platform, performing topological structure matching according to the first observation amount and the second observation amount, and obtaining a topological structure matching error statistic; obtaining an inclination difference statistic, and obtaining a correlation cost statistic of each correlation matching relationship according to the topological structure matching error statistic and the inclination difference statistic; obtaining an angle trajectory correlation result according to the correlation cost statistic of each correlation matching relationship and a preset decision threshold.

[0007] Preferably, in the passive multi-sensor multi-target angle trajectory correlation method, the topological structure matching is performed according to the first observation amount and the second observation amount to obtain a topological structure matching error statistic, including: performing topological structure matching according to the first observation amount and the second observation amount to determine a topological structure matching error; obtaining a topological structure matching error statistic according to the topological structure matching error.

[0008] Preferably, in the passive multi-sensor multi-target angle trajectory correlation method, the angle trajectory correlation relationship set is obtained by traversing all angle trajectory correlation possibilities based on the angle trajectory, including: the angle trajectory correlation relationship set is obtained by traversing all angle trajectory correlation possibilities based on the angle trajectory and a preset correlation criterion, and the specific expression is: ; ; wherein, indicates that all angle trajectory correlation possibilities are traversed based on the angle trajectory of each observation platform at the current moment, indicates all possible angle trajectory correlation relationship sets, indicates an n-th correlation matching relationship in the angle trajectory correlation relationship set, is the number of observation platforms, corresponds to a first observation platform, corresponds to a second observation platform, indicates the number of angle trajectory strips of an observation platform numbered ; is a matrix, , indicates a combination number, indicates the number of angle trajectory strips of a first observation platform, indicates the number of angle trajectory strips of a second observation platform, indicates azimuth angle at the current moment, indicates Pitch angle at all times Representing angular locus The number of measurement points in the middle, Indicates the number is The first observation platform Angle trajectory.

[0009] Preferably, in the passive multi-sensor multi-target angular trajectory association method, the step of performing cross-localization based on each association matching relationship in the angular trajectory association relationship set to obtain the target's three-dimensional position estimation result under each association matching relationship includes: Based on the set of angular trajectory relationships Each associated matching relationship ,like Then, by using cross-location, each associated matching relationship can be obtained. The target's three-dimensional position estimation result is expressed as follows: ; in, The first observation platform represents the... The angular trajectory and the second observation platform's first The trajectories of the bars and corners are related together. This represents the result of the target's three-dimensional position estimation. The first observation platform represents the... Angular trajectory, The second observation platform represents the first Angular trajectory, This represents the function for calculating cross-location.

[0010] Preferably, in the passive multi-sensor multi-target angular trajectory association method, the step of obtaining the distance between the target and the first observation platform based on the target's three-dimensional position estimation result, and projecting the target's three-dimensional position estimation result along the line of sight of the first observation platform to obtain the target's spatial position, includes: Based on the target's three-dimensional position estimation results The distance between the target and the first observation platform is obtained, and the three-dimensional position estimation result of the target is calculated. Projecting along the line of sight of the first observation platform, while ensuring that the observation topology of the first observation platform remains unchanged, yields the target's spatial position, specifically expressed as: ; ; in, Indicates the spatial location of the target. This indicates the distance between the target and the first observation platform. Represents the L2 norm. Indicates the location of the first observation platform. The first observation platform represents the... The line-of-sight vector of the angle trajectory.

[0011] Preferably, in the passive multi-sensor multi-target angular trajectory association method, the expression for the first observation is: ; in, This represents the first observation. Indicates the location of the second observation platform. This represents the observation model of the observation platform to the target. The inputs are the target position and the observation platform position, and the outputs are the measured azimuth and elevation angles. The expression for the second observation is: ; in, This indicates the second observation. express The azimuth angle of the second observation platform at any given time. express The pitch angle of the second observation platform at any given time. Representing angular locus The number of measurement points in the middle, The second observation platform represents the first Angle trajectory.

[0012] Preferably, in the passive multi-sensor multi-target angular trajectory association method, the step of performing topology matching based on the first observation and the second observation, and determining the topology matching error, includes: According to the first observation and the second observation To perform topology matching, the topology matching error is determined based on the definition of a hyperedge in a binary tuple. The specific expression is as follows:

[0013] in, This represents the topology matching error. Indicates matching based on association relationships Find in the first observation Zhongyu Associative matching vertices, Indicates the second observation The Middle One element, Indicates matching based on association relationships Find in the first observation Zhongyu Associative matching vertices, Indicates the second observation The Middle One element, As an indicator function, if matched according to association relationships Unable to obtain from the first observation Find with or If the vertices are associated and matched, then If the value is 0, then take 1; otherwise, take 1. The norm of a vector.

[0014] Preferably, in the passive multi-sensor multi-target angular trajectory association method, obtaining the topology matching error statistic based on the topology matching error includes: Assuming the topology matching error Distance metric in the expression Follows a mean of 0 and a variance of The Gaussian distribution is used to obtain the topology matching error statistic, the specific expression of which is: ; ; in, This represents the statistical value of the topology matching error. Indicates the first observation The total number of elements in This represents the chi-square distribution.

[0015] Preferably, in the passive multi-sensor multi-target angular trajectory association method, obtaining the association cost statistic for each association matching relationship based on the topology matching error statistic and the tilt angle difference statistic includes: Based on the topology matching error statistics And the tilt angle difference statistics, to obtain each association matching relationship. The correlation cost statistic is expressed as follows: ; ; ; ; in, Indicates the relationship between associations and matching. The aforementioned correlation cost statistics, This represents the inclination angle difference statistic. Representing angular locus angular locus Deadline Observational statistics at any given time It follows a chi-square distribution with 1 degree of freedom. Representing angular locus angular locus Deadline The number of co-view trajectory points at any given time. Indicates the difference in tilt angle. for , The angle between the defined plane and the reference plane. for , The angle between the defined plane and the reference plane. Follows a mean of 0 and a variance of Gaussian distribution, This represents the vector pointing from the first observation platform to the second observation platform. This represents the line-of-sight vector of the first observation platform. This represents the line-of-sight vector of the second observation platform. express variance express The variance.

[0016] Preferably, in the passive multi-sensor multi-target angular trajectory association method, the angular trajectory association result is obtained based on the association cost statistics and preset decision threshold for each association matching relationship, including: Each association matching relationship The associated cost statistics As a cost function, the changing pattern of this cost function is monitored, and a preset decision threshold is defined as follows. , And based on the first preset formula, the target association matching relationship is determined from the set of angular trajectory association relationships. As the result of the angular trajectory association, the expression of the first preset formula is: ; in, Indicates the significance level. Indicates the confidence interval. Describing the degrees of freedom as The chi-square distribution.

[0017] The above technical solution involves acquiring the angular trajectories obtained from observations of all targets by the first and second observation platforms, and based on these angular trajectories, traversing all possible angular trajectory associations to obtain a set of angular trajectory association relationships; performing cross-localization based on each association matching relationship in the set to obtain the target's three-dimensional position estimation result under each association matching relationship; obtaining the distance between the target and the first observation platform based on the target's three-dimensional position estimation result, and projecting the target's three-dimensional position estimation result along the line of sight of the first observation platform to obtain the target's spatial position; projecting the target's spatial position onto the observation space of the second observation platform to obtain the first observation; acquiring the second observation of the target in the observation space of the second observation platform, and performing topological structure matching based on the first and second observations to obtain the topological structure matching error statistics; acquiring the tilt angle difference statistics, and obtaining the association cost statistics for each association matching relationship based on the topological structure matching error statistics and the tilt angle difference statistics; and obtaining the angular trajectory association result based on the association cost statistics for each association matching relationship and a preset decision threshold.

[0018] It can be seen that the above technical solution considers the introduction of the target's topological structure features on the basis of the existing tilt angle difference spatial geometric constraints, which can further improve the accuracy of angular trajectory correlation in dense target scenarios. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the tilt angle difference; Figure 2 This is a flowchart illustrating a passive multi-sensor multi-target angular trajectory association method. Figure 3 This is a schematic diagram of topology matching. Figure 4 This is a schematic diagram of a typical simulation scenario; Figure 5 A graph showing the correlation accuracy over time; Figure 6a A schematic diagram of the observation results on the azimuth-elevation plane of the platform; Figure 6b This is a schematic diagram of the projection of the cross-location of the associated matching relationship 1 onto the observation space of platform 2; Figure 6c This is a schematic diagram of the projection of the cross-location of the associated matching relationship 2 into the observation space of platform 2; Figure 6d This is a schematic diagram of the projection of the cross-location of the associated matching relationship 3 into the observation space of platform 2; Figure 7 The graph shows the change in the accuracy of angular trajectory association with angle measurement error. Figure 8 This is a graph showing the change in angular trajectory association accuracy as a function of the initial target spacing. Detailed Implementation

[0021] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] In the embodiments provided in this application, it should be understood that the disclosed system can be implemented in other ways. The system embodiments described below are merely illustrative. For example, the division of units and modules is only a logical functional division, and there may be other division methods in actual implementation. For example, multiple units or modules may be combined, integrated into another system, or some features may be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed may be through some interfaces, indirect coupling or communication connection of devices or modules, and may be electrical, mechanical, or other forms.

[0023] In addition, each functional unit in the various embodiments of this application can be integrated into a single processor, or each unit can be a separate device, or two or more units can be integrated into a single device; each functional unit in the various embodiments of this application can be implemented in hardware or in the form of hardware plus software functional units.

[0024] It should be understood that the use of terms such as "system," "device," "unit," and / or "module" in this application is merely one method of distinguishing different components, elements, parts, sections, or assemblies at different levels. However, if other terms can achieve the same purpose, they may be replaced by other expressions.

[0025] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "a plurality of" or "several" means two or more, unless otherwise explicitly specified.

[0026] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which this application can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size should still fall within the scope of the technical content disclosed in this application, provided that they do not affect the effects and purposes that this application can produce.

[0027] Existing angular trajectory statistical verification and association algorithms based on tilt angle difference essentially utilize the spatial geometric constraint of tilt angle difference. However, relying solely on spatial geometric constraints results in poor association performance in dense target scenarios and is prone to generating erroneous associations.

[0028] An angular trajectory statistical test association algorithm based on tilt angle difference: Spatial consistency assumptions are often used to test the association of angular trajectories. Tilt angle difference is a commonly used spatial consistency constraint, as illustrated in the diagram. Figure 1 As shown.

[0029] definition Tilt angle difference at any moment ,in, for , The angle between the defined plane and the reference plane. for , The angle between the defined plane and the reference plane. This represents the vector pointing from the first observation platform to the second observation platform. This represents the line-of-sight vector of the first observation platform. This represents the observation line-of-sight vector of the second observation platform. Figure 1 In the diagram, the first observation platform is platform S1, and the second observation platform is platform S2. If the two angular trajectories observed by the two platforms originate from the same target, then the tilt angle difference should be 0 if measurement error is not considered. Follows a mean of 0 and a variance of The Gaussian distribution.

[0030] Based on the above definitions, several statistical measures for observation times are given. The expression is as follows: ; ; in, Representing angular locus angular locus Deadline Observational statistics at any given time Obeying a degree of freedom of 1 Chi-square distribution express variance express variance Indicates deadline The number of trajectory points at any given time.

[0031] The embodiments in this application are written in a progressive manner.

[0032] like Figure 2 As shown, this application provides a passive multi-sensor multi-target angular trajectory association method, including: S101. Obtain the angular trajectories obtained by the first and second observation platforms from observing all targets, and based on the angular trajectories, traverse all possible angular trajectory associations to obtain a set of angular trajectory association relationships; In S101, specifically, the angular trajectory measurement information obtained by the first and second observation platforms from observing all targets is acquired. The number of targets can be set based on actual needs; this application does not impose specific limitations on it. These targets are denoted as follows: The first observation platform The expression for the angle locus is: , =1,2, =1,2, ; in, Indicates the number is The first observation platform Angular trajectory, This is the number of the observation platform. The time corresponds to the first observation platform. This corresponds to the second observation platform. Indicates the number is The number of angular trajectories on the observation platform. express Azimuth angle at time, express Pitch angle at all times Representing angular locus The number of measurement points, i.e., the length of the angular trajectory. The purpose of angular trajectory association is to link the angular trajectories of different platform sensors belonging to the same target together. Without considering target occlusion throughout the entire detection process, one angular trajectory can be associated with at most one other angular trajectory.

[0033] In some embodiments, one implementation of this step specifically includes: based on the angular trajectory and a preset association criterion, traversing all possible angular trajectory associations to obtain a set of angular trajectory association relationships.

[0034] Specifically, up to the current moment Based on the angular trajectories observed by the first and second observation platforms, and under the predefined association criteria (e.g., the "one-to-one" association assumption, where an angular trajectory is associated with at most one other angular trajectory), all possible angular trajectory associations are traversed to obtain the set of angular trajectory association relationships, specifically expressed as: ; in, This indicates that, based on the current moment, the angular trajectories of each observation platform have traversed all possible angular trajectory associations. Represents the set of all possible angular trajectory relationships. This represents the nth association match in the set of angular trajectory association relationships. It is The matrix, , Represents the number of combinations. This indicates the number of angular trajectories on the first observation platform. This indicates the number of angular trajectories of the second observation platform. This represents the total number of ways to choose one number from l numbers. It relates to the set of angular locus relationships. Each association matching relationship Then, proceed with the subsequent steps S102-S106 one by one.

[0035] S102. Based on each association matching relationship in the set of angular trajectory association relationships, perform cross-localization to obtain the target's three-dimensional position estimation result under each association matching relationship; In S102, specifically, based on each association matching relationship in the angular trajectory association relationship set... Cross-positioning is performed based on the corresponding angular trajectories of the first and second observation platforms to obtain the target's three-dimensional position estimation results under each associated matching relationship.

[0036] In some embodiments, one implementation of this step specifically includes: based on the set of angular trajectory association relationships. Each associated matching relationship ,like Then, by using cross-location, each associated matching relationship can be obtained. The target's three-dimensional position estimation result is expressed as follows: ; in, The first observation platform represents the... The angular trajectory and the second observation platform's first The trajectories of the bars and corners are related together. This represents the result of the target's three-dimensional position estimation. The first observation platform represents the... Angular trajectory, The second observation platform represents the first Angular trajectory, This represents the function for calculating cross-location.

[0037] S103. Based on the target's three-dimensional position estimation result, obtain the distance between the target and the first observation platform, and project the target's three-dimensional position estimation result along the line of sight of the first observation platform to obtain the target's spatial position; In S103, specifically, based on the target's three-dimensional position estimation result obtained from the cross-positioning solution, the distance between the target and the first observation platform is obtained. The target's three-dimensional position estimation result is projected along the line of sight of the first observation platform. While ensuring that the observation topology of the first observation platform remains unchanged, the target's spatial position is calculated.

[0038] In some embodiments, one implementation of this step specifically includes: based on the target's three-dimensional position estimation result... The distance between the target and the first observation platform is obtained. The estimated three-dimensional position of the target is then projected along the line of sight of the first observation platform. While ensuring that the observation topology of the first observation platform remains unchanged, the spatial position of the target is obtained, specifically expressed as: ; ; in, Indicates the spatial location of the target. This indicates the distance between the target and the first observation platform. Represents the L2 norm. Indicates the location of the first observation platform. The first observation platform represents the... The line-of-sight vector of the angle trajectory.

[0039] S104. Project the target spatial position onto the observation space of the second observation platform to obtain the first observation; In S104, specifically, the target spatial position is projected onto the observation space (azimuth-elevation plane) of the second observation platform to obtain the first observation quantity. In some embodiments, the expression for the first observation quantity is: ; in, Indicates the first observation. Indicates the location of the second observation platform. This represents the observation model of the observation platform on the target. The inputs are the target position and the observation platform position, and the outputs are the measured azimuth and elevation angles. Specifically, taking the above formula as an example, the input target position is the target's spatial position. The input observation platform location is the location of the second observation platform. The output is the measurement value of the target's spatial position by the second observation platform.

[0040] First observation The number of elements in the first observation depends on the angular locus correlation. The total number of elements is: , indicating the number of targets formed under the current association matching relationship.

[0041] S105. Obtain the second observation of the target in the observation space of the second observation platform, and perform topology matching based on the first and second observations to obtain the topology matching error statistics; In S105, specifically, the second observation of the target in the observation space (azimuth-elevation plane) of the second observation platform is first obtained. Then, the first observation obtained in the previous step is matched with the angular trajectory observation (i.e., the second observation) observed by the second observation platform itself in the azimuth-elevation plane of the second observation platform to obtain the topology matching error statistics.

[0042] In some embodiments, the expression for the second observation is: ; in, Indicates the second observation. express The azimuth angle of the second observation platform at any given time. express The pitch angle of the second observation platform at any given time. Representing angular locus The number of measurement points in the middle, The second observation platform represents the first Angle trajectory.

[0043] In other embodiments, one implementation of the step of performing topology matching based on the first and second observations to obtain the topology matching error statistics specifically includes: S1051. Based on the first and second observations, perform topology matching and determine the topology matching error; In S1051, specifically, the first observation... Second observation The matching of topological structures can be viewed as the matching of graphs whose elements are vertices, such as... Figure 3 As shown. By constructing a set of binary hyperedges using the distances between vertices and other vertices, the above topological problem is transformed into a hypergraph matching problem. According to the definition of a binary hyperedge, the first observation can be defined. Second observation The topology matching error. One implementation of this step specifically includes: based on the first observation... Second observation To perform topology matching, the topology matching error is determined based on the definition of a hyperedge in a binary tuple. The specific expression is as follows:

[0044] in, This indicates the topology matching error. Indicates matching based on association relationships Find the first observation Zhongyu Associative matching vertices, Indicates the second observation The Middle One element, Indicates matching based on association relationships Find the first observation Zhongyu Associative matching vertices, Indicates the second observation The Middle One element, As an indicator function, if matched according to association relationships Unable to measure from the first observation Find with or If the vertices are associated and matched, then The value is 0, otherwise the indicator function takes the value 1. The norm of a vector.

[0045] S1052. Based on the topology matching error, obtain the topology matching error statistics.

[0046] In S1052, specifically, if the association matching relationship is correct and measurement error is not considered, the first observation will be... Topology and second observable If the topology is matched, the topology matching error is 0. Based on this, a hypothesis test of the topology matching error is performed to obtain the topology matching error statistic. One implementation of this step specifically includes: Assuming topology matching error Distance metric in the expression Follows a mean of 0 and a variance of The Gaussian distribution is used to obtain the topology matching error statistic, the specific expression of which is: ; in, This represents the topology matching error statistics. This represents the chi-square distribution.

[0047] S106. Obtain the tilt difference statistics, and based on the topology matching error statistics and the tilt difference statistics, obtain the association cost statistics for each association matching relationship; In S106, specifically, the tilt angle difference statistic can be obtained based on the existing tilt angle difference-based angular trajectory statistical test association algorithm. Then, the tilt angle difference statistic and the topology matching error statistic are combined to obtain the association cost statistic corresponding to each association matching relationship.

[0048] In some embodiments, one implementation of the step of obtaining the association cost statistic for each association matching relationship based on the topology matching error statistic and the tilt difference statistic specifically includes: based on the topology matching error statistic... By combining the dip angle difference statistics, we can obtain each association matching relationship. The correlation cost statistic is expressed as follows: ; ; ; ; in, Indicates the relationship between associations and matching. The associated cost statistics, This represents the statistic of the difference in inclination angle. Representing angular locus angular locus Deadline Observational statistics at any given time It follows a chi-square distribution with 1 degree of freedom. Representing angular locus angular locus Deadline The number of co-view trajectory points at any given time. Indicates the difference in tilt angle. for , The angle between the defined plane and the reference plane. for , The angle between the defined plane and the reference plane. Follows a mean of 0 and a variance of Gaussian distribution, This represents the vector pointing from the first observation platform to the second observation platform. This represents the line-of-sight vector of the first observation platform. This represents the line-of-sight vector of the second observation platform. express variance express The variance.

[0049] Furthermore, based on the distribution of the tilt angle difference statistic and the distribution of the topology matching error statistic, the distribution of the association cost statistic can be obtained, with the specific expression as follows:

[0050] S107. Based on the association cost statistics and preset decision threshold for each association matching relationship, obtain the angular trajectory association results.

[0051] In S107, specifically, the association cost statistics of each association matching relationship can be used as a cost function to monitor its changing pattern. Then, based on the preset decision threshold, the target association matching relationship that meets the preset conditions can be determined as the angular trajectory association result.

[0052] In some embodiments, one implementation of this step specifically includes: Each association matching relationship Related cost statistics As a cost function, the changing pattern of this cost function is monitored, and a preset decision threshold is defined as follows. And based on the first preset formula, the target association matching relationship is determined from the set of angular trajectory association relationships. As a result of angular trajectory association, the expression of the first preset formula is: ; in, Indicates the significance level. Indicates the confidence interval. The value can be set based on actual needs. Describing the degrees of freedom as The chi-square distribution, .

[0053] In the above embodiment, the angular trajectories obtained from the observations of all targets by the first and second observation platforms are acquired. Based on the angular trajectories, all possible angular trajectory associations are traversed to obtain a set of angular trajectory association relationships. According to each association matching relationship in the set of angular trajectory association relationships, cross-localization is performed to obtain the target's three-dimensional position estimation result under each association matching relationship. According to the target's three-dimensional position estimation result, the distance between the target and the first observation platform is obtained. The target's three-dimensional position estimation result is projected along the line of sight of the first observation platform to obtain the target's spatial position. The target's spatial position is projected onto the observation space of the second observation platform to obtain the first observation. The second observation of the target in the observation space of the second observation platform is acquired. Based on the first and second observations, topological structure matching is performed to obtain the topological structure matching error statistics. The tilt angle difference statistics are acquired. According to the topological structure matching error statistics and the tilt angle difference statistics, the association cost statistics of each association matching relationship are obtained. According to the association cost statistics of each association matching relationship and the preset decision threshold, the angular trajectory association result is obtained.

[0054] As can be seen, the above embodiments consider introducing the topological features of the target on the basis of the existing tilt angle difference spatial geometric constraints, which can further improve the accuracy of angular trajectory association in dense target scenes.

[0055] In a specific embodiment, a simulation experiment is used to simulate the passive multi-sensor multi-target angular trajectory association method of this application. In a typical simulation scenario, there are 36 dense target groups, starting simultaneously at certain intervals. The initial distance between the targets is... The measurement period is 1 second, and both the azimuth and elevation errors are set to 100 urad. A typical simulation scenario is as follows: Figure 4 As shown.

[0056] In this typical simulation scenario, the curve of association accuracy changing over time is given, such as... Figure 5As shown in the figure, GNN represents the Global Nearest Neighbour association algorithm, and NN represents the Nearest Neighbour association algorithm. From the above results, it can be seen that the passive multi-sensor multi-target angular trajectory association method of this application (corresponding to the method in the figure) introduces topological information on topology based on tilt difference constraints, thus achieving better association accuracy than the Global Nearest Neighbour association algorithm and the Nearest Neighbour association algorithm. Initially, the association accuracy of the proposed method is about 3%~4% higher than that of the Global Nearest Neighbour association algorithm. However, over time, due to the increased spacing caused by target diffusion and the accumulation of information over a longer period, the performance of the proposed method degrades to the same level as the Global Nearest Neighbour association algorithm.

[0057] To further illustrate the gain of topological information in multi-platform angular trajectory correlation, we denote the first observation platform as platform 1 and the second observation platform as platform 2. First, we present a typical simulation scenario. The projections of the observation results and cross-positioning results of targets 1-4 on the azimuth-elevation plane of platform 2 onto the azimuth-elevation plane of platform 2, as shown below. Figure 6a to Figure 6b The topology matching diagram is shown below, where x y represents the relationship between the trajectory x at platform 1 and the trajectory y at platform 2. Figure 6a This is a schematic diagram of the observation results on the azimuth-elevation plane of the platform. Figure 6b For the association matching relationship 1 (1 4,2 3,3 2, 4 1) Schematic diagram of the projection in the observation space of platform 2 after cross-positioning. Figure 6c For the association matching relationship 2 (1 4,2 2, 3 1,4 3) Schematic diagram of the projection in the observation space of platform 2 after cross-positioning. Figure 6d For the association matching relationship 3 (1 1,2 2, 3 3, 4 4) Schematic diagram of the projection in the observation space of platform 2 after cross-positioning.

[0058] Figure 6a Given Observation results on the azimuth-elevation plane of the time platform. Figure 6b to Figure 6d The projections of cross-localization in the observation space of Platform 2 under three different association matching relationships are presented (where association matching relationship 3 is the correct association result), and comparisons are made. Figure 6b to Figure 6d ,and Figure 6a The topological configuration makes it easy to seeFigure 6d and Figure 6a The topological configurations are very similar. By comparing and filtering the topological configurations in the association matching relationships 1 to 3, association matching relationship 3 is selected as the final angular trajectory association result.

[0059] Through the above specific embodiments, we can understand the usefulness of topological structure information in multi-platform angular trajectory association. However, in practice, there are many association matching relationships that need to be traversed. It is possible that similar topological structures will be formed when there are errors in the association matching relationships. Therefore, it is necessary to combine the tilt angle difference statistics with the topological structure matching error for association matching.

[0060] The following are typical scenarios. When platform 1 and platform 2 simultaneously observe targets 1-4, there are a total of 24 possible association matching relationships without considering missed detections (of which association matching relationship 24 is a correct association). The specific values ​​of the tilt angle difference statistic and the topology matching error statistic are shown in the table below: Table 1. Specific values ​​of tilt angle difference statistics and topology matching error statistics.

[0061] According to significance level The confidence level is 0.95. The preset decision threshold in the above simulation scenario is approximately 106.4. The last three columns of the association cost statistics in the table above are less than this threshold. The table shows that association matching relationships 10, 19, and 24 all meet the threshold judgment. If only the tilt angle difference is considered, association matching relationship 19 should be selected. However, the topological matching error statistics of association matching relationship 19 are relatively large. Therefore, considering all factors, association matching relationship 24 is selected because it has the smallest total association cost statistics. Therefore, it is chosen as the final angular trajectory association result, and association matching relationship 24 is indeed the correct association.

[0062] Angle measurement error and initial target spacing are important factors affecting correlation performance. Angle measurement error characterizes the measurement capability of the detection system, while initial target spacing characterizes the density of targets. To further explore the performance boundaries of the algorithm, an analysis of influencing factors was conducted, and the results are as follows: Figure 7 and Figure 8 As shown.

[0063] from Figure 7 As can be seen, the association accuracy of the three methods decreases to varying degrees with the increase of angle measurement error. The method in this paper outperforms other algorithms in association accuracy under different angle measurement error conditions. This is because the introduction of topological information reduces the association ambiguity caused by measurement error. The simulation results verify the scenario robustness of the method in this paper.

[0064] from Figure 8As can be seen, the association performance of the three methods increases with the increase of the initial target spacing. When the target spacing is less than 2km, the method in this paper has a certain performance improvement compared with the global optimal association algorithm, with an improvement of about 1% to 4%. When the target spacing is greater than 2km, since the target spacing is already large enough, the correct association can be achieved by using only the tilt angle difference geometric constraint. Therefore, the performance of the method in this paper degrades to the same level as the global optimal association algorithm.

[0065] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A passive multi-sensor multi-target angular track association method, characterized in that, The method comprises the following steps: obtaining an angular track obtained by observing all targets by a first observation platform and a second observation platform, and traversing all angular track association possibilities based on the angular track to obtain an angular track association relationship set; performing cross positioning according to each association matching relationship in the angular track association relationship set to obtain a target three-dimensional position estimation result under each association matching relationship; obtaining a distance between the target and the first observation platform according to the target three-dimensional position estimation result, projecting the target three-dimensional position estimation result along a line-of-sight direction of the first observation platform to obtain a target spatial position; projecting the target spatial position to an observation space of the second observation platform to obtain a first observation quantity; obtaining a second observation quantity of the target in the observation space of the second observation platform, performing topological structure matching according to the first observation quantity and the second observation quantity to obtain a topological structure matching error statistic; obtaining an inclination difference statistic, and obtaining an association cost statistic of each association matching relationship according to the topological structure matching error statistic and the inclination difference statistic; obtaining an angular track association result according to the association cost statistic of each association matching relationship and a preset decision threshold.

2. The method of claim 1, wherein, The method of performing topological structure matching according to the first observation quantity and the second observation quantity to obtain a topological structure matching error statistic comprises the following steps: performing topological structure matching according to the first observation quantity and the second observation quantity to determine a topological structure matching error; obtaining a topological structure matching error statistic according to the topological structure matching error.

3. The method of claim 2, wherein, The method of traversing all angular track association possibilities based on the angular track to obtain an angular track association relationship set comprises the following steps: traversing all angular track association possibilities based on the angular track and a preset association criterion to obtain an angular track association relationship set, and a specific expression is as follows: ； ； wherein, represents all the angular trajectory association possibilities based on the current time instant of each observation platform angular trajectory, represents the set of all possible angular trajectory association relations, represents the n-th association matching relation in the set of angular trajectory association relations, is the number of observation platforms, corresponds to the first observation platform, corresponds to the second observation platform, represents the number of angular trajectories of the observation platform numbered is a matrix, , represents the combination number, represents the number of angular trajectories of the first observation platform, represents the number of angular trajectories of the second observation platform, represents the azimuth angle at the time instant, represents the pitch angle at the time instant, represents the number of measurement points in the angular trajectory represents the n-th angular trajectory of the observation platform numbered .​​​ 4. The method of claim 3, wherein, The method of performing cross positioning according to each association matching relationship in the angular track association relationship set to obtain a target three-dimensional position estimation result under each association matching relationship comprises the following steps: According to the angle trajectory correlation relationship set Each correlation matching relationship If Then, the target three-dimensional position estimation result under each correlation matching relationship is obtained by using cross positioning, and the specific expression is: ； in, The first observation platform represents the... The angular trajectory and the second observation platform's first The trajectories of the bars and corners are related together. This represents the result of the target's three-dimensional position estimation. The first observation platform represents the... Angular trajectory, The second observation platform represents the first Angular trajectory, This represents the function for calculating cross-location.

5. The method of claim 4, wherein, The method of obtaining a distance between the target and the first observation platform according to the target three-dimensional position estimation result, projecting the target three-dimensional position estimation result along a line-of-sight direction of the first observation platform to obtain a target spatial position comprises the following steps: According to the target three-dimensional position estimation result , the distance between the target and the first observation platform is obtained, the target three-dimensional position estimation result is projected along the line-of-sight direction of the first observation platform, and the spatial position of the target is obtained while ensuring that the observation topology of the first observation platform is unchanged, and the specific expression is as follows: ； ； wherein, denotes the target spatial position, denotes the distance of the target from the first observation platform, denotes the L2 norm, denotes the position of the first observation platform, denotes the first observation platform's first line-of-sight vector of the piecewise angular trajectory.

6. The method of claim 5, wherein, An expression of the first observation quantity is as follows: ； wherein, represents the first observation, represents the position of the second observation platform, represents an observation model of the observation platform to the target, inputting the target position and the observation platform position, and outputting the measured azimuth and elevation. An expression of the second observation quantity is as follows: ； wherein denotes the second observation, denotes the azimuth angle of the second observation platform at the time instant denotes the elevation angle of the second observation platform at the time instant denotes the number of measurement points in the angular trajectory denotes the i-th angular trajectory of the second observation platform denotes the i-th angular trajectory of the second observation platform​ 7. The method of claim 6, wherein, The method of performing topological structure matching according to the first observation quantity and the second observation quantity to determine a topological structure matching error comprises the following steps: According to the first observation and the second observation , topological structure matching is performed, and according to the definition of a binary tuple hyperedge, a topological structure matching error is determined, and the specific expression is: ； in, This represents the topology matching error. Indicates matching based on association relationships Find in the first observation Zhongyu Associative matching vertices, Indicates the second observation The Middle One element, Indicates matching based on association relationships Find in the first observation Zhongyu Associative matching vertices, Indicates the second observation The Middle One element, As an indicator function, if matched according to association relationships Unable to obtain from the first observation Find with or If the vertices are associated and matched, then If the value is 0, then take 1; otherwise, take 1. The norm of a vector.

8. The method of claim 7, wherein, The method of obtaining a topological structure matching error statistic according to the topological structure matching error comprises the following steps: Assume that the topology matching error The distance metric in the expression of Subject to a Gaussian distribution with mean 0 and variance The topology matching error statistics, the specific expression is: ； ； wherein, denotes the topology match error statistics, denotes the first observation element total number, denotes the chi-square distribution.

9. The method of claim 8, wherein, The method of obtaining an association cost statistic of each association matching relationship according to the topological structure matching error statistic and the inclination difference statistic comprises the following steps: According to the topological structure matching error statistics And the dip angle difference statistics, the associated matching relationship of each associated matching relationship The associated cost statistics, the specific expression is: ； ； ； ； in, Indicates the relationship between associations and matching. The aforementioned correlation cost statistics, This represents the inclination angle difference statistic. Representing angular locus angular locus Deadline Observational statistics at any given time It follows a chi-square distribution with 1 degree of freedom. Representing angular locus angular locus Deadline The number of co-view trajectory points at any given time. Indicates the difference in tilt angle. for , The angle between the defined plane and the reference plane. for , The angle between the defined plane and the reference plane. Follows a mean of 0 and a variance of Gaussian distribution, This represents the vector pointing from the first observation platform to the second observation platform. This represents the line-of-sight vector of the first observation platform. This represents the line-of-sight vector of the second observation platform. express variance express The variance.

10. The method of claim 9, wherein, The method of obtaining an angular track association result according to the association cost statistic of each association matching relationship and a preset decision threshold comprises the following steps: The association matching relationship The association cost statistics As a cost function, monitor the change rule of the cost function, define the preset decision threshold as , And according to the first preset formula, determine the target association matching relationship From the set of angular trajectory association relationships as the angular trajectory association result, the expression of the first preset formula is: ； wherein, represents the level of significance, represents the confidence interval, represents the chi-square distribution with degrees of freedom .

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