Space-based optical active and passive task planning method for space situation awareness

Abstract

The invention discloses a space-based optical active and passive task planning method for space situation awareness, and belongs to the field of space situation awareness. The method comprises the following steps: establishing an active and passive detection mode, and using a large-view-field passive sensor and a small-view-field active sensor to realize timely discovery of a new target and accurate perception of a catalogued target state; constructing a single-sensor large-scale target track state determination method, and determining a new target state and a cataloged target state by using a multi-target tracking filter and an initial track determination method; meanwhile, a new target label matching method is constructed and is used for identifying the corresponding relation of new targets among different sensors; afterwards, a multi-sensor information fusion method based on label matching is combined, unification of multi-target information among multiple sensors is achieved, and stable and consistent multi-target state estimation is obtained; and finally, according to a multi-target state estimation result, comprehensively evaluating the urgency of additional observation of a new target and the degree of uncertainty of a cataloged target state, planning a sensor to preferentially observe a target with relatively large uncertainty, and improving the utilization efficiency of observation resources.

Description

Technical Field

[0001] This invention relates to a method for monitoring space targets using both space-based passive and active observation sensors, belonging to the field of space situational awareness. Background Technology

[0002] With the deployment of large low-Earth orbit constellations, led by Starlink, and the frequent occurrence of anti-satellite experiments, satellite collisions, and disintegration events, the number of space objects has increased rapidly. According to NASA's *Orbital Debris Quarterly*, as of February 2025, more than 30,000 space objects had been cataloged. In addition, a large number of smaller or newly deployed space objects remain uncataloged. This surge in the number of space objects is saturating orbital resources, significantly increasing the risk of collisions between space objects. The existence of uncataloged targets further increases the uncertainty of the space environment, seriously threatening the operational safety of our spacecraft in orbit.

[0003] Space situational awareness plays a crucial role in space activities. By continuously and accurately identifying and tracking spacecraft, space debris, and potential threats in orbit, it accurately grasps their orbital status, thereby supporting collision risk assessment, anomaly detection, sensor mission planning, and other functions to ensure spacecraft safety and support the orderly management of space resources. Depending on the object being sensed, new target search and status maintenance of cataloged targets are the two main functions of a space situational awareness system. New target search involves scanning specific space areas to promptly identify non-cooperative targets and improve the cataloging of space targets. Status maintenance of cataloged targets ensures the accuracy and timeliness of the cataloging database, providing critical data support for collision avoidance planning and space traffic management.

[0004] Currently, relevant research mainly focuses on maintaining the status of cataloged targets, and various publications have proposed systematic orbit maintenance methods for satellites in LEO, MEO, and GEO orbits. In contrast, research on orbit determination and maintenance of newly created targets is relatively lagging. Some publications have introduced new target generation methods based on probability hypothesis density filters, but their application in large-scale target continuous identification and management is limited due to the difficulty in establishing individual trajectories. Furthermore, there is currently a lack of systematic and comprehensive research that simultaneously considers the search for new targets and the maintenance of cataloged targets.

[0005] To address the aforementioned issues, this invention proposes a space-based optical active and passive mission planning method for space situational awareness. By combining new target association modeling with multi-sensor information fusion strategies, it significantly improves the system's ability to respond quickly to emerging targets and maintain the continuous state of large-scale cataloged targets, providing strong support for building an efficient and robust space situational awareness system. Summary of the Invention

[0006] To address the shortcomings of existing observation methods in simultaneously searching for new targets and maintaining the state of already cataloged targets, this invention aims to provide a space-based optical active and passive mission planning method for space situational awareness. This method analyzes the state of newly generated targets from passive detection sensors while efficiently planning observation tasks for active detection sensors to maintain the state of targets with high uncertainty, enabling rapid response and accurate cataloging of space objects. Furthermore, to solve the problem of discrepancies in the identity analysis and information of newly generated targets from different sensors, a new target association modeling strategy and a multi-sensor information fusion strategy are constructed. By integrating and analyzing multi-sensor information, a stable and consistent space target state estimate is obtained. This state estimate serves as the information basis for sensor mission planning, thereby recursively realizing space-based optical active and passive mission planning.

[0007] The objective of this invention is achieved through the following technical solution.

[0008] The space-based optical active and passive mission planning method for space situational awareness disclosed in this invention includes the following steps:

[0009] Step 1: Establish an active and passive detection mode, combining a large field-of-view passive sensor with a small field-of-view active sensor to simultaneously achieve timely detection of new targets and accurate perception of the status of cataloged targets.

[0010] Among them, the large field-of-view sensor is fixedly oriented towards the flight velocity direction of the space situational awareness satellite:

[0011] l = v S (1)

[0012] In the formula: l represents the optical axis direction of the large field-of-view passive sensor, v S This represents the velocity vector of a space situational awareness satellite; if the angles of the limiting right ascension and declination offsets of the optical axis within the sensor's field of view are f... R ,f D For a space target to be observed by the large field-of-view sensor, its right ascension α and declination δ relative to the sensor must satisfy the following conditions:

[0013]

[0014] Where α0 and δ0 are the reference right ascension and declination corresponding to the optical axis pointing l, respectively; while the small field-of-view active sensor, based on the state information of the cataloged targets, prioritizes targets with greater uncertainty or newly generated targets from those not covered by the large field-of-view passive sensor, and achieves targeted observation by rotating the lens; at this time, the optical axis pointing ι of the small field-of-view active sensor is:

[0015] ι=x T -x S (3)

[0016] Where, x T and x S These represent the position of the selected target and the position of the sensor, respectively. Since the field of view of the small field of view active sensor is extremely small, it can be approximated that it can only observe the target at any given time.

[0017] Step 2: For tracking cataloged spatial targets, construct an orbital state preservation method. Based on the observations obtained from the sensor detection mode in Step 1, and combined with a multi-target tracking filter, recursively update the state of the cataloged targets. For tracking newly created targets with unknown states, construct a method for determining the state of the newly created targets. Utilize the constraints on the state of the newly created targets to estimate their state. This step provides the data foundation for information fusion in Step 3.

[0018] The multi-target tracking filter used in this invention is a Labeled Multi-Bernoulli (LMB) filter. In this filter, the multi-target state is represented as a labeled multi-Bernoulli random finite set; for a set of existence probabilities r... (l) and state space distribution p (l) The label described is a Bernoulli random finite set π={(r (l) ,p (l) The probability density function of} is expressed as follows:

[0019] π(X)=Δ(X)ω(L(X))p X (4)

[0020] Intermediate variables:

[0021]

[0022] In equations (4) and (5), the indication Δ(X) for distinct labels is 1 only when all targets in the state space have different labels. L (j) is the inclusion function, L is the label space, L is a set of labels, l represents a label, i, j represent labels belonging to a specific label space or set; x represents the spatial target state variable, X represents the spatial target state space;

[0023] Let the random finite set of the posterior of the multi-objective and the random finite set of the newly generated objectives be respectively:

[0024]

[0025] Where: subscript B represents the new target, and the LMB prediction method for this random finite set is:

[0026]

[0027] Where: the subscript + represents the prior state information of the space target, the subscript S represents the surviving space target, and:

[0028]

[0029] p S (·|l) and η S (l) represents the target survival probability and the overall survival probability, respectively; p(·,l) represents the probability density function of the spatial distribution of the target labeled l; and f(x|·,l) represents the target dynamics model. The multi-target state can be further updated based on sensor observations.

[0030]

[0031] Where: L + This represents the set of target labels in the prior state. I represents the correspondence between all observations and labels, where I is also a set of labels, but this set must be L. + A subset of , which is the meaning of Ξ. θ represents a certain correspondence between observations and labels, and this relationship must belong to . Furthermore, Z represents the observation used to update the target state, p θ Then it is calculated using the following formula:

[0032] In this formula, p d The probability that the sensor can detect the target is represented by ρ(·), where P(·) represents the intensity of the Poisson clutter, and ll(·) represents the similarity between observations; z θ(l) This represents the observed value corresponding to the target labeled l, based on the correspondence θ.

[0033] Regarding the determination of the status of newly emerging targets, for a set of observations generated by the sensor at a certain moment, the observations corresponding to the cataloged targets can be filtered out by gating operations, and the observations of newly emerging targets can be extracted.

[0034] The multi-objective state label space obtained after LMB prediction is L + Then the set of gated observations corresponding to each label l in this space is calculated by equation (11):

[0035]

[0036] In this formula, d M This represents the Mahalanobis distance between observations. τ represents the theoretical observation of the target. M This represents the threshold for gating between an observation and a target; for an observation from a certain sensor, if it is not gated with any target, it is considered an observation of a newly emerging target.

[0037]

[0038] Subsequently, based on the probabilistic admissible region method, an LMB random finite set representing the initial orbital state of the newborn target can be generated from the observed values. Based on energy constraints, the distance ρ between the newborn target and the observed values ​​and the rate of change of distance are... satisfy:

[0039]

[0040] In this formula, E represents the energy of the space object, μ is the Earth's gravitational constant, and r represents the position vector of the space object relative to the central celestial body. Simultaneously, the orbit of the newly formed target must also satisfy semi-major axis constraints and eccentricity constraints, based on which several sampling points can be generated:

[0041]

[0042] In this formula, w i a represents the weight of the sampling points. i e is the size of the semi-major axis of the sampling point. i Let N be the magnitude of the eccentricity of the sampling point, and N be the number of sampling points. p(a) and p(e) represent the probability distribution functions satisfied by the semi-major axis and eccentricity values, respectively. The sampling points are projected onto the plane determined by energy constraints. Space, can be obtained Sampling points in space Finally, using the expectation-maximization algorithm, By fitting the sampling points in space with a Gaussian mixture model, the Gaussian mixture of the orbital state of the new target can be obtained:

[0043]

[0044] Where M represents the number of sampling points in the space, p B (x) represents the orbital state of the new target, Q represents the number of Gaussian components that make up the orbital state, and w k μ represents the weight of each Gaussian component. k , Let p represent the mean and variance of each Gaussian component, respectively. B (x) and r B By combining these, a random finite set of LMBs for new targets can be obtained;

[0045] Step 3: Based on the estimation results of the new target state at each time step in Step 2, construct a new target label matching method to identify the correspondence between new targets in different sensors; combine the cataloged target labels to establish a multi-sensor information fusion method based on label matching, realize the unification of multi-target information among multiple sensors, and obtain stable and consistent multi-target state estimation.

[0046] Based on step two, the LMB random finite set of the newly generated targets from the two sensors is obtained. and and The method for calculating the distance between elements is as follows:

[0047] In the above formula, and Let w1 and w2 represent the sets of newly generated target labels generated by sensor 1 and sensor 2, respectively; the fusion weights w1 and w2 satisfy w1 + w2 = 1; based on this distance calculation method, a similarity matrix between elements in the two LMB random finite sets can be constructed; the width of this matrix is... The number of elements in the matrix, with length m+n being the sum of the number of elements in the two LMB random finite sets; where the first m columns of the matrix are... Zhongyu The distances between each element in the matrix, and the last n columns of the matrix are The elements in the middle and The distance to the hollow set, calculated using the elements of the n-column matrix, is as follows:

[0048]

[0049] Where, r β p represents the probability of the target being born. 2,d (x) represents the generation The probability of the sensor detecting the corresponding target;

[0050] Based on the above similarity matrix, we can then... Zhongyu The correspondence between the elements in the model is used to construct a rank distribution problem. The Morty method is used to solve this rank distribution problem, which can identify the correspondence between newly generated targets in different sensors.

[0051] The premise for fusing elements in the LMB random finite set information contained in different sensors is that their labels are the same; since the labels of cataloged targets and newly created targets must be different, this multi-sensor information fusion problem can be divided into two independent sub-problems: information fusion of cataloged targets and information fusion of newly created targets.

[0052] For information fusion of cataloged targets, let the LMB random finite sets of such targets in the two sensors be respectively... and Then for and The targets corresponding to the tags contained in both sensors can be fused, and the fused LMB random finite set is:

[0053]

[0054] in:

[0055]

[0056] For certain targets, if only one of the two sensors contains the corresponding tag, it is considered that the sensor without the tag has missed detection. The information containing the tag is then fused with the empty set. The corresponding calculation method is as follows:

[0057]

[0058] in:

[0059] In the above formula, and The LMB parameter represents a single element. p represents the probability of a missed detection. 3,d (x) represents the probability of a sensor observing the target without the corresponding target state element.

[0060] Will and The fusion result of the target state corresponding to the label contained in both sensors is combined with the calculation result of the corresponding label contained in only one of the two sensors, which is the fusion result of the two sensors on the cataloged target.

[0061] For the information fusion of new targets, the new targets need to be labeled according to Equations (16) and (17). For the new target information that matches each other, the information fusion is performed in the same way as the fusion of cataloged target information contained in both sensors, as shown in Equations (18) and (19). For the new target information that does not match each other, it is assumed that the other sensor has missed detection, and the information fusion is performed in the same way as the missed detection in the fusion of cataloged target information, as shown in Equations (20) and (21). The fused new targets are assigned different labels from the cataloged targets, and then merged with the fusion result of the cataloged target state information as the input of the multi-target tracking filter prediction process in step two.

[0062] Step 4: Based on the multi-target state information fused in Step 3, comprehensively assess the urgency of additional observations of newly emerging targets and the degree of uncertainty in the state of already cataloged targets, guide the sensors to prioritize observations of targets with relatively high uncertainty, improve the efficiency of observation resource utilization while ensuring the stability of the state of newly emerging targets, and realize the planning of space-based optical active and passive missions for space situational awareness.

[0063] For a certain space target, if the probability density functions of the state estimation before and after observation are p k|k-1 and p k The Rényi information gain obtained from this observation behavior is:

[0064]

[0065] In this formula, α is a dimensionless parameter. Substituting the probability density function corresponding to the LMB random finite set, i.e., equation (4), into equation (22), we get:

[0066]

[0067] In the formula:

[0068] In this formula, N k|k-1 and N k These represent the number of Gaussian components in the Gaussian mixture before and after the observation.

[0069] Furthermore, a new target observation priority is introduced and embedded into the Rényi information gain to enhance the active observation's focus on new targets; the new target observation priority is defined as:

[0070]

[0071] Where t represents the current time, t B This indicates the moment of the target's birth. The method for embedding Rényi information gain into the observation priority of the newly born targets is as follows:

[0072]

[0073] In Equation (26), the weight of the Rényi information gain is restricted to a fixed interval, so the embedding method will not destroy its original structure. At the same time, the observation priority of the newly introduced target decays exponentially and non-linearly, so that the new target is given priority observation at multiple times after it is first discovered. After the cataloging accuracy is improved, the observation priority drops rapidly. In addition, the function can also ensure that the priority of the target decreases slowly after it has existed for a long time, avoiding the problem of the observation gain of the cataloged target being too low.

[0074] Based on the Rényi information gain obtained by the above method, mission planning is carried out for space situational awareness sensors. The urgency of additional observation of newly formed targets and the degree of uncertainty of the status of already cataloged targets are comprehensively evaluated. The sensors are guided to prioritize the observation of targets with relatively high uncertainty. While ensuring the stability of the status of newly formed targets, the efficiency of observation resource utilization is improved, and space-based optical active and passive mission planning for space situational awareness is realized.

[0075] Beneficial effects:

[0076] 1. To address the shortcomings of existing observation methods in simultaneously searching for new targets and maintaining the status of cataloged targets, this invention discloses a space-based optical active and passive task planning method for space situational awareness. This method is a multi-sensor space target monitoring method that establishes a collaborative sensing method between active and passive sensors. By analyzing the status of newly emerging targets from passive detection sensors, it simultaneously and efficiently plans observation tasks for active detection sensors to maintain the status of targets with high uncertainty. In other words, it can quickly respond to and accurately catalog space objects.

[0077] 2. To address the issue of discrepancies in the identification and information of newly emerging targets from various sensors, this invention discloses a space-based optical active and passive mission planning method for space situational awareness. This method employs both active and passive detection modes and constructs a new target association modeling strategy and a multi-sensor information fusion strategy by combining the two detection modes. Through integrated analysis of multi-sensor information, it can not only identify newly emerging targets in a timely manner but also effectively maintain the state of already cataloged targets, thereby obtaining a stable and consistent space target state estimate.

[0078] 3. The space-based optical active and passive mission planning method for space situational awareness disclosed in this invention adopts a single-sensor large-scale target orbit state determination method. By establishing an LMB multi-target tracking filter and a new target initial orbit determination method, it can maintain the large-scale target state based on sensor observations and generate the orbit state of new targets.

[0079] 4. The space-based optical active and passive mission planning method for space situational awareness disclosed in this invention identifies the state of the same newly generated target generated by different sensors through a new target label matching method, and further obtains a stable and consistent multi-target state estimate through a multi-sensor information fusion method based on label matching.

[0080] 5. The space-based optical active and passive mission planning method for space situational awareness disclosed in this invention is a sensor mission planning method that takes into account both the state maintenance of newly emerging targets and the state maintenance of already cataloged targets. By simultaneously measuring the observation needs of newly emerging targets and targets with high uncertainty, it guides the sensor network to conduct efficient detection and provides reliable observation data for achieving high-precision estimation of target state in space situational awareness. Attached Figure Description

[0081] Figure 1 This is a multi-sensor, multi-target tracking scenario in this invention;

[0082] Figure 2 This is a schematic diagram of the active-passive combined detection mode in this invention;

[0083] Figure 3 This is a schematic diagram of the similarity matrix for matching newly generated target labels in this invention;

[0084] Figure 4 The graph shows the trend of the number of tracked targets over time in the multi-sensor task planning method proposed in this invention and two commonly used methods.

[0085] Figure 5 This is a trend graph showing the change of OSPA distance between the target position estimate and the true value over time for the multi-sensor task planning method proposed in this invention and two commonly used methods. Detailed Implementation

[0086] To better illustrate the purpose and advantages of the present invention, the specific embodiments and effects of the present invention will be further described in detail below with reference to examples and accompanying drawings.

[0087] This invention addresses scenarios where multiple sensors collaboratively track large-scale space objects. It implements a proposed active-passive combined space-based optical sensor mission planning method to guide sensors in effectively observing space objects, rapidly responding to emerging targets, and maintaining the status of already cataloged targets.

[0088] The specific implementation steps of the space-based optical active and passive mission planning method oriented towards space situational awareness are as follows:

[0089] Step 1: Establish an active and passive detection mode, combining a large field-of-view passive sensor with a small field-of-view active sensor to simultaneously achieve timely detection of new targets and accurate perception of the status of cataloged targets.

[0090] Consider the attached diagram Figure 1 The multi-sensor, multi-target tracking scenario shown depicts 12 low-Earth orbit satellites equipped with sensors, evenly distributed across four orbital planes, with three satellites equidistantly spaced on each plane. Each satellite is equipped with a passive, wide-field-of-view sensor and an active, narrow-field-of-view sensor. The entire tracking process lasts 8 hours, with the sensors performing observations every 60 seconds, for a total of 480 observations.

[0091] First, determine the combined active and passive observation mode, utilizing a large field-of-view passive sensor and a small field-of-view active sensor, such as... Figure 2 As shown, this simultaneously enables the timely detection of new targets and the accurate perception of the status of already cataloged targets. The large field-of-view sensor is fixedly oriented towards the flight velocity direction of the space situational awareness satellite.

[0092] l = v S (27)

[0093] In the formula: l represents the optical axis direction of the large field-of-view sensor, v S This represents the velocity vector of a space situational awareness satellite. If the limiting right ascension and declination angles offset from the optical axis by the sensor's field of view are f... R ,f D For a space target to be observed by the large field-of-view sensor, its right ascension α and declination δ relative to the sensor must satisfy the following conditions:

[0094]

[0095] Where α0 and δ0 are the reference right ascension and declination corresponding to the optical axis pointing l, respectively. For a small field-of-view sensor, based on the state information of the cataloged targets, targets with greater uncertainty or newly generated targets are preferentially selected from those never covered by a large field-of-view sensor, and targeted observation is achieved by rotating the lens. In this case, the optical axis pointing ι of the small field-of-view sensor is:

[0096] ι=x T -x S (29)

[0097] Where, x T and x S These represent the position of the selected target and the position of the sensor, respectively. Since the field of view of a small field-of-view sensor is extremely small, it can be approximated that it can only observe this one target at any given time.

[0098] Step two: For tracking cataloged spatial targets, a trajectory state preservation method is proposed. Based on the observations obtained from the sensor detection mode in step one, and combined with a multi-target tracking filter, the state of the cataloged targets is recursively updated. For tracking newly created targets with unknown states, a method for determining the state of newly created targets is proposed. The state of the newly created targets is estimated using the constraints imposed on their states. This step provides the data foundation for information fusion in step three.

[0099] Based on the active and passive detection mode established in step one, observational information of space objects is acquired, the status of cataloged targets is updated, and new targets are generated accordingly. Space objects are observed using 24 optical sensors on 12 space situational awareness satellites, with each satellite's sensor generating a set of observation values. Let the random finite sets of the multi-target posterior and newly generated targets be:

[0100]

[0101] Where: subscript B represents the new target, and the LMB prediction method for this random finite set is:

[0102]

[0103] Wherein, the subscript + represents the prior state information of the space target, the subscript S represents the surviving space target, and:

[0104]

[0105] p S (·|l) and η S (l) represents the target survival probability and the overall survival probability, respectively; p(·,l) represents the probability density function of the spatial distribution of the target labeled l; and f(x|·,l) represents the target dynamics model. The observations generated by the 24 sensors can be further used to update the multi-target state separately.

[0106]

[0107] in, This represents the set of target labels in the prior state. This represents the correspondence between all observations and labels. I is also a set of labels, but this set must be... A subset of , which is the meaning of Ξ. θ represents a certain correspondence between observations and labels, and this relationship must belong to . Furthermore, Z represents the observation used to update the target state, p θ Then it is calculated using the following formula:

[0108] In this formula, p d represents the probability that the sensor can detect the target, P(·) represents the intensity of the Poisson clutter distribution, and ll(·) represents the similarity between observations. θ(l) This represents the observed value corresponding to the target labeled l, based on the correspondence θ.

[0109] Based on the observations generated by the sensors onboard each space situational awareness satellite, the observations that have not been gated to any target can be determined through the multi-target state obtained after LMB prediction. These observations are considered to be those of newly emerging targets.

[0110]

[0111] Furthermore, the initial orbital state of the newborn target can be generated based on the observations of the newborn target using the probabilistic admissibility region method. Based on energy constraints, the distance and rate of change of distance between the newborn target and the observations satisfy:

[0112]

[0113] In this formula, E represents the energy of the space object, μ is the Earth's gravitational constant, and r represents the position vector of the space object relative to the central celestial body. Simultaneously, the orbit of the newly formed target must also satisfy semi-major axis constraints and eccentricity constraints, based on which several sampling points can be generated:

[0114]

[0115] In this formula, w i a represents the weight of the sampling points. i e is the size of the semi-major axis of the sampling point. i Let be the magnitude of the eccentricity of the sampling point, N be the number of sampling points, and p(a) and p(e) represent the probability distribution functions satisfied by the semi-major axis and eccentricity values, respectively. The sampling points are projected onto the plane determined by energy constraints. Space, can be obtained Sampling points in space Finally, using the expectation-maximization algorithm, By fitting the sampling points in space with a Gaussian mixture model, the Gaussian mixture of the orbital state of the new target can be obtained:

[0116]

[0117] Where M represents the number of sampling points in the space, p B (x) represents the orbital state of the new target, Q represents the number of Gaussian components that make up the orbital state, and w k μ represents the weight of each Gaussian component. k , Let p represent the mean and variance of each Gaussian component, respectively. B (x) and r B By combining these, a random finite set of LMBs for the new target can be obtained.

[0118] Step 3: Based on the estimation results of the newly generated target state at each time point in Step 2, a new target label matching method is constructed to identify the correspondence between new targets across different sensors. Combining the already cataloged target labels, a multi-sensor information fusion method based on label matching is established to unify multi-target information across multiple sensors and obtain stable and consistent multi-target state estimates.

[0119] Based on the state update results of space objects obtained from sensors on each space situational awareness satellite in step two, stable and consistent multi-target state estimates can be obtained through label matching and information fusion. Let any two newly generated targets from the 12 space situational awareness satellites constitute LMB random finite sets. and The method for calculating the distance between elements in the two random finite sets mentioned above is as follows:

[0120] In the above formula, and Let w1 and w2 represent the sets of newly generated target labels generated by sensor 1 and sensor 2, respectively. The fusion weights w1 and w2 satisfy w1 + w2 = 1. Based on this distance calculation method, a similarity matrix between elements in the two LMB random finite sets can be constructed. The width of this matrix is... The number of elements in the matrix is ​​given by a length m+n, which is the sum of the number of elements in the two LMB random finite sets. The first m columns of the matrix are... Zhongyu The distances between each element in the matrix, and the last n columns of the matrix are The elements in the middle and The distance to the hollow set, calculated using the elements of the n-column matrix, is as follows:

[0121]

[0122] Where, r β p represents the probability of the target being born. 2,d (x) represents the generation The similarity matrix constructed using the above method is shown in the diagram below. Figure 3 As shown. Based on this similarity matrix, a rank allocation problem can be constructed according to the correspondence between the elements in B1 and B2. By using the Morty method to solve this rank allocation problem, the elements in the two sets can be associated, and the correspondence between newly generated targets in different sensors can be identified.

[0123] For any two of the 12 space situational awareness satellites, let the information on cataloged targets held by any two satellites be denoted as follows: Let the LMB random finite sets of these targets in the two sensors be respectively... and The merged LMB random finite set is then:

[0124]

[0125] in:

[0126]

[0127] For certain targets, if only one of the two sensors contains the corresponding element, it is considered that the sensor that does not contain the tag has missed detection. The information containing the element is then fused with the spatial data. The corresponding calculation method is as follows:

[0128]

[0129] in:

[0130] In the above formula, and The LMB parameter represents a single element. p represents the probability of a missed detection. 3,d (x) represents the probability of a sensor observing the target without the corresponding target state element.

[0131] The fusion results of the two types of target states are combined to obtain the fusion result of the two sensors for the cataloged targets. For the fusion of newly generated target information, the newly generated targets need to be labeled according to the method described in 3.1. For newly generated target information that matches each other, the information is fused using the same method as the fusion of cataloged target information contained in both sensors. For newly generated target information that does not match each other, it is assumed that the other sensor has missed detection, and the information is fused using the same method as the fusion of cataloged target information where one of them missed detection.

[0132] After sequentially fusing the multi-target information from the 12 sensors, the final result is the multi-target state estimation result for this step. This result serves as the input for the LMB prediction at the next time step and as the information basis for mission planning in step four, and is transmitted to all space situational awareness satellites. This process can be repeated to achieve recursive estimation of the multi-target state.

[0133] Step 4: Based on the multi-target state information fused in Step 3, comprehensively assess the urgency of additional observations of newly emerging targets and the degree of uncertainty of the state of already cataloged targets, guide the sensors to prioritize observations of targets with relatively high uncertainty, improve the efficiency of observation resource utilization, and realize space-based optical active and passive mission planning for space situational awareness.

[0134] Based on the posterior information of the multi-target state obtained in step three, we first analyze the information gain that each target can obtain when it is subsequently observed. If the probability density functions of the posterior information and the ideal updated state after observation are p... k|k-1 and p k The Rényi information gain obtained from this observation behavior is:

[0135]

[0136] In this formula, α is a dimensionless parameter. The probability density function corresponding to the LMB random finite set can be obtained as follows:

[0137]

[0138] In the formula:

[0139]

[0140] In this formula, N k|k-1 and N k These represent the number of Gaussian components in the Gaussian mixture before and after the observation.

[0141] Furthermore, a new target observation priority is introduced and embedded into the Rényi information gain to enhance the active observation's focus on new targets. The new target observation priority is defined as follows:

[0142]

[0143] Where t represents the current time, t B This indicates the moment of the target's birth. The method for embedding Rényi information gain into the observation priority of the newly born targets is as follows:

[0144]

[0145] Based on the Rényi information gain, the 12 sensors determine how to observe to obtain the maximum information gain, and observe in this way to generate target observation values ​​for the next time step target state update.

[0146] Figure 4 The proposed multi-sensor task planning method, a method that does not consider the observation priority of new targets, and a method that does not use small field-of-view sensors are demonstrated to track the change in the number of targets over time. The results show that the method proposed in this invention can quickly identify new targets and has a faster new target identification speed compared with the method that does not use small field-of-view sensors. Figure 5 The accuracy of the target position estimation method proposed in this invention was compared with that of methods that do not consider the observation priority of new targets and methods that do not use small field-of-view sensors. The results show that the position estimation accuracy of the method proposed in this invention has a faster convergence speed and can ensure that the error remains at an extremely low level at the last moment.

[0147] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A space-based optical active-passive task planning method for space situation awareness, characterized in that: The method comprises the following steps, Step one, establishing a passive-active detection mode, combining a large field of view passive sensor with a small field of view active sensor, and simultaneously achieving timely discovery of new targets and accurate perception of the state of cataloged targets; Step two, for cataloged space target tracking, constructing an orbit state maintenance method, based on the observation values obtained by the sensor detection mode in step one, combining a multi-target tracking filter, and recursively updating the state of the cataloged target; For tracking of a new-born target whose state is unknown, a new-born target state determination method is constructed, and the state of the new-born target is estimated by using the constraints on the state of the new-born target; Step three, based on the estimation results of the state of the new-born target at each moment in step two, a new-born target label matching method is constructed, which is used to identify the corresponding relationship of the new-born target between different sensors; In combination with the label of the cataloged target, a multi-sensor information fusion method based on label matching is established, the multi-target information between multiple sensors is unified, and stable and consistent multi-target state estimation is obtained; Step four, based on the multi-target state information fused in step three, the urgency of additional observation of the new-born target and the degree of uncertainty of the state of the cataloged target are comprehensively evaluated, the sensor is guided to preferentially observe the target with relatively large uncertainty, the utilization efficiency of observation resources is improved, and a space-based optical passive-active mission planning for space situation awareness is realized.

2. The space situational awareness oriented space-based optical active-passive task planning method according to claim 1, characterized in that: In step one, the large field of view passive sensor is fixedly directed to the direction of the flight speed of the space situation awareness satellite: l＝v S (1) where l denotes the optical axis pointing of the large field of view passive sensor, v S represents the velocity vector of the space situational awareness satellite; if the limit right ascension and declination covered by the sensor field of view are offset from the optical axis by angles f R ,f D , then the right ascension a and declination d of a space object relative to the sensor must satisfy the following conditions to be observed by the large field of view sensor: Wherein, α0 and δ0 are the reference right ascension and declination corresponding to the optical axis direction l respectively.

3. The space situational awareness oriented space-based optical active-passive task planning method according to claim 1, characterized in that: In step one, the small field of view active sensor selects, from the targets not covered by the large field of view passive sensor, the target with relatively large uncertainty or newly generated target according to the state information of the cataloged target, and realizes targeted observation through a rotating lens; at this time, the optical axis direction ι of the small field of view active sensor is: i = x T -x S (3) where x T and x S represent the position of the selected target and the position of the sensor, respectively; due to the small field of view of the active sensor, the equivalent view is that it can only observe the target at any moment.

4. The space situational awareness oriented space-based optical active-passive task planning method according to claim 1, characterized in that: The implementation method of the multi-target tracking filter in step two is as follows, The multi-target tracking filter used is a labeled multi-Bernoulli (LMB) filter. In this filter, the multi-target state is represented as a labeled multi-Bernoulli random finite set. For a set of existence probabilities r (l) and state space distributions p (l) The labeled multi-Bernoulli random finite set π = {(r (l) , p (l) )} is described by its probability density function as follows: π(X) = Δ(X) ω(L(X))p X (4) Intermediate variables: In formula (4) (5), the indication of different labels Δ(X) is 1 only when the labels of all targets in the state space are different, 1 L (j) is a set function, L is a label space, L is a set consisting of a group of labels, l represents a label, i and j represent labels belonging to a specific label space or set; x represents a state variable of a space target, and X represents a state space of a space target. Let the random finite set of multi-target posterior and the random finite set of new-born target be: Wherein, the subscript B represents a new-born target, and the LMB prediction method of the random finite set is: Wherein, the subscript + represents prior state information of a space target, the subscript S represents a surviving space target, and: p S (·|l) and η S (l) are the target survival probability and the integrated survival probability, respectively, p(·, l) denotes the probability density distribution function of the spatial distribution of the target with label l, and f(x|·, l) denotes the target dynamics model; further update the multi-target state based on the sensor observation value: where: L + represents a set of target label composition in prior state, represents a correspondence between all observations and labels, I is also a set of label composition, but the set needs to be a subset of L + , that is, the meaning of Ξ; θ represents a certain correspondence between observations and labels, which needs to belong to In addition, Z represents the observation value used to update the target state, p θ is calculated by the following formula: In the formula, p d represents the probability that the sensor can detect the target, Ρ(·) represents the intensity of the Poisson distributed clutter, and ll(·) represents the similarity between the observation value and the observation value; z θ(l) represents the observation value corresponding to the target with label l according to the correspondence θ.

5. The space situational awareness oriented space-based optical active-passive task planning method according to claim 1, characterized in that: The implementation of the new-born target state determination method in step two is as follows: For a set of observation values generated by the sensor at a moment, the observation values corresponding to the cataloged target are filtered out through a gating operation, and the observation values of the new-born target are extracted; The multi-target state label space obtained after LMB prediction is The gating observation value set corresponding to each label l in the space is calculated by formula (11): where d M denotes the Mahalanobis distance between observations, denotes the theoretical observation of the target, τ M denotes the gating threshold between observations and targets; for an observation of a sensor, if it is not gated with any target, it is determined as the observation of a new-born target: Based on the probability containment method, a LMB random finite set representing the initial orbit state of the new target can be generated according to the observation value of the new target; based on the energy constraint, the distance p between the new target and the observation value and the distance change rate satisfy: In the formula, E represents the energy of a space object, μ is the earth gravity constant, and r represents the position vector of the space object relative to the central celestial body; at the same time, the orbit of the new-born target also needs to satisfy the semi-major axis constraint and the eccentricity constraint, and a plurality of sampling points can be generated accordingly: In the formula, w i is the weight of the sampling point, a i is the semi-major axis size of the sampling point, e i is the eccentricity size of the sampling point, N is the number of sampling points, and p(a) and p(e) represent the probability distribution functions that the semi-major axis and eccentricity values satisfy, respectively; the sampling points in the space can be obtained by projecting the sampling points to the space determined by the energy constraint The sampling points in the space are fitted by a Gaussian mixture model using the maximum expectation algorithm, i.e., the Gaussian mixture of the new target orbit state is obtained: where M denotes the number of sampling points in the space, p B (x) denotes the track state of the newborn target, Q denotes the number of Gaussian components constituting the track state, w k denotes the weight of each Gaussian component, μ k , denote the mean and variance of each Gaussian component, respectively; p B (x) is combined with r B to obtain the LMB random finite set of the newborn target.

6. The space situational awareness oriented space-based optical active-passive task planning method according to claim 1, characterized in that: The implementation process of the new-born target label matching method in step three is as follows: The LMB random finite set of new born targets generated by two sensors according to step two and and The calculation method of the distance between each element in the inner is as follows: In the above formula, and Let w1 and w2 represent the sets of newly generated target labels generated by sensor 1 and sensor 2, respectively; the fusion weights w1 and w2 satisfy w1 + w2 = 1; based on this distance calculation method, a similarity matrix between elements in the two LMB random finite sets can be constructed; the width of this matrix is... The number of elements in the matrix, with length m+n being the sum of the number of elements in the two LMB random finite sets; where the first m columns of the matrix are... Zhongyu The distances between each element in the matrix, and the last n columns of the matrix are The distance between each element in B1 and the empty set in B2 is calculated using the following method for the elements of this n-column matrix: where r β represents the probability of birth of the target, p 2,d (x) represents the detection probability of the sensor for the corresponding target; Based on the above similarity matrix, the rank assignment problem can be constructed according to the correspondence between the elements in the matrix and the elements in the matrix and the elements in the matrix and the elements in the matrix, and the rank assignment problem is solved by using the Mertens method, that is, the correspondence between the new targets in different sensors is identified.

7. The space situational awareness oriented space-based optical active-passive task planning method according to claim 1, characterized in that: The implementation method of the multi-sensor information fusion based on label matching in step three is as follows: The elements in the LMB random finite set information contained in different sensors can be fused on the premise that the labels are the same; since the labels of the cataloged target and the new-born target are necessarily different, the multi-sensor information fusion problem can be divided into two independent sub-problems: information fusion of the cataloged target and information fusion of the new-born target; For information fusion of catalogued targets, let the LMB random finite sets of such targets in two sensors be and Then for and The targets corresponding to the labels contained in both, i.e. the information fusion of the corresponding targets in two sensors, the fused LMB random finite set is Wherein: When only one of the two sensors contains the corresponding label for some targets, it is determined that the sensor without the label has missed detection, and the information containing the label is fused with the empty set. The corresponding calculation method is: Where: In the above formula, and LMB parameters representing a single element, represents the probability of missing detection, p 3,d (x) represents the probability of observation of the target by the sensor without the corresponding target state element; Will With The fusion result of the target state corresponding to the label contained in both of the two sensors is merged with the calculation result of only one of the two sensors containing the corresponding label, that is, the fusion result of the two sensors for the inventoried target. For the information fusion of new-born targets, label matching is performed on the new-born targets according to formula (16) and formula (17). For the mutually matched new-born target information, the information is fused in the same way as the information fusion of the cataloged target information contained by both sensors, as shown in formula (18) and formula (19). For the mutually unmatched new-born target information, it is determined that the other sensor has missed detection, and the information is fused in the same way as the missed detection of one of the information fusion of the cataloged target information, as shown in formula (20) and formula (21). The fused new-born target is given a different label from the cataloged target, and is combined with the fusion result of the cataloged target state information as the input of the prediction process of the multi-target tracking filter in step two.

8. The space situational awareness oriented space-based optical active-passive mission planning method according to claim 1, characterized in that: The implementation method of the task planning in step four is as follows: For a certain space target, if the state estimation probability density functions before and after observation are p k|k-1 and p k , then the Rényi information gain obtained by the observation behavior is: In the formula, α is a dimensionless parameter; the probability density function corresponding to the LMB random finite set, i.e. formula (4), is brought into formula (22) to obtain: In the formula: In this equation, N k|k-1 and N k respectively represent the number of Gaussian components of the Gaussian mixture representing the state before and after observation. The observation priority of the new-born target is introduced and embedded in the Rényi information gain to improve the attention of active observation to the new-born target. The observation priority of the new-born target is defined as: where t represents the current time, t B denotes the time of birth of the target; and the method for embedding the Rényi information gain of the new target observation priority is: The weight part of the Rényi information gain in formula (26) is limited in a fixed interval, so this embedding method does not destroy the original structure. At the same time, the introduced observation priority of the new-born target is exponentially nonlinearly decaying, so that the new target can obtain priority observation at multiple time points after being discovered for the first time, and the observation priority rapidly decreases after the cataloging accuracy is improved. In addition, the function can also ensure that the priority of the target decreases slowly after a long time, avoiding the problem of low observation gain of the cataloged target; The Rényi information gain obtained based on the above method is used for task planning of the space situation awareness sensor, comprehensively evaluates the urgency of additional observation of the new-born target and the degree of state uncertainty of the cataloged target, guides the sensor to preferentially observe the target with relatively large uncertainty, improves the utilization efficiency of observation resources, and realizes the space-based optical active and passive task planning for space situation awareness.

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