Space debris bistatic detection data fusion method based on Bayesian rule

Abstract

The invention provides a space debris bistatic detection data fusion method based on a Bayesian rule, and the method comprises the following steps: 1, building a detection model: obtaining a detection probability and detection data distribution through a space-based in-situ simulation detection model and a foundation narrow-beam radar simulation detection model based on the orbit parameters of given space debris; step 2, inputting detection data and performing inversion; and step 3, calculating the number of fragments by using a space debris bistatic detection data fusion method based on a Bayesian rule. According to the method, the limitation of a single observation mode is overcome, and the reliability of environment modeling is improved; compared with a single data source, the data obtained by the two detection modes can complement each other, and the obtained information is more complete; and theoretical support is provided for cooperation of fragment monitoring. Data fusion supports data sharing of space monitoring institutions of different countries and regions to cope with challenges brought by space debris together.

Description

Technical Field

[0001] The present invention belongs to the technical field of space debris environment modeling, and in particular relates to a space debris dual-base detection data fusion method based on Bayesian rule. Background Art

[0002] As human space activities increase, the amount of space debris is also increasing year by year. To better understand the current and future state of the debris environment and provide a scientific basis for spacecraft design, risk assessment, collision warning, and debris mitigation and removal strategies, it is necessary to establish a space debris environment model. Detection data is an important data source for establishing space debris environment models. There are two methods for detecting space debris:

[0003] First, narrow-beam dwell-mode radar observations. This type of radar typically produces statistical data that can serve as raw data for space debris modeling. Compared to on-orbit collision detection, radar sampling times are longer, yielding more extensive and detailed data, and allowing for greater flexibility in station placement. However, radar is susceptible to limitations in its transmit power and wavelength, as well as the effects of ground clutter and atmospheric losses.

[0004] Second, space-based direct impact detection uses spacecraft to collide directly with space debris to obtain information on its velocity and position. Compared to radar detection, direct space-based detection data is more accurate, but it cannot provide information on the debris' orbital parameters. The data it can provide is more coarse and statistical.

[0005] While both space-based in-situ collision detection and ground-based narrow-beam dwell mode radar detection have their advantages, they also have their limitations. Using data from only one detection source is subject to the limitations and errors of a single detection method, and cannot fully utilize the detection data obtained from multiple detection methods. Summary of the Invention

[0006] In order to solve the above technical problems, the present invention proposes a space debris dual-base detection data fusion method based on the Bayesian rule, the specific steps are as follows:

[0007] Step 1: Establish a detection model: Based on the orbital parameters of the given space debris, use space-based in-situ simulation and ground-based narrow-beam radar simulation detection models to obtain the detection probability and detection data distribution;

[0008] Step 2: Input detection data and perform inversion;

[0009] Step 3: Calculate the number of debris using the space debris dual-base detection data fusion method based on the Bayesian rule;

[0010] The orbital parameters include the debris orbit perigee height dp, eccentricity, and orbital inclination; the space-based in-situ collision detection data include the mean anomaly angle of the detector at the time of collision, the impact velocity and the impact surface number; the ground-based narrow-beam resident mode radar detection data includes ranging and velocity measurement.

[0011] The process of establishing the space-based in-situ collision simulation detection model is as follows:

[0012] (1) Based on the given distribution of space debris and detectors, the space debris and detectors are discretized into various units in space;

[0013] (2) Calculate the spatial density of space debris and detectors for each unit;

[0014] (3) Combine the molecular kinematics theory to calculate the collision probability, and apply the orbital dynamics theory to calculate the relative collision position, collision speed, magnitude and direction, and detection probability (i.e., the probability of collision between space debris and the detector).

[0015] The process of establishing the ground-based narrow beam radar simulation detection model is as follows:

[0016] (1) Establish a functional in is the latitude of the target obtained from the target's orbital parameters, is the latitude of the target obtained based on the geometric relationship of the target in space observed by the radar, and both are numerical models rather than analytical models;

[0017] (2) Use the bisection method to find the value of θ that makes f = 0, and calculate the position vector and velocity vector of the space target at θ. If this value does not exist, it means that the radar cannot detect this space target;

[0018] (3) Calculate the orbital height r of the space target at θ and the detection limit l of the radar at the orbital height r s , compare the spatial target size l s The size of and determines whether the radar can detect this space target;

[0019] (4) If the radar’s detection performance meets the standards, calculate the radar observation data of the space target, i.e., the range and velocity;

[0020] (5) Calculate the radar detection probability based on the orbital parameters, orbital altitude r, beam angle θ, radar detection time, etc. of the space target.

[0021] The specific steps of step 2 are as follows:

[0022] (1) Discretize the parameters of the debris orbit parameter space to obtain the prior distribution of the debris orbit parameter space and the debris orbit parameter in a certain space unit A iPrior probability

[0023] (2) Input the debris orbit parameters into the space-based in-situ collision simulation detection model and the ground-based narrow-beam radar simulation detection model respectively to obtain the simulated detection sample data and detection probability Furthermore, use the Bayesian formula to calculate the conditional probability

[0024]

[0025] (3) Input the actually detected sample data, discretize the sample data to obtain the probability distribution P[B j , and use the total probability formula to obtain the probability of the debris orbit parameters in the parameter unit A i , that is, the posterior probability P[A i ;

[0026] (4) Subtract the obtained posterior probability P[A i from the prior probability . The difference function is f(i). If the maximum absolute value of the difference function f(i) is within the allowable error range, that is, Maxf(i) < erro, then the obtained posterior probability P[A i can be used as the final posterior probability; otherwise, set the obtained posterior probability P[A i as the prior probability and repeat the above process.

[0027] The debris orbit parameter space refers to the parameter space composed of the orbit inclination i, orbit eccentricity e, and perigee height dp of the debris. Discretize the parameter space by dividing the three parameters at a certain step size, that is, obtain the parameter space unit A i (i = 1, 2…n), where n is the total number of divided space units, and the step size is set to 5 - 20.

[0028] The Bayesian formula in step (2) is as follows:

[0029]

[0030]

[0031] where i is the parameter space unit number and j is the sample space unit number.

[0032] Step three is specifically as follows:

[0033] Using the final posterior probabilities of the space-based in-situ collision simulation detection model and the ground-based narrow-beam radar simulation detection model obtained in step 2, a random variable satisfying the 0-1 distribution is used to characterize whether the debris is in a certain parameter space unit, and its mean and variance are calculated. Then, the central limit theorem is used to calculate its quantitative confidence interval, and the average value of the confidence interval is taken as the number of debris in the space unit. The number of debris N1 and N2 in the space unit of the space-based in-situ collision simulation detection model and the ground-based narrow-beam radar simulation detection model are obtained. The space debris dual-base detection data fusion method based on the Bayesian rule is used to obtain the final number of debris in the space unit.

[0034] The steps for calculating the mean and variance are as follows:

[0035] The probability of the fragments obtained in step 2 being detected in a specific unit is recorded as p, the total number of fragments in this unit is recorded as N, and whether the fragment collides with the detector is recorded as the random variable X. i To describe, let X i If it obeys the (0,1) distribution, its mean and variance are:

[0036] E(X i )=p (3)

[0037] Var(X i )=p(1-p) (4)

[0038] Where i = 1, 2, ... N.

[0039] The confidence interval for the quantity is calculated as follows:

[0040] According to the central limit theorem:

[0041]

[0042] in is the total number of debris detected during the observation duration, so

[0043]

[0044]

[0045] The confidence interval (B1, B2) of the total number of debris N in the orbital parameter space with a confidence level of 1-α can be obtained, where

[0046]

[0047]

[0048] The average of the confidence intervals is taken as the total number of fragments N in the cell.

[0049] The Bayesian rule is:

[0050] The two sets of detection data obtained by space-based in-situ collision detection and ground-based narrow-beam radar detection are respectively processed to obtain the total number of debris N1 and N2, and the probability p1 and p2. Then:

[0051]

[0052]

[0053] Then the estimated value according to the data fusion based on Bayesian rule is:

[0054]

[0055] The beneficial effects of the present invention are as follows:

[0056] 1. Overcome the limitations of a single observation method and improve the reliability of environmental modeling. A single observation method is subject to its own observation principles and equipment accuracy, which will produce corresponding errors. The results obtained by using data fusion can reduce uncertainty and errors and improve the reliability of environmental modeling.

[0057] 2. Improved data integrity: Compared to a single data source, the data obtained from the two detection modes can complement each other, providing more complete information.

[0058] 3. Provide theoretical support for cooperation in debris monitoring. Data fusion supports space monitoring agencies in different countries and regions to share data and jointly address the challenges posed by space debris. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Flowchart of the present invention;

[0060] Figure 2 This is a flow chart of the inversion part of the present invention;

[0061] Figure 3 The results obtained by inverting radar detection data of the simulation example;

[0062] Figure 4 This is the result obtained by inverting the space-based in-situ detection data of the simulation example;

[0063] Figure 5 This is the simulation example data fusion result. DETAILED DESCRIPTION

[0064] The specific implementation of the present invention will be described in detail below with reference to the accompanying drawings.

[0065] The flow chart of the present invention is as follows Figure 1 As shown in Figure 2, the data fusion method is specifically as follows:

[0066] Step 1: Establishment of detection model.

[0067] First, the distribution range of the debris swarm's orbital parameters is determined based on prior information, and a debris swarm with a certain number of debris is generated. The perigee height of the debris swarm follows a normal distribution within the selected range, and the remaining parameters follow a uniform distribution. This is the parameter space.

[0068] Based on the orbital parameters of given space debris, the detection probability and detection data distribution are obtained using space-based in-situ simulation and ground-based narrow-beam radar simulation detection models.

[0069] The process of establishing the space-based in-situ collision simulation detection model is as follows:

[0070] (1) Based on the given distribution of space debris and detectors, the space debris and detectors are discretized into various units in space;

[0071] (2) Calculate the spatial density of space debris and detectors for each unit;

[0072] (3) Combine the molecular kinematics theory to calculate the collision probability, and apply the orbital dynamics theory to calculate the relative collision position, collision speed, magnitude and direction, and detection probability (i.e., the probability of collision between space debris and the detector).

[0073] The process of establishing the ground-based narrow-beam radar simulation detection model is as follows:

[0074] (1) Establish a functional in is the latitude of the target obtained from the target's orbital parameters, is the latitude of the target obtained based on the geometric relationship of the target in space observed by the radar, and both are numerical models rather than analytical models;

[0075] (2) Use the bisection method to find the value of θ that makes f = 0, and calculate the position vector and velocity vector of the space target at θ. If this value does not exist, it means that the radar cannot detect this space target;

[0076] (3) Calculate the orbital height r of the space target at θ and the detection limit l of the radar at the orbital height r s , compare the spatial target size l s The size of and determines whether the radar can detect this space target;

[0077] (4) If the radar’s detection performance meets the standards, calculate the radar observation data of the space target, i.e., the range and velocity;

[0078] (5) Calculate the radar detection probability based on the orbital parameters, orbital altitude r, beam angle θ, radar detection time, etc. of the space target.

[0079] Step 2: Input the detection data and perform inversion, Figure 2 which is the flowchart of the inversion part of the present invention.

[0080] The specific steps of Step 2 are as follows:

[0081] (1) Discretize the parameters in the debris orbit parameter space to obtain the prior distribution of the debris orbit parameter space and the prior probability of the debris orbit parameters in a certain space unit A i ;

[0082] (2) Input the debris orbit parameters into the space-based in-situ collision simulation detection model and the ground-based narrow-beam radar simulation detection model respectively to obtain the simulated detection sample data and the detection probability and then calculate the conditional probability using Bayes' formula

[0083]

[0084] (3) Input the actually detected sample data, perform discretization processing on the sample data to obtain the probability distribution P[B j , and use the total probability formula to obtain the probability of the debris orbit parameters in the parameter unit A i , that is, the posterior probability P[A i ;

[0085] (4) Subtract the obtained posterior probability P[A i from the prior probability , and the difference function is f(i). If the absolute value maximum of the difference function f(i) is within the allowable error range, that is, Maxf(i)<erro, then the obtained posterior probability P[A i can be used as the final posterior probability; otherwise, set the obtained posterior probability P[A i as the prior probability and repeat the above process.

[0086] The debris orbit parameter space refers to the parameter space composed of the orbit inclination i, orbit eccentricity e, and perigee altitude d of the debris. The parameter space is discretized by dividing the three parameters at a certain step size, that is, the parameter space unit A p (i = 1, 2... n) is obtained, where n is the total number of divided space units, and the step size is set to 5 - 20. i ;

[0087] The Bayes' formula in step (2) is:

[0088]

[0089]

[0090] Where i is the parameter space unit number, and j is the sample space unit number.

[0091] Step 3: Calculate the number of debris using the space debris dual-base detection data fusion method based on the Bayesian rule;

[0092] The orbital parameters include the perigee height, eccentricity, and orbital inclination of the debris orbit; the space-based in-situ collision detection data include the mean anomaly angle, impact velocity, and impact surface number of the detector at the time of collision; and the ground-based narrow-beam resident mode radar detection data includes ranging and velocity measurement.

[0093] Step three is as follows:

[0094] Using the final posterior probabilities of the space-based in-situ collision simulation detection model and the ground-based narrow-beam radar simulation detection model obtained in step 2, a random variable satisfying the 0-1 distribution is used to characterize whether the debris is in a certain parameter space unit, and its mean and variance are calculated. Then, the central limit theorem is used to calculate its quantitative confidence interval, and the average value of the confidence interval is taken as the number of debris in the space unit. The number of debris N1 and N2 in the space unit of the space-based in-situ collision simulation detection model and the ground-based narrow-beam radar simulation detection model are obtained. The space debris dual-base detection data fusion method based on the Bayesian rule is used to obtain the final number of debris in the space unit.

[0095] The steps for calculating the mean and variance are as follows:

[0096] The probability of the fragments obtained in step 2 being detected in a specific unit is recorded as p, the total number of fragments in this unit is recorded as N, and whether the fragment collides with the detector is recorded as the random variable X. i To describe, let X i If it obeys the (0,1) distribution, its mean and variance are:

[0097] E(X i )=p (3)

[0098] Var(X i )=p(1-p) (4)

[0099] Where i = 1, 2, ... N.

[0100] The confidence interval for the quantity is calculated as follows:

[0101] According to the central limit theorem:

[0102]

[0103] in is the total number of debris detected during the observation duration, so

[0104]

[0105]

[0106] The confidence interval (B1, B2) of the total number of debris N in the orbital parameter space with a confidence level of 1-α can be obtained, where

[0107]

[0108]

[0109] The average of the confidence intervals is taken as the total number of fragments N in the cell.

[0110] The Bayesian rule is:

[0111] The two sets of detection data obtained by space-based in-situ collision detection and ground-based narrow-beam radar detection are respectively processed to obtain the total number of debris N1 and N2, and the probability p1 and p2. Then:

[0112]

[0113]

[0114] Then the estimated value according to the data fusion based on Bayesian rule is:

[0115]

[0116] Simulation example:

[0117] The present invention provides a specific implementation case. A debris group is generated, and the range of its orbital parameters is shown in Table 1. The right ascension of the ascending node and the angular distance of the perigee are uniformly distributed within the range, and the perigee height, orbital inclination, and eccentricity are randomly generated. The number of debris is 10 6 indivual.

[0118] Table 1 Distribution of orbital parameters of debris clusters

[0119]

[0120] The prior distribution used in this example is uniform distribution, and the number of grid divisions in the debris orbit parameter space, that is, the number of divisions (i.e., step sizes) of the perigee altitude, orbit inclination, and eccentricity within their range are 20, 5, and 10, respectively.

[0121] The radar used for radar observation in this example is the Haystack radar, and its observation area is shown in Table 2.

[0122] Table 2 Haystack radar observation area

[0123]

[0124] The radar observation model is used to simulate the observation at an elevation angle of 75° due east, and the simulated detection data is obtained for inversion. The distribution of the number of debris in each parameter space unit is obtained, such as Figure 3 shown.

[0125] The orbital parameters of the detector used in the space-based in-situ detection in this example are shown in Table 3. The inversion results are as follows Figure 4 shown.

[0126] Table 3 Detector orbit parameters

[0127]

[0128] The result after data fusion is as follows Figure 5 shown.

Claims

1. A space debris dual-base detection data fusion method based on Bayesian rule, the specific steps are as follows: Step 1: Establishment of detection model: Based on the orbital parameters of given space debris, the detection probability and detection data distribution are obtained by using space-based in-situ simulation and ground-based narrow beam radar simulation detection models respectively; Step 2: Input detection data and perform inversion; Step 3: Calculate the number of debris using the space debris dual-base detection data fusion method based on the Bayesian rule; The orbital parameters include the debris orbit perigee height dp, eccentricity, and orbital inclination; the space-based in-situ collision detection data include the mean anomaly angle of the detector at the time of collision, the impact velocity and the impact surface number; the ground-based narrow beam resident mode radar detection data includes ranging and velocity measurement.

2. The space debris dual-base detection data fusion method based on Bayesian rule according to claim 1 is characterized in that: The process of establishing the space-based in-situ collision simulation detection model is as follows: (1) Based on the given distribution of space debris and detectors, the space debris and detectors are discretized into various units in space; (2) Calculate the spatial density of space debris and detectors for each unit; (3) The collision probability is calculated by combining the molecular kinematics theory, and the orbital dynamics theory is used to calculate the relative collision position, collision velocity, magnitude and direction, and detection probability.

3. The space debris dual-base detection data fusion method based on Bayesian rule according to claim 1 is characterized in that: The process of establishing the ground-based narrow beam radar simulation detection model is as follows: (1) Create a functional in is the latitude of the target obtained from the orbital parameters of the target, is the latitude of the target obtained based on the geometric relationship of the space target observed by the radar; (2) Use the binary method to find the value of θ that makes f = 0, and calculate the position vector and velocity vector of the space target at. If this value does not exist, it means that the radar cannot detect this space target; (3) Calculate the orbital height r of the space target at θ and the detection limit l of the radar at the orbital height r s , compare the spatial target size l s and the size of the target to determine whether the radar can detect the space target; (4) If the radar detection performance meets the standard, calculate the radar observation data of the space target, i.e., the range and speed measurement; (5) Calculate the radar detection probability based on the orbital parameters of the space target, orbital altitude r, beam angle θ, radar detection time, etc.

4. The space debris dual-base detection data fusion method based on Bayesian rule according to claim 1 is characterized in that: The specific steps of step 2 are as follows: (1) Discretize the parameters of the debris orbit parameter space to obtain the prior distribution of the debris orbit parameter space and the debris orbit parameter in a certain space unit A. i The prior probability (2) Input the debris orbit parameters into the space-based in-situ collision simulation detection model and the ground-based narrow beam radar simulation detection model to obtain the simulated detection sample data and detection probability Then, the conditional probability is calculated using the Bayesian formula (3) Input the sample data actually detected, discretize the sample data, and obtain the probability distribution P[B j ], using the total probability formula to obtain the debris orbit parameters in parameter unit A i The probability in, that is, the posterior probability P[A i ]; (4) Subtract the obtained posterior probability \(P[A i \) from the prior probability The difference function is \(f(i)\). If the maximum absolute value of the difference function \(f(i)\) is within the allowable error range, that is, \(Maxf(i)<erro\), then the obtained posterior probability \(P[A i \) can be used as the final posterior probability; otherwise, assume that the obtained posterior probability \(P[A i \) is the prior probability Repeat the above process.

5. The method for fusion of space debris dual-base detection data based on Bayesian rule according to claim 4 is characterized in that: The debris orbit parameter space refers to the parameter space composed of the debris orbit inclination i, orbit eccentricity e, and perigee height dp. The parameter space is discretized by dividing the three parameters according to a certain step size, that is, the parameter space unit A is obtained. i (i=1, 2...n), wherein n is the total number of divided space units, and the step size is set to 5-20.

6. The method for fusion of space debris dual-base detection data based on Bayesian rule according to claim 4 is characterized in that: The Bayesian formula in step (2) is: Where i is the parameter space unit number and j is the sample space unit number.

7. The space debris dual-base detection data fusion method based on Bayesian rule according to claim 1 is characterized in that: Step three is as follows: Using the final posterior probabilities of the space-based in-situ collision simulation detection model and the ground-based narrow-beam radar simulation detection model obtained in step 2, use a random variable satisfying the 0-1 distribution to characterize whether the debris is in a certain parameter space unit, find its mean and variance, and then use the central limit theorem to find its quantitative confidence interval, take the average value of the confidence interval as the number of debris in the space unit, and get the number of debris N1 and N2 in the space unit of the space-based in-situ collision simulation detection model and the ground-based narrow-beam radar simulation detection model. Use the space debris dual-base detection data fusion method based on the Bayesian rule to get the final number of debris in the space unit.

8. The method for fusion of space debris dual-base detection data based on Bayesian rule according to claim 7 is characterized in that: The steps for calculating the mean and variance are as follows: The probability of the fragment obtained in step 2 being detected in a specific unit is recorded as p, the total number of fragments in this unit is recorded as N, and whether the fragment collides with the detector is expressed as a random variable X. i To describe, let X i It follows a (0,1) distribution, and its mean and variance are: FORMER i )=p (3) There is(X i )=p(1-p) (4) Where i=1,2,...N.

9. The method for fusion of space debris dual-base detection data based on Bayesian rule according to claim 7 is characterized in that: The calculation method of the quantitative confidence interval is as follows: From the central limit theorem we get: in is the total number of debris detected during the observation duration, so The confidence interval (B1, B2) of the total number of debris N in the orbital parameter space with a confidence level of 1-α can be obtained, where The average of the confidence intervals is taken as the total number of fragments N within the cell.

10. The method for dual-base detection data fusion of space debris based on Bayesian rule according to claim 7, characterized in that: The Bayesian rule is: The two sets of detection data obtained by space-based in-situ collision detection and ground-based narrow beam radar detection are respectively used to obtain the total number of debris N1, N2, and the probability p1, p2. Then: Then the estimated value according to the data fusion based on Bayesian rule is:

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