Time-matched Poisson multi-Bernoulli filtering multi-target tracking method
Through the time-matched Poisson multi-Bernoulli filtering method, the problem of sampling time mismatch in radar target tracking is solved, the filtering accuracy and robustness are improved, the time complexity is reduced, and efficient multi-target tracking is achieved.
Patent Information
- Application Number
- CN202410361650.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-03-27
- Publication Date
- 2025-09-30
AI Technical Summary
In radar target tracking, the problem of reduced filtering accuracy caused by sampling time mismatch is difficult to be effectively solved by existing technologies.
A time-matched Poisson-multi-Bernoulli filtering method is adopted. Through the Gaussian mixture Poisson-multi-Bernoulli mixture filter, time matching is achieved under the linear Gaussian dynamic and measurement models. Combined with the KLD divergence approximation, the Poisson-Bernoulli filter is optimized, which is suitable for the scanning and tracking mode and reduces the impact of sampling time diversity.
The estimation accuracy of target state and cardinality is improved, filtering time is reduced, and the method has high robustness, which is superior to the performance of other filters in unidirectional electronic scanning mode.
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Figure CN120722339A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a multi-target tracking method using time-matched Poisson multi-Bernoulli filtering, and in particular to an improved Gaussian mixture Poisson multi-Bernoulli (PMB) filtering tracking method. The method is based on Bayesian filtering technology, belongs to the field of radar data processing technology, and can be used in radar systems such as phased arrays, traffic control, and unmanned driving. Background Art
[0002] Target tracking refers to the process of estimating the target state based on measurements obtained by sensors (such as radar). Target tracking is typically performed using Bayesian filtering, which involves two models and two steps: a motion model and a measurement model, and a prediction step and an update step. The prediction step primarily utilizes the motion model to describe how the target's motion state changes over time, while the update step primarily utilizes the measurement model to adjust the target's state. Depending on the number of targets to be tracked, target tracking can be divided into single-target tracking and multi-target tracking. Single-target methods primarily use Kalman filtering and particle filtering, while multi-target methods use data association algorithms and random finite sets. Multi-target methods are also based on single targets.
[0003] In recent years, the random finite set method (RFS) has developed rapidly, from probability hypothesis density filtering (PHD), potential probability hypothesis density filtering (CPHD), multi-Bernoulli filtering (MB), generalized label multi-Bernoulli filtering (GLMB) to trajectory probability hypothesis density filtering (TPHD), Poisson multi-Bernoulli mixture filtering (PMBM) and Poisson multi-Bernoulli filtering (PMB) in recent years. These filters accurately capture the problems of target and measurement difficulty, target missed detection or false detection, and difficulty in determining the birth position of new targets during target tracking, demonstrating their good problem-solving capabilities.
[0004] However, methods based on random finite sets assume that measurements are acquired at the same instant in time during each scan, at the very end of the scan. This differs from the target measurement sampling during the radar scan. Ignoring the sampling time of each measurement leads to a mismatch between the prediction time and the measurement time, resulting in degraded filtering performance. Considering the timestamp issue, time matching methods have been introduced into random finite set target tracking. PHD and GLMB have been used to time match point and extended targets. Time-matched RFS filtering can effectively address the sampling time diversity issue in radar target tracking. Summary of the Invention
[0005] To address the problem of inaccurate tracking and reduced filtering accuracy caused by sampling time mismatch in radar target tracking, the present invention provides a multi-target tracking method using a time-matched Poisson multi-Bernoulli filter. The core technology of the method lies in providing a TM-PMBM filter based on a Gaussian mixture Poisson multi-Bernoulli mixture (PMBM) filter and an implementation method of the TM-PMBM filter under the KLD divergence approximation under a linear Gaussian dynamic and measurement model. The performance of the TM-PMB filter is compared with other time-matched RFS filters in a track-while-scan (TWS) unidirectional scanning mode. The proposed filter can effectively reduce the impact of sampling time diversity, improve the estimation accuracy of target state and cardinality, require less filtering time, and has high robustness.
[0006] The present invention adopts the following technical solutions to solve the above technical problems:
[0007] 1. The present invention provides a multi-target tracking method using time-matched Poisson multi-Bernoulli filtering, comprising the following steps:
[0008] Step 1. Initialization of multi-target state:
[0009] Assume that the given target follows a Gaussian linear motion model and the measurement model is also a Gaussian linear model. In the filter, the survival probability and detection probability are independent of the target's temporal state and are set to constants. Let the posterior Poisson intensity and posterior Bernoulli component density at the end of the k-1 scanning period be: and
[0010] Step 2 is the sampling time set within the k-1th scanning cycle, where the predicted time component is based on the single measurement time t m Assigned. The prediction step of the detectable target is as follows:
[0011] (2a) The Poisson point process component (PPP) is predicted based on the measurement time, which is mainly the PPP of the previous moment plus the new PPP. A PPP prediction is performed at each measurement time.
[0012] (2b) The Bernoulli component (MB) also needs to be predicted based on the measurement time, and an MB prediction must be performed for each measurement time.
[0013] Step 3: Update the detectable targets. The detected potential targets are composed of two parts: the new Bernoulli component generated by the measurement, which may generate a new track, and the previous Bernoulli component related to the measurement. The specific steps are:
[0014] (3a) The PPP component generates the potential first detected target, i.e. a new Bernoulli component is created for each measurement:
[0015] (3b) After the Bayesian update of the potential new trajectory, the relevant measurements should be considered to connect with the previous trajectory, that is, the measurement update of the Bernoulli component.
[0016] Step 4: We will uniformly set the time t at the end of the k-th scanning cycle e As the filtering moment of the PPP component and the Bernoulli component, because it cannot find a suitable time to match them, and the Poisson component and the Bernoulli component take the entire scanning time to filter. The prediction step of the undetected target is as follows:
[0017] (4a) The Poisson point process component (PPP) is calculated based on the end time of the period t e Make predictions;
[0018] (4b) The Bernoulli component (MB) also needs to be calculated based on the end time of the cycle t e Make predictions.
[0019] Step 5: Update step for undetected targets. Specific steps:
[0020] (5a) Poisson point process component (PPP) update;
[0021] (5b) Bernoulli component (MB) update.
[0022] Step 6: Determine the new global hypothesis, mainly through the Murty algorithm to select the formation and deletion of the global hypothesis, and select the new global hypothesis with the highest weight. Generate the cost matrix C based on the association weights of the generated potential detection targets and the measurement value Z j :
[0023] Step 7: Delete and recycle unnecessary global assumptions and Bernoulli components:
[0024] First, global hypotheses with weights above a threshold are retained. Second, hypotheses with no necessary connections are removed. Third, if the sum of all Bernoulli components with a smaller probability than the sum of all connections increases the computational burden, these should be removed as appropriate. Fourth, global hypotheses are weighted and merged.
[0025] Step 8: Perform KLD minimization approximation on the multi-Bernoulli mixture approximation components, and reduce multiple global hypotheses to a single global hypothesis.
[0026] Step 9: Extract states from the global hypothesis and Bernoulli components with higher weights.
[0027] 2. As a further technical solution of the present invention, the setting of the two linear Gaussian models in step 1 and the detection probability and survival probability are:
[0028] f(x,t|x′,t′)=N(x;F(t|t′)x′,Q(t|t′)),
[0029] h(z,t|x,t)=N(z;H(t)x,R),
[0030] p S，k (x′, t′)=p S，k , p D，k (x, t) = p D，k
[0031] 3. As a further technical solution of the present invention, the prediction of the PPP component in step 2 is specifically as follows:
[0032]
[0033]
[0034] in
[0035]
[0036]
[0037]
[0038] Where, and J p They represent the new Poisson intensity, the number of new components and the weight respectively.
[0039] The prediction of the Bernoulli component is:
[0040]
[0041]
[0042] in
[0043]
[0044]
[0045]
[0046] 4. As a further technical solution of the present invention, the PPP measurement update in step 3 is specifically as follows:
[0047]
[0048]
[0049] in
[0050]
[0051]
[0052]
[0053]
[0054]
[0055]
[0056]
[0057] The measurement update of the Bernoulli component is as follows:
[0058]
[0059]
[0060] in
[0061]
[0062]
[0063]
[0064]
[0065]
[0066]
[0067] 5. As a further technical solution of the present invention, the prediction of the PPP of the undetected portion in step 4 is specifically as follows:
[0068]
[0069]
[0070] The prediction of the Bernoulli component of the undetected part is:
[0071]
[0072]
[0073] 6. As a further technical solution of the present invention, the updating of the undetected portion of PPP in step 5 is specifically as follows:
[0074]
[0075] in
[0076]
[0077]
[0078]
[0079] The update of the Bernoulli component of the undetected part is as follows:
[0080]
[0081]
[0082]
[0083] in
[0084]
[0085]
[0086] 7. As a further technical solution of the present invention, the determination of the global hypothesis in step 6 is specifically as follows:
[0087] C j =-ln[W o , W N ]
[0088] in
[0089]
[0090]
[0091]
[0092] Where is the weight matrix after removing clutter from the updated n old tracks in m measurements, and is the diagonal matrix of pure measurement weights.
[0093] 8. As a further technical solution of the present invention, the unique global hypothesis generated in step 7 is specifically:
[0094]
[0095]
[0096] in
[0097] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:
[0098] (1) Based on the Poisson-Multi-Bernoulli filter (PMB), the time matching method is used to improve the Poisson-Bernoulli filter to address the problem of sampling time differentiation during the sensor scanning process. The calculation formulas for different types of time-tagged targets are given, and a reasonable conjugate prior representation is used for the union of the Poisson point process and the Multi-Bernoulli mixture.
[0099] (2) The Gaussian mixture implementation of the linear-Gaussian dynamic model and the measurement model TM-PMBM as well as the TM-PMB filter is given in detail from the perspective of sampling time;
[0100] (3) The simulation results verify the superiority of the time-matched Poisson-Bernoulli hybrid filter structure and the conjugate prior form, solving the time problem of mismatch between prediction and update. In the TWS scanning mode with unidirectional electronic scanning, the TM-PMB filter outperforms other filters. BRIEF DESCRIPTION OF THE DRAWINGS
[0101] Figure 1 It is a basic flow chart of the present invention.
[0102] Figure 2 It is a real trajectory diagram of simulation 1 in an embodiment of the present invention.
[0103] Figure 3 is a trajectory estimation diagram of simulation 1 in an embodiment of the present invention.
[0104] Figure 4 3 is a comparison chart of the average OSPA errors of 200 Monte Carlo experiments in simulation 1 in an embodiment of the present invention.
[0105] Figure 5 3 is a comparison chart of the average OSPA positioning distances after 200 Monte Carlo experiments in simulation 1 of the embodiment of the present invention.
[0106] Figure 6 3 is a comparison chart of the average OSPA cardinality of 200 Monte Carlo experiments in simulation 1 in an embodiment of the present invention.
[0107] Figure 7 3 is a comparison chart of average cardinalities of 200 Monte Carlo experiments in simulation 1 according to an embodiment of the present invention.
[0108] Figure 8 3 is a comparison chart of the average time required for simulating 1 through 200 Monte Carlo experiments in an embodiment of the present invention. DETAILED DESCRIPTION
[0109] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limiting the present invention.
[0110] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as such, will not be interpreted in an idealized or overly formal sense.
[0111] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings:
[0112] The invention adopts a time matching framework and takes the measurement sampling time into consideration in Bayesian conjugate prior filtering to perform recursive iteration to obtain a multi-target tracking method of time-matched Poisson multi-Bernoulli filtering.
[0113] The multi-target tracking method using a time-matched Poisson multi-Bernoulli filter employs specific labels for different target types after increasing the sampling time, and utilizes a reasonable conjugate prior representation for the combination of a Poisson point process and a multi-Bernoulli mixture. Simulation experiments based on a Gaussian mixture model demonstrate the superiority of the structure and conjugate prior formulation of the time-matched Poisson multi-Bernoulli mixture filter and the time-matched Poisson multi-Bernoulli filter, further verifying their effectiveness in addressing the temporal mismatch between the prediction and update scanning processes.
[0114] The present invention is a multi-target tracking method using time-matched Poisson multi-Bernoulli filtering, comprising the following steps:
[0115] Step 1. Initialization of multi-target state:
[0116] Assuming that the given target follows a Gaussian linear motion model, the measurement model is also a Gaussian linear model, as follows:
[0117] f(x,t|x′,t′)=N(x;F(t|t′)x′,Q(t|t′)),
[0118] h(z,t|x,t)=N(z;H(t)x,R),
[0119] In the filter, the survival probability and detection probability are independent of the time state of the target and are set to constants, which are specifically expressed as follows:
[0120] pS，k (x′, t′)=p S，k , p D，k (x, t) = p D，k
[0121] Let the posterior Poisson intensity and posterior Bernoulli component density at the end of k-1 scanning cycles be: and
[0122] Step 2 is the sampling time set within the k-1th scanning cycle, where the predicted time component is based on the single measurement time t m Assigned. The prediction step of the detectable target is as follows:
[0123] (2a) The Poisson point process component (PPP) is predicted based on the measurement time. It is mainly the PPP of the previous moment plus the new PPP. A PPP prediction is performed for each measurement time. The specific steps are as follows:
[0124]
[0125]
[0126] in
[0127]
[0128]
[0129]
[0130] Where w q and J p They represent the new Poisson intensity, the number of new components and the weight respectively.
[0131] (2b) The Bernoulli component (MB) also needs to be predicted based on the measurement time, and an MB prediction must be performed for each measurement time.
[0132] The prediction of the Bernoulli component is:
[0133]
[0134]
[0135] in
[0136]
[0137]
[0138]
[0139] Step 3: Update the detectable targets. The detected potential targets are composed of two parts: the new Bernoulli component generated by the measurement, which may generate a new track, and the previous Bernoulli component related to the measurement. The specific steps are:
[0140] (3a) The PPP component generates the potential first detected target, that is, a new Bernoulli component is created for each measurement. The specific measurement update is as follows:
[0141]
[0142]
[0143] in
[0144]
[0145]
[0146]
[0147]
[0148]
[0149]
[0150]
[0151] (3b) After the Bayesian update of the potential new track, the relevant measurements should be considered to connect with the previous track, that is, the measurement update of the Bernoulli component. The specific Bernoulli measurement update is as follows:
[0152]
[0153]
[0154] in
[0155]
[0156]
[0157]
[0158]
[0159]
[0160]
[0161] Step 4: We will uniformly set the time t at the end of the k-th scanning cycle e As the filtering moment of the PPP component and the Bernoulli component, because it cannot find a suitable time to match them, and the Poisson component and the Bernoulli component take the entire scanning time to filter. The prediction step of the undetected target is as follows:
[0162] (4a) The Poisson point process component (PPP) is calculated based on the end time of the period t e Make predictions;
[0163]
[0164]
[0165] (4b) The Bernoulli component (MB) also needs to be calculated based on the end time of the cycle t e Make predictions.
[0166]
[0167]
[0168] Step 5: Update step for undetected targets. Specific steps:
[0169] (5a) The Poisson point process component (PPP) is updated as follows:
[0170]
[0171] in
[0172]
[0173]
[0174]
[0175] (5b) The Bernoulli component (MB) is updated as follows:
[0176]
[0177]
[0178]
[0179] in
[0180]
[0181]
[0182] Step 6: Determine the new global hypothesis, mainly through the Murty algorithm to select the formation and deletion of the global hypothesis, and select the new global hypothesis with the highest weight. Generate the cost matrix C based on the association weights of the generated potential detection targets and the measurement value Z j :
[0183] C j =-ln[W o , W N ]
[0184] in
[0185]
[0186]
[0187]
[0188] Where is the weight matrix after removing clutter from the updated n old tracks in m measurements, and is the diagonal matrix of pure measurement weights.
[0189] Step 7: Delete and recycle unnecessary global assumptions and Bernoulli components:
[0190] First, global hypotheses with weights above a threshold are retained. Second, hypotheses with no necessary connections are removed. Third, if the sum of all Bernoulli components with a smaller probability than the sum of all connections increases the computational burden, these should be removed as appropriate. Fourth, global hypotheses are weighted and merged.
[0191] Step 8: Perform KLD minimization approximation on the multi-Bernoulli mixture approximation components, and reduce multiple global hypotheses to a single global hypothesis:
[0192]
[0193]
[0194] in
[0195] Step 9: Extract states from the global hypothesis and Bernoulli components with higher weights.
[0196] The algorithm and processing method of the present invention have been verified and achieved satisfactory application results:
[0197] 1. Experimental conditions: Assume that there are multiple targets moving in a uniform linear motion on the horizontal rectangular coordinate system XY plane. The target's motion state can be expressed as {x, v x , a x ,y,v y , a y}, where {x, y} are the position information of the target in the X and Y directions in the horizontal rectangular coordinate system, {v x , v y} are the speed information of the target in the X direction and Y direction in the horizontal rectangular coordinate system, {a x , a y} are the acceleration information of the target in the X and Y directions in the horizontal rectangular coordinate system. Initialize the state transfer matrix F, process noise Q, measurement transfer matrix H, and survival probability p S , detection probability p D , the clutter rate and area size in the scene are λ C and V, the time interval T = tt′, and the maximum number of hypotheses is set to 5.
[0198]
[0199]
[0200] P S =0.99
[0201] P D =0.85
[0202] λ C =10 V=4000×2000m 2
[0203] Evaluation parameters ospa: c = 200, p = 1
[0204] 2. Simulation content:
[0205] Simulation 1: Six targets are designed to move with uniform acceleration. The birth position and velocity information of each target are {1000, -13, 0.01, 100, 2, 0.35}, {-1500, 20, 0.15, 1000, -5, 0.16}, {-1200, 23, 0, 100, 16, 0}, {-1200, 13, 0.2, 100, 6, -0.1}, {-1200, 15, -0.3, 100, 10, 0.25}, {1000, -8, 0.15, 100, 8, 0.35}, and the birth and death times are {1, 75}, {1, 100}, {20, 100}, {20, 100}, {40, 100}, {40, 100}, and the tracking time is set to 100. Figure 2 This is the actual trajectory diagram of this scene. The circle represents the starting point and the triangle represents the end. Figure 3This is the trajectory estimation diagram for this scenario. The top shows the X-position estimation, and the bottom shows the Y-position estimation. The performance of the four filters used in this scenario, PHD, joint-GLMB, PMBM, and PMB, and their time-matched versions, TM-PHD, TM-joint-GLMB, TM-PMBM, and TM-PMB, are compared. Figure 4 This is the OSPA error comparison chart for this scenario. The OSPA error can be obtained by Figure 5 OSPA positioning error and Figure 6 The sum of the OSPA cardinality errors is: Figure 7 This is a comparison chart of the four filter bases mentioned above for this scenario. Figure 8 Reflects the time required for the four filters.
[0206] 3. Analysis of simulation results:
[0207] from Figure 3 and Figure 8 It can be seen that the method proposed in this patent can well achieve multi-target tracking while dealing with the diversity of sampling time.
[0208] from Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 It can be seen that the method proposed in this patent not only improves the estimation accuracy of the position and cardinality of the PMB filter, and significantly reduces the OSPA error, but also makes the filtering performance of TM-PMB significantly better than other filters, almost on par with TM-PMBM.
[0209] from Figure 8 It can be seen that the time complexity of the TM-PMB filter proposed in this patent is almost equivalent to that of the TM-PHD filter, and the filtering accuracy is greatly improved; compared with the TM-PMBM filter, the TM-PMB filter can greatly shorten the required filtering time under the same filtering accuracy, thereby improving real-time performance.
[0210] The simulation results demonstrate the effectiveness of the multi-target tracking method with time-matched Poisson multi-Bernoulli filtering proposed in this patent.
[0211] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person familiar with the technology can understand and think of any changes or replacements within the technical scope disclosed by the present invention, which should be included in the scope of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.
Claims
1. The present invention provides a multi-target tracking method using time-matched Poisson multi-Bernoulli filtering, comprising the following steps: Step 1. Initialization of multi-target state: Assume that the given target follows a Gaussian linear motion model and the measurement model is also a Gaussian linear model. In the filter, the survival probability and detection probability are independent of the target's temporal state and are set to constants. Let the posterior Poisson intensity and posterior Bernoulli component density at the end of the k-1 scanning period be: and Step 2 is the sampling time set within the k-1th scanning cycle, where the predicted time component is based on the single measurement time t m Assigned. The prediction step of the detectable target is as follows: (2a) The Poisson point process component (PPP) is predicted based on the measurement time, which is mainly the PPP of the previous moment plus the new PPP. A PPP prediction is performed at each measurement time. (2b) The Bernoulli component (MB) also needs to be predicted based on the measurement time, and an MB prediction must be performed for each measurement time. Step 3: Update step of detectable targets. The detected potential targets are composed of two parts: The new Bernoulli components generated by the measurement may generate new tracks, as well as the previous Bernoulli components related to the measurement. The specific steps are: (3a) The PPP component generates the potential first detected target, i.e. a new Bernoulli component is created for each measurement: (3b) After the Bayesian update of the potential new trajectory, the relevant measurements should be considered to connect with the previous trajectory, that is, the measurement update of the Bernoulli component. Step 4: We will uniformly set the time t at the end of the k-th scanning cycle e As the filtering moment of the PPP component and the Bernoulli component, because it cannot find a suitable time to match them, and the Poisson component and the Bernoulli component take the entire scanning time to filter. The prediction step of the undetected target is as follows: (4a) The Poisson point process component (PPP) is calculated based on the end time of the period t e Make predictions; (4b) The Bernoulli component (MB) also needs to be calculated based on the end time of the cycle t e Make predictions. Step 5: Update step for undetected targets. Specific steps: (5a) Poisson point process component (PPP) update; (5b) Bernoulli component (MB) update. Step 6: Determine the new global hypothesis, mainly through the Murty algorithm to select the formation and deletion of global hypotheses, and select the new global hypothesis with the highest weight. Generate the cost matrix Cj based on the association weights of the generated potential detection targets and the measurement value Z: Step 7: Delete and recycle unnecessary global assumptions and Bernoulli components: First, global hypotheses with weights above a threshold are retained. Second, hypotheses with no necessary connections are removed. Third, if the sum of all Bernoulli components with a smaller probability than the sum of all connections increases the computational burden, these should be removed as appropriate. Fourth, global hypotheses are weighted and merged. Step 8: Perform KLD minimization approximation on the multi-Bernoulli mixture approximation components, and reduce multiple global hypotheses to a single global hypothesis. Step 9: Extract states from the global hypothesis and Bernoulli components with higher weights.
2. As a further technical solution of the present invention, the setting of the two linear Gaussian models in step 1 and the detection probability and survival probability are: f(x,t|x′,t′)=N(x;F(t|t′)x′,Q(t|t′)), h(z,t|x,t)=N(z;H(t)x,R), p S.k (x′,t′)=p S，k ,p D，k (x,t)=p D.k 。 3. As a further technical solution of the present invention, the prediction of the PPP component in step 2 is specifically as follows: in Where, and J b They represent the new Poisson intensity, the number of new components and the weight respectively. The prediction of the Bernoulli component is: in 4. As a further technical solution of the present invention, the PPP measurement update in step 3 is specifically as follows: in The measurement update of the Bernoulli component is as follows: in 5. As a further technical solution of the present invention, the prediction of the PPP of the undetected portion in step 4 is specifically as follows: The prediction of the Bernoulli component of the undetected part is:
6. As a further technical solution of the present invention, the updating of the undetected portion of PPP in step 5 is specifically as follows: in The update of the Bernoulli component of the undetected part is as follows: in 7. As a further technical solution of the present invention, the determination of the global hypothesis in step 6 is specifically as follows: C j =-ln[W O ,W N ] in Where is the weight matrix after removing clutter from the updated n old tracks in m measurements, and is the diagonal matrix of pure measurement weights.
8. As a further technical solution of the present invention, the unique global hypothesis generated in step 7 is specifically: in