Angle measurement data association method based on pseudo baseline direction consistency

Abstract

The invention provides an angle measurement data association method based on pseudo baseline direction consistency. The method comprises the following steps: inputting angle measurement of two optical sensors; randomly generating a series of possible association results through a Monte Carlo method; constructing an association cost function based on the pseudo baseline direction vector, and calculating the cost of each association result; and taking the result with the minimum cost as an optimal association result. According to the method, the consistency of the pseudo baseline directions determined by any two pairs of association relationships in the association result is taken as a cost function, so that sensor position information is not involved in the calculation process, the influence of sensor position errors is avoided, the requirement on data integrity is reduced, the method has relatively good robustness on missing detection or false alarm, and the method is suitable for large-scale popularization and application. The method is suitable for many-to-many combat scenes based on a low-cost mobile platform, such as unmanned aerial vehicle swarm confrontation, and a data association result can provide information support for target distribution and collaborative strike.

Description

Technical Field

[0001] The present invention relates to the field of sensor information processing, and particularly to an angular measurement data association method based on the consistency of pseudo-baseline directions. Background Art

[0002] Utilizing multi-platform collaborative defense against swarm targets such as unmanned aerial vehicle swarms and warhead swarms can effectively improve the interception efficiency. Data association technology can determine the corresponding relationships between target data of different platforms, laying a foundation for target allocation and collaborative strikes. Considering factors such as accuracy, volume, weight, cost, and power consumption, many platforms will choose optical sensors (infrared or visible light) for target detection. Due to the small size and long distance of the targets, they often have only a few pixels (i.e., point targets) on the imaging plane of the optical sensor. Moreover, the targets in a swarm or warhead swarm often have the same appearance, making it difficult to associate them through color, shape, and texture features. Angular measurement has become an important way for target data association.

[0003] Currently, researchers usually judge the correlation between angular measurements based on the distance between the lines of sight. The so-called line of sight refers to a ray determined by the angular measurement direction of the target starting from the position of the optical sensor. Under ideal conditions without measurement errors, the lines of sight corresponding to the same target intersect at the position of the target, and the distance between them is zero. Therefore, the closer the distance between the lines of sight, the greater the possibility that they correspond to the same target. Calculating the target line of sight requires accurate coordinates of the sensor's own position. The higher the spatial density of the target group, the higher the requirement for the accuracy of the sensor's own position in the data association algorithm. For mobile platforms, satellite navigation or inertial navigation systems are usually used to determine their own position coordinates. Satellite signals may be interfered with or blocked, and the positioning error of inertial navigation accumulates over time and often fails to meet the accuracy requirements for the intersection of the lines of sight.

[0004] For the case where there are errors in the sensor's own positioning, the usual approach is to first correct the sensor's position and then perform data association. Typical calibration sources include observed celestial bodies, beacons, or "special targets". For scenarios without specific calibration sources, the threshold method is often used to find several candidate association relationships with higher probabilities, and then these association relationships are used to correct the sensor's position. The problem with such methods is that the threshold method is only applicable to scenarios where the targets are relatively sparse, and its performance degrades severely when the spatial distribution of the targets is dense.

[0005] For the case where the sensor positions are unknown, the mutual topological relationships between the target data are usually utilized for data association. Some studies perform grid processing on the space and use a 0-1 matrix to represent the mutual topological relationships between the targets; some studies assign values to the elements in the grid based on the target existence probabilities. The problem with the methods used in these studies is that they all assume that the sensor can obtain complete target position information, and essentially solve the correlation problem between point sets. However, what the present invention aims to solve is the correlation problem between angular measurements, infer the association relationships between three-dimensional targets through two-dimensional measurements, and infer high-dimensional states using low-dimensional information. Summary of the Invention

[0006] Aiming at the deficiencies of the prior art, the present invention provides an angular measurement data association method based on the consistency of pseudo-baseline directions.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] The present invention provides an angular measurement data association method based on the consistency of pseudo-baseline directions, including the following steps:

[0009] Input the angular measurements of two optical sensors;

[0010] Randomly generate a series of possible association results through the Monte Carlo method;

[0011] Construct an association cost function based on the pseudo-baseline direction vectors and calculate the cost of each association result;

[0012] Take the one with the minimum cost as the best association result.

[0013] Furthermore, the pseudo-baseline direction vectors are calculated according to the following steps:

[0014] Obtain the 1 ith angular measurement of the first optical sensor and the 2 ith angular measurement of the second optical sensor where i 1 = 1,..., M 1 , i 2 = 1,..., M 2 ; M 1 represents the number of angular measurements in the angular measurement set of the first optical sensor, and M 2 represents the number of angular measurements in the angular measurement set of the second optical sensor;

[0015] Calculate the corresponding angular measurement direction vectors

[0016]

[0017] Among them, β is the deflection angle of the target in the world coordinate system; α is the pitch angle of the target in the world coordinate system;

[0018] Calculate the pseudo-baseline direction vector with any two pairs of angular measurement direction vectors of the two optical sensors, i 1 ≠ i 1 ′, i 2 ≠ i 2 ′,

[0019] l F = q g × q g′

[0020]

[0021] Among them, × represents the vector cross product; l F is the pseudo-baseline direction vector.

[0022] Furthermore, the association cost function is:

[0023]

[0024] Among them, represents the estimation of l F ; A is a function of the association result a; ||·|| represents the L1 norm of the calculation vector.

[0025] Furthermore, the association result is:

[0026]

[0027] Among them, a divides the angular measurements obtained by the two sensors into n T subsets. The angular measurements in each subset are regarded as corresponding to the same target. The binary group records the numbers of the angular measurements in the h-th subset. The function ξ describes the mapping relationship between h and the binary group (i 1 , i 2 ); n T represents the number of binary groups in a.

[0028] Furthermore, the A is

[0029]

[0030]

[0031] Among them, the function ξ describes the mapping relationship between the number g of q and the binary group (i 1 , i 2 ).

[0032] Further, the is the least - squares solution of the homogeneous equation AX = 0, obtained by performing singular - value decomposition on A:

[0033]

[0034] The smallest singular value σ in Σ 3 corresponding singular - value vector v in V 3 is the estimated pseudo - baseline vector That is

[0035]

[0036] Further, for the case of missed detection or false alarm, the association cost function is:

[0037]

[0038]

[0039] a R = a\a D

[0040] a D = {((i 1 , i 2 ):(i 1 , i 2 ) ∈ a, and either i 1 or i 2 is 0)}

[0041] where a R is the remainder of a except a D ; a D is the set of pairs containing virtual measurements in a; n σ represents a multiple of the standard deviation σ A of the target - angle measurement error; n D is the number of pairs containing virtual measurements in a, and c D is the cost of virtual measurement.

[0042] Further, the best association result is obtained according to the following steps:

[0043] Regard the association result a as a state, regard the set of all feasible solutions as the state space, and let π(a) represent the probability distribution of state a in this space ;

[0044] Based on the proposal distribution q PR (a, a′) to obtain the newly proposed state a′ to be transferred from the existing state a;

[0045] Calculate the correlation costs Cost(a) and Cost(a′) of a and a′ respectively;

[0046] Calculate the state transition acceptance probability A M (a, a′);

[0047] Generate a random number U within the interval [0, 1] according to a uniform distribution, and determine the magnitude between U and A M (a, a′). If U < A M (a, a′), then transfer to state a′; otherwise, stay in state a;

[0048] Save all the received states and generate a set

[0049] Output The state with the minimum correlation cost in is used as the correlation result.

[0050] Furthermore, the ways to transfer the existing state a to the new state a′ include the exchange, splitting, and concatenation of the binary tuples in a; the probabilities of performing the exchange, splitting, and concatenation operations on the proposed distribution q PR (a, a′) are all 1 / 3.

[0051] Furthermore, the state transition acceptance probability A M (a, a′) is calculated according to the following formula:

[0052]

[0053] Among them,

[0054] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0055] The angle measurement data association method based on the pseudo-baseline direction consistency provided by the present invention uses the consistency of the pseudo-baseline directions determined by any two pairs of association relationships in the association result as the cost function. Not only does the calculation process not involve sensor position information, avoiding the influence of sensor position errors, but it also reduces the requirement for data integrity, has good robustness to missed detections or false alarms, and can avoid the problem of performance degradation of the data association algorithm caused by the failure or insufficient accuracy of the platform navigation and positioning function in an electromagnetic interference environment. It is applicable to multi-to-multi combat scenarios based on low-cost mobile platforms such as UAV swarm confrontation. The data association result can provide information support for target allocation and cooperative strikes. Brief Description of the Drawings

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on the structures shown in these drawings.

[0057] Figure 1 Schematic flow chart of the angle measurement data association method based on the consistency of the pseudo-baseline direction provided for an embodiment;

[0058] Figure 2 Design idea diagram of the association cost function provided for an embodiment;

[0059] Figure 3 Baseline characteristic analysis diagram provided for an embodiment;

[0060] Figure 4 Analysis diagram of the influence of missed detection or false alarm on the association result provided for an embodiment, where Figure 4 (a) is the correct association result, Figure 4 (b) is the incorrect association result;

[0061] Figure 5 Simulation scenario diagram under the condition of limited sensor position accuracy provided for an embodiment;

[0062] Figure 6 Influence diagram of the sensor position measurement error standard on the association correct rate provided for an embodiment;

[0063] Figure 7 Influence diagram of the included angle between the sensor optical axes on the association correct rate under the condition of position error provided for an embodiment;

[0064] Figure 8 Influence diagram of the change in the number of targets on the association correct rate provided for an embodiment;

[0065] Figure 9 Influence diagram of the target detection probability on the association correct rate under the condition of error provided for an embodiment;

[0066] Figure 10 Influence diagram of the target angle measurement error on the association correct rate under the condition of position error provided for an embodiment;

[0067] Figure 11 Sensor position error robustness simulation result diagram provided for an embodiment;

[0068] Figure 12 Experimental scenario design diagram provided for an embodiment, where Figure 12(a) Side view of pose combination 1, Figure 12 (b) Front view of pose combination 1, Figure 12 (c) Front view of pose combination 2, Figure 12 (d) Front view of pose combination 3, Figure 12 (e) Front view of pose combination 4

[0069] Figure 13 Experimental scenario diagram provided for an embodiment, where Figure 13 (a) Schematic diagram of sensor pose combination 1, Figure 13 (b) Schematic diagram of sensor pose combination 2, Figure 13 (c) Schematic diagram of sensor pose combination 3, Figure 13 (d) Schematic diagram of sensor pose combination 4;

[0070] Figure 14 is Figure 13 The physical diagram of the clothes hanger shown in the attached figure annotation 3 in

[0071] Figure 15 is Figure 13 The physical diagram of the luminous bead shown in the attached figure annotation 4 in

[0072] Figure 16 is Figure 13 The physical diagram of the camera shown in the attached figure annotation 1 in Figure 16 (a) Overall schematic diagram of the camera, Figure 16 (b) Physical diagram of the camera, Figure 16 (c) Physical diagram of the attitude sensor;

[0073] Figure 17 Experimental result diagram provided for an embodiment, where Figure 17 (a) Example diagram of the association result of pose combination 1, Figure 17 (b) Example diagram of the association result of pose combination 2, Figure 17 (c) Example diagram of the association result of pose combination 3, Figure 17 (d) Example diagram of the association result of pose combination 4.

[0074] Attached figure annotation:

[0075] 1. Camera; 2. Attitude sensor; 3. Clothes hanger; 4. Luminous bead. Detailed implementation manner

[0076] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0077] Referring to Figure 1 , in one embodiment, an angle measurement data association method based on the consistency of pseudo-baseline directions is provided, including the following steps:

[0078] Input the angle measurements of all optical sensors;

[0079] Randomly generate a series of possible association results by the Monte Carlo method;

[0080] Construct an association cost function based on the pseudo-baseline direction vector and calculate the cost of each association result;

[0081] Take the one with the minimum cost as the best association result.

[0082] Denote the set of angle measurements of the s-th optical sensor as

[0083]

[0084] where represents the i-th (s) angle measurement in the set Z; M s represents the number of angle measurements in Z; s represents Z; (s) ;

[0085]

[0086] where respectively represent the deflection angle and pitch angle of the target in the world coordinate system; w A represents the angle measurement error.

[0087] The association result a divides the sets of angle measurements of two optical sensors into n T subsets, and uses the binary tuple to record the numbers of the angle measurements in the h-th subset.

[0088]

[0089] where ξ records the mapping relationship between h and its corresponding binary tuple (i 1 , i 2 ).

[0090] The association result is denoted as a

[0091]

[0092] Since each target can form at most one angular measurement on an optical sensor, and each pair can only correspond to one target, there should be a one-to-one mapping constraint between the indices of the angular measurements. If a target corresponding to a certain pair is missed by an optical sensor, a virtual (Dummy) measurement number 0 is added at the corresponding index position of the pair.

[0093] If a certain association result a and the pairs it contains satisfy the above constraints, then a is called a feasible solution, and the set of all feasible solutions is denoted as Usually, the association result cost function Cost(a) is used to evaluate the correctness of a. Generally speaking, the greater the possibility that the association result is correct, the smaller the corresponding cost value. Based on the above, solving the data association problem is equivalent to finding a feasible solution a that minimizes the cost of the association result, and the solving process can be expressed as

[0094]

[0095] where a * represents the optimal association result.

[0096] The straight line connecting the position coordinates of two sensors is called the baseline. Assuming there is no influence of angular measurement error, a correctly associated pair of sight lines intersect at the target location and determine a plane at the same time. If another pair of correctly associated sight lines is known, the plane they determine will intersect the previous plane at the baseline. That is to say, two pairs of correctly associated sight lines can determine the baseline. Further analysis shows that the baseline direction can be calculated through the directions of two pairs of correctly associated sight lines. If there are multiple targets in the scene, the baseline directions calculated by any two pairs of correctly associated sight line directions should be the same. Referring to Figure 2 , the above process is illustrated, and are two pairs of correctly associated measurements. The baseline direction calculated through them is the same as the baseline direction calculated through another two pairs of correctly associated measurements ( and and ). Based on this, the correctness of the association result can be evaluated, and then the corresponding association cost function can be designed. The above process does not involve sensor position information and is thus not affected by sensor position error.

[0097] In one embodiment, the pseudo baseline direction vector is calculated according to the following steps:

[0098] Obtain the i 1 th angular measurement of the first optical sensor and the i-th angular measurement of the second optical sensor 2 angular measurement where i 1 = 1,..., M 1 i 2 = 1,..., M 2 ; M 1 represents the number of angular measurements in the set of angular measurements of the first optical sensor, and M 2 represents the number of angular measurements in the set of angular measurements of the second optical sensor;

[0099] Obtain the corresponding angular measurement direction vector

[0100]

[0101] where β is the yaw angle of the target in the world coordinate system; α is the pitch angle of the target in the world coordinate system;

[0102] Refer to Figure 3 q 1 represents and the vector obtained by cross product, that is q 2 represents and the vector obtained by cross product, that is where the symbol × represents vector cross product. The pairs (1,1) and (2,2) both correspond to the correct association relationship. According to spatial geometry knowledge, the angular measurement direction vectors with correct association are coplanar with the baseline vector, so the vector obtained by cross product of the angular measurement direction vectors with correct association is orthogonal to the baseline vector l. Therefore, q 1 × l = 0, q 2 × l = 0. Since l is orthogonal to both q 1 and q 2 , so l = q 1 × q 2 . It can be seen that if the angular measurement direction vectors from two different sensors are called a pair of angular measurement direction vectors, then in the absence of angular measurement errors, two pairs of correctly associated angular measurement direction vectors can determine the baseline direction.

[0103] Then for any two pairs of angular measurement direction vectors, the vector obtained by cross multiplying the vector obtained by cross product of one pair with the vector obtained by cross product of the other pair is the pseudo-baseline direction vector l F .

[0104] Calculate the pseudo-baseline direction vector with any two pairs of angular measurement direction vectors of the two optical sensors, i 1 ≠ i1 ′, i 2 ≠ i 2 ′,

[0105] l F = q g × q g′

[0106]

[0107] wherein, × represents the vector cross product; l F is the pseudo baseline direction vector.

[0108] Obviously, if the two pairs of angular measurement direction vectors that determine the pseudo baseline direction vector are correctly associated, then their corresponding pseudo baseline vectors are the baseline vectors. Since these two pairs of measurements may not be correctly associated, the direction of the obtained l F will be different from the baseline direction, so l F is called the pseudo baseline direction vector. For the correct association result a * , calculate the pseudo baseline direction vectors corresponding to any two pairs of angular measurement direction vectors among them, and the obtained results are consistent and all equal to the baseline direction vector.

[0109] The association result is:

[0110]

[0111] wherein, a divides the angular measurements obtained by the two sensors into n T subsets, the angular measurements in each subset are regarded as corresponding to the same target, and the binary tuple records the numbers of the angular measurements in the h-th subset, and the function ξ describes the mapping relationship between h and the binary tuple (i 1 , i 2 ), and n T represents the number of binary tuples in a.

[0112] Construct a function A according to the association result a, and the A is

[0113]

[0114] wherein, the function ξ describes the mapping relationship between the number g of q and the binary tuple (i 1 , i 2 ), and n T represents the number of binary tuples in a.

[0115] According to the definition of the pseudo baseline direction vector, any two vectors q g and q g′ in A can determine a pseudo baseline vector l F = qg × q g′ , and satisfy the following constraints

[0116]

[0117] Traverse any two row vectors in A. If the corresponding pseudo-baseline direction vectors they generate are the same, both being l F , then l F should satisfy

[0118] Al F = 0

[0119] If the generated pseudo-baseline direction vectors are not the same, then Al F ≠ 0. The degree of consistency of these pseudo-baseline direction vectors can be evaluated by calculating the residual sum of squares.

[0120] The is the least squares solution of the homogeneous equation AX = 0, obtained by performing a singular value decomposition on A:[[]]

[0121]

[0122] The smallest singular value σ in Σ 3 corresponding singular value vector v in V 3 is the estimated pseudo-baseline vector That is

[0123]

[0124] can reflect the quality of the estimation , and at the same time reflect the consistency of the pseudo-baseline direction vectors estimated from any two row vectors in A. ||·|| represents the calculation of the L1 norm of the vector, that is, the sum of the absolute values of the elements in the vector. If a is the correct association result and the influence of angular measurement error is not considered, then

[0125]

[0126] affected by angular measurement error usually is not equal to 0. If the association result represented by a is incorrect the value of will be larger. Therefore

[0127]

[0128] where represents l FEstimation; A is a function of the association result a; ||·|| represents the calculation of the L1 norm of a vector.

[0129] Then the process of solving the optimal association result can be expressed as

[0130]

[0131] where is the set of feasible solutions for a.

[0132] The association cost function is expanded into the following form

[0133]

[0134] It can be seen from the expansion that only the target angle measurement is used in the association cost function, and the sensor position information is not involved, so it is not affected by the sensor position error.

[0135] Referring to Figure 4 , for the cases of missed detection or false alarm in the two-sensor scenario, the data association algorithm treats missed detection or false alarm in the same way, that is, associating a certain angle measurement with a virtual measurement. Figure 4 In, both 2 sensors obtain 4 angle measurements, Figure 4 (a) reflects the correct association result, that is, due to missed detection or false alarm, and should have been associated with the virtual measurement. Figure 4 (b) reflects the wrong association result, which wrongly associates and together. The corresponding values for these two cases are both greater than 0. Figure 4 (a) The corresponding value is only caused by the measurement noise, while Figure 4 (b) The corresponding value is mainly caused by the wrong association. For these two cases, a threshold is used for discrimination. If the value corresponding to the association result is within the threshold, it is considered that the value is caused by the measurement noise, otherwise it is considered that the value is caused by the wrong association. Assuming that the angle measurement error follows a zero-mean Gaussian distribution, the residual value is approximately expressed as a linear function of the measurement error, so as to reasonably calculate the change range of the residual value caused by the angle measurement error.

[0136] In this embodiment, The corresponding angle measurement direction vectors are respectively and If correspond to the same target, then

[0137] ||qg T ·l||<||δg T (nσ)·l

[0138] Among them, l represents the baseline direction vector;

[0139]

[0140]

[0141] ||δ g T (n σ )·l|| reflects the residual value range caused by measurement errors; n σ represents a multiple of the standard deviation σ of the target angle measurement error. By setting the value of n A , the strength of the constraint ||q σ ·l||<||δ g T ·l|| can be adjusted. Usually, n g T (n σ )·l|| is taken as n σ ≥3. Since different and correspond to different q g , each q g needs to calculate the corresponding δ g T (nσ) respectively.

[0142] For the association result a, use a R to represent the remaining part of a except a D ; use a D to represent the set composed of the binary tuples containing virtual measurements in a

[0143] a R = a\a D

[0144] a D = {((i 1 , i 2 ): (i 1 , i 2 ) ∈ a, and one of i 1 or i 2 is 0)}.

[0145] If a is the correct association result, then

[0146]

[0147] For the data association results of the two sensors, each binary tuple can contain at most one virtual measurement. Since the true baseline direction vector l is unknown, is used instead. Therefore, for the cases of missed detections or false alarms, the association cost function is

[0148]

[0149] where n D is the number of binary tuples in a that contain virtual measurements, and c D is the cost of the virtual measurement. This association cost function consists of two parts. For the virtual measurement part, its cost is equal to the number of virtual measurements n D (i.e., the number of binary tuples in a that contain virtual measurements) multiplied by the cost c D of the virtual measurement; for the remaining part, if satisfies the threshold constraint, it means that the residual sum is caused by measurement errors, and its cost is set to Otherwise, it means that the residual sum is caused by incorrect associations, and its value is set to infinity.

[0150] The best association result is obtained according to the following steps:

[0151] Regard the association result a as a state, and regard the set of all feasible solutions as the state space. Let π(a) represent the probability distribution of state a in this space ;

[0152] Based on the proposal distribution q PR (a, a′), obtain the newly proposed state a′ to be transferred from the existing state a;

[0153] Calculate the association costs Cost(a) and Cost(a′) of a and a′ respectively;

[0154] Calculate the state transition acceptance probability A M (a, a′);

[0155] Generate a random number U uniformly distributed in the interval [0, 1], and judge the size between U and A M (a, a′). If U < A M (a, a′), then transfer to state a′, otherwise stay in state a;

[0156] Save all the accepted states to generate the set

[0157] Output the state with the minimum association cost in as the association result.

[0158] The ways to transfer the existing state a to the new state a' include swapping, splitting, and concatenating the pairs in a; the proposed distribution q PR (a, a') has a probability of 1 / 3 for each of the swap, split, and concatenate operations. The swap means converting the pairs (i 1 , i 2 ) and (i 1 ', i 2 ') into (i 1 ', i 2 ) and (i 1 , i' 2 ); the split means splitting the pair (i 1 , i 2 ) into (i 1 , 0) and (0, i 2 ); the concatenation is the inverse operation of the split, that is, merging (i 1 , 0) and (0, i 2 ) into (i 1 , i 2 ).

[0159] The state transition receiving probability A M (a, a') is calculated according to the following formula:

[0160]

[0161] where

[0162] Referring to Figure 5 , in one embodiment, the potential application scenarios are abstracted through simulation. It is assumed that the targets are randomly distributed near the origin of the world coordinate system and are surrounded by drones in a "C" shape on a sphere about 800 m away. Taking 2 of them as an example for analysis. It is assumed that the measurement sets obtained by two sensors at the same moment are Z (1) and Z (2), the task of the data association algorithm is to solve the association relationship between the measurements in two sets. Through simulations with different measurement errors, missed detections (or false alarms), the included angle between the optical axes of sensors, etc., the performance of the algorithm is analyzed and investigated. To illustrate the advantages of the angle measurement data association method based on the pseudo-baseline direction consistency proposed in this paper (Data Association based on pseudo-Baseline direction Consistency, DABC algorithm), classical data association algorithms are also selected for comparison in the simulation, namely the SDA algorithm, the DABE (Data Association based on Bias Estimation) algorithm with the function of correcting sensor position deviation, the reference pattern REP (Reference Pattern) algorithm based on the relative position relationship of targets in the image plane, and the MADS (Minimum Angular Distance Sum) algorithm based on the minimum angular distance sum.

[0163] Assume that the true position coordinates of the s-th sensor are y s =(y s,x , y s,y , y s,z ) T , and the position coordinates of the i-th target are x i =(x i,x , x i,y , x i,z ) T , where x i,x , x i,y , and x i,z are uniformly distributed in the intervals [-100m, 100m], [-100m, 100m], and [-100m, 100m], respectively. For the DABC algorithm, SDA algorithm, DABE algorithm, and MADS algorithm, the target angle measurement generation model is

[0164]

[0165] where H P represents the sensor angle measurement generation function;

[0166]

[0167] w A represents the angle measurement error, which follows a Gaussian distribution with a mean of 0 and a covariance matrix R A , that is

[0168]

[0169] where σ Ais the standard deviation of the target angle measurement error. For the REP algorithm, the input of the algorithm is the coordinates of the target on the imaging plane. The simulation assumes that the optical axis of the optical sensor points from the true position of the sensor to the center of the target generation area (i.e., the origin of the world coordinate system), the imaging resolution is 800x600 pixels, and the field of view angle is 45 degrees. Based on this, the camera projection matrix can be obtained. Combining the projection matrix and the target position, the coordinates of the target on the imaging plane can be obtained. Assume that the position coordinates of the optical sensor obtained by the navigation and positioning system are w P represents the positioning error of the navigation system, which follows a Gaussian distribution with a mean of 0 and a covariance matrix of R P That is

[0170]

[0171]

[0172] where σ P represents the standard deviation of the sensor position measurement error, which is mainly affected by the accuracy of the platform's own navigation and positioning system.

[0173] To fully evaluate the algorithm performance, the target position, angle measurement error, and position measurement error used in each test are randomly generated. The algorithm performance is evaluated by the association correct rate (ACC), which is defined as

[0174]

[0175] The correct association result means that the number of pairs obtained by the association algorithm is equal to the number of true targets in the scene, and the measurements in each pair correspond to the same target. If the result of a certain test is correct, the number of correct association results is incremented by 1. The total number of tests is 1000 times.

[0176] In terms of algorithm parameter configuration, for the DABE algorithm, the threshold used when screening calibration sources is 3σ A . For the REP algorithm, it uses the coordinates of the target in the image plane as the input of the algorithm for data association, the penalty cost is set to 10000, and the order is set to 1.

[0177] Referring to Figure 6 , which is the first simulation result graph. The first simulation is to analyze the robustness of the algorithm to sensor position errors. Currently, the positioning accuracy provided by satellite navigation systems for mobile platforms is about 10m. Based on this, the standard deviation of the position error σ P is incremented from 2 meters to 10 meters. In terms of other parameter settings, the number of targets is set to 5, the standard deviation of the target angle measurement error σ A is set to 0.1mrad, the target detection probability is set to 1, and the included angle between the optical axes of the sensors (defined as Figure 12shown) is less than 10 degrees.

[0178] As Figure 6 shown, the simulation results show that in an almost ideal situation without the influence of missed detections or false alarms and with almost the same sensor observation angles, all algorithms can withstand a position error of about 10 m, and the association correct rate is above 97%. For the SDA algorithm and the DABE algorithm, this is because the assignment algorithm can utilize global information for data association, and the sensor position error has the same influence on the measurements generated by it. Therefore, the global-based algorithms can still obtain correct results. For the REP algorithm, the MADS algorithm, and the DABC algorithm, they are designed to be independent of the sensor position and are thus not affected by the sensor position error.

[0179] The purpose of the second simulation is to analyze the influence of different sensor observation angles on the association correct rate. The included angle ranges between the optical axes of the two sensors are set to be less than 10 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees respectively. In terms of other parameter settings, the standard deviation σ P of the sensor position error is set to 10 m, the number of targets is set to 5, the target detection probability is 1, and the standard deviation σ A of the target angle measurement error is set to 0.1 mrad.

[0180] Referring to Figure 7 , the simulation results show that as the included angle range between the sensor optical axes increases, the performance of the REP algorithm drops rapidly, indicating that the reference pattern cannot cope with the influence brought by perspective transformation. The other algorithms are less affected by the difference in sensor observation angles and all maintain a high correct rate.

[0181] The purpose of the third simulation is to examine the influence of the change in the number of targets on the algorithm performance. The number of targets increases from 6 to 10. In terms of other parameter settings, the standard deviation σ P of the sensor position error is set to 10 m, the included angle between the sensor optical axes is set to be less than 90 degrees, the target detection probability is 1, and the standard deviation σ A of the target angle measurement error is set to 0.1 mrad.

[0182] Referring to Figure 8 , the simulation results show that as the number of targets increases, the association correct rates of the SDA algorithm and the DABE algorithm both decrease. The main reason is the influence of "ghosting", that is, the misintersection of lines of sight without an actual association relationship. The increase in the number of targets increases the probability of "ghosting" and leads to a decrease in the correct rate of the line-of-sight-based data association algorithm.

[0183] The purpose of the fourth simulation is to analyze the robustness of the algorithm to the target detection probability. For the two-sensor scenario, the data association algorithm treats missed detections and false alarms in the same way, so a simulation scenario for false alarms is not specifically set up. In terms of parameter settings, the number of targets is set to 10, the standard deviation σ P of the sensor position error is set to 10 m, the included angle between the optical axes of the sensors is set to be less than 90 degrees, and the standard deviation σ A of the target angle measurement error is set to 0.1 mrad. The target detection probability decreases from 98% to 90%.

[0184] Referring to Figure 9 , the simulation results show that, except for the DABC algorithm, the association correct rates of other algorithms decrease rapidly as the target detection probability decreases. For the SDA algorithm, the present invention specifically analyzes the impact of missed detections on it, and the simulation results are consistent with the analyzed situation. For the DABE algorithm, although it has a certain effect on sensor position correction, since the threshold method is used to select the calibration source, the improvement of the association correct rate is very limited. For the MADS algorithm, its description of the correspondence between measurements highly depends on the data integrity, and missed detections will break this correspondence, resulting in a sharp drop in the association correct rate. However, for the DABC algorithm proposed in this paper, its cost function is designed based on the consistency of the pseudo-baseline direction, reducing the requirement for data integrity. At the same time, by reasonably estimating the range of changes in the cost value of the correct association result, it rejects the wrong association results caused by missed detections (or false alarms), thus ensuring a relatively high association correct rate.

[0185] The purpose of the fifth simulation is to analyze the impact of the angle measurement error on the association correct rate. The standard deviation σ A of the angle measurement error increases from 1 mrad to 5 mrad. In terms of other parameter settings, the number of targets is set to 10, the included angle between the optical axes of the sensors is less than 90 degrees, the target detection probability is set to 90%, and the standard deviation σ P of the sensor position error is set to 10 m.

[0186] Referring to Figure 10 , the simulation results show that as the standard deviation of the target angle measurement error increases, the association correct rate of the DABC algorithm decreases. Similar to the case of forming "ghost images", the pseudo-baselines formed by unassociated measurements may also be close to the direction of the actual baseline, and the corresponding cost of the association result may even be smaller, thus generating wrong association results. The increase in the angle measurement error will increase the probability of this situation occurring, resulting in a downward trend in the association correct rate. Both position measurement errors and angle measurement errors will increase the probability of "ghost images" appearing. The SDA algorithm is affected by both errors, so the association correct rate starts to decrease in the third simulation, while the DABC algorithm is only affected by the angle measurement error and is affected accordingly in the fifth simulation.

[0187] To fully illustrate the robustness of the DABC algorithm to sensor position errors, the 6th simulation was designed. The standard deviation of the sensor position error was gradually increased to 100,000 m. In terms of other parameter settings, the number of targets was set to 10, the included angle between the optical axes of the sensors was less than 90 degrees, and the target detection probability was set to 90%, and the standard deviation σ A of the angular measurement error was set to 2 mrad.

[0188] Referring to Figure 11 , the simulation results show that the association correct rate of the DABC algorithm is not affected by the sensor position error and remains at about 92%.

[0189] Referring to Figure 12 , in one embodiment, in the experimental scenario, there are two cameras (i.e., optical sensors), denoted as S 1 and S 2 respectively. Each camera is equipped with 1 attitude sensor for measuring the camera attitude. Glow beads are used to simulate the targets and are tied to the hanging rack with transparent thin lines. The distance between the hanging rack and the cameras is 1.8 m, as shown in Figure 12 (a). To verify the effectiveness of the algorithm under different observation angle difference conditions, 4 different sensor pose combinations were designed in the experiment, as shown in Figure 12 (b)- Figure 12 (e). In pose combination 1, the two cameras face the target group directly, with a spacing of about 0.1 m and a height from the ground of about 0.3 m. Compared with pose combination 1, in pose combination 2, camera S 1 rolled about 30 degrees around the optical axis direction. In pose combinations 3 and 4, the included angle between the optical axes of the sensors was gradually increased.

[0190] Referring to Figure 13 , 14 , 15, 16, the actual experimental scenario is shown. The image resolution of both cameras is 1600 pixels * 1200 pixels, and the internal parameters are obtained through the Zhang Zhengyou calibration method. The specific values are shown in Table 1. Among them, cu and cv represent the coordinates of the camera principal point, and fu and fv represent the dimensions that convert the focal length into pixel coordinates in the u and v directions. In pose combinations 1-4, the attitude sensor readings of cameras S 1 and S 2 are shown in Table 2. The diameter of glow bead 4 is 0.08 m, and it is distinguished by circular stickers of different colors.

[0191] Table 1 Camera internal parameter table

[0192]

[0193] Table 2 Camera attitude sensor data table

[0194]

[0195] The experimental process includes three steps

[0196] Step 1: Turn off all the lights in the room. Two cameras take pictures of the targets respectively, detect the targets on the images, and obtain their coordinates on the images. Based on these coordinates, the internal parameters of the cameras, and the poses of the cameras, the angular measurements of the targets in the world coordinate system can be calculated.

[0197] Step 2: Use the method described in the present invention to solve the correlation relationship between the angular measurements of the targets obtained by the two sensors, and number the targets in the scene according to the correlation results.

[0198] Step 3: Turn on the lights in the room, and compare the data association results with the real scene. If the sticker colors corresponding to the targets with the same number are the same, it indicates that the association results are correct.

[0199] The experimental results are as Figure 17 shown. Taking Figure 17 (d) as an example for specific illustration:

[0200] Experimental results of Step 1: According to the operations in Step 1, S 1 and S 2 respectively obtain their respective sets of target angular measurements

[0201] Experimental results of Step 2: After calculation by the method described in the present invention, the association result a = {(1, 2), (2, 1), (3, 0), (4, 5), (5, 3), (0, 4)} is obtained. Number the targets in the scene accordingly, and the corresponding relationship between the angular measurements of each sensor and the targets is shown in Table 3, where the targets are numbered according to the sorting of the binary tuples in the association result. In this article, the targets detected by both sensors are confirmed as targets, and the measurements not associated with other data are recorded as NA.

[0202] Table 3 Corresponding relationship table between angular measurements and targets

[0203]

[0204]

[0205] Experimental results of Step 3: Check whether the sticker colors corresponding to the targets with the same number in the two sensors are the same. The check results are shown in Table 4.

[0206] Table 4 Correctness check table of association results

[0207]

[0208] As can be seen from Table 4, the sticker colors corresponding to the same numbered targets are the same, and the association results are correct. The experimental results show that the data association algorithm assigns the same number to the same target detected by different sensors, enabling different sensors to form a unified understanding of the targets in the scene. By making judgments in the same way, the association results of the other 3 pose combinations are all correct.

[0209] Matters not covered by this invention are well-known technologies.

[0210] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0211] The above-described embodiments merely represent several implementation manners of this application. The description is relatively specific and detailed, but it should not be construed as a limitation to the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of this application, several modifications and improvements can still be made, and these all belong to the protection scope of this application. Therefore, the protection scope of this application should be subject to the appended claims.

[0212] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An angle measurement data association method based on pseudo baseline direction consistency, characterized in that: The following steps are involved: Input angle measurements from two optical sensors; A series of possible correlation results are randomly generated through the Monte Carlo method; Construct an association cost function based on the pseudo baseline direction vector and calculate the cost of each association result; The one with the lowest cost is taken as the best association result.

2. The angle measurement data association method based on pseudo baseline direction consistency according to claim 1, characterized in that: The pseudo baseline direction vector is calculated according to the following steps: Get the i1th angle measurement of the 1st optical sensor And the second optical sensor's i2nd angle measurement Wherein, i1=1, ..., M1, i2=1, ..., M2; M1 represents the number of angle measurements in the first optical sensor angle measurement set, and M2 represents the number of angle measurements in the second optical sensor angle measurement set; calculate The corresponding angle measurement direction vector Among them, β is the deflection angle of the target in the world coordinate system; α is the pitch angle of the target in the world coordinate system; The pseudo baseline direction vector is calculated by measuring the direction vectors of any two pairs of angles of the two optical sensors, i1≠i1′, i2≠i2′, l F =q g ×q g′ Among them, × represents vector cross product; l F is the pseudo baseline direction vector.

3. The angle measurement data association method based on pseudo baseline direction consistency according to claim 1, characterized in that: The associated cost function is: in, Indicates l F An estimate of ; A is a function of the associated result a; ||·|| represents the L1 norm of the calculated vector.

4. The angle measurement data association method based on pseudo baseline direction consistency according to claim 1, characterized in that: The association results are: Where a divides the angle measurements obtained by the two sensors into n T subsets, and the angle measurements in each subset are considered to correspond to the same target, consisting of a binary Record the number of the angle measurement in the hth subset. The function ξ describes the mapping relationship between h and the binary (i1, i2). T Represents the number of 2-tuples in a.

5. The angle measurement data association method based on pseudo baseline direction consistency according to claim 3, characterized in that: The A is Among them, the function ξ describes the mapping relationship between the number g of q and the tuple (i1,i2).

6. The angle measurement data association method based on pseudo baseline direction consistency according to claim 3, characterized in that: Said is the least squares solution of the homogeneous equation AX=0, obtained by performing singular value decomposition on A: The singular value vector v3 in V corresponding to the smallest singular value σ3 in Σ is the estimated pseudo baseline vector Right now 7. The angle measurement data association method based on pseudo baseline direction consistency according to claim 1, characterized in that: For the case of missed detection or false alarm, the associated cost function is: a R =a\a D a D ={((i1,i2):(i1,i2)∈a, and one of i1 or i2 is 0)} Among them, a R for a except a D the remainder of D is the set of two-tuples in a that contain virtual measurements; n σ Represents the standard deviation of the target angle measurement error σ A Multiples of n D is the number of pairs containing virtual measurements in a, c D The cost of virtual measurement.

8. The angle measurement data association method based on pseudo baseline direction consistency according to claim 1, characterized in that: Follow these steps to get the best correlation results: Consider the associated result a as a state, and construct a set of all feasible solutions Considered as a state space, let π(a) represent the state a in this space The probability distribution of Based on the proposed distribution q PR (a, a′) Get the new state a′ to be transferred from the current state a; Calculate the associated costs Cost(a) and Cost(a′) of a and a′ respectively; Calculate the state transition acceptance probability A M (a,a′); Generate a random number U in the interval [0,1] according to uniform distribution, and determine whether U is equal to A. M (a, a′) between the size, if U<A M (a,a′), then transfer to state a′, otherwise stay in state a; Save all received states and generate a collection Output The state with the minimum association cost is taken as the association result.

9. The angle measurement data association method based on pseudo baseline direction consistency according to claim 8, characterized in that: The ways to transfer the existing state a to the new state a′ include exchanging, splitting, and connecting the two tuples in a; the recommended distribution q PR The probability of performing swap, split, and connect operations on (a, a′) is 1 / 3.

10. The angle measurement data association method based on pseudo baseline direction consistency according to claim 8, characterized in that: The state transition acceptance probability A M (a,a′) is calculated according to the following formula: in,

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