Multi-station multi-target angle correlation positioning method

Abstract

The invention discloses a multi-station multi-target angle correlation positioning method, which comprises the following steps of: classifying angle measurement sets from different aircrafts to obtain a plurality of groups of angle measurement value sets of different aircrafts possibly from the same target, and providing a reliable measurement set for a coupling weight least square angle positioning algorithm; secondly, establishing a group of overdetermined nonlinear angle measurement equations including position estimation errors and angle measurement errors of the aircraft, and proposing a coupling error weight least square angle positioning algorithm; and finally, each target angle measurement set obtained through classification by using an angle correlation screening algorithm is used as input of a coupling error weight least square angle positioning algorithm, a multi-target position estimation result is obtained, and a multi-target positioning process is completed. According to the method, the calculation complexity of the angle measurement set association process in the multi-target angle positioning process can be greatly reduced, the measurement association operation time is effectively shortened, and the multi-target angle positioning real-time performance and the positioning precision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of space exploration and positioning, and in particular, to a multi-station multi-target angle correlation positioning method. Background Art

[0002] In many current advanced fields, such as military operations, aerospace exploration, and robot collaboration, the multi-station multi-target positioning technology undoubtedly plays a crucial role. In the military field, accurately knowing the specific positions of multiple enemy targets is an important basis for formulating strategic decisions and carrying out tactical operations, which is related to the success or failure of the entire combat operation; in the aerospace field, when an aircraft performs tasks such as air traffic control and search and rescue, accurately positioning multiple targets is a key prerequisite for successfully completing these missions; positioning refers to the process of estimating the target position by obtaining a series of positioning parameters and relying on the relationship between the positioning parameters and the target position. The angle positioning process usually uses the angle information between the measurement station and the unknown target to estimate the actual position of the target.

[0003] When multiple aircraft perform positioning operations on multiple targets, the lack of angle source information is a very difficult problem. Due to the lack of clear indication of the angle source, the correlation between measurement data becomes extremely complex. When processing the measurement data obtained by each aircraft, it is very difficult to clearly distinguish which angle measurement values correspond to the same target, which is likely to cause interference from false targets, and then lead to a large deviation between the estimated number of targets and the actual situation, and it is also difficult to ensure the accuracy of the estimated target position. Secondly, the mutual coupling between the self-position estimation error and the angle measurement error of multiple aircraft also has a serious negative impact on the positioning accuracy. This coupling effect makes it difficult to accurately determine the target position, and ultimately has an adverse effect on the actual execution effect of related tasks.

[0004] At the present stage, for the problem of data association, although some studies use clustering algorithms and other methods for processing, most clustering algorithms have an increasing computational complexity when facing a complex measurement environment and massive data, and it is difficult to meet the real-time requirements. For the positioning accuracy problem caused by error coupling, existing improved angle positioning methods have been carried out by improving the sensor position estimation accuracy or reducing the influence of the sensor position error on the angle measurement quantity. Their essence is to improve the angle measurement result, and they do not improve the positioning accuracy when the sensor already has errors from the perspective of positioning. In addition, algorithms starting from improving the angle measurement result mostly impose constraints on the sensor position, which limits the application freedom of angle positioning.

[0005] To meet the urgent need for high-precision and high-efficiency multi-target positioning at present, it is necessary to develop a new multi-station multi-target angle positioning method. Summary of the Invention

[0006] The object of the present invention is to provide a multi-station multi-target angle correlation positioning method to achieve a fast and high-precision multi-target positioning process.

[0007] The technical solution for achieving the object of the present invention is: a multi-station multi-target angle correlation positioning method, comprising the following steps:

[0008] S1. Based on the geometric relationship between the target point and the corresponding angle measurement values measured by different aircraft, an angle correlation screening algorithm is used to classify the angle measurement sets from different aircraft, and multiple sets of different multi-aircraft angle measurement value sets that may originate from the same target are obtained;

[0009] S2. Establish a set of overdetermined non-linear angle measurement equations including the aircraft's own position estimation error and angle measurement error, and propose a coupled error weighted least squares angle positioning algorithm;

[0010] S3. Using each target angle measurement set classified by the angle correlation screening algorithm as the input of the coupled error weighted least squares angle positioning algorithm, the multi-target position estimation result is obtained, and the multi-target positioning is completed.

[0011] Further, the pairwise angle correlation screening process in step S1 specifically includes:

[0012] In the scenario of dual-station multi-target positioning, at any given moment, aircraft P i Position coordinates (x i , y i , z i ) and its any angle observation data a(θ i , φ i ), i = 1, 2; where θ i , φ i are respectively the azimuth angle observation value and the elevation angle observation value of the aircraft to the target;

[0013] Step 1-1: Calculate the observation vector of aircraft P 1 Observation vector of aircraft P Aircraft P 2 Observation vector And the distance vector

[0014] Step 1-2: Calculate And the unit normal vector corresponding to the plane formed by μ 1 And calculate Projection of On the plane formed by And On the plane

[0015] Step 1-3: Judge And μ1 Whether they are on the same side. If they are on the same side and not parallel, go to step 1-4 for judgment. Otherwise, it is considered that and there is no possibility of data association;

[0016] Step 1-4: Calculate the included angle If |Δ| ≤ Δ max , it is considered that and there is a possibility of data association, and perform positioning calculation; otherwise, it is considered that and there is no possibility of data association; where Δ max is the association judgment threshold, and the judgment ends;

[0017] Output the final judgment result and the absolute value of the included angle |Δ|; "Yes" indicates the possibility of association, and "No" indicates no.

[0018] Furthermore, the angle association screening algorithm in step S1 specifically includes:

[0019] Obtain the position coordinates s 1 of the main aircraft P 1 = [x 1 , y 1 , z 1 T at any moment and its angle observation data from the aircraft P k , k = 2, …, M, position coordinates s k = [x k , y k , z k T and its angle observation data M is the number of aircraft in the missile group, and the number of angle measurements measured by the aircraft is N i , i = 1, …, M;

[0020] Step 1: Initialize, let j = 1, k = 2, the two-aircraft angle association set the multi-aircraft angle association result set where is the angle association result set of aircraft j;

[0021] Step 2: Select the main aircraft as the reference association angle;

[0022] Step 3: Select the kth slave aircraft as the association object, and sequentially use its angle measurement value and the reference association angle Perform pairwise matching and screening, that is, through the pairwise angle correlation screening process, make a judgment. If the correlation possibility is met, save the absolute value of the included angle |Δ| corresponding to the pair (k, p) and the correlation to the set ;

[0023] Step 4: Judge whether the number of elements in the set is greater than 1. If it is greater, it means that there are multiple correlations. Then, find the correlation with the smallest absolute value of the included angle |Δ| in the set as the final correlation result, and save the correlation in the set . If not, directly save the elements in the set to the set ;

[0024] Step 5: Set the set k = k + 1, and repeat steps 2, 3, 4, and 5 until k > M;

[0025] Step 6: Update the reference correlation angle of the main aircraft, that is, j = j + 1, and repeat steps 2, 3, 4, 5, and 6 until j > N 1 ;

[0026] Step 7: End the correlation calculation. Any subset in the set is the correlation angle corresponding to the measurement of the main aircraft . Use this correlation result for positioning calculation; Output: The final correlation result set

[0027]

[0028]

[0029]

[0030] o Considering the coupling error of the sensor's own position estimation error and angle measurement error, denote Ψ o = [cosθ o , sinθ o , sinφ o , g o o T as the unknown true value of the angle positioning result, where θ o , φ o , g o are the azimuth angle, pitch angle, and inverse distance of the target in the modified polar coordinates. The multi-station single-target nonlinear measurement equation is:

[0030] GΨ o = ε ​

[0031] In the formula,

[0032]

[0033] ε = Bn a + CΔs

[0034] where G is the measurement matrix and ε is the coupling error quantity; B = blkdiag{B θ , B φ}, G θ , B θ , C θ are parameter matrices related to the single-target azimuth angle information θ = [θ 1 , …, θ M obtained by the sensor group; G φ , B φ , C φ are parameter matrices related to the single-target elevation angle information φ = [φ 1 , …, φ M ; the parameter matrices are in turn:

[0035]

[0036] where G θ is the cluster azimuth angle measurement matrix, and G φ is the cluster elevation angle measurement matrix; B θ is the angle noise driving matrix related to the cluster azimuth angle, and B φ is the angle noise driving matrix related to the cluster elevation angle; C θ is the site error driving matrix related to the cluster azimuth angle, and C φ is the site error driving matrix related to the cluster elevation angle; where, are the azimuth angle measurement value and elevation angle measurement value of the target by the sensor of the aircraft i; is the projection of the distance vector between the target and the sensor i on the xy plane; r i o is the two-norm of the distance vector between the target and the sensor i;

[0037] In the above measurement equation, the error quantity ε describes the systematic error coupled by the angle measurement error n a and the sensor's own position estimation error Δs, and its weight matrix W satisfies

[0038]

[0039] Q a is the multi-sensor angle measurement noise covariance matrix, Qs is the position estimation error covariance matrix of multiple aircraft.

[0040] Furthermore, the coupled error weighted least squares angle positioning algorithm in step S2 specifically includes:

[0041] Based on the overdetermined nonlinear angle measurement equation containing the aircraft's own position estimation error and angle measurement error, using the weighted least squares solution method to solve the unknown quantity Ψ of the above measurement equation o ; Assume that the multi-sensor angle measurement noise covariance matrix Q a and the position estimation error covariance matrix Q of multiple aircraft s are known;

[0042] First, calculate the coupled weight measurement system error matrix W. Matrices B and C contain the unknown quantity ψ = [cosθcosφ, sinθcosφ, sinφ, g] T of the target angle measurement value, where θ, φ, and g are the azimuth angle, elevation angle, and inverse range of the target in the modified polar coordinates; Calculate the target position quantity Ψ o corresponding estimated value using the homogeneous measurement equation that ignores the system error ε

[0043] The measurement equation after ignoring the coupled error term ε is:

[0044]

[0045] where, is consistent with the unknown quantity ψ, representing the approximate estimated value of its result; Use the above formula to construct an optimization problem and obtain:

[0046]

[0047] The Lagrangian function of this problem is:

[0048]

[0049] where, is the Lagrangian function and λ is the Lagrangian coefficient;

[0050] Take the partial derivative of the above calculation,

[0051]

[0052] If the constraint is minimized, the solution of the above equation is G T the eigenvector corresponding to the minimum eigenvalue solution of G; Considering the physical meaning constraint of the target positioning position parameter :

[0053]

[0054] In the formula, represents the approximate estimated value of g o ; Using the above formula, establish the initial estimation result of the cluster judgment rule, and then obtain the positioning solution. The estimation judgment rule is as follows:

[0055]

[0056] Among them, represents the 1st to 3rd elements; represents the 4th element of

[0057] Solve the approximate result using the above process to obtain the weight matrix W. Subsequently, use the complete measurement equation to re - establish the coupled weight least - squares cost function:

[0058]

[0059] Among them, is the least - squares cost value;

[0060] At this time, construct the optimization problem under the coupled weight as:

[0061] minψ T G T WGψ

[0062] s.t.ψ T ψ = 1

[0063] Referring to the positioning solution calculation process under the condition of ignoring errors, obtain the final positioning result ψ;

[0064] Finally, obtain the positioning estimation result u o as:

[0065] u o =(1 / ψ(4))[ψ(1),ψ(2),ψ(3)] T .

[0066] Among them, represents the i - th element;

[0067] The above - mentioned solution process of the coupled weight least - squares method is designed as a two - step solution. The first step is to calculate the approximate value to obtain the accurate weight matrix, and the second step is to use the obtained weight matrix to solve the final positioning result. The two - step solution process ensures the accuracy of each estimated value in the angle calculation process, thereby improving the accuracy of the final angle positioning result.

[0068] A computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the above method are implemented.

[0069] A computer-readable storage medium stores a computer program thereon. When the program is executed by a processor, the steps of the above method are implemented.

[0070] A computer program product includes a computer program. When the computer program is executed by a processor, the steps of the above method are implemented.

[0071] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0072] (1) A multi-objective angle correlation screening algorithm is proposed. By using the relationship between angle positioning schematic lines and based on the vector projection principle, fast screening and matching of multi-objective angle measurement sets are realized, providing reasonable target measurement values for subsequent positioning calculation.

[0073] (2) A coupled weight least squares angle positioning method is established. Considering the influence of the coupled error formed by the station site error and angle measurement error caused by inaccurate estimation of the aircraft's own position on the angle positioning accuracy, high-precision target positioning under the condition of coupled error is realized.

[0074] (3) The multi-objective angle correlation screening algorithm and the coupled weight least squares positioning method are fused, avoiding the complex calculation process of the original method, and realizing the fast and high-precision positioning process of multiple stations and multiple targets under angle measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a flowchart of the multi-station multi-objective angle correlation screening and positioning method in the specific embodiment of the present invention.

[0076] Figure 2 It is a schematic diagram of ideal angle positioning in the specific embodiment of the present invention.

[0077] Figure 3 It is a schematic diagram of actual angle positioning in the specific embodiment of the present invention.

[0078] Figure 4 It is a schematic diagram of the same-side situation of the angle positioning relationship in the specific embodiment of the present invention.

[0079] Figure 5 It is a schematic diagram of the different-side situation of the angle positioning relationship in the specific embodiment of the present invention.

[0080] Figure 6 It is a schematic diagram of two-step calculation in the specific embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0081] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0082] Aiming at the complex association problem caused by the lack of angle source information in the process of positioning multiple targets by multiple aircraft carrying angle measurement sensors, as well as the positioning accuracy problem caused by the coupling of the position estimation error of the multiple aircraft themselves and the angle measurement error, the present invention proposes a multi-station multi-target angle association positioning method. The method mainly consists of two parts: angle association screening and coupling weighted least squares positioning method. The relationship between the parts is shown in the attached figure. Figure 1 As shown, it can be divided into three main steps:

[0083] (1) Starting from the geometric relationship between the target point and its corresponding angle measurement values ​​measured by different aircraft, the pairwise angle association screening process is explored with the help of the vector projection method. An angle association screening algorithm is proposed to classify the angle measurement sets from different aircraft. Multiple sets of angle measurement values ​​from different aircraft that may come from the same target are obtained, providing a reliable measurement set for the coupled weighted least squares angle positioning algorithm.

[0084] (2) A set of overdetermined nonlinear angle measurement equations that include the aircraft's own position estimation error and angle measurement error are established, and their closed-form solution method is studied, and a coupled error weighted least squares angle positioning algorithm is proposed.

[0085] (3) The angle measurement set of each target obtained by classification using the angle association screening algorithm is used as the input of the coupled error weighted least squares angle positioning algorithm to obtain the multi-target position estimation result and complete the multi-target positioning process.

[0086] The specific implementation methods of the above steps are described in detail below:

[0087] Step 1: Angle correlation screening process

[0088] In the process of multi-aircraft multi-target angle positioning, at least two aircrafts need to observe the angle of the same target to obtain the positioning result of a single target. Therefore, the problem of associating the angle measurement sets of multiple targets by multiple aircraft can actually be divided into the process of associating and fusing the angle measurement sets of multiple targets by different dual-aircraft combinations. Therefore, considering dual-aircraft positioning as the simplest combination in the multi-aircraft measurement process, the problem of associating the angle measurement sets of multiple targets by dual-aircraft is first explored.

[0089] Consider the observation process of any two observation aircraft on the target in a three-dimensional space scene. Figure 2 This is a schematic diagram of two observation aircraft locking onto the same target, where P 1 is the position of aircraft 1, P 2 is the position of aircraft 2, T is the target position, $\vec{v}_1$ is the unit vector of the observation direction of the aircraft 1 towards the target, which can be obtained using the angular measurement $a(\theta$ 1 , $\varphi$ 1 ), that is where $\theta$ 1 is the azimuth measurement of the aircraft 1 towards the target, and $\varphi$ 1 is the elevation measurement of the aircraft 1 towards the target; $\vec{v}_2$ is the unit vector of the observation direction of the aircraft 2 towards the target, which can also be obtained using the angular measurement $a(\theta$ 2 , $\varphi$ 2 ), where $\theta$ 2 is the azimuth measurement of the aircraft 2 towards the target, and $\varphi$ 2 is the elevation measurement of the aircraft 2 towards the target.

[0090] Without considering the observation error and the aircraft's own position estimation error, the position of the target T can be described as the intersection of the ray emitted from P 1 in the direction of and the ray emitted from P 2 in the direction of . Therefore, the process of observing and positioning a target by two aircraft in three-dimensional space can be abstracted as a problem of calculating the intersection position of two known rays in three-dimensional space.

[0091] The positional relationship between rays in space, according to whether they are in the same plane is divided into two types: coplanar and skew. When two rays are coplanar, there are three relationships: intersecting, parallel, and non-intersecting and non-parallel, and there is an intersection between the rays only in the case of intersection. In the skew state, there is no intersection between the rays.

[0092] In the ideal positioning scenario without considering the observation error and the aircraft's own position estimation error, the positional relationship between the abstracted observation angle rays satisfies the above description. When and only when the rays are coplanar and intersecting, they originate from the same target. However, considering the actual scenario, due to the existence of observation error and the aircraft's own estimation error, the strict intersection condition when the observation rays originate from the same target is broken, and a situation as shown in Figure 3 occurs. The observation vector 1 from P and the observation vector 2 from P are generated due to the same target T, but due to the existence of observation error, the rays represented by do not satisfy the collinear condition, and are different from and P 1 P 2There is a small angle Δ between the formed planes. At this time, the intersection conditions under ideal conditions cannot cover all the possibilities of data association in the actual angle positioning scenario. Therefore, the ray position relationships in three-dimensional space are reclassified and discussed.

[0093] Taking and the formed plane x'z' as the analysis reference plane, denote as the plane normal vector of the plane x'z', as the azimuth vector of any ray emitted from P 2 (i.e., any angle observation vector from P 2 ). Its distribution in three-dimensional space is as shown in Figure 4 , Figure 5 . In the figure, is parallel to and is a unit vector, is the projection of on the plane x'z', Δ is the angle between and , is the plane normal vector parallel to x'y' and is a unit vector. Denote and the plane formed by passing through P 2 as Taking the plane as the demarcation line, the distribution of in space can be divided into three categories, namely and are on one side of the plane , that is, and are on the same side; and are on both sides of the plane , that is, and are on different sides; is on the plane . Figure 4 shows the case where and are on the same side; Figure 5 shows the case where and are on different sides.

[0094] When and are on different sides or is on the plane , the ray and have no possibility of intersection, that is, their corresponding observation angles do not originate from the same target. And On the same side as, then the ray and have the possibility of originating from the same target, but not all rays that meet the conditions are further related to and further discussion is needed. When is on the same side as and , the positional relationship between and the plane x'z' can be measured by the angle Δ between the vector and the plane. In an ideal situation, intersects with then Δ = 0. However, in the actual measurement environment, there are angle observation errors and aircraft own position estimation errors, so the angle Δ is not constantly zero, and its variation range should have a threshold related to the angle observation error and the own position estimation error. When the angle Δ between and the plane is within this threshold range, then it is considered that and come from the same target, otherwise, it is considered that they come from two targets, and then the angle correlation screening process between two aircraft is completed.

[0095] Table 1 Pairwise angle correlation screening steps

[0096]

[0097] Considering the observation process of multiple aircraft in the actual space for multiple targets, the pairwise angle screening steps are extended to the multi-aircraft scenario of an aircraft cluster to complete the collaborative multi-aircraft angle screening algorithm. For the above scenario, the following assumptions are proposed:

[0098] (1) The aircraft cluster monitors the same area, and each aircraft has a detection probability for a single target, and there is a possibility of non-detection, that is, the maximum detection numbers of the aircraft cluster are the same, and the individual detection numbers are unknown;

[0099] (2) During the aircraft monitoring process, a single measurement value corresponds to a single target, and different targets with the same angle measurement produce two identical measurement values;

[0100] For the collaborative positioning process of the aircraft cluster, let the number of aircraft in the missile cluster be M, and the number of angle measurements measured by each aircraft be N i , i = 1,..., M, and the corresponding angle measurement values are denoted as where is the azimuth angle measurement of aircraft i for target j, is the elevation angle measurement of aircraft i for target j.

[0101] Taking any individual in the aircraft group as the research object, it is denoted as the master aircraft, and the remaining aircraft are slave aircraft. Taking the measurement values of each angle of the master aircraft as the matching benchmark, they are sequentially matched with the measurement values of the remaining slave aircraft. When a certain measurement value of the master aircraft satisfies the association possibility after the pairwise angle association screening process introduced by a certain measurement value of the slave aircraft, the associated individuals are saved. If there are multiple groups of association results between a certain measurement value of the master aircraft and the measurement value of a single slave aircraft, the calculation of the absolute value of the included angle |Δ| is used for further discrimination. The one with the smallest absolute value of the included angle among multiple groups of association results is selected as the final association result. The above angle association screening algorithm is described in the following pseudocode form.

[0102] Table 2 Angle Association Screening Algorithm

[0103]

[0104]

[0105] Step 2: Coupled Weighted Least Squares Localization Algorithm

[0106] First, a single-target overdetermined nonlinear angle measurement equation containing the aircraft's own position estimation error and angle measurement error is established.

[0107] Assume that there are M aircraft in the multi-station single-target localization scenario, and their true position coordinates are expressed as Each aircraft is equipped with an angle measurement sensor to be able to obtain the angle observation value a of the target in a timely manner i (θ i , φ i ), i = 1,..., M, where θ i is the azimuth angle observation value of aircraft i for the target, and φ i is the elevation angle observation value of aircraft i for the target. Denote the multi-aircraft azimuth angle measurement vector as θ = [θ 1 , θ 2 ,..., θ M T , and the elevation angle measurement vector as φ = [φ 1 , φ 2 ,..., φ M T . The overall angle measurement vector of the cluster is:

[0108] a = [θ T , φ T T = a o + n a

[0109] where a represents the cluster angle measurement value, a o = [θ oT , φ​​​oT T represents the true value of the cluster angle measurement; n θ = [n θ,1 , n θ,2 ,..., n θ,M T ; n φ = [n φ,1 , n φ,2 ,..., n φ,M T , where n θ,i , n φ,i , i = 1,…, M represents the angle measurement noise of the vehicle i; n a is the measurement noise. Assume that n a is zero-mean Gaussian distributed noise, and its covariance matrix is Q a .

[0110] During the vehicle positioning measurement process, the self-position obtained by the system is the estimated value of the true position obtained by using the navigation element. Therefore, the estimated position s of each vehicle i and the true position have a difference Δs i , then the cluster position vector is expressed as:

[0111]

[0112] In the formula, is the true value of the vehicle position in the vehicle cluster; is the error vector of the self-position estimation of multiple vehicles. Considering the vehicle position estimation process, it is reasonably assumed that Δs is zero-mean Gaussian noise, and its noise covariance matrix is denoted as Q s .

[0113] Denote the target position as u o = [x o , y o , z o T , and establish the measurement relationship connecting the target position and the angle measurement value as:

[0114]

[0115] where i = 1, 2,..., M,

[0116] Expand the above azimuth measurement pseudo-linear equation, then there is:

[0117]

[0118] Let Then the above formula can be rewritten as:​​​​

[0119]

[0120] Introduce the inverse range g o = 1 / ||u o ||,

[0121]

[0122] where The above measurement equation contains the ideal azimuth angle and the true value of the aircraft position Both are unknown during the positioning process. Considering their relationship with the measured values, an azimuth measurement equation with errors is established.

[0123] Since then

[0124]

[0125] where Considering the position error of a single aircraft After sorting out, we get:

[0126]

[0127] Simplify the first term on the right side of the above formula:

[0128]

[0129] In the formula, is The projection on the xy plane. Furthermore, the final azimuth measurement value θ i and the target positioning parameter g o The pseudo-linear relationship of:

[0130]

[0131] Combining the azimuth measurement values of M multi-aircraft, assuming the unknown vector of the target position The azimuth measurement equation for this cluster is obtained as follows:

[0132] G θ ψ o = B θ n θ + C θ Δs

[0133] where,

[0134]

[0135] Establish the pitch angle pseudo-linear measurement relationship with reference to the above process. The specific derivation process is as follows:

[0136] Since Then there is

[0137]

[0138] Among them, Since the true value of the pitch angle measurement Under the first-order approximation condition, use the measured value α with noise φ,i And the measurement noise n a,i Characterize

[0139]

[0140] Among them, n a,i =[n θ,i , n φ,i T , and

[0141]

[0142] Substitute the above formula and consider the aircraft position estimation error Simplify to get:

[0143]

[0144] Among them,

[0145]

[0146] Combine M measurement equations to obtain the cluster pitch angle measurement equation:

[0147] G φ ψ o =B φ n φ +C φ Δs

[0148] Among them,

[0149]

[0150] Combine the azimuth angle measurement equation and the pitch angle measurement equation of multiple aircraft. Then, considering the coupling error of the sensor's own position estimation error and the angle measurement error, the multi-station single-target non-linear measurement equation is:

[0151] GΨ o =ε

[0152] In the formula,

[0153] ​

[0154] ε = Bn a + CΔs

[0155] where B = blkdiag{B θ , B φ}, G θ , B θ , C θ are parameter matrices related to the single-target azimuth angle information θ = [θ 1 , …, θ M obtained by the sensor group; G φ , B φ , C φ are parameter matrices related to the single-target elevation angle information φ = [φ 1 , …, φ M obtained by the sensor group.

[0156] In the above measurement equation, the error quantity ε describes the system error coupled by the angle measurement error n a and the sensor's own position estimation error Δs, and its weight matrix W satisfies

[0157]

[0158] Secondly, based on the above overdetermined nonlinear equation, the coupled weight least squares positioning method is obtained.

[0159] Based on the overdetermined nonlinear angle measurement equation containing the aircraft's own position estimation error and angle measurement error, referring to the weighted least squares solution method, the unknown quantity Ψ o in the above measurement equation is solved. Assume that the multi-sensor angle measurement noise covariance matrix Q a and the multi-aircraft position estimation error covariance matrix Q s are known.

[0160] First, calculate the coupled weight measurement system error matrix W. Since the matrices B and C contain elements related to the unknown quantity ψ, to improve the calculation accuracy and ensure that the estimated value of the unknown quantity is close to the true value. Use the homogeneous measurement equation that ignores the system error ε to calculate the target position quantity Ψ o corresponding estimated value

[0161] After ignoring the coupling error term ε, the measurement equation is:

[0162]

[0163] where is consistent with the unknown quantity ψ and represents an approximate estimated value of its result; use the above formula to construct an optimization problem and obtain:

[0164]

[0165] The Lagrangian function for this problem is:

[0166]

[0167] Take the partial derivative of the above calculation,

[0168]

[0169] If the constraint is to be minimized, the solution of the above equation is G T The eigenvector corresponding to the minimum eigenvalue solution of G. Further consider the physical meaning constraint of the target positioning position parameter :

[0170]

[0171] In the formula, represents the approximate estimated value of g o . Using the above formula, establish the initial estimation result judgment rule of the cluster, and then obtain the positioning solution. The estimation judgment rule is as follows:

[0172]

[0173] Use the above process to solve the approximate result to obtain the weight matrix W, and then use the complete measurement equation to re-establish the coupled weight least squares cost function:

[0174]

[0175] At this time, the optimization problem under the coupled weight is constructed as:

[0176] minψ T G T WGψ

[0177] s.t.ψ T ψ = 1

[0178] Refer to the positioning solution calculation process under the condition of ignoring errors to obtain the final positioning result ψ.

[0179] Finally, the positioning estimation result u o is:

[0180] u o =(1 / ψ(4))[ψ(1),ψ(2),ψ(3)] T .

[0181] The above-mentioned solution process of the coupled weight least squares method is designed for a two-step solution. The approximate value is calculated for the first time to obtain the accurate weight matrix, and the weight matrix obtained is used to solve the final positioning result for the second time. The two-step solution process ensures the accuracy of each estimated value during the angle calculation process, thereby improving the accuracy of the final angle positioning result. The two-step operation process is as Figure 6 shown.

[0182] Step 3: Obtaining the multi-target positioning result

[0183] Using the final association result set obtained in Step 1 successively use the coupled weight least squares positioning algorithm described in Step 2 to calculate the estimated positions of each target, and obtain the multi-station multi-target positioning result.

[0184] The present invention will be described in detail below with reference to the embodiments and the accompanying drawings.

[0185] Embodiment

[0186] Based on numerical simulation to verify the contents of the claims of the present invention, the following design experiments are carried out for calculation and simulation to fully display the method process and the universality of the law.

[0187] Carry out a simulation experiment to verify the performance of the multi-station multi-target angle association positioning algorithm. Assume that there are three aircraft in the positioning scenario, and their true positions whose true value coordinates are randomly generated, and the generation range satisfies Assume that the individuals in the aircraft group are isomorphic and are equipped with angle measurement sensors and navigation positioning components with the same performance. Communication is possible between individuals within the cluster, and the positions and corresponding angle observation results of individuals within the cluster can be obtained in real time. The number of targets tracked by the cluster at this moment is N, and its true position coordinates

[0188] Assume that each aircraft can detect all targets completely. Denote the angle measurement set of aircraft i for multiple targets as The position coordinate vector of aircraft i itself is s i . Considering the position estimation error and angle measurement error of the aircraft itself, using the true value of the position of aircraft i and the true value of the target position to obtain the set A i and the vector s i . By adding random noise with a mean of zero and a variance of to the true value of the position of each aircraft randomly generated at this moment to simulate the estimated value s of the position of each aircraft within the cluster at this moment i . Using the true value of the position of each aircraft and the true value of the target position the true value of the angle measurement of each aircraft for each target can be calculated Add random noise with a mean of zero and a variance of to the true value of the angle measurement to simulate the angle measurement values of each aircraft for each target at this moment to obtain the angle measurement set of the i-th aircraft for multiple targets

[0189] To simulate the set of real measurement results, sort the elements in the angle measurement set A i and disrupt the order in which the measured elements in the set correspond to the targets one by one. In the sorting process, first use the azimuth angle measurement value for ascending sorting. When are the same, sort in ascending order according to the pitch angle measurement value . The sorted angle measurement set A i is used as the set of true angle measurement values of the i-th aircraft for multiple targets. The performance of the algorithm is verified by multiple Monte Carlo tests, and the number of tests T s = 1000.

[0190] The experiment sets 10 fixed-position targets for positioning verification. The positions of 3 aircraft are randomly generated within the generated range. The angle measurement error is selected, and the aircraft position estimation error is selected. The target positions are shown in the following table.

[0191] Table 3 True values of multi-target positions

[0192]

[0193] The experiment first conducts correlation screening on the different angle measurement values obtained by each aircraft. Taking aircraft 1 as the main one, use the angle correlation screening algorithm for screening to form a multi-aircraft angle measurement set for different targets. Subsequently, use the multiple target measurement sets as the input of the coupled weight least squares positioning algorithm to calculate the multi-target positions.

[0194] For several Monte Carlo tests, statistically analyze the angle correlation screening results. It is agreed that during the multi-aircraft correlation screening process, if the measurement results from different aircraft are correlated and all come from the same target, it is considered a correct correlation. The correlation results are shown in Table 4.

[0195] Table 4 Results of multi-target angle correlation screening

[0196]

[0197] According to the principle of probability statistics, in the vast majority of scenarios, the number of correct correlations of the algorithm is greater than 7, meeting the requirements of the actual scenario. Subsequently, for several Monte Carlo tests, statistically analyze the results of the algorithm's estimation of each target position. The statistical results are shown in Table 5.

[0198] Table 5 Multi-target positioning results

[0199]

[0200] According to the 1σ principle, the ratio of the maximum positioning error of each target of the multi-station multi-target positioning algorithm to the true value is statistically calculated using the above table, as shown in Table 5.

[0201] Table 5 Multi-target positioning error

[0202]

[0203] Analyzing the above positioning results, in the vast majority of scenarios, the positioning error of the algorithm for a single target is less than 5% compared to the true value result. In some cases, due to the small true value of the target, the error ratio is relatively large. For example, the position of the target on the 5Y axis is -55 meters, the average positioning error is 5.79 meters, and the error ratio (1σ) is 22.63%. Except for some exceptions, the positioning accuracy of the algorithm for each target on each axis is less than 16 meters under the current error, meeting the high-precision positioning requirements. As the angle measurement error and the self-position estimation error of the aircraft increase, the proposed algorithm can obtain better positioning accuracy.

[0204] Finally, the single operation time of the algorithm is statistically calculated. Under the environment of Intel Core i5-8300H in the Windows 11 system, the average single-step operation time of the algorithm is 2.5 ms, meeting the requirement of rapidity.

Claims

1. A multi-station multi-target angle association positioning method, characterized in that: The following steps are involved: S1. Based on the geometric relationship between the target point and its corresponding angle measurement values ​​measured by different aircraft, an angle association screening algorithm is used to classify the angle measurement sets from different aircraft to obtain multiple sets of angle measurement values ​​from different aircraft that may come from the same target. S2. Establish a set of overdetermined nonlinear angle measurement equations that include the aircraft's own position estimation error and angle measurement error, and propose a coupling error weighted least squares angle positioning algorithm; S3. The angle measurement set of each target obtained by classification using the angle association screening algorithm is used as the input of the coupled error weighted least squares angle positioning algorithm to obtain the multi-target position estimation result and complete the multi-target positioning.

2. A multi-station multi-target angle association positioning method according to claim 1, characterized in that: The pairwise angle association screening process in step S1 specifically includes: In the dual-station multi-target positioning scenario, at any given moment, the aircraft P i Position coordinates (x i ,y i ,z i ) and its arbitrary angle observation data a(θ i ,φ i ), i=1,2; where θ i ,φ i They are the azimuth angle observation and pitch angle observation of the aircraft to the target respectively; Step 1-1: Calculate the aircraft P1 observation vector Aircraft P2 observation vector With distance vector Step 1-2: Calculation The unit normal vector corresponding to the plane formed by μ1 And calculate exist and The projection on the plane Step 1-3: Judgement Is it on the same side as μ1? If they are on the same side and not parallel, proceed to step 1-4. Otherwise, it is considered and There is no possibility of data association; Step 1-4: Calculate the angle If |Δ|≤Δ max , then it is believed that and If there is a possibility of data association, the positioning calculation is performed; otherwise, it is considered and There is no data association possible; among them, Δ max is the association judgment threshold, and the judgment ends; Output the final judgment result and the absolute value of the angle |Δ|; "yes" indicates that there is a possibility of association, "no" indicates that there is no association.

3. A multi-station multi-target angle association positioning method according to claim 2, characterized in that: The angle association screening algorithm in step S1 specifically includes: Get the position coordinates of the main aircraft P1 at any time s1 = [x1, y1, z1] T Observation data with its angle From the aircraft P k ,k=2,…,M position coordinates s k =[x k ,y k ,z k ] T Observation data with its angle p=1,…,N i ; M is the number of aircraft in the swarm, and the number of angle measurements measured by the aircraft is N i ,i=1,…,M; Step 1: Initialize, set j = 1, k = 2, and the angle association set of the two machines Multi-machine angle association result set in is the angle association result set of aircraft j; Step 2: Select the main aircraft is the reference association angle; Step 3: Select the kth slave aircraft as the associated object and use its angle measurement value in turn p=1,…,N k Angle associated with the base Perform pairwise matching screening, that is, through the pairwise angle association screening process, make a judgment. If the association possibility is met, save the absolute value of the angle between (k, p) and the pair of associations |Δ| to the set middle; Step 4: Determine the set Is the element in greater than 1? If so, it means there are multiple associations, so find the set from them. The association with the smallest absolute value of the angle |Δ| is taken as the final association result, and the association is saved in the set If not, directly set The elements are stored in the collection middle; Step 5: Set up the collection k=k+1, repeat steps 2, 3, 4, 5 until k>M; Step 6: Update the reference angle of the main aircraft, that is, j=j+1, and repeat steps 2, 3, 4, 5, 6 until j>N1; Step 7: End the association calculation and set Any subset of Measured for the main aircraft The correlation angle is calculated by using the correlation result to perform positioning calculation; Output: Final association result set 4. A multi-station multi-target angle association positioning method according to claim 3, characterized in that: In step S2, a set of overdetermined nonlinear angle measurement equations including the aircraft's own position estimation error and angle measurement error specifically includes: Considering the coupling error of the sensor's own position estimation error and angle measurement error, let Ψ o =[cosθ o cosφ o ,sinθ o cosφ o ,sinφ o ,g o ] T is the unknown value of the angle positioning result, where θ o ,φ o ,g o is the azimuth, elevation and reverse range of the target in the corrected polar coordinates. The nonlinear measurement equation for a single target at multiple stations is: GΨ o =e In the formula, e=Bn a +CΔs Where G is the measurement matrix, ε is the coupling error; B = blkdiag{B θ ,B φ }, G θ ,B θ ,C θ is the single target azimuth information θ = [θ1,…,θ M ] related parameter matrix; G φ ,B φ ,C φ is the single target pitch angle information φ=[φ1,…,φ M ] related parameter matrices; the parameter matrices are: Among them, G θ is the cluster azimuth measurement matrix, G φ B is the cluster pitch angle measurement matrix; θ is the cluster azimuth-correlated angle noise driving matrix, B φ C is the cluster pitch angle related angle noise driving matrix; θ is the cluster azimuth-related site error driving matrix, C φ is the cluster elevation angle related site error driving matrix; in, is the azimuth and pitch angle measurements of the target by the aircraft i sensor; is the projection of the distance vector between the target and sensor i on the xy plane; is the second norm of the distance vector between the target and sensor i; The error quantity ε in the above measurement equation describes the angle measurement error n a The system error coupled with the sensor's own position estimation error Δs has a weight matrix W that satisfies: Q a is the multi-sensor angle measurement noise covariance matrix, Q s is the error covariance matrix of multi-vehicle position estimation.

5. A multi-station multi-target angle association positioning method according to claim 4, characterized in that: The coupling error weighted least squares angle positioning algorithm in step S2 specifically includes: Based on the overdetermined nonlinear angle measurement equation including the aircraft's own position estimation error and angle measurement error, the weighted least squares solution method is used to solve the unknown quantity Ψ in the above measurement equation. o Solve; Assume that the multi-sensor angle measurement noise covariance matrix Q a And the covariance matrix Q of multi-aircraft position estimation errors s known; First, calculate the coupling weight measurement system error matrix W. The matrices B and C contain the unknown quantities of the target angle measurement value ψ = [cosθcosφ, sinθcosφ, sinφ, g] T Related elements, where θ, φ, g are the azimuth, pitch angle, and reverse range of the target in the corrected polar coordinates; the target position Ψ is calculated using the homogeneous measurement equation ignoring the system error ε o Corresponding estimated value After ignoring the coupling error term ε, the measurement equation is: in, is consistent with the unknown quantity ψ, indicating an approximate estimate of its result; using the above formula to construct the optimization problem, we get: The Lagrangian function of this problem is: in, is the Lagrangian function, λ is the Lagrangian coefficient; For the above calculation partial derivative, If the constraint is minimized, the solution of the above equation is G T G The eigenvector corresponding to the minimum eigensolution; Consider the target positioning position parameters Physical constraints: In the formula, Express g o The approximate estimated value of; Using the above formula, establish the preliminary estimation result of the cluster The judgment rules are used to obtain the positioning solution. The estimated judgment rules are as follows: in, express The 1st to 3rd elements; express The fourth element of ; Use the above process to solve the approximate result The weight matrix W is obtained, and then the coupling weight least squares cost function is re-established using the complete measurement equation: in, is the least squares cost; At this time, the optimization problem under the coupling weight is constructed as follows: minψ T G T WGψ stψ T ψ=1 Get the final positioning result ψ; Finally, the positioning estimation result u is obtained o for: you o =(1 / ψ(4){ψ(1),ψ(2),ψ(3)] T in, i=1,2,3,4 means The i-th element; The above-mentioned coupled weight least squares solution process is designed to be solved in two steps. The first step is to solve the approximate value to obtain the accurate weight matrix, and the second step is to use the obtained weight matrix to solve the final positioning result.

6. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method described in any one of claims 1 to 5 are implemented.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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