A target direction finding method based on short baseline unified model

Abstract

The application discloses a target direction finding method based on a short baseline unified model, which is realized by a computer and comprises the following steps: firstly, an improved polar coordinate representation (MPR) unified model is constructed; secondly, a closed-form initial solution of direction finding under the MPR model is obtained; then, an improved successive unconstrained minimization method based on the MPR is used to solve a quadratic constraint optimization problem to obtain the angle of the target source; thirdly, a direction finding initial solution is used to guide source deployment; fourthly, time-space reference system error calculation is performed; finally, target source TDOA measurement and time-space reference system error elimination and final solution solving are performed; the application effectively avoids the threshold effect of the short baseline positioning system based on the far-field direction finding unified model of the modified polar coordinates, so that the far-field target direction finding method of the unmanned aerial vehicle group based on the time difference of arrival measurement becomes possible; the calibration source and the target source are jointly monitored, the time-space reference system error is eliminated through the time difference measurement of the calibration source, and thus the direction finding precision is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned aerial vehicle direction finding, and particularly relates to a target direction finding method based on a short baseline unified model. BACKGROUND

[0002] The basic principle of the existing unmanned aerial vehicle group cooperative TDOA positioning is that multiple unmanned aerial vehicles receive target source signals and measure TDOA positioning parameters under the condition of clock synchronization, and then multiple hyperboloids with the unmanned aerial vehicles as the foci are obtained, and the intersection of the hyperboloids is the target source position. However, in actual application, many non-ideal factors will cause the positioning performance to deteriorate, such as: the unmanned aerial vehicle signal receiving measurement noise is too large, the target source far field and near field prior conditions are unknown, the unmanned aerial vehicle position drift caused by the unmanned aerial vehicle maneuvering, and the clock of the unmanned aerial vehicles is not synchronized.

[0003] In view of the problem of whether the target source is located in the far field or the near field, the traditional electronic reconnaissance signal processing divides it into two research fields: for the far field target, the direction of arrival (DOA) of the target transmitted signal is usually estimated, and for the near field signal, the TDOA positioning method can be used to construct the equation between the target position and the TDOA parameter to solve the target position. However, in the actual environment, the prior information of whether the signal source is located in the far field or the near field is often missing, and the problem of mismatch between the positioning or direction finding method and the long-short baseline model of the system may occur, which causes the positioning or direction finding performance to deteriorate seriously. SUMMARY

[0004] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide a target direction finding method based on a short baseline unified model. The modified polar representation (MPR) far-near field direction finding unified model effectively avoids the threshold effect of the short baseline positioning system, making it possible for the unmanned aerial vehicle group far field target direction finding method based on the time difference of arrival (TDOA) measurement. The unified model fully utilizes the advantage of the same space-time reference system error when the calibration source and the target source are jointly monitored, and eliminates the space-time reference error in the target source time difference measurement value through the calibration source time difference measurement, so as to improve the direction finding accuracy.

[0005] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0006] A target direction finding method based on a short baseline unified model, realized based on a computer, comprising the following steps:

[0007] Step 1, modified polar representation (MPR) unified model construction;

[0008] Step 2, closed-form initial solution of direction finding under the MPR model;

[0009] Step 3, the angle of the target source is solved by solving a quadratic constraint optimization problem by using an improved successive unconstrained minimization (Improved SUM-MPR) method based on MPR;

[0010] Step 4, the direction finding initial solution guides the calibration source deployment;

[0011] Step 5, the space-time reference system error is calculated;

[0012] Step 6, the target source TDOA measurement is eliminated with the space-time reference system error, and the target source final solution is solved.

[0013] The present application has the following beneficial effects:

[0014] The present application provides a scheme for effectively avoiding the threshold effect of a short baseline positioning system: the present application uses a method of modified polar coordinate representation, constructs a unified model of near-field positioning and far-field direction finding, avoids the threshold effect of target position estimation of the short baseline positioning system under the Cartesian coordinate system and DOA estimation under the polar coordinate system, and simultaneously does not require prior information of the target being located in the near field or the far field.

[0015] Higher direction finding accuracy and lower calculation complexity: the present application uses an algebraic closed-form solution method, represents the direction of arrival (DOA) of the target signal as a set of positive sine functions, thereby reconstructs the measurement equation and solves the problem by using two linear WLS optimization methods, converts the positioning problem under MPR into a quadratic optimization problem, and proposes a closed-form solution method: an improved successive unconstrained minimization (Improved SUM-MPR) method based on MPR, which effectively reduces the calculation complexity compared with an iterative algorithm, and the direction finding accuracy is superior to that of other closed-form solution algorithms.

[0016] The present application provides a scheme for effectively avoiding the space-time reference system error caused by the position error of a UAV and the clock synchronization error between the UAVs: the present application avoids the clock time error of the position information and the internal clock synchronization information of the UAV from the Beidou or GPS module due to the number and state of satellites, deployment environment shielding, spectrum disturbance and other factors by introducing a calibration source and scientifically deploying the UAVs, makes the clocks of the UAVs unsynchronized, and further seriously deteriorates the TDOA measurement accuracy, and even makes the TDOA positioning completely invalid; avoids the problem that the Beidou or GPS module is difficult to give the position information of the UAV itself in real time due to the maneuvering characteristics of the UAV itself, causes a large position drift error in the self-positioning result of the UAV, and seriously reduces the target direction finding accuracy based on the TDOA measurement. Attached Figure Description

[0017] Figure 1 This is a flowchart of an embodiment of the present invention.

[0018] Figure 2 This is the direction-finding scenario configuration in the simulation of this embodiment of the invention.

[0019] Figure 3 The curves show how the direction-finding performance of various algorithms in the embodiments of this invention changes with the increase of RDOA measurement error.

[0020] Figure 4 These are the simulation curves of the direction-finding performance of various algorithms in the embodiments of the present invention as the distance to the target source increases.

[0021] Figure 5 These are the curves showing the change in direction-finding performance of various algorithms as a function of UAV position error, as simulated in embodiments of the present invention. Detailed Implementation

[0022] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] Reference Figure 1 A target direction finding method based on a short baseline unified model, implemented using a computer, includes the following steps:

[0024] Step 1, Construction of the Modified Polar Representation (MPR) Unified Model: The geometric relationship between the UAV and the target being located in the near-field localization model and the far-field direction finding model is mathematically described in a unified manner, and the target position is represented by the MPR modified polar coordinate system;

[0025] The location of the target is represented by MPR coordinates as follows:

[0026]

[0027] Where, θ o and φ o These are the azimuth and pitch angles of the target relative to the reference UAV in the polar coordinate system, respectively, g o The inverse distance is defined as:

[0028]

[0029] Among them, u o and Let be the position coordinates of the target and the reference UAV in the Cartesian coordinate system, respectively, denoted as: The Euclidean distance between the target and the reference drone;

[0030] Step 2, Closed-form solution of Direction Finding under MPR model:

[0031] (2.1) Relative position of target u i to the UAVs in the swarm s

[0032]

[0033] where M is the number of UAVs participating in the positioning, u o is the position of the target to be located, is the real position of the UAVs, s i is the measured position of the UAVs, Δs i is the measurement error of the UAVs' position, is the real RDOA value of the target to be located, n i1 is the measurement error of the RDOA of the target to be located, n t,i1 is the RDOA error caused by time synchronization error between UAVs, which is the quantity to be eliminated;

[0034] The Euclidean distance between the UAV s i and the target to be located u o is represented as:

[0035]

[0036] where, Collecting all M-1 RDOA measurements gives the matrix form:

[0037] r = r o + n t

[0038] where r = [r 21 , r 31 ,..., r M1 ] T , n = [n 21 , n 31 ,..., n M1 ] T is the RDOA measurement error vector with zero mean, satisfying Gaussian random distribution, and its covariance matrix is Q n , n t = [n t,21 , n t,31 ,..., n t,M1 ] T is the RDOA error vector caused by time synchronization error of the UAV swarm, satisfying Gaussian random distribution, and its covariance matrix is Qt ;

[0039] (2.2) Set the origin of the coordinate system to the position of the UAV s1, i.e. and drones i With the target u o Expanding the distance relationship yields:

[0040]

[0041] in, For the target u o The true distance to the origin, r i1 For the target u o To drones i The distance between the target u and the target u o The distance difference to drone s1, n i1 For r i1 Measurement error, n t,i1 For the target u o To drones i Distance error caused by clock synchronization error with UAV S1;

[0042] Representing the above formula using MPR coordinates, and Substitute into the above equation and divide both sides by 2r o Ignoring higher-order noise terms, we obtain the value r containing the measured value. i1 The basic equations related to MPR variables:

[0043]

[0044] in, Let n be the noise vectors n and ... t and Δs i The total error caused This is the unit vector pointing from the origin to the target, and it is related to the direction of arrival (DOA) of the target signal. In 2D and 3D cases, these vectors are respectively... and

[0045] (2.3) By defining the target position vector as The basic equation in step (2.2) is pseudo-linearized. After collecting M-1 RDOA measurements, the basic equation is written in matrix form:

[0046]

[0047] in, Includes the target RDOA measurement error n and the clock synchronization error nt the joint influence of is the UAV's own position error, h1=-r,

[0048] (2.4) Introducing the weighting matrix W1 to balance the clock synchronization error n t and the UAV's own position error Δs, ignoring the second-order noise in ∈1, we have W1=(B1(Q n +Q t )B1+ΓQ s Γ T ) -1 Since the unknowns are linear in the matrix equation and are solved by the linear least squares criterion, the solution is to solve a quadratic optimization problem with quadratic constraints, described as:

[0049]

[0050]

[0051] where, h1is the RDOA measurement matrix, G1is the regression matrix, W1is the weighting matrix, and ψ1is the unknown to be solved;

[0052] Step 3: Use the improved weight SUM-MPR method to solve the constrained optimization problem described in step (2.4) to obtain the initial estimate of the target source in the MPR coordinate system

[0053] (3.1) Use the Improved SUM-MPR method based on MPR to solve the quadratic constrained optimization problem to obtain the angle of the target source:

[0054] Step 3.1.1: Ignore the constraints in the quadratic optimization problem and assume that the elements in are independent to obtain Assuming that the errors in G1are small enough and the bias can be ignored, we have At this time, the 2-D MPR and 3-D MPR of the target position are: and

[0055] where, tan -1 () is the inverse tangent function, and ψ 11 is the solution in step 3.1.1;

[0056] Step 3.1.2: The solution in step 3.1.1 is denoted as Δψ 11 To estimate the error, square the first N elements on both sides of the equation:

[0057]

[0058] Considering the constraint, add the last element of to get: 11

[0059]

[0060]

[0061]

[0062] where, is the error introduced by Δψ 11 unknowns By constructing the following optimization problem:

[0063]

[0064] Solve; Weighted matrix Then the WLS estimate is:

[0065]

[0066] Its covariance matrix is:

[0067]

[0068] By ψ 12 The target's 2-D MPR and 3-D MPR coordinates are obtained as:

[0069]

[0070] where sgn() is the sign function, defined as: ψ 12 is the solution in step 3.1.2;

[0071] Step 4, Direction finding initial solution guide calibration source deployment: The calibration source is represented in the MPR coordinate system as The calibration source is guided to be deployed at the initial estimated position of the target in the MPR coordinate system, i.e. let Then The corresponding Cartesian coordinates are

[0072] ​​Step 5, space-time reference system error calculation: the distance from the calibration source to each UAV is known from the RDOA measurement value:

[0073]

[0074] wherein ξ i1 is the RDOA measurement error of the calibration source, and the set is denoted as ξ, ξ = [ξ 21 , ξ 31 ,..., ξ M1 ] T is the calibration source RDOA measurement error vector with a mean of zero, satisfying Gaussian random distribution, and the covariance matrix thereof is Q ξ ;

[0075] The positioning UAVs carry monitoring receivers that simultaneously monitor the positioning target signals and calibration signals in a high sampling rate mode, i.e., each UAV monitoring data contains both target signals and calibration signals, so the clock synchronization error n t,i1 of the target signal RDOA measurement value is contained in the calibration signal RDOA measurement value; the RDOA calculation value of the calibration source arriving at each UAV is obtained from the actual position of the deployed calibration source and the UAVs with error positions, and is At this time, the system error is:

[0076]

[0077] wherein Δs is the to-be-calibrated quantity introduced by the UAV position error Δs i , Δs1, n t,i1 is the to-be-calibrated quantity introduced by the clock synchronization error;

[0078] Step 6, target source TDOA measurement and space-time reference system error elimination and final solution: M-1 system error calibration quantities are collected to obtain Δr c = [Δr c,21 , Δr c,31 ,..., Δr c,M1 ] T Δr c is introduced into the target signal RDOA measurement value r, and the target signal RDOA correction value after eliminating the system error is:

[0079]

[0080] Finally, after eliminating the RDOA system uncertainty of the source, we obtain Since it contains n i1 , and ξ i1Three error terms, the residual error terms above are solved by two closed-form solutions, will be substituted into and Taylor series expansion is applied to the first order term to obtain:

[0081]

[0082] where, is the unit direction vector, pointing to s i . Substitute into to obtain:

[0083]

[0084] Define n d,i1 as follows

[0085]

[0086] M-1 RDOA sets are obtained:

[0087]

[0088] where, n d = [n d,21 , n d,31 ,..., n d,M1 ] T ; Square both sides of the above expression to obtain:

[0089]

[0090] Substitute into the above equation to obtain:

[0091]

[0092] Divide both sides of the above equation by and substitute and to obtain:

[0093]

[0094] where,

[0095]

[0096] The above equation only retains the first order noise term, so define the following matrix:

[0097] ​

[0098] wherein,

[0099]

[0100]

[0101]

[0102] 2=[∈ 2,2 ,∈ 2,3 ,...,∈ 2,M ] T

[0103] Let ∈2be defined as:

[0104]

[0105] The above formula is solved by weighted least squares, wherein the weighted matrix is represented as E[∈2∈2 T ]; the above quadratic optimization problem can be represented as:

[0106]

[0107]

[0108] The weighted matrix can be represented as:

[0109]

[0110] wherein,

[0111]

[0112] The RDOA of the source after eliminating the error is reconstructed into a quadratic minimization problem with quadratic constraints, which can be solved by Improved SUM-MPR based on MPR; and then G2, W2 and ψ2 are brought into the Improved SUM-MPR in step (3) for solving, and the performance-optimized target source direction finding result can be obtained.

[0113] The beneficial effects of the present application can be further proved by the following simulation experiment:

[0114] 1. Simulation conditions:

[0115] The simulation verifies the algorithm performance in a three-dimensional scene, and is also applicable to a two-dimensional scene; the simulation scene contains 7 unmanned aerial vehicles (M=7), the positions of which are shown in Table 1, and the arrival direction angle DOA of the target signal is randomly selected as θ°=22.13°, φ°=14.41°, and the target source RDOA measurement error covariance matrix is set as in The unit is m 2 The calibration source is fixed at a distance of 10km from the coordinate origin, and its RDOA measurement error σ ξ RDOAσ of the target source n The measurement error is less than 15dB (equivalent to Its covariance matrix is in The unit is m 2 When the UAV clock synchronization error follows a Gaussian distribution, Its covariance matrix is in The unit is m 2 When the UAV clock synchronization error satisfies a uniform distribution, Where ρ is in meters; the covariance matrix of the UAV's self-localization position error is... To simulate the randomness of the UAV's position error, P is set here. s =diag(17), where The unit is m 2 The number of Monte Carlo simulations was K=2000, and the performance was measured using MSE (mean squared error), defined as follows:

[0116]

[0117] Where K is the number of Monte Carlo simulations, θ k , These are the estimated values ​​of the azimuth and elevation angles obtained from the k-th simulation, respectively.

[0118] Direction finding scenario configuration as follows Figure 2 As shown, Figure 2 The center circle represents the drone, the cross represents the target source, the pentagram represents the randomly deployed calibration source, and the diamond represents the calibration source deployed in the direction of the first Improved SUM-MPR coarse estimation.

[0119] To verify the performance of the method of the present invention, under the condition of UAV position error Δs and clock synchronization error n t Under the conditions of the RDOA measurement error ξ of the calibration source and the RDOA measurement error n of the target being located, the following comparative algorithms are selected for positioning performance comparison simulation: the classic closed algorithm CFS based on TDOA measurement; the closed algorithms SUM-MPR and GTRS-MPR; the WEC-MPR algorithm; the method of this invention introduces a single UAV as the calibration source, but the calibration source is deployed arbitrarily, which is represented as: the method proposed in this paper (random deployment of calibration source); the direction finding performance limit CRLB (Cramér-Rao Low Bound).

[0120] Table 1. Location coordinates of the UAV

[0121]

[0122] 2. Simulation results:

[0123] Simulation 1: The target source distance coordinate is set as 50km, and the RDOA measurement error of the target source is changed in a logarithmic form from-40dB to 30dB; when the average clock synchronization error between UAVs is 200ns, which is converted into the RDOA measurement error is set as 35.56dB (i.e., σ t = 60m); when the RDOA measurement error is converted into 10logρ 2 is set as 35.56dB (i.e., ρ = 60m); and the UAV self-positioning position error σ s = 1m. The curves of the performance of the above-mentioned comparison algorithm and the performance of the method of the present application with the change of the RDOA measurement error of the target source are shown in Figure 3 , Figure 3 the horizontal coordinate axis in the figure represents the RDOA measurement error, Figure 3 and the vertical coordinate axis represents the RMSE of the target azimuth and elevation angle in °.

[0124] Figure 3 The left subgraph in the figure shows the direction finding performance when the clock synchronization error is Gaussian distribution, and the right subgraph shows the direction finding performance when the clock synchronization error is uniform distribution. As shown in the left subgraph, Figure 3 when no calibration source is referenced, the root mean square error of the direction finding results of the SUM-MPR, GTRS-MPR and WEC-MPR algorithms is all more than 5°, and the direction finding performance is difficult to meet the requirements of practical application; after the introduction of the calibration source, when and the RDOA measurement error is 0.316m, the direction finding error of the method of the present application under the guided deployment of the calibration source is less than 0.03°, which is improved by about 5.25° compared with the direction finding precision of the SUM-MPR, GTRS-MPR and WEC-MPR without the calibration source; and the direction finding precision is improved by about 0.15° compared with the direction finding precision of the method of the present application under the random deployment of the calibration source; when , the direction finding error of the method of the present application under the guided deployment of the calibration source is about 0.52°, which is improved by about 4.77° compared with the direction finding precision of the SUM-MPR, GTRS-MPR and WEC-MPR without the calibration source. As shown in the right subgraph, Figure 3 when no calibration source is referenced, the root mean square error of the direction finding results of the SUM-MPR, GTRS-MPR, CFS and WEC-MPR algorithms is all more than 3°, and the direction finding performance is difficult to meet the requirements of practical application; after the introduction of the calibration source, when and the RDOA measurement error is 0.316 meters, the direction finding error is less than 0.03° in the calibration source guided deployment using the method of the present application, which is about 3.11° higher than the direction finding precision of the SUM-MPR, GTRS-MPR and WEC-MPR without calibration source; compared with the calibration source randomly deployed and using the method of the present application, the direction finding precision is about 0.01° higher; when , the direction finding error of the method of the present application in the calibration source guided deployment is about 0.52°, which is about 2.643° higher than the direction finding precision of the SUM-MPR, GTRS-MPR and WEC-MPR without calibration source. It is shown that the introduction of the calibration source well eliminates the time synchronization error deterioration effect between the unmanned aerial vehicles and is suitable for the case where the clock synchronization error satisfies the Gaussian distribution and the uniform distribution; when the calibration source is guided and deployed on the initial direction finding azimuth, the direction finding error is always less than the case where the calibration source is randomly deployed, because when the calibration source is guided and deployed on the initial direction finding azimuth, the radial component of the positioning unmanned aerial vehicle position error relative to the positioned target is almost the same as the radial component relative to the calibration source, and the calibration effect of the positioning unmanned aerial vehicle position error is better; when , the direction finding performance of the calibration source randomly deployed and the calibration source guided deployment is similar, because the RDOA measurement error is too large at this time and almost covers the performance impact of the unmanned aerial vehicle position error, but the two cases are still better than the case without calibration source, because at this time the clock synchronization error between the unmanned aerial vehicles is relatively large compared with the measurement error, which has covered the performance impact of the RDOA measurement error. In summary, the method of the present application can use the guided deployment of the calibration source to effectively eliminate the clock synchronization error between the unmanned aerial vehicles and the self-positioning position error of the unmanned aerial vehicle, so as to improve the direction finding estimation precision.

[0125] Simulation 2: Based on the direction finding scene configuration shown in Figure 2 , the direction finding performance with the change of the target source distance in the cases of no calibration source, calibration source guided deployment and calibration source randomly deployed is verified. The RDOA measurement error of the target source is set to , and the RDOA measurement error is 0.1 meters, and the unmanned aerial vehicle position error and the clock synchronization error are set to be the same as in simulation 1. When the distance of the target source relative to the coordinate origin changes from 5km to 50km. Figure 4 The horizontal coordinate axis in the figure represents the distance of the target source from the center, Figure 4 The vertical coordinate axis in the figure represents the RMSE of the target azimuth angle and the elevation angle in °.

[0126] Figure 4 The left subgraph in the figure plots the direction finding performance when the clock synchronization error is Gaussian distribution, and the right subgraph plots the direction finding performance when the clock synchronization error is uniform distribution. It is shown from Figure 4From the left subgraph, it can be seen that the two cases of calibration source random deployment and calibration source guided deployment are much better than the case without calibration source. When the target relative coordinate origin distance is 10 km, the direction finding error of the calibration source guided deployment and the use of the method of the present application is about 0.013°, which is improved by 5.06° than the direction finding precision of the SUM-MPR and GTRS-MPR methods without calibration source, and is improved by 0.17° than the direction finding error of the calibration source random deployment and the use of the method of the present application. When the target relative coordinate origin distance is up to 200 km, the direction finding error of the calibration source guided deployment and the use of the method of the present application is about 0.012°, which is improved by 5.31° than the direction finding precision of the SUM-MPR and GTRS-MPR methods without calibration source, and is improved by 0.17° than the direction finding error of the calibration source random deployment and the use of the method of the present application. From the left subgraph, Figure 4 From the right subgraph, it can be seen that the two cases of calibration source random deployment and calibration source guided deployment are much better than the case without calibration source. When the target relative coordinate origin distance is 10 km, the direction finding error of the calibration source guided deployment and the use of the method of the present application is about 0.012°, which is improved by 3.02° than the direction finding precision of the SUM-MPR and GTRS-MPR methods without calibration source, and is improved by 0.02° than the direction finding error of the calibration source random deployment and the use of the method of the present application. When the target relative coordinate origin distance is up to 200 km, the direction finding error of the calibration source guided deployment and the use of the method of the present application is about 0.013°, which is improved by 3.16° than the direction finding precision of the SUM-MPR and GTRS-MPR methods without calibration source, and is improved by 0.019° than the direction finding error of the calibration source random deployment and the use of the method of the present application. Figure 4 It is shown that the direction finding error is greatly eliminated, because the introduction of the calibration source well eliminates the time synchronization error between the unmanned aerial vehicles; in addition, the direction finding performance of the calibration source guided deployment and the use of the method of the present application is obviously better than that of the calibration source random deployment, which shows that the guided deployment of the calibration source can better eliminate the influence of the position error of the unmanned aerial vehicle itself; with the gradual increase of the target relative coordinate origin distance, the performance of the method of the present application in the case of calibration source guided deployment is almost unchanged, which shows that the method of the present application can be well applied to the demand for accurate direction finding of super long distance target, and has good adaptability to long and short distance targets.

[0127] Simulation 3: The target source distance coordinate origin is set to 50 km, and the position error of the unmanned aerial vehicle The logarithmic form is changed from -40 dB to 30 dB; when The average clock synchronization error between the unmanned aerial vehicles is 200 ns, which is converted into RDOA measurement error It is set to 35.56 dB (i.e. σ t = 60 m); when The RDOA measurement error is converted into 10logρ 2 It is set to 35.56 dB (i.e. ρ = 60 m); without RDOA measurement error σn =0.1m. The performance curves of the above comparison algorithm as a function of UAV position error and the direction-finding performance curve of the proposed method as a function of UAV position error are shown below. Figure 5 As shown. Figure 5 The horizontal coordinate axis represents the UAV's position error in logarithmic form. Figure 5 The vertical coordinate axes represent the RMSE of the target's azimuth and elevation angles, in degrees.

[0128] Figure 5 The left subplot shows the direction-finding performance when the clock synchronization error has a Gaussian distribution, and the right subplot shows the direction-finding performance when the clock synchronization error has a uniform distribution. Figure 5 As shown in the left-middle sub-figure, without a calibration source, the root mean square error of the direction finding results for both SUM-MPR, GTRS-MPR, and WEC-MPR algorithms exceeds 5°, making it difficult to meet the requirements of practical applications. With the introduction of a calibration source, when... When the UAV position error is 1m, the direction finding error is less than 0.01° when using the method proposed in this paper with calibration source guidance. This represents an improvement of approximately 5.27° in direction finding accuracy compared to SUM-MPR, GTRS-MPR, and WEC-MPR without calibration sources; and an improvement of approximately 0.17° compared to direction finding accuracy when using the method proposed in this paper with arbitrary calibration source deployment. When the UAV's position error is 10m, the direction finding error of the method presented in this paper is approximately 0.09° under the guidance of the calibration source, which is about 5.12° higher than the direction finding accuracy of the uncalibrated SUM-MPR, GTRS-MPR, and WEC-MPR methods. Figure 5 As shown in the right-middle subfigure, without a calibration source, the root mean square error of the direction finding results for both SUM-MPR, GTRS-MPR, CFS, and WEC-MPR algorithms exceeds 3°, making it difficult to meet the requirements of practical applications. With the introduction of a calibration source, when... When the UAV position error is 1m, the direction finding error is less than 0.013° when using the method proposed in this paper with calibration source guidance. This represents an improvement of approximately 3.13° compared to SUM-MPR, GTRS-MPR, and WEC-MPR without calibration sources; and an improvement of approximately 0.02° compared to arbitrary calibration source deployment using the method proposed in this paper. When the time error and the UAV position error are 10 m, the direction finding error of the method in the calibration source guided deployment condition is about 0.12°, which is improved by about 0.23° compared with the direction finding precision of the SUM-MPR, GTRS-MPR and WEC-MPR methods without calibration source. In addition, the direction finding performance of the method in the calibration source guided deployment condition is obviously better than that in the calibration source random deployment condition, which shows that the guided deployment of the calibration source can better eliminate the influence of the UAV position error. With the gradual increase of the sensor position error, the performance of the method in the calibration source guided deployment condition is almost unchanged, which shows that the method can be well applied to the demand of far-field target direction finding in the UAV position drift condition.

Claims

1. A method for target direction finding based on short baseline unified model, based on computer implementation, characterized in that, Comprise the following steps: Step 1, the modified polar representation (MPR) unified model construction is improved; The specific steps 1 are: The geometric relationship between the unmanned aerial vehicle and the positioned target in the near-field positioning model and the far-field direction finding model is mathematically described, and the target position is represented by using the MPR modified polar coordinate system; The position of the positioned target is represented by using the MPR coordinate as follows: where θ o and φ o are the azimuth and the pitch angle of the reference UAV in the target relative polar coordinate system, respectively, and g o is the inverse distance, defined as: wherein u o and are the position coordinates of the positioned target and the reference drone in the Cartesian coordinate system, respectively, denoted as: u o = [x o , y o , z o ] T , is the Euclidean distance of the target relative to the reference drone; Step 2, the direction finding closed-form initial solution under the MPR model; The specific steps 2 are: (2.1) The relative distance between the target and the group of drones s i The Range Difference of Arrival (RDOA) measurement between the drone s1 and the target is expressed as: wherein M is the number of UAVs participating in positioning in the fleet, u o is the target position to be located, s i o = s i - Δs i is the real position of the UAV to be located, s i is the measured known position of the UAV, Δs i is the position measurement error of the UAV, is the real value of the RDOA of the target to be located, n i1 is the measurement error of the RDOA of the target to be located, n t,i1 is the distance of arrival error caused by the time synchronization error between the UAVs; Unmanned aerial vehicle s i The Euclidean distance between the positioned target u o The true value is represented as: wherein, After all M-1 RDOA measurements are collected, the matrix form is obtained: r = r o + n + n t wherein r = [r 21 ,r 31 ,...,r M1 ] T , n = [n 21 ,n 31 ,...,n M1 ] T is a RDOA measurement error vector with zero mean, satisfying Gaussian random distribution, and its covariance matrix is Q n ; n t = [n t,21 ,n t,31 ,...,n t,M1 ] T is a RDOA error vector caused by UAV group time synchronization error with zero mean, satisfying Gaussian random distribution, and its covariance matrix is Q t ; (2.2) Set the coordinate origin as the position of the UAV s1, that is and the distance between the UAV s i The distance relationship of the positioned target is expanded as wherein, is the positioned target u o the real distance to the coordinate origin, r i1 is the positioned target u o the distance to the unmanned aerial vehicle s i the distance difference between the positioned target u o and the unmanned aerial vehicle s1, n i1 is the measurement error of r i1 , n t,i1 is the distance error caused by the clock synchronization error between the positioned target u o and the unmanned aerial vehicle s i and the unmanned aerial vehicle s1; Expressing the above equation in terms of MPR coordinates, we have s i o = s i - Δs i and Substituting into the above equation and dividing both sides by 2r o , and neglecting the higher order noise terms, we obtain the basic equation involving the MPR variables and the measured value r i1 : wherein is a noise vector n, n t and Δs i the sum of errors caused by, is a unit vector pointing from the coordinate origin to the target being located, related to the direction of arrival DOA of the target signal, in 2-D and 3-D cases respectively and (2.3) By defining the target position vector as The basic equation in step (2.2) is pseudo-linearized, and after M-1 RDOA measurements are collected, the basic equation is written in matrix form: wherein, including the combined effect of the positioning target RDOA measurement error n and the clock synchronization error n t is the UAV's own position error, h1= -r, ​ (2.4) Introducing a weighted matrix W1 to balance the clock synchronization error n t The space-time reference error is composed of the UAV's own position error Δs and the clock synchronization error n. Ignoring the second-order noise in ∈1, we get W1 = (B1(Q n + Q t )B1 + ΓQ s Γ T ) -1 Since the unknown quantity In the matrix equation, it is linear and solved by the linear least squares criterion. At this time, the solution is to solve a quadratic optimization problem with a quadratic constraint, described as: wherein, hi is the RDOA measurement matrix, G1 is the regression matrix, W1 is the weighting matrix, and ψ1 is the quantity to be solved. Step 3, the angle of the target source is obtained by using the improved successive unconstrained minimization (Improved SUM-MPR) method based on the MPR to solve the quadratic constraint optimization problem; The specific steps 3 are: Solve the constrained optimization problem described in step (2.4) using the improved weight SUM-MPR method to obtain the initial estimated value of the positioned target source in the MPR coordinate system (3.1) Improved SUM-MPR method based on MPR: Step 3.1.1 : Ignore the constraints in the quadratic optimization problem and assume Assuming the errors in G1 are small enough and the bias is negligible, then The 2-D MPR and 3-D MPR of the target position are and ​ where tan -1 () is the arctangent function, ψ 11 is the solution in step 3.1.1; Step 3.1.2: The solution in step 3.1.1 is represented as Δψ 11 To estimate the error, square the first N elements on both sides of the equation: Taking into account the constraints, the last element of ψ 11 is added to the result: where for Δψ 11 introduced error, unknowns By constructing the following optimization problem: solving; weighting matrix The WLS estimate is then The covariance matrix is as follows: By ψ 12 The target 2-D MPR and 3-D MPR coordinates are obtained as follows: where sgn() is the sign function defined as: Ψ 12 is the solution in step 3.1.2; Step 4, the direction finding initial solution guides the calibration source deployment; Step 5, the space-time reference system error calculation; Step 6, the target source TDOA measurement and the space-time reference system error elimination and final solution solving.

2. The method of claim 1, wherein, The specific steps 4 are: The calibration source is represented in the MPR coordinate system as The calibration source is directed to be deployed at the initial estimated position of the positioned target in the MPR coordinate system, i.e. let Then The corresponding Cartesian coordinates are 3. The method of claim 2, wherein, The specific steps 5 are: The distance from the calibration source to each unmanned aerial vehicle is as follows: wherein ξ i1 is the RDOA measurement error of the calibration source, the set is denoted as ξ, ξ = [ξ 21 , ξ 31 ,..., ξ M1 ] T is a zero-mean calibration source RDOA measurement error vector, satisfying a Gaussian random distribution, and the covariance matrix thereof is Q ξ ; The positioning unmanned aerial vehicle carries a monitoring receiver which simultaneously monitors the positioning target signal and the calibration signal through a high sampling rate operation mode, that is, the target signal and the calibration signal are simultaneously contained in each unmanned aerial vehicle monitoring data, so that the clock synchronization error n which is the same as the target signal RDOA measurement value is contained in the calibration signal RDOA measurement value t,i1 The RDOA calculation value of the calibration source to each unmanned aerial vehicle is obtained from the actual position of the deployed calibration source and the position of the unmanned aerial vehicle with an error, and is At this time, the system error is: wherein, Δs is the position error of the UAV i Δs1 is the to-be-calibrated quantity introduced by the clock synchronization error, n t,i1 Δs1 is the to-be-calibrated quantity introduced by the clock synchronization error.

4. The method of claim 3, wherein, The specific steps 6 are: After collecting M-1 system error calibration quantities, Δr c = [Δr c,21 , Δr c,31 ,..., Δr c,M1 ] T Introducing Δr c into the target signal RDOA measurement value r, the target signal RDOA correction value after eliminating system error is: After eliminating the RDOA system uncertainty of the source, we get Since it contains n i1 , and ξ i1 three error terms, by two closed-form solutions to solve the above residual error terms, substitute into and apply Taylor series expansion to the first order term to get: wherein is the unit directional vector, given by points to s i ; substituting into yields: Definition of n d,i1 As shown in the following equation M-1 RDOA sets are obtained as follows: in, n d =[n d,21 ,n d,31 ,...,n d,M1 ] T ; to be on Squaring both sides of the expression yields: Substitute to the above equation gives: Dividing both sides of the above equation by and substituting and yields: Wherein, The above formula only retains the first-order noise term, and therefore the following matrix is defined: Wherein, ∈2＝[∈ 2,2 ,∈ 2,3 ,...,∈ 2,M ] T The following is defined as: ∈2 = B1n d + Γ Δs The above equation is solved by weighted least squares, where the weighting matrix is represented as E[∈2∈2 T ]; the above quadratic optimization problem is represented as: The weighted matrix is represented as follows: W2 = ((B1G c )Q s (B1G c ) T +ΓQ s Γ T +B1(Q n +Q ξ )B1) 1 Wherein, G c (i,:) = [-p c,1 , O N＝(i-2) , p c,i , O N×(M-i) ] T The RDOA of the source after eliminating the error is reconstructed as a quadratic minimization problem with quadratic constraints, and is solved by Improved SUM-MPR based on MPR G2, W2 and ψ2 are brought back into the Improved SUM-MPR in step (3) to obtain the target direction finding result of the target source after performance optimization.

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