Multi-target association and fusion localization method and equipment

Abstract

This invention provides a multi-target association and fusion positioning method and device. The method includes: acquiring the received measurement parameters of each receiving station radar, the coordinates of the transmitting station, and the coordinates of the receiving station; combining the received measurement parameters to obtain a combined measurement vector, and combining the transmitting station coordinates and the receiving station coordinates to obtain a station location vector; based on the combined measurement vector and the station location vector, using an improved least squares method to solve for the target position, obtaining the target least squares solution corresponding to the target position; based on the target least squares solution and the station location vector, calculating the homogeneity hypothesis measurement for each receiving station radar, and generating a likelihood function penalty term using the homogeneity hypothesis measurement; constructing a multidimensional allocation optimization model using the likelihood function penalty term, and solving the multidimensional allocation optimization model using a Lagrange relaxation algorithm to obtain the association result; and determining the true position of the target based on the association result.

Description

Technical Field

[0001] This invention relates to the field of radar data processing technology, specifically to a multi-target association and fusion positioning method and device. Background Technology

[0002] With the continuous development of radar technology, multistatic radar systems have been widely used in both defense and civilian fields. Compared with traditional monostatic radar systems, multistatic radar systems, through the coordinated operation of multiple transmitting and receiving nodes, can effectively improve target detection and identification capabilities. In complex three-dimensional scenes, the localization and correlation of multiple targets become a key challenge in achieving accurate target tracking and situational awareness.

[0003] Targets in 3D scenes are complexly distributed, and sensor measurement data and sensor position coordinates often contain significant errors, making it difficult to guarantee the accuracy of target association and positioning precision. Secondly, because base radar systems involve the coordinated operation of multiple transmitters and receivers, the amount of data transmission and processing is large, making efficient computation while ensuring real-time performance a crucial issue. Existing technologies rarely combine target association and positioning in the radar field, making methods to simultaneously address these two problems in complex environments particularly important. Summary of the Invention

[0004] To address the aforementioned problems in the prior art, this invention provides a multi-target association and fusion localization method and device.

[0005] The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a multi-target association and fusion localization method, applied to a three-dimensional scene with one-to-many radar cooperating, including:

[0007] Obtain the receiving measurement parameters of each receiving station radar, the coordinates of the transmitting station site, and the coordinates of the receiving station site;

[0008] The received measurement parameters are combined to obtain a combined measurement vector, and the coordinates of the transmitting station and the receiving station are combined to obtain a station location vector.

[0009] Based on the combined measurement vector and station address vector, an improved least squares method is used to solve for the target position, and the target least squares solution corresponding to the target position is obtained. The improved least squares method is based on the approximate linear equation constructed by trigonometric function transformation, Taylor expansion processing and neglecting quadratic noise processing.

[0010] Based on the target least squares solution and the station location vector, the same source hypothesis measurement of each receiving station radar is calculated, and the same source hypothesis measurement is used to generate the likelihood function penalty term.

[0011] A multidimensional allocation optimization model is constructed by using the likelihood function penalty term, and the Lagrange relaxation algorithm is used to solve the multidimensional allocation optimization model to obtain the association results;

[0012] The true location of the target is determined based on the correlation results.

[0013] Optionally, the received measurement parameters include: time delay difference τ, elevation angle θ, and azimuth angle. The time delay difference is the time delay between the direct wave and the reflected wave.

[0014] Optionally, the received measurement parameters are combined to obtain a combined measurement vector, and the coordinates of the transmitting station and the receiving station are combined to obtain a station vector, including:

[0015] The received measurement parameters are fused to obtain the initial measurement combination; the initial measurement combination is expressed as:

[0016]

[0017] in, Indicates the initial measurement combination. Represents the i-th radar of the s-th receiving station. s There are three received measurement parameters, s = 1, ..., N, i s =1,...,n s n s This represents the total number of received measurement parameters of the radar at the s-th receiving station. Represents the i-th radar of the s-th receiving station. s Delay difference under each received measurement parameter Represents the i-th radar of the s-th receiving station. s The azimuth angle of the reflected wave under a given receiver measurement parameter. Represents the i-th radar of the s-th receiving station. s The elevation angle of the reflected wave under each received measurement parameter, [·] T Represents the transpose of a matrix;

[0018] The initial measurement combination is reorganized to obtain the combined measurement vector; the combined measurement vector is represented as:

[0019]

[0020] Denotes the combined measurement vector, τ1,...,τ N Indicates in Under the assumption of common origin, the time delay difference corresponding to the radars of the 1st to Nth receiving stations, θ1,...,θ N Indicates in Under the assumption of common origin, the elevation angles corresponding to the radars of the 1st to Nth receiving stations are... Indicates in The azimuth angles corresponding to the radars of the 1st to Nth receiving stations under the same source assumption;

[0021] The coordinates of the transmitting station and the receiving station are combined using a pre-defined method to obtain a station address vector; the station address vector is represented as:

[0022]

[0023] Where p represents the site vector, t represents the coordinates of the launching station site, and r1,...,r N This represents the coordinates of the receiving station locations corresponding to the radars of receiving stations 1 through N.

[0024] Optionally, based on the combined measurement vector and station location vector, an improved least squares method is used to solve for the target location, obtaining the target least squares solution corresponding to the target location, including:

[0025] Based on the first-order Taylor expansion and ignoring the quadratic noise term, the time delay difference in the combined measurement vector is linearly transformed to obtain the first approximate linear equation.

[0026] Based on trigonometric function transformation, first-order Taylor expansion and neglecting quadratic noise terms, linear transformation is performed on the azimuth and elevation angles in the combined measurement vector to obtain the second approximate linear equation.

[0027] By combining the first and second approximate linear equations, a bus linear equation is obtained.

[0028] The initial least squares solution of the objective is obtained by calculating the bus linear equations;

[0029] The third approximate linear equation is obtained based on the first-order Taylor expansion, neglecting the quadratic noise term, and the relationship between elements in the initial least squares solution of the objective.

[0030] The objective least squares solution is obtained by calculating the third approximate linear equation.

[0031] Optionally, the first approximate linear equation is expressed as:

[0032] B τ n τ =h τ -G τ α o ;

[0033] Among them, B τ This represents the correlation matrix between the target's true location and the receiving station's coordinates, n. τh represents the error vector related to the site error vector Δp ​​and the time delay error vector Δτ. τ G represents a vector related to the delay error vector, the coordinates of the transmitting station site, and the coordinates of the receiving station site. τ α represents the matrix related to the time delay error vector, the coordinates of the transmitting station site, and the coordinates of the receiving station site. o Indicates the first parameter;

[0034] α o =[u oT ,||u o -t|| 2 ] T ;

[0035] u o The target's actual location is represented by t, which represents the coordinates of the launch station.

[0036] The second approximate linear equation is expressed as:

[0037]

[0038] in, Represents the pitch angle error vector Δθ and the azimuth angle error vector And the error vector related to the site error vector Δp, This represents a vector related to the coordinates of the launch station site, elevation angle, and azimuth angle. This represents a matrix related to the coordinates of the launch station site, elevation angle, and azimuth angle.

[0039] Alternatively, the bus linear equation can be expressed as:

[0040] n = h1 - G1α o ;

[0041] n represents the total error vector, h1 represents the second parameter, and G1 represents the third parameter.

[0042]

[0043] Among them, 0 N This represents an N×1 dimensional column vector of all zeros.

[0044] Alternatively, the objective least squares solution can be expressed as:

[0045]

[0046] in, Let W2 represent the objective least squares solution, W2 represent the weighting matrix, G2 represent the fourth parameter, h2 represent the fifth parameter, and (·) represent the objective least squares solution. -1 This indicates taking the inverse of the matrix;

[0047]

[0048]

[0049] Indicates taking The first three items, This represents the initial least squares solution to the objective. Indicates taking The fourth term, I3, represents the 3×3 identity matrix.

[0050] Optionally, the likelihood function penalty term is expressed as:

[0051]

[0052] This represents the penalty term of the likelihood function. Let represent the detection probability of the radar at the s-th receiving station. This represents the volume of the observation airspace of the radar at the s-th receiving station. This represents the error covariance matrix of the received measurement parameters corresponding to the radar of the s-th receiving station. Indicates different initial measurement combinations The measurement of the corresponding receiving station radar is based on the same source assumption.

[0053] Alternatively, the multidimensional allocation optimization model can be expressed as:

[0054]

[0055] in, Indicates the associated result. Let n represent the likelihood function penalty term. N This represents the total number of received measurement parameters of the radar at the Nth receiving station, where... It is a binary variable, and its value can be 0 or 1.

[0056] In a second aspect, the present invention provides a multi-target association and fusion positioning device, comprising: a processor, a storage medium and a bus, wherein the storage medium stores machine-readable instructions executable by the processor, and when the multi-target association and fusion positioning device is running, the processor communicates with the storage medium via the bus, and the processor executes the machine-readable instructions to perform the steps of the multi-target association and fusion positioning method of the first aspect described above.

[0057] This invention provides a multi-target association and fusion localization method and device. The multi-target association and fusion localization method, applied to a three-dimensional scene with multiple receiving radars, includes: acquiring the received measurement parameters, transmitter station coordinates, and receiver station coordinates of each receiving radar; combining the received measurement parameters to obtain a combined measurement vector; combining the transmitter station coordinates and receiver station coordinates to obtain a station coordinate vector; based on the combined measurement vector and station coordinate vector, using an improved least squares method to solve for the target position, obtaining the target least squares solution; the improved least squares method is based on an approximate linear equation constructed using trigonometric function transformation, Taylor expansion, and neglecting quadratic noise; based on the target least squares solution and station coordinate vector, calculating the homogeneity hypothesis measurement for each receiving radar, and generating a likelihood function penalty term using the homogeneity hypothesis measurement; constructing a multidimensional allocation optimization model using the likelihood function penalty term, and solving the multidimensional allocation optimization model using a Lagrange relaxation algorithm to obtain the association result; and determining the true position of the target based on the association result. In this embodiment of the invention, the target location is solved by an improved least squares method based on the combined measurement vector and the station address vector, resulting in a closed-form solution for positioning - the target least squares solution, which improves the positioning accuracy and speed of the target. In addition, by constructing a multidimensional allocation optimization model and using the Lagrange relaxation algorithm to solve the optimization problem, the computational load of the fusion calculation process is reduced, which improves the calculation speed of the target's true location.

[0058] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating a multi-target association and fusion localization method provided in an embodiment of the present invention;

[0060] Figure 2 A schematic diagram of a three-dimensional scene in the one-to-three-receive mode is shown.

[0061] Figure 3 A schematic diagram illustrating the positioning results obtained according to the method of the present invention when a single target exists in the one-send-three-receive mode;

[0062] Figure 4 The diagram schematically illustrates the relationship between target spacing and the probability of successful target association.

[0063] Figure 5 The diagram schematically illustrates the relationship between measurement errors of different distance differences (obtained from time delay differences) and the probability of successful target association.

[0064] Figure 6 The diagram schematically illustrates the relationship between measurement errors at different azimuth angles and the probability of successful target association.

[0065] Figure 7 This is a schematic diagram of the structure of a multi-target association and fusion positioning device provided in an embodiment of the present invention. Detailed Implementation

[0066] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0067] To improve the calculation speed and accuracy of the target's true location, this invention provides a multi-target association and fusion localization method. Figure 1 This is a flowchart illustrating a multi-target association and fusion localization method provided in an embodiment of the present invention. Figure 1 As shown, it includes:

[0068] S101. Obtain the receiving measurement parameters of each receiving station radar, the coordinates of the transmitting station site, and the coordinates of the receiving station site.

[0069] Optionally, the received measurement parameters include: time delay difference τ, elevation angle θ, and azimuth angle. The time delay difference is the time delay between the direct wave and the reflected wave.

[0070] S102. Combine the received measurement parameters to obtain a combined measurement vector. Combine the coordinates of the transmitting station and the receiving station to obtain a station vector.

[0071] Optionally, S102 may specifically include:

[0072] The received measurement parameters are fused to obtain the initial measurement combination; the initial measurement combination is expressed as:

[0073]

[0074] in, Indicates the initial measurement combination, z sis Represents the i-th radar of the s-th receiving station. s There are three received measurement parameters, s = 1, ..., N, i s =1,...,n s n s This represents the total number of received measurement parameters of the radar at the s-th receiving station. Represents the i-th radar of the s-th receiving station. s Delay difference under each received measurement parameter Represents the i-th radar of the s-th receiving station. s The azimuth angle of the reflected wave under a given receiver measurement parameter. Represents the i-th radar of the s-th receiving station. sThe elevation angle of the reflected wave under each received measurement parameter, [·] T Represents the transpose of a matrix;

[0075] The initial measurement combination is reorganized to obtain the combined measurement vector; the combined measurement vector is represented as:

[0076]

[0077] Denotes the combined measurement vector, τ1,...,τ N Indicates in Under the assumption of common origin, the time delay difference corresponding to the radars of the 1st to Nth receiving stations, θ1,...,θ N Indicates in Under the assumption of common origin, the elevation angles corresponding to the radars of the 1st to Nth receiving stations are... Indicates in The azimuth angles corresponding to the radars of the 1st to Nth receiving stations under the same source assumption;

[0078] The coordinates of the transmitting station and the receiving station are combined using a pre-defined method to obtain a station address vector; the station address vector is represented as:

[0079]

[0080] Where p represents the site vector, t represents the coordinates of the launching station site, and r1,...,r N This represents the coordinates of the receiving station locations corresponding to the radars of receiving stations 1 through N.

[0081] S103. Based on the combined measurement vector and station address vector, an improved least squares method is used to solve for the target position, and the target least squares solution corresponding to the target position is obtained.

[0082] The improved least squares method is based on an approximate linear equation constructed by trigonometric function transformation, Taylor expansion, and neglecting quadratic noise.

[0083] Optionally, S103 may specifically include:

[0084] Based on the first-order Taylor expansion and ignoring the quadratic noise term, the time delay difference in the combined measurement vector is linearly transformed to obtain the first approximate linear equation.

[0085] Based on trigonometric function transformation, first-order Taylor expansion and neglecting quadratic noise terms, linear transformation is performed on the azimuth and elevation angles in the combined measurement vector to obtain the second approximate linear equation.

[0086] By combining the first and second approximate linear equations, a bus linear equation is obtained.

[0087] The initial least squares solution of the objective is obtained by calculating the bus linear equations;

[0088] The third approximate linear equation is obtained based on the first-order Taylor expansion, neglecting the quadratic noise term, and the relationship between elements in the initial least squares solution of the objective.

[0089] The objective least squares solution is obtained by calculating the third approximate linear equation.

[0090] Optionally, the first approximate linear equation is expressed as:

[0091] B τ n τ =h τ -G τ α o ;

[0092] Among them, B τ This represents the correlation matrix between the target's true location and the receiving station's coordinates, n. τ h represents the error vector related to the site error vector Δp ​​and the time delay error vector Δτ. τ G represents a vector related to the delay error vector, the coordinates of the transmitting station site, and the coordinates of the receiving station site. τ α represents the matrix related to the time delay error vector, the coordinates of the transmitting station site, and the coordinates of the receiving station site. o Indicates the first parameter;

[0093] α o =[u oT ,||u o -t|| 2 ] T ;

[0094] u o The target's actual location is represented by t, which represents the coordinates of the launch station.

[0095] The second approximate linear equation is expressed as:

[0096]

[0097] in, Represents the pitch angle error vector Δθ and the azimuth angle error vector And the error vector related to the site error vector Δp, This represents a vector related to the coordinates of the launch station site, elevation angle, and azimuth angle. This represents a matrix related to the coordinates of the launch station site, elevation angle, and azimuth angle.

[0098] It should be noted that, in the embodiments of the present invention, n τ Represented as n τ=cΔτ+D1Δp.

[0099]

[0100]

[0101] c is the speed of light. Indicates from u o The normalized direction vector to t, and Similarly, Furthermore, It can also be expressed as: Specifically, B θ , D2、 as well as They are represented as follows:

[0102]

[0103]

[0104] Alternatively, the bus linear equation can be expressed as:

[0105] n = h1 - G1α o ;

[0106] n represents the total error vector, h1 represents the second parameter, and G1 represents the third parameter.

[0107]

[0108] Among them, 0 N This represents an N×1 dimensional column vector of all zeros.

[0109] Furthermore, α is obtained using ordinary least squares. o with u o The initial estimate,

[0110] in Indicates taking The first three items.

[0111] Will Replace u o Calculation parameters Obtain the weight matrix have

[0112]

[0113] Among them, Q τ For [τ1,...,τ] N ] T The corresponding noise covariance matrix, With Qθ Similarly, Q P for Based on the corresponding noise covariance matrix and the parameters sought, the preliminary least-squares solution of the objective is obtained:

[0114]

[0115] according to The relationship between the first term and the last three terms, derived through Taylor expansion and neglecting quadratic noise terms, yields the third approximate linear equation, as follows:

[0116] B2Δα=h2-G2u o ;

[0117] in,

[0118]

[0119] Finally obtained The following is the target least squares solution for the target location.

[0120] Alternatively, the objective least squares solution can be expressed as:

[0121]

[0122] in, Let W2 represent the objective least squares solution, W2 represent the weighting matrix, G2 represent the fourth parameter, h2 represent the fifth parameter, and (·) represent the objective least squares solution. -1 This indicates taking the inverse of the matrix;

[0123]

[0124] Indicates taking The first three items, This represents the initial least squares solution to the objective. Indicates taking The fourth term, I3, represents the 3×3 identity matrix.

[0125] Among them, W2 is composed of Calculated.

[0126] S104. Based on the target least squares solution and the station location vector, calculate the homogeneity hypothesis measurement for each receiving station radar, and use the homogeneity hypothesis measurement to generate a likelihood function penalty term.

[0127] Specifically, the initial measurement combination The corresponding receiving station radar homogeneous hypothesis measurement It can be expressed by the following formula:

[0128]

[0129] in, This represents the i-th signal obtained by the radar of the s-th receiving station. s At the moment of measurement, Indicates in The mapping of measurements is based on the geometric positional relationship between the target and the receiving station radar at all times. This mapping relationship is obtained from the following formulas:

[0130]

[0131] in They represent The coordinates of r in the three dimensions of a Cartesian coordinate system s,x ,r s,y ,r s,z Let represent the coordinates of the radar at the s-th receiving station in three dimensions in a Cartesian coordinate system, and ||·|| denotes the L2 norm of the vector. Indicates taking only vectors The first two elements.

[0132] The initial measurement combination is calculated based on the following formula. The likelihood function penalty term for homologous measurements

[0133] Optionally, the likelihood function penalty term is expressed as:

[0134]

[0135] This represents the penalty term of the likelihood function. Let represent the detection probability of the radar at the s-th receiving station. This represents the volume of the observation airspace of the radar at the s-th receiving station. This represents the error covariance matrix of the received measurement parameters corresponding to the radar of the s-th receiving station. Indicates different initial measurement combinations The measurement of the corresponding receiving station radar is based on the same source assumption.

[0136] S105. Construct a multidimensional allocation optimization model through the likelihood function penalty term, and solve the multidimensional allocation optimization model using the Lagrange relaxation algorithm to obtain the association results.

[0137] Alternatively, the multidimensional allocation optimization model can be expressed as:

[0138]

[0139] in, Indicates the associated result. Let n represent the likelihood function penalty term. NThis represents the total number of received measurement parameters of the radar at the Nth receiving station, where... It is a binary variable, and its value can be 0 or 1.

[0140] S106. Determine the true location of the target based on the association results.

[0141] Specifically, in the embodiments of the present invention, Measurement combination corresponding to a value of 1 As a homologous measurement.

[0142] Will The corresponding homologous measurement is represented as follows: Will The corresponding objective least squares solution The actual location of the target.

[0143] This invention provides a multi-target association and fusion localization method applied to a three-dimensional scene with a single-transmitter, multi-receiver radar. The method includes: solving for target positions using an improved least squares method based on combined measurement vectors and station location vectors, obtaining a closed-form localization solution – a target least squares solution, thus improving the localization accuracy and speed of subsequent targets; furthermore, by constructing a multi-dimensional allocation optimization model and using the Lagrange relaxation algorithm to solve the optimization problem, the computational load of the fusion calculation process is reduced, improving the calculation speed for the true position of the target.

[0144] To verify the effectiveness of the multi-target association and fusion localization method, simulation experiments were also conducted in this embodiment of the invention, as follows:

[0145] 1. Simulation conditions

[0146] The simulation experiments of this invention used an AMD Ryzen 9 7945HX CPU@2.50GHz, a 64-bit Windows operating system, and MATLAB (R 2023b) as the simulation software.

[0147] 2. Simulation Experiment Content

[0148] The simulation experimental conditions and experimental parameter settings for the process of this invention are as follows:

[0149] The radar network operates in a one-transmit, three-receive mode. Figure 2 A schematic diagram of a 3D scene in a one-to-three-receiver mode is shown, in which... Figure 2 Figure (a) is the main view of the 3D scene in the one-to-three-receiver mode. Figure 2Figure (b) is a top-down view of a three-dimensional scene in the one-transmit, three-receive mode. The coordinates of the transmitting radar are [0,0,0] km, the coordinates of receiving radar 1 are [-40,0,29] km, the coordinates of receiving radar 2 are [36,15,1] km, and the coordinates of receiving radar 3 are [0,20,1] km. There are four densely packed targets forming a square within the spatial observation area, with spatial coordinates of [50,50,70] km, [50.5,50,70] km, [50,50.5,70] km, and [50.5,50.5,70] km, respectively. The distance between the targets is [not specified]. The range is 500m. The electromagnetic waves emitted by the transmitting radar are reflected by four targets and can be received and detected by the receiving radar station. The time delay difference, azimuth angle, and elevation angle of the targets are obtained. The measurement errors of the three receiving radar stations are the same. The error of the time delay difference measurement converted into the range difference measurement is 50m. The azimuth angle measurement error is 0.06°, the elevation angle measurement error is 0.06°, the station location error is 50m, the detection probability of each receiving radar station is 0.9, and the airspace observation volume is 12200 cubic kilometers.

[0150] Figure 3 The diagram illustrates the positioning results obtained according to the method of the present invention when a single target exists in the one-launch-three-receive mode. Figure 3 Figure (a) corresponds to Figure 2 The result from the perspective of (a) figure. Figure 3 Figure (b) corresponds to Figure 2 The results are shown in Figure (b). The target's true spatial location is [50, 50, 70] km. The measurement error and station location error are the same as the experimental conditions described above. The blue star-shaped points in space represent the positioning results repeated 500 times. Figure 3 (a) and Figure 3 (b) It can be seen that, in the case of a single target, the average value of the positioning result obtained by using the distance difference, elevation angle, azimuth angle measurement and station coordinates of multiple receiving stations is close to the true value, and has a high positioning accuracy.

[0151] Figures 4-6 The diagram schematically illustrates the correlation effect obtained according to the method of this invention when there are four targets in a one-send-three-receive mode. Specifically, Figure 4 The diagram schematically illustrates the relationship between target spacing and the probability of successful target association. Figure 5 The diagram schematically illustrates the relationship between measurement errors of different distance differences (obtained from time delay differences) and the probability of successful target association. Figure 6 The diagram schematically illustrates the relationship between measurement errors at different azimuth angles and the probability of successful target association. Figure 4The horizontal axis represents the target spacing, i.e., the sparsity, in meters (m), and the vertical axis represents the probability of successful association, in percent (%). In this experiment, only the target spacing varied from 40m to 500m; all other experimental conditions remained constant. Figure 4 It can be seen that when the target spacing is small (e.g., 0-100m), the probability of successful association is low. As the target spacing increases, the probability of successful association rises rapidly. At around 200m, the probability of successful association reaches above 0.8, and after 300m, it gradually stabilizes, approaching 1. Figure 5 The distance between the targets was set to 300m, and an experiment was conducted to measure the distance difference error from 10m to 300m, while keeping the other experimental conditions unchanged. Figure 5 The horizontal axis represents the distance difference error in meters (m), and the vertical axis represents the success rate of association in percent (%). Figure 5 It can be seen that the success rate of association is over 90% when the distance difference measurement error is within 50m, the probability drops rapidly when the distance difference measurement error is greater than 80m, and tends to stabilize when the error is greater than 200m, gradually approaching 0. Figure 6 With the target spacing set at 300m and other experimental conditions remaining unchanged, an experiment was conducted to test the variation of azimuth measurement error from 0.05° to 1.2°. Figure 6 The horizontal axis represents the azimuth measurement error in meters (m), and the vertical axis represents the success rate of association in percentage (%). Figure 6 It can be seen that as the azimuth measurement error increases, the probability of successful association decreases rapidly. When the azimuth measurement error is greater than 0.45°, the impact of the measurement error slows down, and the probability of successful association basically stabilizes at 0.45°.

[0152] In summary, this invention provides a multi-target association and fusion localization method. This method utilizes time delay difference measurement and two-dimensional angle measurement, obtaining a closed-form solution for localization through linear approximation and multiple least squares. It exhibits good localization accuracy and speed even for single-target scenarios with station location and measurement errors. Based on the maximum likelihood criterion, an association optimization problem is established and solved. When the measurement error is within a certain range and the multi-target sparsity is high, the probability of successful association approaches 1. The use of the Lagrange relaxation algorithm to solve the optimization problem effectively reduces the computational load and basically meets the real-time requirements of radar systems.

[0153] The method provided in this embodiment of the invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc., and this embodiment of the invention does not limit the application to such devices.

[0154] Based on the same inventive concept, embodiments of the present invention also provide a multi-target association and fusion positioning device. Figure 7A schematic diagram of a multi-target association and fusion positioning device provided in an embodiment of the present invention includes: a processor 710, a storage medium 720, and a bus 730. The storage medium 720 stores machine-readable instructions executable by the processor 710. When the multi-target association and fusion positioning device is running, the processor 710 and the storage medium 720 communicate via the bus 730. The processor 710 executes the machine-readable instructions to perform the steps of the above-described method embodiment. Specific implementation methods and technical effects are similar and will not be repeated here.

[0155] The storage medium may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the storage medium may also be at least one storage device located remotely from the aforementioned processor.

[0156] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0157] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0158] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0159] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the accompanying drawings and the disclosure, will understand and implement other variations of the disclosed embodiments in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0160] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the inventive concept, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A multi-target association and fusion localization method, applied to a three-dimensional scene with one-to-many radar cooperating, characterized in that, include: Obtain the receiving measurement parameters of each receiving station radar, the coordinates of the transmitting station site, and the coordinates of the receiving station site; The received measurement parameters are combined to obtain a combined measurement vector, and the coordinates of the transmitting station and the receiving station are combined to obtain a station address vector. Based on the combined measurement vector and the station address vector, an improved least squares method is used to solve for the target position, and the target least squares solution corresponding to the target position is obtained; the improved least squares method is based on an approximate linear equation constructed by trigonometric function transformation, Taylor expansion processing and neglecting quadratic noise processing; Based on the target least squares solution and the station location vector, calculate the same source hypothesis measurement for each receiving station radar, and use the same source hypothesis measurement to generate a likelihood function penalty term; A multidimensional allocation optimization model is constructed using the likelihood function penalty term, and the Lagrange relaxation algorithm is used to solve the multidimensional allocation optimization model to obtain the association results. The true location of the target is determined based on the correlation results.

2. The multi-target association and fusion localization method according to claim 1, characterized in that, The received measurement parameters include: time delay difference τ, elevation angle θ, and azimuth angle. The time delay difference is the time delay between the direct wave and the reflected wave.

3. The multi-target association and fusion localization method according to claim 2, characterized in that, The received measurement parameters are combined to obtain a combined measurement vector. The transmitter station coordinates and the receiver station coordinates are combined to obtain a station address vector, including: The received measurement parameters are fused to obtain an initial measurement combination; the initial measurement combination is expressed as: in, This indicates the initial measurement combination. Represents the i-th radar of the s-th receiving station. s There are three received measurement parameters, s = 1, ..., N, i s =1,...,n s n s This represents the total number of received measurement parameters of the radar at the s-th receiving station. Represents the i-th radar of the s-th receiving station. s Delay difference under each received measurement parameter Represents the i-th radar of the s-th receiving station. s The azimuth angle of the reflected wave under a given receiver measurement parameter. Represents the i-th radar of the s-th receiving station. s The elevation angle of the reflected wave under each received measurement parameter, [·] T Represents the transpose of a matrix; The initial measurement combination is reorganized to obtain the combined measurement vector; the combined measurement vector is represented as follows: Let τ1,…,τ represent the combined measurement vector. N Indicates in Under the assumption of common origin, the time delay difference corresponding to the radars of the 1st to Nth receiving stations, θ1,…,θ N Indicates in Under the assumption of common origin, the elevation angles corresponding to the radars of the 1st to Nth receiving stations are... Indicates in The azimuth angles corresponding to the radars of the 1st to Nth receiving stations under the same source assumption; The coordinates of the transmitting station and the coordinates of the receiving station are combined using a preset method to obtain the station address vector; the station address vector is represented as: Where p represents the station address vector, t represents the coordinates of the transmitting station address, and r1,…,r N This represents the coordinates of the receiving station locations corresponding to the radars of receiving stations 1 through N.

4. The multi-target association and fusion localization method according to claim 1, characterized in that, Based on the combined measurement vector and the station address vector, an improved least squares method is used to solve for the target location, obtaining the target least squares solution corresponding to the target location, including: Based on the first-order Taylor expansion and the neglect of quadratic noise terms, the time delay difference in the combined measurement vector is linearly transformed to obtain the first approximate linear equation. Based on trigonometric function transformation, first-order Taylor expansion and neglecting quadratic noise terms, the azimuth and elevation angles in the combined measurement vector are linearly transformed to obtain the second approximate linear equation. The first approximate linear equation and the second approximate linear equation are combined to obtain the bus linear equation; The preliminary least squares solution of the objective is obtained by calculating the bus linear equations. Based on the first-order Taylor expansion, neglecting the quadratic noise term, and the relationship between elements in the preliminary least squares solution of the objective, a third approximate linear equation is obtained. The objective least squares solution is obtained by calculating the third approximate linear equation.

5. The multi-target association and fusion localization method according to claim 4, characterized in that, The first approximate linear equation is expressed as: B τ n τ =h τ -G τ a o ; Among them, B τ This represents the correlation matrix between the target's true location and the receiving station's coordinates, n. τ h represents the error vector related to the site error vector Δp ​​and the time delay error vector Δτ. τ G represents a vector related to the delay error vector, the coordinates of the transmitting station site, and the coordinates of the receiving station site. τ α represents the matrix related to the time delay error vector, the coordinates of the transmitting station site, and the coordinates of the receiving station site. o Indicates the first parameter; α o =[u oT ,||u o -t|| 2 ] T ; u o The target's actual location is represented by t, which represents the coordinates of the launch station's location. The second approximate linear equation is expressed as: in, Represents the pitch angle error vector Δθ and the azimuth angle error vector And the error vector related to the site error vector Δp, This represents a vector related to the coordinates of the launch station site, elevation angle, and azimuth angle. This represents a matrix related to the coordinates of the launch station site, elevation angle, and azimuth angle.

6. The multi-target association and fusion localization method according to claim 5, characterized in that, The bus linear equation is expressed as: n=h1-G1α o ; n represents the total error vector, h1 represents the second parameter, and G1 represents the third parameter. Among them, 0 N This represents an N×1 dimensional column vector of all zeros.

7. The multi-target association and fusion localization method according to claim 6, characterized in that, The objective least squares solution is expressed as: in, Let W2 represent the objective least squares solution, W2 represent the weighting matrix, G2 represent the fourth parameter, h2 represent the fifth parameter, and (·) represent the fifth parameter. -1 This indicates taking the inverse of the matrix; Indicates taking The first three items, This represents the initial least-squares solution to the objective. Indicates taking The fourth term, I3, represents the 3×3 identity matrix.

8. The multi-target association and fusion localization method according to claim 7, characterized in that, The likelihood function penalty term is expressed as follows: This represents the penalty term of the likelihood function. Let represent the detection probability of the radar at the s-th receiving station. This represents the volume of the observation airspace of the radar at the s-th receiving station. This represents the error covariance matrix of the received measurement parameters corresponding to the radar of the s-th receiving station. Indicates different initial measurement combinations The measurement of the corresponding receiving station radar is based on the same source assumption.

9. The multi-target association and fusion localization method according to claim 8, characterized in that, The multidimensional allocation optimization model is expressed as follows: in, This indicates the association result. Let n represent the likelihood function penalty term. N This represents the total number of received measurement parameters of the radar at the Nth receiving station, where... It is a binary variable, and its value can be 0 or 1.

10. A multi-target association and fusion positioning device, characterized in that, include: The device includes a processor, a storage medium, and a bus. The storage medium stores machine-readable instructions executable by the processor. When the multi-target association and fusion localization device is running, the processor communicates with the storage medium via the bus, and the processor executes the machine-readable instructions to perform the steps of the multi-target association and fusion localization method as described in any one of claims 1-9.

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