Whirling target multi-station positioning method based on whirling electromagnetic wave

Abstract

The application discloses a rotating target multi-station positioning method based on vortex electromagnetic waves, and comprises the following steps: a multi-station radar detection scene is established, and an estimated measurement value model of a rotating target in the multi-station radar detection scene is obtained; based on the estimated measurement value model, a target center is positioned by using a geometric solution solving method or a positioning method based on positioning error correction, and position coordinates of a target rotating center are obtained; and a Cramer-Rao bound value is taken as a lower limit of unbiased estimation, and effectiveness of the geometric solution solving method and the positioning method based on positioning error correction is verified. By using the orbital angular momentum characteristics of vortex electromagnetic waves, a Doppler frequency shift generated in an azimuth direction, i.e. a rotating Doppler frequency shift, is obtained, so that more abundant information than traditional plane waves is obtained, and the position of the rotating target is estimated by using a multi-station measurement method.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a multi-station positioning method for rotating targets based on vortex electromagnetic waves. Background Technology

[0002] The introduction of the concept of Orbital Angular Momentum (OAM) has injected new vitality into the field of perception. Unlike spin angular momentum (i.e., polarization effect), OAM essentially describes the macroscopic physical properties of electromagnetic waves, characterizing the degree of rotation around an axis during propagation, and thus defining electromagnetic vortex waves. Based on electromagnetic field theory, vortex waves have a concise mathematical description corresponding to the propagation equation: At a propagation factor e jkr Based on this, a phase factor related to the azimuth angle is superimposed. (Distance r in spherical coordinate system - azimuth angle) - Elevation angle θ), its macroscopic manifestation is that the propagation equiphase surface is distorted into a helical surface. The mode number l can be positive or negative, and its magnitude characterizes the vortex amplitude and direction of rotation. Vortex waves with different integer modes are in azimuth angle The eigenstates are mutually orthogonal; therefore, theoretically, the range of OAM mode values ​​can be infinitely large, becoming a completely new dimension outside the time, frequency, and polarization domains.

[0003] Vortex electromagnetic waves, carrying orbital angular momentum, possess azimuth-directed phase information modulation capabilities due to their annular radiation field intensity distribution and helical phase wavefront. Therefore, vortex electromagnetic waves have garnered increasing attention in radar imaging and rotating target detection in recent years. In conventional radar systems, the detection of rotating objects is primarily based on the micro-Doppler effect induced by the relative motion between the radar and the object along the line of sight (LOS), resulting in a frequency shift known as linear Doppler shift. However, limited by the characteristics of planar waves, conventional narrowband radars can only obtain the maximum projection of the rotational frequency and radius relative to the line of sight. This is a one-dimensional information acquisition method, making it difficult to obtain more detailed rotational parameters such as rotation radius and tilt angle. Unlike traditional planar electromagnetic wave illumination, vortex electromagnetic waves, due to their OAM (Operational Aspect-Directed Motion) characteristics, generate not only a linear Doppler shift in the radial direction but also a Doppler shift in the azimuth direction when detecting targets—a rotational Doppler shift—providing another dimension of azimuth information. By jointly processing the two-dimensional information of linear Doppler and rotational Doppler, a richer amount of information can be obtained than that of traditional plane wave detection, thus enabling a more accurate estimation of the target motion parameters.

[0004] However, existing studies on the estimation of micro-motion parameters for vortex electromagnetic wave radar are based on the assumption that the position of the rotation center is known, which is impractical. The limited radar resolution depends on the signal bandwidth and array aperture, making the position of the rotation center inaccurate. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a multi-station positioning method for rotating targets based on vortex electromagnetic waves. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a multi-station positioning method for rotating targets based on vortex electromagnetic waves, comprising:

[0007] Establish a multi-station radar detection scenario and obtain an estimated measurement model of the rotating target under the multi-station radar detection scenario;

[0008] Based on the estimated measurement model, the target center is located using a geometric solution method or a positioning method based on positioning error correction, and the position coordinates of the target rotation center are obtained.

[0009] By using the Cramer-Rao boundary value as the lower bound of the unbiased estimate, the effectiveness of the geometric solution method and the positioning method based on positioning error correction are verified.

[0010] In one embodiment of the present invention, a multi-station radar detection scenario is established, and an estimated measurement model of a rotating target under the multi-station radar detection scenario is obtained, including:

[0011] Establish a radar coordinate system (U, V, W), a reference coordinate system (X, Y, Z), and a local coordinate system (x, y, z). The radar coordinate system is a Cartesian coordinate system with the radar's receiving element Q as its origin. The local coordinate system is a Cartesian coordinate system with the target's rotation center O as its origin, obtained by translation and rotation of the radar coordinate system. The reference coordinate system is a Cartesian coordinate system with the same origin as the local coordinate system, and it has the same translation as the radar coordinate system but no rotation relative to the local coordinate system.

[0012] Assuming that the M multi-transmitter single-receiver radars generating vortex electromagnetic waves point in the same direction, the target's rotation radius r is obtained. P and the off-axis distance D relative to radar station i i Estimated measurement of coupling h i for:

[0013]

[0014] Where, n i This indicates the measurement error caused by Gaussian noise. The estimated measurement h represents radar station i. i The true value, [U i V i W i ] TRepresents the coordinates of radar station i in the radar coordinate system, [U O V O W O ] T Represents the coordinates of the target's rotation center;

[0015] Obtain the measurement equation in vector form:

[0016] h = h o +n,

[0017] in, The measurement noise n follows a Gaussian distribution with zero mean and covariance matrix C':

[0018] C'=diag{σ1,σ2,...,σ i ,...,σ M},

[0019] Where, σ i This represents the calculated estimated measurement value h. i Clamelo boundary

[0020] In one embodiment of the present invention, the target center is located using a geometric solution method, including:

[0021] The estimated measurement value h corresponding to different radar stations i among the M multi-shot single-receive radars. i Perform joint calculations to remove the influence of the rotation radius and establish intermediate estimates;

[0022] A general expression for the target rotation center position is obtained by constructing a position information matrix of multiple radar stations and combining it with the intermediate estimate;

[0023] The position coordinates of the target's rotation center are obtained based on the general expression for the target's rotation center position.

[0024] In one embodiment of the present invention, the estimated measurement value h corresponding to different radar stations i among the M multi-transmitter single-receiver radars is... i Joint calculations are performed to remove the influence of the rotation radius and establish intermediate estimates, specifically including:

[0025] Assume the location coordinates of radar station i in the local coordinate system are (x... i ,y i ,z i ) T The true value of the estimated measurement at radar station i is obtained.

[0026] Using the radar station located at the origin of the radar coordinate system as the reference station, an intermediate estimate k is established. i0 :

[0027]

[0028] Where h0 represents the measured true value of the radar coordinate system origin, D0 represents the off-axis distance of the radar coordinate system origin, and x and y represent the coordinates of the target rotation center O in the local coordinate system. i y i This represents the coordinates of radar station i in the local coordinate system.

[0029] In one embodiment of the present invention, constructing a position information matrix of multiple radar stations and combining it with the intermediate estimate to obtain a general expression for the target rotation center position includes:

[0030] The intermediate estimate k i0 After sorting, we get:

[0031]

[0032] Let s i =(x i ,y i ) T p = (x, y) T ,get:

[0033]

[0034] in, Represents the square value of the L2 norm;

[0035] The location coordinate information of multiple radar stations is used to construct a matrix S = [s1, s2, ..., s i ,…,s N ] T ,

[0036] The intermediate estimate k i0 Constructing vectors get:

[0037]

[0038] The general expression for the position of the rotation center is obtained by the least squares method:

[0039]

[0040] In one embodiment of the present invention, target center localization is performed using a localization method based on localization error correction, including:

[0041] Measure the true value After squaring, substitute the noisy estimated measurement value h. iIgnoring the second-order noise term, we obtain the coordinates P of the target rotation center position. O =(U O V O ) T Pseudolinear equations:

[0042]

[0043] Where, r P The radius of rotation of the target, s i =(x i ,y i ) T P represents the coordinates of radar station i in the local coordinate system. O =(U O V O ) T This indicates the position coordinates of the target's rotation center in the radar coordinate system;

[0044] make Transform the pseudolinear equation into vector form:

[0045]

[0046] Where B1 = diag{h1,h2,...,h i ,...,h M}, G1 is defined as:

[0047]

[0048] in, The weighted least squares estimate is W1 is a weighted matrix. C' represents the covariance matrix of the measurement noise n;

[0049] get Weighted least squares estimate The covariance matrix is:

[0050]

[0051] The Taylor series is used to estimate the error of the positioning result, so as to correct the positioning result of the target rotation center and obtain the estimated value of the final target center coordinates.

[0052] In one embodiment of the present invention, the positioning result is corrected by estimating the error of the positioning result using Taylor series, including:

[0053] We will use weighted least squares estimates The covariance matrix obtained and Expressed as the true value plus the estimation error:

[0054]

[0055]

[0056]

[0057] in, express The estimation error, express The estimation error, express The estimation error; express The estimated value, express The estimated value, express The estimated value;

[0058] Taylor series expansion yields:

[0059]

[0060] in, Indicates to The estimate, express The error, express The error;

[0061] The equivalent error is derived as follows:

[0062]

[0063] in:

[0064]

[0065] Among them, I 3×3 Represents a third-order identity matrix;

[0066] The weighted least squares value of the estimation error after Taylor expansion is obtained:

[0067]

[0068] Where W2 is the weighting matrix,

[0069] The estimated coordinates of the center of the rotated target are:

[0070]

[0071] in, express The true value;

[0072] The covariance matrix obtained from the estimated coordinates of the rotating target center is:

[0073]

[0074] Obtain the estimated coordinates of the center of the rotated target:

[0075]

[0076] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0077] This invention proposes a multi-station localization method for rotating targets based on vortex electromagnetic waves. Utilizing the orbital angular momentum characteristics of vortex electromagnetic waves, it obtains the Doppler frequency shift generated in the azimuth direction, i.e., the rotational Doppler frequency shift, thus acquiring richer information than traditional plane waves. The position of the rotating target is estimated through multi-station measurement. Furthermore, the modal purity remains unaffected, resulting in high localization accuracy. It also incorporates traditional TDOA (Time Difference of Arrival) technology for positioning. When radar detects targets, plane electromagnetic waves can estimate the target's velocity information through the radial Doppler effect. However, under the vortex electromagnetic wave system, the target's motion in the radar's line-of-sight also generates a rotational Doppler effect. The rotational Doppler frequency is related not only to the rotational angular velocity but also to the relative position of the radar and the target. Using vortex beams to detect targets, the relationship between the radar and the target position can be obtained by analyzing the rotational Doppler frequency characteristics. Through multi-station target scanning, precise localization of the rotating target's center can be achieved.

[0078] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0079] Figure 1 This is a flowchart of a multi-station positioning method for a rotating target based on vortex electromagnetic waves provided in an embodiment of the present invention;

[0080] Figure 2 This is a schematic diagram of a detection scenario for a single radar for vortex electromagnetic waves provided in an embodiment of the present invention;

[0081] Figure 3 This is a comparison chart of the mean square error of the rotating target position obtained through multi-radar station positioning. Detailed Implementation

[0082] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following detailed description of the multi-station positioning method for rotating targets based on vortex electromagnetic waves proposed in accordance with the present invention is provided in conjunction with the accompanying drawings and specific embodiments.

[0083] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0084] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element.

[0085] In a vortex electromagnetic wave system, the target's motion induces a rotating Doppler effect. The target's angular velocity can be estimated using the rotating Doppler frequency. This rotating Doppler frequency is modulated not only by the target's rotational angular velocity but also by the relative geometric relationship between the radar and the target. By describing the characteristics of the rotating Doppler frequency, its relationship with the target's position can be analyzed, i.e., the location of the target's rotation center.

[0086] Please see Figure 1 , Figure 1 This is a flowchart of a multi-station positioning method for a rotating target based on vortex electromagnetic waves, provided by an embodiment of the present invention. The rotating target center positioning method includes the following steps:

[0087] S1: Establish a multi-station radar detection scenario and obtain an estimated measurement model of the rotating target under the multi-station radar detection scenario.

[0088] Step S1 in this embodiment specifically includes:

[0089] S1.1: Establish the radar coordinate system, reference coordinate system, and local coordinate system.

[0090] Please see Figure 2 , Figure 2This is a schematic diagram of a detection scenario using a single vortex electromagnetic wave radar, provided for an embodiment of the present invention. In this embodiment, a typical detection scenario is established, where the radar is stationary and the vortex electromagnetic wave transmitting device is a multi-transmitter single-receiver radar with N ring-arranged transmitting units. A radar coordinate system (U, V, W), a reference coordinate system (X, Y, Z), and a local coordinate system (x, y, z) are established to obtain a mathematical model of the target's distance, azimuth, and elevation angle relative to the radar in the radar coordinate system.

[0091] Among them, the radar coordinate system is a rectangular coordinate system with the receiving element Q of a radar as the origin; the local coordinate system is a rectangular coordinate system with the rotation center O of the target as the origin, obtained by translation and rotation of the radar coordinate system; the reference coordinate system is a rectangular coordinate system with the same origin as the target coordinate system (i.e., the local coordinate system), which has the same translation as the radar coordinate system and the target coordinate system, but no rotation, and the rotating target is point P.

[0092] S1.2: Assuming that the M multi-transmitter single-receiver radars generating vortex electromagnetic waves point in the same direction, the target's rotation radius r is obtained. P and the off-axis distance D relative to radar station i i Estimated measurement of coupling h i .

[0093] Specifically, considering M multi-transmitter single-receiver radars s under three-dimensional positioning. i =[U i V i W i ] T (i = 1, 2, 3, ..., M), and simultaneously receive signals around the fixed point O = [U O V O W O ] T The target signal is rotated, where [U i V i W i ] T This represents the coordinates of the i-th multi-transmitter single-receiver radar in the radar coordinate system, where O is the target's rotation center, [U O V O W O ] T Indicates the coordinates of the target's rotation center.

[0094] In a multi-station system, assuming that the M multi-transmitter single-receiver radars generating vortex electromagnetic waves point in the same direction, the target's rotation radius r is obtained. P and off-axis distance D i Estimated measurement of coupling h i for:

[0095]

[0096] Where, n i This indicates the measurement error caused by Gaussian noise. The estimated measurement value h for radar station i i The true value. Essentially, multiple estimates involve illuminating a rotating target with multiple beams in either the time or spatial dimensions. This embodiment uses a multi-station system for detection.

[0097] S1.3: Obtain the measurement equation in vector form:

[0098] h = h o +n (2)

[0099] in,

[0100]

[0101] Without loss of reasonableness, assuming that the observations at each radar station are statistically independent and that the measurement noise n follows a Gaussian distribution with zero mean and covariance matrix C', it can be expressed as:

[0102] C'=diag{σ1,σ2,...,σ i ,...,σ M}

[0103] Where, σ i This represents the calculated estimated measurement value h. i Cramer-Rao Lower Bound (CRB)

[0104] S2: Based on the estimated measurement model, the target center is located using a geometric solution method or a positioning method based on positioning error correction, and the position coordinates of the target rotation center are obtained.

[0105] This embodiment provides two target center localization methods: a geometric solution (GS) method and a positioning method based on positioning error (PE) method. The processing procedures of the two methods are described in detail below.

[0106] (I) Geometric Solution Method

[0107] In this method, the geometric solution solving method includes the following steps:

[0108] (1) Estimated measurement values ​​h corresponding to different radar stations i in M ​​multi-transmit single-receive radars iPerform joint calculations to remove the influence of the rotation radius and establish intermediate estimates.

[0109] Specifically, the unknown rotation radius must first be eliminated to obtain the position of the rotation center before estimating the rotation radius. Assume the position coordinates of radar station i in the local coordinate system are (x... i ,y i ,z i ) T The true value of the estimated measurement at radar station i is obtained. Where, r P D represents the target's rotation radius. i D represents the off-axis distance of the target relative to radar station i. i The estimated measurements can be obtained from two radar stations i and j. Temporarily eliminate the effect of the rotation radius.

[0110]

[0111] Where x and y represent the coordinates of the target rotation center O in the local coordinate system, x i y i This represents the coordinates of radar station i in the local coordinate system, x j y j This represents the coordinates of radar station j in the local coordinate system.

[0112] Without compromising versatility, the radar station located at the origin of the radar coordinate system is used as the reference station to establish the intermediate estimate k. i0 :

[0113]

[0114] Where h0 represents the measured true value of the origin of the radar coordinate system, and D0 represents the off-axis distance of the origin of the radar coordinate system.

[0115] (2) Construct a position information matrix of multiple radar stations and combine it with intermediate estimates to obtain a general expression for the position of the target rotation center.

[0116] By constructing a position information matrix of multiple radar stations and simultaneously establishing a general expression for the target's rotation center position, the position coordinates of the target's rotation center can be obtained. From an algebraic geometric perspective, solving for target parameters using multiple sets of observations is represented in three-dimensional space as finding the intersection points of multiple sets of parallel cylindrical surfaces, and in two-dimensional space as finding the intersection points of multiple circles.

[0117] Specifically, in order to obtain a general expression for the position of the target rotation center, the above equation (4) can be rearranged to obtain:

[0118]

[0119] Let s i =(x i ,y i ) T p = (x, y) T Substituting into equation (5) above, we get:

[0120]

[0121] in, This represents the square value of the L2 norm.

[0122] Since it is impossible to solve directly from equation (6), the position coordinate information of multiple radar stations is used to construct a matrix S = [s1, s2, ..., s i ,…,s N ] T ,

[0123] The intermediate estimate k i0 Constructing vectors Equation (6) above can be reformulated as:

[0124]

[0125] The general expression for the position of the center of rotation is obtained by the least squares method:

[0126]

[0127] Furthermore, it can be deduced that:

[0128]

[0129] in, Let represent the fourth power of the L2 norm.

[0130] p can be solved using equation (9) above, thus obtaining the position coordinates of the target's rotation center. From an algebraic geometric perspective, solving p using multiple sets of observations is represented in three-dimensional space as finding the intersection points of multiple sets of cylindrical surfaces with parallel axes, and in two-dimensional space as finding the intersection points of multiple circles. Based on the formula, to solve p without auxiliary information, at least the intermediate estimates k from four radar stations are required. i0 .

[0131] (ii) Using a positioning method based on positioning error correction to locate the target rotation center.

[0132] In this step, a positioning method based on positioning error correction is used to obtain the rotation center position P. O =(U O V O ) TThe pseudolinear equation is derived, and the covariance matrix of the error is obtained. Specifically, based on traditional parameter measurements, some prior information about the position of the rotation center can be obtained, and this prior information can be used to reduce the number of stations, reduce the system burden, and reduce the complexity of the problem.

[0133] First, measure the true value After squaring, substitute the noisy estimated measurement value h. i Ignoring the second-order noise term, we can obtain the coordinates P of the rotation center position. O =(U O V O ) T Pseudolinear equations:

[0134]

[0135] Where, r P The radius of rotation of the target, s i =(x i ,y i ) T P represents the coordinates of radar station i in the local coordinate system. O =(U O V O ) T This indicates the position coordinates of the target's rotation center in the radar coordinate system.

[0136] At the same time, Representing the equivalent error, the above pseudolinear equation can be written in vector form as follows:

[0137]

[0138] Where B1 = diag{h1,h2,...,h i ,...,h M}, G1 is defined as:

[0139]

[0140] in, The WLS (Weighted Least Squares) estimate is:

[0141]

[0142] Where W1 is the weighting matrix, which can be defined as:

[0143]

[0144] Where C' represents the covariance matrix of the measurement noise n.

[0145] Therefore, we can obtain Weighted least squares estimate The covariance matrix is:

[0146]

[0147] Furthermore, to avoid performing nonlinear operations such as squared estimation errors on the positioning results, the positioning error is estimated using Taylor series to correct the positioning result of the target rotation center. A positioning method based on positioning error correction is adopted. Therefore, the above-obtained... and Expressed as the true value plus the estimation error:

[0148]

[0149] in, express The estimation error, express The estimation error, express The estimation error; express The estimated value, express The estimated value, express The estimated value.

[0150] Will Depend on Taylor series expansion yields:

[0151]

[0152] in, Indicates to The estimate, express The error, express The error, after series expansion, estimates the target parameter from become

[0153]

[0154] The equivalent error can then be derived:

[0155]

[0156] in:

[0157]

[0158] Among them, I 3×3This represents a third-order identity matrix.

[0159] The weighted least squares value of the estimation error after Taylor expansion is:

[0160]

[0161] Where W2 is the weighting matrix, The covariance matrix estimated after Taylor expansion is:

[0162]

[0163] Finally, the estimated coordinates of the center of the rotated target can be obtained as follows:

[0164]

[0165] therefore:

[0166]

[0167] in, express The true value.

[0168] The covariance matrix for estimating the coordinates of the rotated target center is:

[0169]

[0170] It should be noted that this method is applicable to... The estimate will be biased and is not an efficient estimator. However, the variable we are interested in is U. o V o Because of The estimate is unbiased, therefore:

[0171]

[0172] S3: Using the Cramer-Rao boundary value as the lower bound of the unbiased estimate, we verify the effectiveness of the geometric solution method and the positioning method based on positioning error correction.

[0173] Specifically, if the second-order error term is ignored, the estimation bias of the method is:

[0174]

[0175] The Jacobian matrix is:

[0176]

[0177] By calculating the Jacobian matrix, the diagonal elements of its inverse matrix are obtained as Cramerau thresholds.

[0178] Please see Figure 3, Figure 3 This is a comparison chart of the mean square error (MSE) of the rotating target position obtained through multi-radar site localization. Under different noise levels (σ), the mean square error (MSE) estimated by the geometric solution (GS) and the localization error-based solution (PE) is compared with the Cramerau threshold. At high signal-to-noise ratios, both target localization estimation methods can achieve the localized Cramerau threshold (CRB), validating the correctness and effectiveness of the multi-beam scanning estimation method.

[0179] This invention relates to a multi-station positioning method for rotating targets based on vortex electromagnetic waves. It utilizes the orbital angular momentum characteristics of vortex electromagnetic waves to obtain the Doppler frequency shift generated in the azimuth direction, i.e., the rotational Doppler frequency shift, thereby obtaining richer information than traditional plane waves. The position of the rotating target is estimated through multi-station measurement. Furthermore, the modal purity remains unaffected, resulting in high positioning accuracy, and it incorporates traditional TDOA for positioning.

[0180] Another embodiment of the present invention provides a storage medium storing a computer program for executing the steps of the multi-station positioning method for rotating targets based on vortex electromagnetic waves described in the above embodiments. A further aspect of the present invention provides an electronic device including a memory and a processor. The memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the multi-station positioning method for rotating targets based on vortex electromagnetic waves described in the above embodiments. Specifically, the integrated modules implemented as software functional modules can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0181] 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 concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A multi-station positioning method for a rotating target based on vortex electromagnetic waves, characterized in that, include: Establish a multi-station radar detection scenario and obtain an estimated measurement model of the rotating target under the multi-station radar detection scenario; Based on the estimated measurement model, the target center is located using a geometric solution method or a positioning method based on positioning error correction, and the position coordinates of the target rotation center are obtained. The Cramer-Rao threshold is used as the lower bound of the unbiased estimate to verify the effectiveness of the geometric solution method and the positioning method based on positioning error correction. Establish a multi-station radar detection scenario and obtain an estimated measurement model of a rotating target under the multi-station radar detection scenario, including: Establish radar coordinate system Reference coordinate system and local coordinate system The radar coordinate system is based on the radar's receiving array elements. A rectangular coordinate system with the origin at the origin; the local coordinate system is centered on the rotation center of the target. The origin is a Cartesian coordinate system obtained by translation and rotation of the radar coordinate system; the reference coordinate system is a Cartesian coordinate system with the same origin as the local coordinate system, and has the same translation but no rotation relative to the radar coordinate system and the local coordinate system. Assuming that vortex electromagnetic waves are generated M Multiple single-receiver radars pointing in the same direction yield the target's rotation radius. and relative to radar stations i Off-axis distance Estimated measurements of coupling for: in, This indicates the measurement error caused by Gaussian noise. Indicates radar station i Estimated measurement value The true value, Indicates radar station i Coordinates in the radar coordinate system Represents the coordinates of the target's rotation center; Obtain the measurement equation in vector form: ， in, Measure noise The zero-mean covariance matrix is Gaussian distribution: ， in, This represents the calculated estimated measurement value. Clamelo boundary ; Target center localization using geometric solution methods includes: The M Different radar sites in a multi-receiver single-receiver radar i Corresponding estimated measurement value Perform joint calculations to remove the influence of the rotation radius and establish intermediate estimates; A general expression for the target rotation center position is obtained by constructing a position information matrix of multiple radar stations and combining it with the intermediate estimate; Based on the general expression for the position of the target's rotation center, obtain the position coordinates of the target's rotation center; Target center localization is performed using a localization method based on localization error correction, including: Measure the true value After squaring, substitute the estimated measurement value containing noise. Ignoring second-order noise terms, we obtain the coordinates of the target rotation center position. Pseudolinear equations: in, Indicates the target's rotation radius. Indicates radar station i Coordinates in the local coordinate system This indicates the position coordinates of the target's rotation center in the radar coordinate system; make The pseudo-linear equation is transformed into vector form: in, , , Defined as: in, The weighted least squares estimate is , For weighted matrices, , Indicates measurement noise The covariance matrix; get Weighted least squares estimate The covariance matrix is: ； The Taylor series is used to estimate the error of the positioning result, so as to correct the positioning result of the target rotation center and obtain the estimated value of the final target center coordinates.

2. The multi-station positioning method for rotating targets based on vortex electromagnetic waves according to claim 1, characterized in that, The M Different radar sites in a multi-receiver single-receiver radar i Corresponding estimated measurement value Joint calculations are performed to remove the influence of the rotation radius and establish intermediate estimates, specifically including: Assuming a radar site The position coordinates in the local coordinate system are: , obtained radar site The true value of the estimated measurement is ; Using the radar station located at the origin of the radar coordinate system as the reference station, intermediate estimates are established. : ， in, This represents the actual measured value of the origin of the radar coordinate system. This represents the off-axis distance from the origin of the radar coordinate system. x , y Indicates the center of rotation of the target Coordinates in the local coordinate system x i , y i Indicates radar station i Coordinates in the local coordinate system.

3. The multi-station positioning method for rotating targets based on vortex electromagnetic waves according to claim 2, characterized in that, A general expression for obtaining the target rotation center position by constructing a position information matrix of multiple radar stations and combining it with the intermediate estimate includes: The intermediate estimate After sorting, we get: ； make , ,get: ； in, This represents the square value of the L2 norm; The location coordinate information of multiple radar stations is used to construct a matrix. , ; intermediate estimate Constructing vectors ,get: ， The general expression for the position of the rotation center is obtained by the least squares method: 。 4. The multi-station positioning method for rotating targets based on vortex electromagnetic waves according to claim 3, characterized in that, The Taylor series is used to estimate the error in the positioning results, and the positioning results of the target rotation center are corrected accordingly, including: We will use weighted least squares estimates The covariance matrix obtained , and Expressed as the true value plus the estimation error: in, express The estimation error, express The estimation error, express The estimation error; express The estimated value, express The estimated value, express The estimated value; Taylor series expansion yields: in, Indicates to The estimate, express The error, express The error; The equivalent error is derived as follows: ， in: ， ， in, Represents a third-order identity matrix; The weighted least squares value of the estimation error after Taylor expansion is obtained: ， in, For weighted matrices, ; The estimated coordinates of the center of the rotated target are: in, express The true value; The covariance matrix obtained from the estimated coordinates of the rotating target center is: ； Obtain the estimated coordinates of the center of the rotated target: ， 。

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