Space target parameter estimation method and system based on distributed broadband radar networking

Abstract

This invention discloses a method for estimating space target parameters based on a distributed broadband radar network. The method includes acquiring data from the distributed radar; constructing and decomposing a micro-range model of the space target under the distributed broadband radar; deriving the Cramer-Rao lower bounds for the estimation accuracy of the cone apex and cone base parameters and selecting the parameters for space target parameter estimation; solving for the cone apex and cone base scattering center coefficients; performing correlation matching of scattering centers; and estimating the space target parameters based on the distributed broadband radar network using an optimization method. This invention also discloses a system for implementing the aforementioned method for estimating space target parameters based on a distributed broadband radar network. This invention ensures the effectiveness and noise robustness of the parameter estimation process, and also achieves higher correlation accuracy, better real-time performance, higher reliability, and better precision.

Description

Technical Field

[0001] This invention belongs to the field of digital signal processing, specifically relating to a method and system for estimating spatial target parameters based on distributed broadband radar networking. Background Technology

[0002] In ballistic missile offensive and defensive confrontations, target feature extraction and effective identification are crucial for defense; among these, target geometric structure features and micro-motion features are two important characteristics. Single radar identification of ballistic targets suffers from attitude sensitivity and low accuracy in extracting target micro-motion parameters, because the precession angle is usually difficult to obtain accurately in practice, and such solutions typically require knowledge of certain structural parameters of the target, such as target length and semi-cone angle.

[0003] Multi-view micro-Doppler can provide complementary and redundant information, which is beneficial for target feature extraction and identification. In terms of space target micro-models, existing space target parameter estimation schemes based on distributed broadband radar networks mainly use the cone scattering center or the projected length of the target axis to approximate the true target projection length, while approximating the target length variation information as a sine function, failing to fully utilize the information of the micro-curves of each scattering center.

[0004] Regarding the correlation matching of scattering centers, since the scattering centers at the bottom of the cone have sliding characteristics on the bottom surface of the ring and can transform into each other, most existing methods only match the micro-curves of the scattering centers at the top of the cone; this makes the accuracy of existing methods poor.

[0005] Regarding the impact of the occlusion effect, existing methods generally only use the micro-range curve of the cone apex or the length change information between the cone apex and the scattering center of the cone base near the radar to extract micro-motion features. However, in actual observation, due to the occlusion effect, at different radar observation angles, only the scattering center of the cone base near the radar can be observed, while the other scattering centers may not be visible; this may cause the existing scheme to fail.

[0006] Regarding the selection of scattering center coefficients, existing schemes do not evaluate the effectiveness and robustness of this parameter when selecting the apex or basal scattering center coefficients for feature extraction. However, in reality, the degree of influence of noise on different parameters varies. Therefore, the accuracy of existing schemes is poor.

[0007] Finally, regarding the accumulation time, existing methods require the accumulation time to be greater than half of the precession period. In order to achieve higher accuracy, the accumulation time needs to be greater than the precession period, which also limits the application of existing methods. Summary of the Invention

[0008] One of the objectives of this invention is to provide a highly reliable and accurate method for estimating spatial target parameters based on distributed broadband radar networks.

[0009] The second objective of this invention is to provide a system for implementing the aforementioned spatial target parameter estimation method based on distributed broadband radar networking.

[0010] The spatial target parameter estimation method based on distributed broadband radar networking provided by this invention includes the following steps:

[0011] S1. Acquire data information from the distributed radar, including bandwidth, power, and other information;

[0012] S2. Construct a micro-range model of a space target under a distributed bandwidth radar and decompose it;

[0013] S3. Derive the Cramer-Rao lower bounds for the accuracy of the cone apex parameter estimation and the cone base parameter estimation, thereby selecting the parameters for space target parameter estimation;

[0014] S4. The least squares method is used to solve for the scattering center coefficients at the apex and base of the cone;

[0015] S5. Based on the obtained data, perform correlation matching of scattering centers;

[0016] S6. Based on the correlation matching results of the scattering centers, the spatial target parameters based on the distributed broadband radar network are estimated using the optimization method.

[0017] Step S2, which involves constructing and decomposing a micro-model of a spatial target under a distributed bandwidth radar, specifically includes the following steps:

[0018] The initial distance between the spatial cone-shaped target and the radar and the target's center of gravity O is set as r0; the angle between the target's spin axis and precession axis is the precession angle θ; the cone apex scattering center A is the ideal scattering center, and the cone bottom scattering centers B and C are both sliding scattering centers, with B being the scattering center closest to the radar on the bottom surface;

[0019] Due to the reference distance r in linear frequency modulation ref Due to the influence of the distance, the micro-distances of each scattering center are represented in the range compression results as follows:

[0020] r A (t)=r0-(Hh)(a+bx(t))-r ref

[0021]

[0022]

[0023] In the formula r A(t) is the micro-curve of the scattering center A at the top of the cone; H is the height of the cone; h is the distance from the center of the cone to the center of the cone's ground circle; a is the product of the precession angle and the cosine of the horizon angle, and a = cosθcosγ, where γ is the angle between the radar line of sight and the cone's spin axis, i.e., the horizon angle; b is the product of the precession angle and the sine of the horizon angle, and b = sinθsinγ; x(t) is the cosine function of time t, and x(t) = cos(ωt + φ0), where ω is the precession angular frequency, t is time, φ0 is the initial phase angle; r is the radius of the cone's base circle.

[0024] For the cone-shaped scattering center near the radar base, according to Weierstrass's theorem, r B It can be expressed in the following generalized polynomial form through Taylor series expansion:

[0025]

[0026] In the formula, K is the decomposition order; C k is the coefficient of the Taylor series expansion term; k is the index of the Taylor series expansion term.

[0027] Step S3, which derives the Cramer-Rao lower bounds for the estimation accuracy of the cone apex and cone base parameters to select the parameters for space target parameter estimation, specifically includes the following steps:

[0028] Derive the Cramero lower bound of the accuracy of cone apex parameter estimation to determine the variables ultimately used to estimate the parameters of the space target:

[0029] Accuracy of cone apex parameter estimation:

[0030] The cone-top micro-curve is simplified to obtain:

[0031]

[0032] In the formula r A The cone apex micro-curve; The amplitude of the curve; The precession frequency; This is the initial phase; For curve offset terms;

[0033] The Cramérault bound of the cosine function is then expressed as:

[0034]

[0035]

[0036]

[0037]

[0038] In the formula for Clameros lower bound; σ 2 The variance of signal and noise is denoted as N; N is the number of sampling points. for The lower realm of Clameros; Let be the precession frequency; η be the signal-to-noise ratio, and The amplitude of the curve; for The lower realm of Clameros; This is the initial phase; for The lower realm of Clameros; For curve offset terms;

[0039] Accuracy of cone base parameter estimation:

[0040] The cone-bottom micro-curve is simplified to obtain:

[0041]

[0042] In the formula r B The scattering center micro-curve is shown below; w is the precession angular frequency; φ0 is the initial phase; d r The bias term is represented by w(t), which is Gaussian white noise, and w(t) ~ N(0,σ). 2 );

[0043] When the sampling period is T r Then, the obtained observation sequence Z(n) is represented as:

[0044] Z(n) = V(n) + w(n)

[0045] In the formula, n is the sampling index, and n = 0, 1, 2, ..., N-1, where N is the number of sampling points; V(n) is the cone-base micro-curve, and w(n) is Gaussian white noise;

[0046] At this point, the coefficients C of the observed sequence Z(n) and the Taylor series expansion term are... k The joint probability density function is:

[0047]

[0048] In the formula, p(Z(n); Θ) is the joint probability density function of parameter Θ; Θ is the parameter vector, and Θ=[C1,...,C K ,d r ] T ;

[0049] The coefficients C of the Taylor series expansion terms kThe specific formula for calculating each element of the Fisher information matrix J is as follows:

[0050]

[0051]

[0052]

[0053] In the formula For the parameters C in the Fisher information matrix J i C j The corresponding elements; i and j are the coefficients of the Taylor series expansion terms; For the parameters C in the Fisher information matrix J i ,d r The corresponding element; For the parameter d in Fisher information matrix J r ,d r The corresponding element;

[0054] The coefficients C of the Taylor series expansion terms k The lower bound is the diagonal elements of the inverse matrix of matrix J;

[0055] Based on the lower bound of the Cramérault curve estimated by parameters, the parameter A of the cone-top micro curve is... A w, φ and D A The estimation accuracy meets the set requirements, and the parameters C1, C2, and d of the cone-bottom micro curve are... r The estimation accuracy meets the set requirements; therefore, A is selected. A w, φ, D A C1, C2 and d r As parameters, design a parameter estimation algorithm.

[0056] Step S4, which involves solving for the scattering center coefficient at the cone apex, specifically includes the following steps:

[0057] The micro-curve of scattering center A is represented as follows:

[0058]

[0059] In the formula, v is the target velocity; a is the target acceleration;

[0060] The corresponding Taylor expansion is expressed as:

[0061]

[0062] In the formula, P represents the fitting order; a p The coefficients are those of the p-th order Taylor expansion;

[0063] Construct matrix A from the coefficients of the Taylor expansion. p =[a1,...,a p ,...,a P ] T , will r A Represented in matrix form r A =[r A (1),...,r A (N)] T r A (N) represents the Nth sample of the micro-curve A; the corresponding Taylor expansion is expressed in the following matrix form:

[0064] FA p =r A

[0065] In the formula r A Let F be the vector of the cone-shaped micro-curve; and F be the coefficient matrix. It is the P-th power at time N;

[0066] Applying the least squares method to matrix A p By fitting the data, we obtain A. p The expression is A p =(F T F) -1 F T r A ;

[0067] The higher the order p, the higher the corresponding parameter a. p The higher the estimation accuracy, the higher the fitting order P, and the higher the matrix A. p The higher the overall fitting accuracy, the better; the root mean square error between the fitted curve and the original curve is used as the evaluation index to determine the optimal fitting order.

[0068] By using the fitting coefficients, a system of equations is established to solve for the parameters of the parameter estimation algorithm.

[0069] Step S4, which involves solving for the scattering center coefficient at the bottom of the cone, specifically includes the following steps:

[0070] After translational compensation, the micro-curve of the scattering center B is expressed as follows:

[0071]

[0072] The corresponding Taylor expansion is expressed as:

[0073]

[0074] The coefficients of the first two Taylor expansions are expressed as follows:

[0075]

[0076]

[0077] In the formula, C1 represents the coefficients of the first-order Taylor expansion expression; C2 represents the coefficients of the second-order Taylor expansion expression.

[0078] set up get:

[0079] RC = r B

[0080] In the formula r B Let be the micro-curve vector of the scattering center B; R is the coefficient matrix, and R k =cos(wt+φ0) k Let k = 1, ..., K; C be the parameter vector to be determined, and C = [C1, C2, ..., C]. K ,d r ] T ;r B Represented as r B =[r2(1),r2(2),...,r2(N)] T ;

[0081] R is calculated from w and φ0 obtained from the micro-curve of the cone apex scattering center;

[0082] Finally, the coefficient matrix C is calculated as follows: r B for

[0083]

[0084] Step S5, which involves performing correlation matching of scattering centers based on the obtained data information, specifically includes the following steps:

[0085] The relationship between the occlusion of the scattering center and the horizon angle β and the semi-cone angle γ is shown below:

[0086] If 0 ≤ β < γ, then scattering centers A, B and C are all blocked;

[0087] If γ≤β(t)<π / 2, then scattering centers A and B are blocked, while scattering center C is not blocked.

[0088] If π / 2≤β(t)<π-γ, then scattering centers A, B and C are all blocked;

[0089] If π-γ≤β(t)<π, then scattering centers B and C are blocked, while scattering center A is not blocked.

[0090] In summary, the variation in the number of scattering centers can be categorized into three cases: (1) all are visible; (2) A and B are visible; (3) B and C are visible.

[0091] When the number of scattering centers is equal to 3, it corresponds to case (1); at this time, the least squares fitting method is used to fit all the micro curves, and the root mean square error between the fitted curve and the original curve is used as the matching degree evaluation index. The smallest root mean square error corresponds to the cone apex scattering center A; then, the cone bottom scattering micro curve decomposition coefficient estimation method is used to calculate the decomposition coefficients of the remaining two scattering centers. Among them, the scattering center with the second-order coefficient less than 0 is the scattering center B close to the radar, and the scattering center with the second-order coefficient greater than 0 is the scattering center C far away from the radar.

[0092] When the number of scattering centers is equal to 2, it corresponds to case (2) or case (3); a new distance curve r is introduced. BC For r BC =(r B +r C ) / 2; For the existing two micro-curves r B and r C And the new distance curve r BC Perform fitting and then make a judgment: if r BC The corresponding root mean square error is the smallest, then in case (3), the two micro curves correspond to the scattering center of the cone bottom scattering center, and then the scattering center B and scattering center C are determined according to the sign of the second-order decomposition coefficients to determine the corresponding micro curves; if r BC If the corresponding root mean square error is not the minimum, then the curve with the minimum root mean square error corresponds to the cone scattering center A, and the other curve corresponds to the scattering center B.

[0093] Step S6, which involves estimating spatial target parameters based on distributed broadband radar networking using an optimization method based on the correlation matching results of scattering centers, specifically includes the following steps:

[0094] Distributed radar micro-range observation data is used to estimate the target's micro-motion and size and structural parameters. All parameters are solved using data acquired by two radars.

[0095] The line-of-sight angle of the first radar is set as γ1, and the line-of-sight angle of the second radar is set as γ2.

[0096] If both radars exhibit condition (2), then the estimated frequency is obtained by using the signal amplitude as the weighting factor.

[0097]

[0098] In the formula, w is the desired precession angular frequency; The amplitude parameters are obtained from the first radar estimation. The amplitude parameter obtained from the second radar estimation; w (1) The precession frequency estimated by the first radar; w (2) The precession frequency estimated by the second radar;

[0099] Then, the parameters are estimated using the following equation:

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] In the formula, a1 is the first parameter corresponding to the first radar, b1 is the second parameter corresponding to the first radar, and b1 = sinθsinγ1, a1 = cosθcosγ1; This is the difference between the initial distance and the reference distance observed by the first radar. The amplitude of the cone-top micro-range curve estimated by the first radar; The offset of the cone-shaped micro-range curve in the first radar; denoted as the first Taylor expansion coefficient of the micro-range curve at the bottom of the first radar cone; a2 and b2 are the parameters corresponding to the second radar, and a2 = cosθcosγ2, b2 = sinθsinγ2; The amplitude of the cone-top micro-range curve estimated by the second radar; The offset of the cone-bottom micro-range curve in the second radar; The first Taylor expansion coefficient of the cone-bottom micro-range curve in the second radar; This is the difference between the initial range and the reference range observed by the second radar;

[0109] If the i-th radar exhibits condition (3), then the following equation is used for parameter estimation:

[0110]

[0111]

[0112] In the formula, the superscript (i) represents the i-th radar, and i takes the value of 1 or 2;

[0113] If the i-th radar occurs in case (1), then the cone apex micro-curve and the cone basal micro-curve near the radar are selected for parameter estimation, which is equivalent to the i-th radar occurrence case (2).

[0114] This invention also provides a system for implementing the aforementioned spatial target parameter estimation method based on distributed broadband radar networking, comprising a data acquisition module, a model building module, a parameter selection module, a coefficient solving module, an association matching module, and a parameter estimation module; the data acquisition module, model building module, parameter selection module, coefficient solving module, association matching module, and parameter estimation module are connected in series; the data acquisition module is used to acquire data information from the distributed radar, including bandwidth, power, etc., and upload the data to the model building module; the model building module is used to construct a spatial target micro-model under distributed broadband radar based on the received data information, decompose it, and upload the data to the parameter selection module; the parameter selection module is used to... The received data is used to derive the Cramer-Rao lower bounds for the estimation accuracy of the cone apex and cone base parameters, thereby selecting the parameters for space target parameter estimation. The data is then uploaded to the coefficient solving module. This module uses the least squares method to solve for the cone apex and cone base scattering center coefficients based on the received data and uploads the data to the association matching module. The association matching module performs association matching of scattering centers based on the received and obtained data and uploads the data to the parameter estimation module. Finally, the parameter estimation module uses optimization methods to estimate the space target parameters based on a distributed broadband radar network, using the association matching results of the scattering centers.

[0115] The spatial target parameter estimation method and system based on distributed broadband radar networking provided by this invention decomposes the micro-range model and derives the Cramer-Rao lower bound to select the parameters for spatial target parameter estimation, ensuring the effectiveness and noise robustness of the invention. By estimating, solving, and correlating the cone apex and cone base scattering center coefficients using the least squares method, the correlation accuracy is improved. Furthermore, by using optimization methods for parameter estimation, this invention eliminates the need for long-term data accumulation, ensuring its real-time performance. Therefore, this invention has higher reliability and better accuracy. Attached Figure Description

[0116] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0117] Figure 2 This is a schematic diagram showing the relationship between the parameters and micro-motion characteristics in cases (1) and (2) of the method of the present invention.

[0118] Figure 3This is a schematic diagram showing the relationship between the parameters and micro-motion features in case (3) of the method of the present invention.

[0119] Figure 4 This is a schematic diagram of the functional modules of the system of the present invention. Detailed Implementation

[0120] like Figure 1 The diagram shown illustrates the method flow of this invention: The spatial target parameter estimation method based on distributed broadband radar networking provided by this invention includes the following steps:

[0121] S1. Acquire data information from the distributed radar, including bandwidth, power, and other information;

[0122] S2. Construct a micro-range model of a space target under a distributed bandwidth radar and decompose it; specifically, this includes the following steps:

[0123] The initial distance between the spatial cone-shaped target and the radar and the target's center of gravity O is set as r0; the angle between the target's spin axis and precession axis is the precession angle θ; the cone apex scattering center A is the ideal scattering center, and the cone bottom scattering centers B and C are both sliding scattering centers, with B being the scattering center closest to the radar on the bottom surface;

[0124] Due to the reference distance r in linear frequency modulation ref Due to the influence of the distance, the micro-distances of each scattering center are represented in the range compression results as follows:

[0125] r A (t)=r0-(Hh)(a+bx(t))-r ref

[0126]

[0127]

[0128] In the formula r A (t) is the micro-curve of the scattering center A at the top of the cone; H is the height of the cone; h is the distance from the center of the cone to the center of the cone's ground circle; a is the product of the precession angle and the cosine of the horizon angle, and a = cosθcosγ, where γ is the angle between the radar line of sight and the cone's spin axis, i.e., the horizon angle; b is the product of the precession angle and the sine of the horizon angle, and b = sinθsinγ; x(t) is the cosine function of time t, and x(t) = cos(ωt + φ0), where ω is the precession angular frequency, t is time, φ0 is the initial phase angle; r is the radius of the cone's base circle.

[0129] For the cone-shaped scattering center near the radar base, according to Weierstrass's theorem, r B It can be expressed in the following generalized polynomial form through Taylor series expansion:

[0130]

[0131] In the formula, K is the decomposition order; C k is the coefficient of the Taylor series expansion term; k is the index of the Taylor series expansion term;

[0132] S3. Derive the Cramer-Rao lower bounds for the accuracy of the cone apex and cone base parameter estimations, thereby selecting the parameters for space target parameter estimation; specifically including the following steps:

[0133] Derive the Cramero lower bound of the accuracy of cone apex parameter estimation to determine the variables ultimately used to estimate the parameters of the space target:

[0134] Accuracy of cone apex parameter estimation:

[0135] The cone-top micro-curve is simplified to obtain:

[0136]

[0137] In the formula r A The cone apex micro-curve; The amplitude of the curve; The precession frequency; This is the initial phase; For curve offset terms;

[0138] The Cramérault bound of the cosine function is then expressed as:

[0139]

[0140]

[0141]

[0142]

[0143] In the formula for Clameros lower bound; σ 2 The variance of signal and noise is denoted as N; N is the number of sampling points. for The lower realm of Clameros; Let be the precession frequency; η be the signal-to-noise ratio, and The amplitude of the curve; for The lower realm of Clameros; This is the initial phase; for The lower realm of Clameros; For curve offset terms;

[0144] Accuracy of cone base parameter estimation:

[0145] The cone-bottom micro-curve is simplified to obtain:

[0146]

[0147] In the formula r B The scattering center micro-curve is shown below; w is the precession angular frequency; φ0 is the initial phase; d r The bias term is represented by w(t), which is Gaussian white noise, and w(t) ~ N(0,σ). 2 );

[0148] When the sampling period is T r Then, the obtained observation sequence Z(n) is represented as:

[0149] Z(n) = V(n) + w(n)

[0150] In the formula, n is the sampling index, and n = 0, 1, 2, ..., N-1, where N is the number of sampling points; V(n) is the cone-base micro-curve, and w(n) is Gaussian white noise;

[0151] At this point, the coefficients C of the observed sequence Z(n) and the Taylor series expansion term are... k The joint probability density function is:

[0152]

[0153] In the formula, p(Z(n); Θ) is the joint probability density function of parameter Θ; Θ is the parameter vector, and Θ=[C1,...,C K ,d r ] T ;

[0154] The coefficients C of the Taylor series expansion terms k The specific formula for calculating each element of the Fisher information matrix J is as follows:

[0155]

[0156]

[0157]

[0158] In the formula For the parameters C in the Fisher information matrix J i C j The corresponding elements; i and j are the coefficients of the Taylor series expansion terms; For the parameters C in the Fisher information matrix J i ,d rThe corresponding element; For the parameter d in Fisher information matrix J r ,d r The corresponding element;

[0159] The coefficients C of the Taylor series expansion terms k The lower bound is the diagonal elements of the inverse matrix of matrix J;

[0160] Based on the lower bound of the Cramérault curve estimated by parameters, the parameter A of the cone-top micro curve is... A w, φ and D A The estimation accuracy meets the set requirements, and the parameters C1, C2, and d of the cone-bottom micro curve are... r The estimation accuracy of the parameter meets the set requirements, while the accuracy of the other parameters remains low even under conditions of low noise. Therefore, the parameter estimation algorithm should avoid using these parameters as much as possible; thus, A is selected. A w, φ, D A C1, C2 and d r Design a parameter estimation algorithm;

[0161] S4. The least squares method is used to solve for the scattering center coefficients at the apex and base of the cone;

[0162] In practice, the process of solving for the scattering center coefficient at the cone apex includes the following steps:

[0163] The micro-curve of scattering center A is represented as follows:

[0164]

[0165] In the formula, v is the target velocity; a is the target acceleration;

[0166] Directly fitting using this function requires careful selection of initial frequency values. For more complex functions, higher-order polynomials are generally used for approximation; the corresponding Taylor expansion is expressed as:

[0167]

[0168] In the formula, P represents the fitting order; a p The coefficients are those of the p-th order Taylor expansion;

[0169] Construct matrix A from the coefficients of the Taylor expansion. p =[a1,...,a p ,...,a P ] T , will r A Represented in matrix form r A =[r A (1),...,r A(N)] T r A (N) represents the Nth sample of the micro-curve A; the corresponding Taylor expansion is expressed in the following matrix form:

[0170] FA p =r A

[0171] In the formula r A Let F be the vector of the cone-shaped micro-curve; and F be the coefficient matrix. It is the P-th power at time N;

[0172] Applying the least squares method to matrix A p By fitting the data, we obtain A. p The expression is A p =(F T F) -1 F T r A ;

[0173] The higher the order p, the higher the corresponding parameter a. p The higher the estimation accuracy, the higher the fitting order P, and the higher the matrix A. p The higher the overall fitting accuracy, the better; the root mean square error between the fitted curve and the original curve is used as the evaluation index to determine the optimal fitting order; finally, this invention needs to use the coefficient matrix to solve for A. A ,w,φ,D A Since there are 6 parameters including v, a, etc., only the first 6 order fitting coefficients are needed to establish a system of equations to solve the problem.

[0174] By using the fitting coefficients, a system of equations is established to solve for the parameters of the parameter estimation algorithm.

[0175] The process of solving for the scattering center coefficient at the bottom of the cone includes the following steps:

[0176] As the view angle changes, the scattering center at the base of the target cone remains visible. Information about B is crucial for estimating the parameters of the space target; however, due to its complex modulation characteristics, it has not received sufficient attention in previous studies. After translational compensation, the micro-curve of the scattering center B is expressed as follows:

[0177]

[0178] The corresponding Taylor expansion is expressed as:

[0179]

[0180] The coefficients of the first two Taylor expansions are expressed as follows:

[0181]

[0182]

[0183] In the formula, C1 represents the coefficients of the first-order Taylor expansion expression; C2 represents the coefficients of the second-order Taylor expansion expression.

[0184] set up get:

[0185] RC = r B

[0186] In the formula r B Let be the micro-curve vector of the scattering center B; R is the coefficient matrix, and R k =cos(wt+φ0) k Let k = 1, ..., K; C be the parameter vector to be determined, and C = [C1, C2, ..., C]. K ,d r ] T ;r B Represented as r B =[r2(1),r2(2),...,r2(N)] T ;

[0187] R is calculated from w and φ0 obtained from the micro-curve of the cone apex scattering center;

[0188] Finally, the coefficient matrix C is calculated as follows: r B for

[0189] In theory, a closed-form solution can be obtained when the order is less than or equal to the signal sampling length, which can always be satisfied in practice; in addition, parameters of order two and above have relatively small values, and the accuracy of the solved parameters is low, making them unsuitable for parameter estimation.

[0190] S5. Based on the obtained data, perform correlation matching of scattering centers; specifically including the following steps:

[0191] The relationship between the occlusion of the scattering center and the horizon angle β and the semi-cone angle γ is shown below:

[0192] If 0 ≤ β < γ, then scattering centers A, B and C are all blocked;

[0193] If γ≤β(t)<π / 2, then scattering centers A and B are blocked, while scattering center C is not blocked.

[0194] If π / 2≤β(t)<π-γ, then scattering centers A, B and C are all blocked;

[0195] If π-γ≤β(t)<π, then scattering centers B and C are blocked, while scattering center A is not blocked.

[0196] In summary, the variation in the number of scattering centers can be categorized into three cases: (1) all are visible; (2) A and B are visible; (3) B and C are visible.

[0197] When the number of scattering centers is equal to 3, it corresponds to case (1); at this time, the least squares fitting method is used to fit all the micro curves, and the root mean square error between the fitted curve and the original curve is used as the matching degree evaluation index. The smallest root mean square error corresponds to the cone apex scattering center A; then, the cone bottom scattering micro curve decomposition coefficient estimation method is used to calculate the decomposition coefficients of the remaining two scattering centers. Among them, the scattering center with the second-order coefficient less than 0 is the scattering center B close to the radar, and the scattering center with the second-order coefficient greater than 0 is the scattering center C far away from the radar.

[0198] When the number of scattering centers is equal to 2, it corresponds to case (2) or case (3); a new distance curve r is introduced. BC For r BC =(r B +r C ) / 2; For the existing two micro-curves r B and r C And the new distance curve r BC Perform fitting and then make a judgment: if r BC The corresponding root mean square error is the smallest, then in case (3), the two micro curves correspond to the cone-bottom scattering center and the scattering center. Then, the correspondence between the two micro curves and the scattering center B and the scattering center C is determined according to the sign of the second-order decomposition coefficients; if r BC If the corresponding root mean square error is not the minimum, then the curve with the minimum root mean square error corresponds to the cone scattering center A, and the other curve corresponds to the scattering center B.

[0199] S6. Based on the correlation matching results of the scattering centers, perform spatial target parameter estimation using an optimization method based on a distributed broadband radar network; specifically including the following steps:

[0200] Distributed radar micro-range observation data is used to estimate the target's micro-motion and size and structural parameters. All parameters are solved using data acquired by two radars.

[0201] The line-of-sight angle of the first radar is set as γ1, and the line-of-sight angle of the second radar is set as γ2.

[0202] If both radars exhibit condition (2) (conditions (1), (2), or (3) refer to each radar individually), then the estimated frequency is obtained by using the signal amplitude as the weighting factor.

[0203]

[0204] In the formula, w is the desired precession angular frequency; The amplitude parameters are obtained from the first radar estimation. The amplitude parameter obtained from the second radar estimation; w (1) The precession frequency estimated by the first radar; w (2) The precession frequency estimated by the second radar;

[0205] Finally, other parameters are estimated, and the relationship between the scattering center micro-curve coefficients and target parameters is as follows: Figure 2 As shown; then, the parameters are estimated using the following equation:

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214] In the formula, a1 is the first parameter corresponding to the first radar, b1 is the second parameter corresponding to the first radar, and b1 = sinθsinγ1, a1 = cosθcosγ1; This is the difference between the initial distance and the reference distance observed by the first radar. The amplitude of the cone-top micro-range curve estimated by the first radar; The offset of the cone-shaped micro-range curve in the first radar; denoted as the first Taylor expansion coefficient of the micro-range curve at the bottom of the first radar cone; a2 and b2 are the parameters corresponding to the second radar, and a2 = cosθcosγ2, b2 = sinθsinγ2; The amplitude of the cone-top micro-range curve estimated by the second radar; The offset of the cone-bottom micro-range curve in the second radar; The first Taylor expansion coefficient of the cone-bottom micro-range curve in the second radar; The difference between the initial range and the reference range observed by the second radar; θ, γ1, γ2, h, H, r, The parameters that need to be solved;

[0215] If the i-th radar exhibits condition (3), the relationship between the micro-range curve coefficient of the scattering center and the target parameters is as follows: Figure 3 As shown; therefore, the following equation is used for parameter estimation:

[0216]

[0217]

[0218] In the formula, the superscript (i) represents the i-th radar, and i takes the value of 1 or 2;

[0219] If the i-th radar is in situation (1), then the cone apex micro-curve and the cone basal micro-curve near the radar are selected for parameter estimation, which is equivalent to the radar being in situation (2).

[0220] This invention derives the Cramer-Rao lower bound for estimating the scattering center parameters of space targets based on a space target macro model, and selects scattering center parameters with a low and robust Cramer-Rao lower bound for space target parameter estimation. This invention utilizes the Taylor expansion method to expand the cone-top macro curve into a high-order polynomial summation and the cone-bottom macro curve into a high-order power of a cosine function summation, representing them in matrix form. Finally, the least squares algorithm is used to estimate the space target scattering center parameters. This invention uses the estimated space target scattering center parameters to achieve scattering center correlation matching under different obstruction conditions. The root mean square error between the original macro curve and the sinusoidally fitted macro curve is used as the evaluation index to determine the cone-top scattering center, and the second-order decomposition coefficient of the macro curve is used to determine the cone-bottom scattering center. This invention utilizes distributed radar to obtain the space target's macro curves from different viewpoints and estimates its scattering center parameters. Using the relationship between the scattering center parameters, space target structural parameters, and micro-motion parameters, a system of equations is established, and the target parameter estimation results are obtained by solving the equations using optimization methods.

[0221] This invention first utilizes Taylor decomposition to decompose the micro-curve of the cone-shaped scattering center into a sum of high powers of sinusoidal parameters. Based on this, the Cramer-Rao lower bound of each scattering center parameter is derived, thereby selecting the parameters for micro-motion feature extraction and ensuring the effectiveness and noise robustness of the algorithm. Second, the least squares method is used to estimate the coefficients of each scattering center under distributed radar. The relationship between the root mean square error of the fitted sine curve and the scattering center coefficients is used to perform scattering center association matching, resulting in higher association accuracy. Finally, based on the relationship between the selected parameters and micro-motion features under distributed radar at each time step, a system of equations is established, and micro-motion feature extraction is achieved through optimization methods, eliminating the need for long-term accumulation.

[0222] like Figure 4The diagram shows the functional modules of the system of this invention: The system disclosed in this invention, which implements the spatial target parameter estimation method based on distributed broadband radar networking, includes a data acquisition module, a model building module, a parameter selection module, a coefficient solving module, an association matching module, and a parameter estimation module; these modules are connected in series. The data acquisition module acquires data information from the distributed radar, including bandwidth, power, etc., and uploads the data to the model building module. The model building module constructs a micro-model of the spatial target under the distributed broadband radar based on the received data information, decomposes it, and uploads the data to the parameter selection module. The parameter selection module... The first module derives the Cramer-Rao lower bounds for the estimation accuracy of the cone apex and cone base parameters based on the received data, thereby selecting the parameters for space target parameter estimation, and then uploads the data to the coefficient solving module. The coefficient solving module solves the cone apex and cone base scattering center coefficients using the least squares method based on the received data, and then uploads the data to the association matching module. The association matching module performs association matching of scattering centers based on the received data and the obtained data, and then uploads the data to the parameter estimation module. The parameter estimation module performs space target parameter estimation based on distributed broadband radar networking using optimization methods based on the received data and the association matching results of the scattering centers.

Claims

1. A method for estimating spatial target parameters based on distributed broadband radar networking, comprising the following steps: S1. Acquire data information from the distributed radar; S2. Construct a micro-range model of a space target under a distributed bandwidth radar and decompose it; S3. Derive the Cramer-Rao lower bounds for the accuracy of the cone apex and cone base parameter estimations, thereby selecting the parameters for space target parameter estimation; specifically including the following steps: Derive the Cramero lower bound of the accuracy of cone apex parameter estimation to determine the variables ultimately used to estimate the parameters of the space target: Accuracy of cone apex parameter estimation: The cone-top micro-curve is simplified to obtain: In the formula The cone apex micro-curve; The amplitude of the curve; The precession frequency; This is the initial phase; For curve offset terms; The Cramérault bound of the cosine function is then expressed as: In the formula for The lower realm of Clameros; The variance of signal and noise; This represents the number of sampling points; for The lower realm of Clameros; The precession frequency; For signal-to-noise ratio, and , The amplitude of the curve; for The lower realm of Clameros; This is the initial phase; for The lower realm of Clameros; For curve offset terms; Accuracy of cone base parameter estimation: The cone-bottom micro-curve is simplified to obtain: In the formula The micro-curve of the cone-bottom scattering center; The precession angular frequency; This is the initial phase; For bias terms; It is Gaussian white noise, and K is the decomposition order; is the coefficient of the Taylor series expansion term; k is the index of the Taylor series expansion term. When the sampling period is At that time, the obtained observation sequence Represented as: In the formula For sampling index, and N is the number of sampling points; It is a cone-shaped micro-curve, and ; It is Gaussian white noise; At this time, the observation sequence and the coefficients of the Taylor series expansion terms The joint probability density function is: In the formula For parameters The joint probability density function; Let be the parameter vector, and ; coefficients of the terms in a Taylor series expansion Fisher Information Matrix The specific calculation formulas for each element are as follows: In the formula Fisher Information Matrix Medium parameters The corresponding elements; i and j are the coefficients of the Taylor series expansion terms; Fisher Information Matrix Medium parameters The corresponding element; Fisher Information Matrix Medium parameters The corresponding element; coefficients of the terms in a Taylor series expansion The lower bound is the matrix The diagonal elements of the inverse matrix; Based on the lower bound of Cramero's curve estimated by parameters, the parameters of the cone-top micro curve are... , , and The estimation accuracy meets the set requirements, and the parameters of the cone-bottom micro curve are... , and The estimation accuracy meets the set requirements; therefore, the selected... , , , , , and Design a parameter estimation algorithm; S4. The least squares method is used to solve for the scattering center coefficients at the apex and base of the cone; S5. Based on the obtained data, perform correlation matching of scattering centers; S6. Based on the correlation matching results of the scattering centers, the parameters of spatial targets based on distributed broadband radar networking are estimated using optimization methods.

2. The spatial target parameter estimation method based on distributed broadband radar networking according to claim 1, characterized in that... Step S2, which involves constructing and decomposing a micro-model of a spatial target under a distributed bandwidth radar, specifically includes the following steps: Position the spatial cone-shaped target relative to the radar and the target's center of gravity. The initial distance between them is The angle between the target's spin axis and precession axis is the precession angle. The cone apex scattering center A is an ideal scattering center, while the cone base scattering centers B and C are both sliding scattering centers, with B being the scattering center closest to the radar on the bottom surface. Due to the reference distance in linear frequency modulation Due to the influence of the distance, the micro-distances of each scattering center are represented in the range compression results as follows: In the formula The micro-curve is for the scattering center A at the cone apex; The height of the cone; This is the distance from the center of the cone to the center of the cone's surface circle; It is the product of the precession angle and the cosine of the horizon angle, and , The angle between the radar line-of-sight direction and the cone's spin axis is the field of view angle. It is the product of the precession angle and the sine of the horizon angle, and ; For time The cosine function, and , The precession angular frequency, For time, The initial phase angle; The radius of the base circle of the cone; For the cone-shaped scattering center near the radar, according to Weierstrass's theorem, It can be expressed in the following generalized polynomial form through Taylor series expansion: In the formula, K is the decomposition order; is the coefficient of the Taylor series expansion term; k is the index of the Taylor series expansion term.

3. The spatial target parameter estimation method based on distributed broadband radar networking according to claim 2, characterized in that... Step S4, which involves solving for the scattering center coefficient at the cone apex, specifically includes the following steps: The micro-curve of scattering center A is represented as follows: In the formula For target speed; Accelerate towards the target; The corresponding Taylor expansion is expressed as: In the formula, P represents the fitting order; The coefficients are those of the p-th order Taylor expansion; Construct a matrix from the coefficients of the Taylor expansion. ,Will Represented in matrix form , Let N be the Nth sample of the macro curve A; then the corresponding Taylor expansion is expressed in the following matrix form: In the formula The vector of the cone apex micro-curve; Let be the coefficient matrix, and , It is the P-th power at time N; Applying the least squares method to the matrix By fitting, we can obtain The expression is ; The higher the order p, the higher the corresponding parameters. The higher the estimation accuracy, the higher the fitting order P, and the better the matrix. The higher the overall fitting accuracy, the better; the root mean square error between the fitted curve and the original curve is used as the evaluation index to determine the optimal fitting order. By using the fitting coefficients, a system of equations is established to solve for the parameters of the parameter estimation algorithm.

4. The spatial target parameter estimation method based on distributed broadband radar networking according to claim 3, characterized in that... Step S4, which involves solving for the scattering center coefficient at the bottom of the cone, specifically includes the following steps: After translational compensation, the micro-curve of the scattering center B is expressed as follows: The corresponding Taylor expansion is expressed as: The coefficients of the first two Taylor expansions are expressed as follows: In the formula The coefficients of the first-order Taylor expansion expression; The coefficients of the second-order Taylor expansion expression; set up ,get: In the formula Let B be the micro-curve vector of the scattering center B; Let be the coefficient matrix, and , , ; Let be the parameter vector to be determined, and ; Represented as ; Calculated from the micro-curve of the cone scattering center and Calculations yielded ; Finally, the coefficient matrix is ​​calculated. for , for .

5. The spatial target parameter estimation method based on distributed broadband radar networking according to claim 4, characterized in that... Step S5, which involves performing correlation matching of scattering centers based on the obtained data information, specifically includes the following steps: Occlusion of the scattering center and the field of view Half cone angle The relationship is as follows: like Then the scattering centers A, B and C are all blocked; like If , then scattering centers A and B are blocked, while scattering center C is not blocked; like Then the scattering centers A, B and C are all blocked; like If , then scattering centers B and C are blocked, while scattering center A is not blocked; In summary, the number of scattering centers can be categorized into three cases: (1) all are visible; (2) A and B are visible; (3) B and C are visible. When the number of scattering centers is equal to 3, it corresponds to case (1); at this time, the least squares fitting method is used to fit all the micro curves, and the root mean square error between the fitted curve and the original curve is used as the matching degree evaluation index. The smallest root mean square error corresponds to the cone scattering center A. Then, the decomposition coefficients of the remaining two scattering centers are calculated using the cone-bottom scattering micro-curve decomposition coefficient estimation method. The scattering center with a second-order coefficient less than 0 is the scattering center B closer to the radar, and the scattering center with a second-order coefficient greater than 0 is the scattering center C farther away from the radar. When the number of scattering centers is equal to 2, it corresponds to case (2) or case (3); a new distance curve is introduced. for For the existing two micro curves and and the new distance curve Perform fitting and then make a judgment: if The corresponding root mean square error is the smallest, then in case (3), the two micro curves correspond to the scattering center of the cone bottom scattering center, and the correspondence between the scattering center B and the scattering center C and the two micro curves is determined according to the sign of the second-order decomposition coefficients; if If the corresponding root mean square error is not the minimum, then the curve with the minimum root mean square error corresponds to the cone scattering center A, and the other curve corresponds to the scattering center B.

6. The spatial target parameter estimation method based on distributed broadband radar networking according to claim 5, characterized in that... Step S6, which involves estimating spatial target parameters based on distributed broadband radar networking using an optimization method based on the correlation matching results of scattering centers, specifically includes the following steps: Distributed radar micro-range observation data is used to estimate the target's micro-motion and size and structural parameters. All parameters are solved using data acquired by two radars. Set the field of view of the first radar as The second radar's field of view is ; If both radars exhibit condition (2), then the estimated frequency is obtained by using the signal amplitude as the weighting factor. In the formula The desired precession angular frequency; The amplitude parameters are obtained from the first radar estimation. The amplitude parameters obtained from the second radar estimation; The precession frequency estimated by the first radar; The precession frequency estimated by the second radar; Then, the parameters are estimated using the following equation: In the formula The first parameter corresponds to the first radar. The second parameter corresponds to the first radar, and , ; This is the difference between the initial distance and the reference distance observed by the first radar. The amplitude of the cone-top micro-range curve estimated by the first radar; The offset of the cone-shaped micro-range curve in the first radar; The first Taylor expansion coefficient of the micro-range curve at the bottom of the first radar cone; and For the parameters corresponding to the second radar, and , ; The amplitude of the cone-top micro-range curve estimated by the second radar; The offset of the cone-bottom micro-range curve in the second radar; The first Taylor expansion coefficient of the cone-bottom micro-range curve in the second radar; This is the difference between the initial range and the reference range observed by the second radar; If the i-th radar exhibits condition (3), then the following equation is used for parameter estimation: superscript This represents the i-th radar, where i can be 1 or 2; If the i-th radar occurs (1), then the cone apex micro-curve and the cone base micro-curve near the radar are selected for parameter estimation, which is equivalent to the i-th radar occurrence (2).

7. A system for implementing the spatial target parameter estimation method based on distributed broadband radar networking as described in any one of claims 1 to 6, characterized in that... It includes a data acquisition module, a model building module, a parameter selection module, a coefficient solving module, an association matching module, and a parameter estimation module; these modules are connected in series. The data acquisition module acquires data information from the distributed radar and uploads it to the model building module. The model building module constructs a micro-model of a spatial target under the distributed bandwidth radar based on the received data information, decomposes it, and uploads the data to the parameter selection module. The parameter selection module is used to derive the Cramer-Rao lower bound of the estimation accuracy of the cone apex parameter and the cone base parameter based on the received data information, thereby selecting the parameters for space target parameter estimation, and uploading the data to the coefficient solving module; The coefficient solving module is used to solve the scattering center coefficients at the top and bottom of the cone using the least squares method based on the received data information, and then uploads the data to the association matching module. The association matching module is used to perform association matching of scattering centers based on the received data information and the obtained data information, and then upload the data to the parameter estimation module; The parameter estimation module is used to estimate the parameters of spatial targets based on distributed broadband radar networks by means of optimization methods, based on the received data and the correlation matching results of the scattering centers.

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