Radar resource allocation method based on minimum effective time width

Abstract

The invention discloses a radar resource allocation method based on the minimum effective time width, and the method comprises the steps: S1, initializing networking phased array radar system parameters, constructing a target motion model, and obtaining a target state; s2, constructing a measurement equation, and obtaining target measurement; s3, estimating and updating the target state and the target measurement by using an SCKF algorithm to obtain target state estimation, and fusing the target state estimation; s4, deducing PCRLB according to the target state estimation to obtain a tracking precision constraint; s5, constructing an optimization model; s6, designing a radar-target assignment algorithm to solve the optimization model, and obtaining an optimal effective time width allocation result of the networking radar to all targets; and S7, feeding back an allocation result to a radar transmitting end, thereby controlling radar transmitting parameters and realizing allocation of radar resources. The method has the advantages that radar resources can be effectively distributed in the networking radar multi-target tracking process, the effective time width is minimized, and the tracking capacity is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar tracking and identification, and in particular relates to a radar resource allocation method based on minimizing effective time width. Background Art

[0002] There is a contradiction between the limited radar tracking resources and the large demand for radar resources in target tracking tasks. Radar resource management technology is to give the optimal solution between the two under consideration of actual application scenarios, in order to consume the least radar resources and achieve the maximum radar performance. Compared with single-base phased array radars, the structure between nodes of networked phased array radars is complex. Not only the tracking resources of the nodes must be considered, but also the information fusion architecture, which brings greater challenges to resource management technology. Reasonable scheduling of phased array radar resources is one of the key technologies to improve radar resource utilization. Faced with difficulties such as complex tasks and limited resources, how to coordinate the allocation of radar resources such as waveform, power, dwell time, bandwidth, etc. to obtain better tracking performance has become a problem that needs to be solved urgently. Summary of the invention

[0003] The purpose of the present invention is to provide a radar resource allocation method based on minimizing the effective time width, which has the characteristics of effectively allocating radar resources, minimizing the effective time width, and improving the tracking capacity during the multi-target tracking process of the networked radar.

[0004] The technical solution adopted by the present invention is a radar resource allocation method based on minimizing the effective time width, which specifically includes the following steps:

[0005] S1: Initialize the system parameters of the networked phased array radar, build the target motion model, and obtain the target state;

[0006] S2: construct the measurement equation to obtain the target measurement;

[0007] S3: Use the SCKF algorithm to estimate and update the target state and target measurement, obtain the target state estimate, and perform fusion;

[0008] S4: derive PCRLB based on the target state estimate to obtain the tracking accuracy constraint;

[0009] S5: construct an optimization model by combining tracking accuracy constraints and radar-target allocation resource constraints;

[0010] S6: Design a radar-target assignment algorithm to solve the optimization model and obtain the optimal effective time bandwidth allocation result of the networked radar to all targets;

[0011] S7: Feedback the optimal effective time width allocation results of the networked radar to all targets to the radar transmitter, thereby controlling the radar transmission parameters and realizing the allocation of radar resources.

[0012] The present invention is also characterized in that:

[0013] The parameters of the networked phased-control radar system in S1 include the number of radars, the total number of targets, the initial position, speed and acceleration of each target;

[0014] In S1, the target motion model is constructed to obtain the target state, which is expressed as:

[0015]

[0016] In the formula, represents the motion state vector of target q at time k, including the position, velocity and acceleration of target q at time k, represents the motion state vector of target q at time k-1, F q is the state transfer matrix of target q; It means that the target q has zero mean and covariance at time k-1. Gaussian process noise, where for:

[0017]

[0018] Where I3 is the 3×3 unit matrix; T s To track the interval, is the Kronecker product, κ q is the noise intensity of the target q.

[0019] The measurement equation is constructed in S2 to obtain the target measurement, which is expressed as follows:

[0020]

[0021] In the formula, represents the measurement vector of radar i to target q at time k, Represents a nonlinear transformation function containing the angle information and distance information of the target; It means that it has zero mean and covariance is Gaussian process noise, It is expressed as:

[0022]

[0023] Where: blkdiag(·) represents the matrix operation to generate the specified diagonal elements; and are the Cramer-Rao bounds of the distance, azimuth and elevation of target q relative to radar i, respectively.

[0024] S3 uses the SCKF algorithm to estimate and update the target state and target measurement to obtain the target state estimation, which specifically includes the following steps:

[0025] S3.1: Prediction;

[0026] S3.1.1: Decomposition of the target state estimation error covariance matrix:

[0027]

[0028] In the formula, represents the error covariance matrix of the state estimation of radar i to target q at the end of time k-1, represents the error covariance matrix The square root of

[0029] S3.1.2: Calculate volume points and perform nonlinear transformation:

[0030]

[0031] In the formula, It is expressed as the state estimation of radar i to target q at the end of time k-1, For volume point, is the volume point propagated through the state equation; m = 2n x is the total number of volume points; n x For vector The dimension of ξ j To take the matrix The jth column in n x dimensional identity matrix;

[0032] S3.1.3: Compute the target state prediction mean and the square root of the prediction error covariance matrix:

[0033]

[0034] In the formula, represents the state estimation of radar i to target q at time k obtained by estimating at time k-1, Chol(·) represents Cholesky decomposition of the matrix; Tria(·) represents triangulation of the matrix; the weighted central matrix Defined as:

[0035]

[0036] Step 3.2: Update;

[0037] Step 3.2.1: Calculate volume points and perform nonlinear transformation based on the measurement model:

[0038]

[0039] Step 3.2.2: Calculate the measured predicted mean:

[0040]

[0041] In the formula, represents the mean of m measurement vectors;

[0042] Step 3.2.3: Calculate the square root of the measurement covariance matrix:

[0043]

[0044] In the formula, Expressed as the square root of the measurement covariance matrix, the weighted center matrix for:

[0045]

[0046] Step 3.2.4: Calculate the measurement covariance matrix:

[0047]

[0048] In the formula, Expressed as the measurement covariance matrix;

[0049] Step 3.2.5: Calculate the cross-covariance matrix between the target state and the target measurement:

[0050]

[0051] Weighted Center Matrix satisfy:

[0052]

[0053] Step 3.2.6: Calculate the filter gain:

[0054]

[0055] In the formula, Expressed as filter gain;

[0056] Step 3.2.7: The square root coefficients of the posterior state estimate and the estimation error covariance matrix are:

[0057]

[0058] S3 fuses the obtained states, and each radar fuses the state estimation and estimation error covariance of the target using the covariance insertion rule information, which is expressed as:

[0059]

[0060] In the formula, represents the state estimation of the target q after fusion; represents the estimated error covariance matrix of the fused target q, and I represents the total number of radars.

[0061] The PCRLB is derived from the target state estimate and is expressed as:

[0062]

[0063] In the formula, It is expressed as the predicted Bayesian information matrix of target q at time k, It is expressed as the Jacobian matrix of radar i to target q at time k, and Respectively and exist The estimated value at is the state prediction vector of radar i for target q at time k-1, represents the tracking status of radar i on target q at time k; (·) -1 Represents the inverse operation of a matrix;

[0064] The tracking error is expressed as:

[0065]

[0066] In the formula, It is expressed as the tracking error of target q at time k, tr pos [·] means to find the trace of the matrix.

[0067] In S5, the optimization model is constructed by combining the constraints, specifically:

[0068] Target tracking accuracy constraint: That is, the tracking accuracy of the networked phased-control radar for the target q needs to meet the following requirements:

[0069]

[0070] In the formula, is the tracking accuracy constraint, which is directly given by the tracking requirement; Q represents the total number of targets;

[0071] Radar-target allocation resource constraints include:

[0072] To assign variable constraints:

[0073]

[0074] In the formula, the variable is assigned n c Indicates the maximum number of radars;

[0075] Target constraints:

[0076]

[0077] Tracking target constraints:

[0078]

[0079] In the formula, represents the dwell time of radar i on target q, Expressed as the total dwell time of radar i;

[0080] Combined with the above constraints, the optimization model is constructed as follows:

[0081]

[0082] The specific steps of S6 are:

[0083] S61: Relax the {0,1} discrete variable to a continuous variable: Convert formula (30) into the following form:

[0084]

[0085] S62: Solve equation (31) using a convex optimization algorithm to obtain the optimal solution set u k,opt , the optimal solution set u k,opt The optimal effective time width allocation result of the networked radar for all targets is obtained under the premise of only considering the tracking accuracy constraint and not considering the fixed radar transmission effective time width parameters;

[0086] S63: Design a radar-target assignment algorithm to set the upper limit n of the number of radars that exist in the model for the qth target. c and the upper limit n of the number of targets arranged for the i-th radar i,r , first set the empty set u k,optset Assign a set of radar-targets; when the constraint n is satisfied c and n i,r At the same time, select the optimal solution set u in turn k,opt The largest element in the column is set to 1; when an element is set to 1, the corresponding column is set to 0 I×1 , to ensure that at least one target is assigned to a radar; the output result is u that satisfies the constraint k Feasible solution; finally output a series of alternative solutions;

[0087] S64: Compare the objective function values ​​corresponding to the candidate solutions obtained by each radar-target assignment algorithm to obtain the optimal effective time width allocation result of the networked radar for all targets:

[0088]

[0089] In the formula, It is represented as the optimal effective time bandwidth allocation result of the networked radar for all targets, and J is the radar-target assignment set u k,optset The number of alternatives.

[0090] The beneficial effects of the present invention are:

[0091] 1. The present invention is based on a radar resource allocation method that minimizes effective time width, obtains more accurate target state information according to information fusion technology, and uses the predicted PCRLB as a constraint to optimize resource allocation, so that the target parameter estimation at the next moment is more accurate.

[0092] 2. The present invention is based on a radar resource allocation method that minimizes the effective time width. In order to improve the utilization rate of radar resources, on the basis of meeting the tracking accuracy required by the task, resources are reasonably allocated, a multi-radar target joint tracking accuracy resource scheduling model is established, and variable relaxation and constraint relaxation methods are used for solving the problem to improve the solution efficiency of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 It is a flow chart of the radar resource allocation method based on minimizing the effective time width of the present invention;

[0094] Figure 2 It is a closed-loop tracking flow chart of the radar resource allocation method based on minimizing the effective time width of the present invention;

[0095] Figure 3 It is a two-dimensional plane diagram of the target position of the radar in the simulation experiment in the radar resource allocation method based on minimizing the effective time width of the present invention;

[0096] Figure 4 It is the position tracking error of the 25th batch of targets after the simulation experiment optimization in the radar resource allocation method based on minimizing the effective time width of the present invention;

[0097] Figure 5 It is the position tracking error of the 32nd batch of targets after the simulation experiment optimization in the radar resource allocation method based on minimizing the effective time width of the present invention;

[0098] Figure 6 It is the position tracking error of the 75th batch of targets after the simulation experiment optimization in the radar resource allocation method based on minimizing the effective time width of the present invention;

[0099] Figure 7 The present invention is based on the radar resource allocation method of minimizing the effective time width in the simulation experiment to effectively track the number of targets.

[0100] Figure 8 The invention is based on the effective time width consumption of the radar resource allocation method simulation experiment based on minimizing the effective time width. DETAILED DESCRIPTION

[0101] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0102] The present invention is based on a radar resource allocation method that minimizes effective time width, such as Figure 1 As shown, the specific steps include:

[0103] S1: Initialize the system parameters of the networked phased array radar, build the target motion model, and obtain the target state;

[0104] The parameters of the networked phased-control radar system include the number of radars, the total number of targets, the initial position, speed and acceleration of each target;

[0105] Assume that the motion equation of the target q can be described as an approximate constant acceleration motion model, expressed as:

[0106]

[0107] In the formula, represents the motion state vector of target q at time k,

[0108] and Represent the position, velocity and acceleration of the target on the x, y and z axes respectively. Contains the position, velocity and acceleration of the target q at time k. represents the motion state vector of target q at time k-1, F q is the state transfer matrix of target q; It means that the target q has zero mean and covariance at time k-1. Gaussian process noise, where for:

[0109]

[0110] Where I3 is the 3×3 unit matrix; T s To track the interval, is the Kronecker product, κ q is the noise intensity of the target q.

[0111] S2: construct the measurement equation to obtain the target measurement;

[0112] Using the nonlinear measurement model, at time k, the process of radar i obtaining target measurement satisfies:

[0113]

[0114] In the formula, represents the measurement vector of radar i to target q at time k, Represents a nonlinear transformation function containing the angle information and distance information of the target; are the distance, azimuth and elevation of the target relative to the radar respectively; It means that it has zero mean and covariance is Gaussian process noise, It is expressed as:

[0115]

[0116] Where: blkdiag(·) represents the matrix operation to generate the specified diagonal elements; and are the Cramér-Rao lower bound (CRLB) of the distance, azimuth and elevation of the target q relative to the radar i, respectively.

[0117] S3: Use the SCKF algorithm to estimate and update the target state and target measurement, obtain the target state estimate, and perform fusion;

[0118] Since the measurement data of the radar system is obtained in the polar coordinate system, and the Kalman filter is only applicable to linear systems, it is necessary to process the nonlinear transformation. The square-root CKF (SCKF) algorithm introduces orthogonal triangular decomposition based on the CKF. By iteratively calculating the square root of the error covariance matrix, the symmetry and semi-positive definiteness of the covariance matrix are guaranteed, and the filtering accuracy and stability are further improved. Therefore, SCKF is selected to estimate the target state.

[0119] To describe the filtering process of SCKF, first, the Tria(·) operation is defined as follows: Let R be the matrix A T The upper triangular matrix obtained by QR decomposition, the QR decomposition algorithm of matrix A can be expressed as S = Tria (A) = R T , S is a lower triangular matrix. If the state estimation and covariance matrix of target q in radar i at the end of time k-1 are recorded as and The SCKF algorithm process of using radar i to track target q at time k can be summarized as:

[0120] S3.1: Prediction;

[0121] S3.1.1: Decomposition of the target state estimation error covariance matrix:

[0122]

[0123] In the formula, represents the error covariance matrix of the state estimation of radar i to target q at the end of time k-1, represents the error covariance matrix The square root of

[0124] S3.1.2: Calculate volume points and perform nonlinear transformation:

[0125]

[0126] In the formula, It is expressed as the state estimation of radar i to target q at the end of time k-1, For volume point, is the volume point propagated through the state equation; m = 2n x is the total number of volume points; n x For vector The dimension of ξ j To take the matrix The jth column in n x dimensional identity matrix;

[0127] S3.1.3: Compute the target state prediction mean and the square root of the prediction error covariance matrix:

[0128]

[0129] In the formula, represents the state estimation of radar i to target q at time k obtained by estimating at time k-1, Chol(·) represents Cholesky decomposition of the matrix; Tria(·) represents triangulation of the matrix; the weighted central matrix Defined as:

[0130]

[0131] Step 3.2: Update;

[0132] Step 3.2.1: Calculate volume points and perform nonlinear transformation based on the measurement model:

[0133]

[0134] Step 3.2.2: Calculate the measured predicted mean:

[0135]

[0136] In the formula, represents the mean of m measurement vectors;

[0137] Step 3.2.3: Calculate the square root of the measurement covariance matrix:

[0138]

[0139] In the formula, Expressed as the square root of the measurement covariance matrix, the weighted center matrix for:

[0140]

[0141] Step 3.2.4: Calculate the measurement covariance matrix:

[0142]

[0143] In the formula, Expressed as the measurement covariance matrix;

[0144] Step 3.2.5: Calculate the cross-covariance matrix between the target state and the target measurement:

[0145]

[0146] Weighted Center Matrix satisfy:

[0147]

[0148] Step 3.2.6: Calculate the filter gain:

[0149]

[0150] In the formula, Expressed as filter gain;

[0151] Step 3.2.7: The square root coefficients of the posterior state estimate and the estimation error covariance matrix are:

[0152]

[0153] Information fusion based on covariance insertion:

[0154] The method of the present invention adopts a distributed filtering framework, that is, each radar is equipped with a filter. Each radar sends the state estimation and estimation error covariance of the target to the information fusion center, and uses the covariance insertion rule to perform information fusion:

[0155]

[0156] In the formula, represents the state estimation of the target q after fusion; represents the estimated error covariance matrix of the fused target q, and I represents the total number of radars.

[0157] S4: derive PCRLB based on the target state estimate to obtain the tracking accuracy constraint;

[0158] After using SCKF and information fusion technology to obtain more accurate target state information, the predicted PCRLB is used as the optimization criterion to optimize resource allocation, so that the target parameter estimation at the next moment is more accurate, thus forming a closed-loop feedback tracking system. Figure 2 shown.

[0159] Introducing Radar-Target Assignment Variables In the formula, At this time, the predicted PCRLB for the target q is expressed as:

[0160]

[0161] In the formula, It is expressed as the predicted Bayesian information matrix of target q at time k, It is expressed as the Jacobian matrix of radar i to target q at time k, and Respectively and exist The estimated value at is the state prediction vector of radar i for target q at time k-1, represents the tracking status of radar i on target q at time k; (·) -1 Represents the inverse operation of a matrix;

[0162] The predicted CRLB at this time Assign variables to the target The tracking error is expressed as:

[0163]

[0164] In the formula, It is expressed as the tracking error of target q at time k, tr pos [·] means to find the trace of the matrix.

[0165] S5: Construct an optimization model by combining tracking accuracy constraints and radar-target allocation resource constraints;

[0166] Target tracking accuracy constraint: That is, the tracking accuracy of the networked phased-control radar for the target q needs to meet the following requirements:

[0167]

[0168] In the formula, is the tracking accuracy constraint, which is directly given by the tracking requirement; Q represents the total number of targets;

[0169] Radar-target allocation resource constraints include:

[0170] Assignment variable constraint: For a target, at least one radar needs to be assigned to track it at every moment, and there is an upper limit on the number of assignments. That is, for a {0,1} binary assignment variable The following constraints exist:

[0171]

[0172] In the formula, the variable is assigned n c Indicates the maximum number of radars;

[0173] Target constraint: For radar, at least one group of targets must be arranged:

[0174]

[0175] In addition, there is an upper limit on the number of radar tracks, which is determined by the radar's detection waveform dwell time for targets in different distance ranges. That is, the tracking target constraint:

[0176]

[0177] In the formula, represents the dwell time of radar i on target q, Expressed as the total dwell time of radar i;

[0178] Combined with the above constraints, the optimization model is constructed as follows:

[0179]

[0180] S6: Design a radar-target assignment algorithm to solve the optimization model and obtain the optimal effective time bandwidth allocation result of the networked radar to all targets;

[0181] Since the target-radar assignment is a binary {0,1} discrete variable, the model is non-convex. That is, formula (30) can be summarized as a Boolean multidimensional assignment problem, which is a typical NP-hard problem and it is difficult to obtain the optimal solution within an effective time. The method of the present invention proposes a second-order relaxation solution algorithm to obtain a more satisfactory suboptimal solution while meeting the real-time requirements.

[0182] The specific steps include:

[0183] S61: Relax the {0,1} discrete variable to a continuous variable: Convert formula (30) into the following form:

[0184]

[0185] S62: Solve equation (31) using a convex optimization algorithm, such as the interior point method, to obtain the optimal solution set u k,opt , the optimal solution set u k,opt The optimal effective time width allocation result of the networked radar for all targets is obtained under the premise of only considering the tracking accuracy constraint and not considering the fixed radar transmission effective time width parameters;

[0186] Since the optimal solution can be in fractional form. The relaxed optimization model (31) is no longer equivalent to the original problem (30). However, since the feasible domain of equation (30) is contained in equation (31), the optimal objective function value of equation (31) provides a lower bound for the original problem (30). Therefore, the optimal solution of equation (31) can be used as the initial solution set to design a specific assignment scheme. Intuitively, the optimal solution u of equation (31) is k,opt That is, the optimal effective time width allocation result of the networked radar to all targets under the premise of considering the tracking accuracy constraint and not considering the fixed radar transmission effective time width parameters. Based on this, we design a target-radar assignment algorithm.

[0187] S63: Design a radar-target assignment algorithm to set the upper limit n of the number of radars that exist in the model for the qth target. c and the upper limit n of the number of targets arranged for the i-th radar i,r , first set the empty set u k,optset Assign a set of radar-targets; when the constraint n is satisfied c and n i,r At the same time, select the optimal solution set u in turn k,opt The largest element in the column is set to 1; when an element is set to 1, the corresponding column is set to 0 I×1 , to ensure that at least one target is assigned to a radar; the output result is u that satisfies the constraint k Feasible solution; finally output a series of alternative solutions;

[0188] S64: Compare the objective function values ​​corresponding to the candidate solutions obtained by each radar-target assignment algorithm to obtain the optimal effective time width allocation result of the networked radar for all targets:

[0189]

[0190] In the formula, It is represented as the optimal effective time bandwidth allocation result of the networked radar for all targets, and J is the radar-target assignment set u k,optset The number of alternatives.

[0191] S7: Feedback the optimal effective time width allocation results of the networked radar to all targets to the radar transmitter, thereby controlling the radar transmission parameters and realizing the allocation of radar resources.

[0192] Example 1

[0193] This embodiment provides a radar resource allocation method based on minimizing effective time width, which specifically includes the following steps:

[0194] S1: Initialize the system parameters of the networked phased array radar, build the target motion model, and obtain the target state;

[0195] S2: construct the measurement equation to obtain the target measurement;

[0196] S3: Use the SCKF algorithm to estimate and update the target state and target measurement, obtain the target state estimate, and perform fusion;

[0197] S4: derive PCRLB based on the target state estimate to obtain the tracking accuracy constraint;

[0198] S5: construct an optimization model by combining tracking accuracy constraints and radar-target allocation resource constraints;

[0199] S6: Design a radar-target assignment algorithm to solve the optimization model and obtain the optimal effective time bandwidth allocation result of the networked radar to all targets;

[0200] S7: Feedback the optimal effective time width allocation results of the networked radar to all targets to the radar transmitter, thereby controlling the radar transmission parameters and realizing the allocation of radar resources.

[0201] Example 2

[0202] This embodiment provides a radar resource allocation method based on minimizing effective time width, which is characterized by specifically comprising the following steps:

[0203] S1: Initialize the system parameters of the networked phased array radar, build the target motion model, and obtain the target state;

[0204] The number of networked radars is set to I = 5, the total number of targets is set to Q = 75, and the initial position, velocity, and acceleration of each batch of targets are randomly generated.

[0205] The constructed target motion model is expressed as:

[0206]

[0207] In the formula, represents the motion state vector of target q at time k, including the position, velocity and acceleration of target q at time k, represents the motion state vector of target q at time k-1, F q is the state transfer matrix of target q; It means that the target q has zero mean and covariance at time k-1. Gaussian process noise, where for:

[0208]

[0209] Where I3 is the 3×3 unit matrix; T s To track the interval, is the Kronecker product, κ q is the noise intensity of the target q.

[0210] S2: construct the measurement equation to obtain the target measurement;

[0211] The constructed measurement equation is expressed as follows:

[0212]

[0213] In the formula, represents the measurement vector of radar i to target q at time k, Represents a nonlinear transformation function containing the angle information and distance information of the target; It means that it has zero mean and covariance is Gaussian process noise, It is expressed as:

[0214]

[0215] Where: blkdiag(·) represents the matrix operation to generate the specified diagonal elements; and are the Cramer-Rao bounds of the distance, azimuth and elevation of target q relative to radar i, respectively.

[0216] S3: Use the SCKF algorithm to estimate and update the target state and target measurement, obtain the target state estimate, and perform fusion;

[0217] S3.1: Prediction;

[0218] S3.1.1: Decomposition of the target state estimation error covariance matrix:

[0219]

[0220] In the formula, represents the error covariance matrix of the state estimation of radar i to target q at the end of time k-1, represents the error covariance matrix The square root of

[0221] S3.1.2: Calculate volume points and perform nonlinear transformation:

[0222]

[0223] In the formula, It is expressed as the state estimation of radar i to target q at the end of time k-1, For volume point, is the volume point propagated through the state equation; m = 2n x is the total number of volume points; n x For vector The dimension of ξ j To take the matrix The jth column in n x dimensional identity matrix;

[0224] S3.1.3: Compute the target state prediction mean and the square root of the prediction error covariance matrix:

[0225]

[0226] In the formula, represents the state estimation of radar i to target q at time k obtained by estimating at time k-1, Chol(·) represents Cholesky decomposition of the matrix; Tria(·) represents triangulation of the matrix; the weighted central matrix Defined as:

[0227]

[0228] Step 3.2: Update;

[0229] Step 3.2.1: Calculate volume points and perform nonlinear transformation based on the measurement model:

[0230]

[0231] Step 3.2.2: Calculate the measured predicted mean:

[0232]

[0233] In the formula, represents the mean of m measurement vectors;

[0234] Step 3.2.3: Calculate the square root of the measurement covariance matrix:

[0235]

[0236] In the formula, Expressed as the square root of the measurement covariance matrix, the weighted center matrix for:

[0237]

[0238] Step 3.2.4: Calculate the measurement covariance matrix:

[0239]

[0240] In the formula, Expressed as the measurement covariance matrix;

[0241] Step 3.2.5: Calculate the cross-covariance matrix between the target state and the target measurement:

[0242]

[0243] Weighted Center Matrix satisfy:

[0244]

[0245] Step 3.2.6: Calculate the filter gain:

[0246]

[0247] In the formula, Expressed as filter gain;

[0248] Step 3.2.7: The square root coefficients of the posterior state estimate and the estimation error covariance matrix are:

[0249]

[0250] Information fusion is the process of fusing the state estimation and estimation error covariance of each radar for the target using the covariance insertion rule, which can be expressed as:

[0251]

[0252] In the formula, represents the state estimation of the target q after fusion; represents the estimated error covariance matrix of the fused target q, and I represents the total number of radars.

[0253] S4: derive PCRLB based on the target state estimate to obtain the tracking accuracy constraint;

[0254] The PCRLB is derived from the target state estimate, denoted as, which is expressed as:

[0255]

[0256] In the formula, It is expressed as the predicted Bayesian information matrix of target q at time k, It is expressed as the Jacobian matrix of radar i to target q at time k, and Respectively and exist The estimated value at is the state prediction vector of radar i for target q at time k-1, represents the tracking status of radar i on target q at time k; (·) -1 Represents the inverse operation of a matrix;

[0257] The tracking error is expressed as:

[0258]

[0259] In the formula, It is expressed as the tracking error of target q at time k, tr pos [·] means to find the trace of the matrix.

[0260] S5: Construct an optimization model by combining tracking accuracy constraints and radar-target allocation resource constraints;

[0261] Target tracking accuracy constraint: That is, the tracking accuracy of the networked phased-control radar for the target q needs to meet the following requirements:

[0262]

[0263] In the formula, is the tracking accuracy constraint, which is directly given by the tracking requirement; Q represents the total number of targets;

[0264] Radar-target allocation resource constraints include:

[0265] To assign variable constraints:

[0266]

[0267] In the formula, the variable is assigned n c Indicates the maximum number of radars;

[0268] Target constraints:

[0269]

[0270] Tracking target constraints:

[0271]

[0272] In the formula, represents the dwell time of radar i on target q, Expressed as the total dwell time of radar i;

[0273] Combined with the above constraints, the optimization model is constructed as follows:

[0274]

[0275] S6: Design a radar-target assignment algorithm to solve the optimization model and obtain the optimal effective time bandwidth allocation result of the networked radar to all targets;

[0276] S61: Relax the {0,1} discrete variable to a continuous variable: Convert formula (30) into the following form:

[0277]

[0278] S62: Solve equation (31) using a convex optimization algorithm to obtain the optimal solution set u k,opt , the optimal solution set u k,opt The optimal effective time width allocation result of the networked radar for all targets is obtained under the premise of only considering the tracking accuracy constraint and not considering the fixed radar transmission effective time width parameters;

[0279] S63: Design a radar-target assignment algorithm to set the upper limit n of the number of radars that exist in the model for the qth target. c and the upper limit n of the number of targets arranged for the i-th radar i,r , first set the empty set u k,optset Assign a set of radar-targets; when the constraint n is satisfied c and n i,r At the same time, select the optimal solution set u in turn k,opt The largest element in the column is set to 1; when an element is set to 1, the corresponding column is set to 0 I×1 , to ensure that at least one target is assigned to a radar; the output result is u that satisfies the constraint k Feasible solution; finally output a series of alternative solutions;

[0280] S64: Compare the objective function values ​​corresponding to the candidate solutions obtained by each radar-target assignment algorithm to obtain the optimal effective time width allocation result of the networked radar for all targets:

[0281]

[0282] In the formula, It is represented as the optimal effective time bandwidth allocation result of the networked radar for all targets, and J is the radar-target assignment set u k,optset The number of alternatives.

[0283] S7: Feedback the optimal effective time width allocation results of the networked radar to all targets to the radar transmitter, thereby controlling the radar transmission parameters and realizing the allocation of radar resources.

[0284] Simulation experiment:

[0285] Set the number of networked radars I = 5, the total number of targets Q = 75, the initial position, velocity, and acceleration of each batch of targets are randomly generated, and the motion model obeys the constant acceleration motion model. The target tracking interval is T s = 1s, each simulation lasts K = 85 frames, the first 4 frames are used for tracking initialization, and the resources are assumed to be evenly distributed during this period. The effective dwell time available to each radar is equal, that is, for satisfy Assume that each radar has a target dwell time at different distances is a fixed value, as shown in Table 1; the unit of each residence time is That is, normalization. For the proposed algorithm, the fixed irradiation time for a batch of targets is set to 10 frames. Figure 3 A two-dimensional plane diagram of the radar target position is given, where the black line represents the target trajectory, and the target flies northeast by default. Radar 3 is an X-band radar, and the other radars are P- and L-band radars.

[0286] Table 1 Radar dwell time usage for targets at different distances

[0287]

[0288]

[0289] In addition to the PCRLB of the target location, the root mean square error (RMSE) of the target location estimation is introduced for comparison, which is defined as:

[0290]

[0291] In the formula, is the posterior estimate of the target state in the jth Monte Carlo experiment; NMC=50 is the number of trials.

[0292] Figure 4-Figure 8 They are the position tracking errors of each batch of targets after optimization. Due to the large number of targets, only the position RMSE and corresponding PCRLB of 5 batches of typical targets are given here. As can be seen from the figure, the RMSE and PCRLB of the target are very close, which indirectly proves the correctness of using the predicted PCRLB as the optimization indicator.

[0293] Figure 7 The number of effective tracking targets is compared between the present invention and the randomly assigned one. Figure 8This is the total effective bandwidth consumption comparison between the present invention and the random allocation. Here, if the PCRLB of a batch of targets is not greater than the tracking accuracy constraint, then the batch of targets is an effective tracking target. Figure 7 and Figure 8 It can be seen from the comparison that the method of the present invention can more effectively utilize resources to track targets and improve the target tracking capacity under the condition of smaller effective time width. It is worth noting that the total time width consumption of the networked radar does not exceed 2, and the PCRLB of all 75 batches of targets meets the preset threshold constraints.

[0294] Based on the distributed phased array radar system, the method of the present invention proposes a networked radar target assignment algorithm based on minimizing the effective time width. The algorithm obtains relatively accurate target state information based on information fusion technology, and uses the predicted PCRLB as the optimization standard to optimize the resource allocation model, so that the target parameter estimation at the next moment is more accurate. In order to improve the utilization rate of radar resources, on the basis of meeting the target tracking accuracy, resources are reasonably allocated, and a multi-radar target joint tracking accuracy resource scheduling model is established. In order to better solve the model, the first step is to use the variable relaxation method to convert the non-convex model into a convex optimization model that can be solved by the interior point method, and obtain the suboptimal solution of the original problem. The radar target is assigned based on this as the initial solution set, and the optimal solution of radar resource allocation is obtained to guide the networked radar to track and estimate the target at the next moment. The simulation results show that the method in this paper maximizes the utilization rate of radar resources and improves the tracking capacity under the constraints of meeting the equipment performance and tracking accuracy.

Claims

1. A radar resource allocation method based on minimizing effective time width, characterized in that: The specific steps include: S1: Initialize the system parameters of the networked phased array radar, build the target motion model, and obtain the target state; S2: construct the measurement equation to obtain the target measurement; S3: Use the SCKF algorithm to estimate and update the target state and target measurement, obtain the target state estimate, and perform fusion; S4: derive PCRLB based on the target state estimate to obtain the tracking accuracy constraint; S5: construct an optimization model by combining tracking accuracy constraints and radar-target allocation resource constraints; S6: Design a radar-target assignment algorithm to solve the optimization model and obtain the optimal effective time bandwidth allocation result of the networked radar to all targets; S7: Feedback the optimal effective time width allocation results of the networked radar to all targets to the radar transmitter, thereby controlling the radar transmission parameters and realizing the allocation of radar resources.

2. The radar resource allocation method based on minimizing effective time width according to claim 1, characterized in that: The parameters of the networked phased-control radar system in S1 include the number of radars, the total number of targets, the initial position, speed and acceleration of each target; In S1, the target motion model is constructed to obtain the target state, which is expressed as: In the formula, represents the motion state vector of target q at time k, including the position, velocity and acceleration of target q at time k, represents the motion state vector of target q at time k-1, F q is the state transfer matrix of target q; It means that the target q has zero mean and covariance at time k-1. Gaussian process noise, where for: Where I3 is a 3×3 unit matrix; T s To track the interval, is the Kronecker product, κ q is the noise intensity of the target q.

3. The radar resource allocation method based on minimizing effective time width according to claim 2, characterized in that: The measurement equation is constructed in S2 to obtain the target measurement, which is expressed as follows: In the formula, represents the measurement vector of radar i to target q at time k, Represents a nonlinear transformation function containing the angle information and distance information of the target; It means that it has zero mean and covariance is Gaussian process noise, It is expressed as: Where: blkdiag(·) represents the matrix operation to generate the specified diagonal elements; and are the Cramer-Rao bounds of the distance, azimuth and elevation of target q relative to radar i, respectively.

4. The radar resource allocation method based on minimizing effective time width according to claim 3 is characterized in that: S3 uses the SCKF algorithm to estimate and update the target state and target measurement to obtain the target state estimation, which specifically includes the following steps: S3.1: Prediction; S3.1.1: Decomposition of the target state estimation error covariance matrix: In the formula, represents the error covariance matrix of the state estimation of radar i to target q at the end of time k-1, represents the error covariance matrix The square root of S3.1.2: Calculate volume points and perform nonlinear transformation: In the formula, It is expressed as the state estimation of radar i to target q at the end of time k-1, For volume point, is the volume point propagated through the state equation; m = 2n x is the total number of volume points; n x For vector The dimension of ξ j To take the matrix The jth column in n x dimensional identity matrix; S3.1.3: Compute the target state prediction mean and the square root of the prediction error covariance matrix: In the formula, represents the state estimation of radar i to target q at time k obtained by estimating at time k-1, Chol(·) represents Cholesky decomposition of the matrix; Tria(·) represents triangulation of the matrix; the weighted central matrix Defined as: Step 3.2: Update; Step 3.2.1: Calculate volume points and perform nonlinear transformation based on the measurement model: Step 3.2.2: Calculate the measured predicted mean: In the formula, represents the mean of m measurement vectors; Step 3.2.3: Calculate the square root of the measurement covariance matrix: In the formula, Expressed as the square root of the measurement covariance matrix, the weighted center matrix for: Step 3.2.4: Calculate the measurement covariance matrix: In the formula, Expressed as the measurement covariance matrix; Step 3.2.5: Calculate the cross-covariance matrix between the target state and the target measurement: Weighted Center Matrix satisfy: Step 3.2.6: Calculate the filter gain: In the formula, Expressed as filter gain; Step 3.2.7: The square root coefficients of the posterior state estimate and the estimation error covariance matrix are:

5. The radar resource allocation method based on minimizing effective time width according to claim 4, characterized in that: S3 fuses the obtained states, and each radar fuses the state estimation and estimation error covariance of the target using the covariance insertion rule information, which is expressed as: In the formula, represents the state estimation of the target q after fusion; represents the estimated error covariance matrix of the fused target q, and I represents the total number of radars.

6. The radar resource allocation method based on minimizing effective time width according to claim 5, characterized in that: The PCRLB is derived from the target state estimate and is expressed as: In the formula, It is expressed as the predicted Bayesian information matrix of target q at time k, It is expressed as the Jacobian matrix of radar i to target q at time k, and Respectively and exist The estimated value at is the state prediction vector of radar i for target q at time k-1, represents the tracking status of radar i on target q at time k; (·) -1 Represents the inverse operation of a matrix; The tracking error is expressed as: In the formula, It is expressed as the tracking error of target q at time k, tr pos [·] means to find the trace of the matrix.

7. The radar resource allocation method based on minimizing effective time width according to claim 6, characterized in that: In S5, the optimization model is constructed by combining the constraints, specifically: Target tracking accuracy constraint: That is, the tracking accuracy of the networked phased-control radar for the target q needs to meet the following requirements: In the formula, is the tracking accuracy constraint, which is directly given by the tracking requirement; Q represents the total number of targets; Radar-target allocation resource constraints include: To assign variable constraints: In the formula, the variable is assigned n c Indicates the maximum number of radars; Target constraints: Tracking target constraints: In the formula, represents the dwell time of radar i on target q, Expressed as the total dwell time of radar i; Combined with the above constraints, the optimization model is constructed as follows:

8. The radar resource allocation method based on minimizing effective time width according to claim 7, characterized in that: The specific steps of S6 are: S61: Relax the {0,1} discrete variable to a continuous variable: Convert formula (30) into the following form: S62: Solve equation (31) using a convex optimization algorithm to obtain the optimal solution set u k,opt , the optimal solution set u k,opt The optimal effective time width allocation result of the networked radar for all targets is obtained under the premise of only considering the tracking accuracy constraint and not considering the fixed radar transmission effective time width parameters; S63: Design a radar-target assignment algorithm to set the upper limit n of the number of radars that exist in the model for the qth target. c and the upper limit n of the number of targets arranged for the i-th radar i,r , first set the empty set u k,optset Assign a set of radar-targets; when the constraint n is satisfied c and n i,r At the same time, select the optimal solution set u in turn k,opt The largest element in the column is set to 1; when an element is set to 1, the corresponding column is set to 0 I×1 , to ensure that at least one target is assigned to a radar; the output result is u that satisfies the constraint k Feasible solution; finally output a series of alternative solutions; S64: Compare the objective function values ​​corresponding to the candidate solutions obtained by each radar-target assignment algorithm to obtain the optimal effective time width allocation result of the networked radar for all targets: In the formula, It is represented as the optimal effective time bandwidth allocation result of the networked radar to all targets, and J is the radar-target assignment set u k,optset The number of alternatives.

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