Joint Beam-Power-Bandwidth Allocation Method for Multi-Target Tracking in Centralized MIMO Radar

Abstract

The present invention discloses a beam-power-bandwidth joint allocation method in centralized MIMO radar multi-target tracking. Aiming at the multi-target tracking task, the problem of combining beam selection with power and bandwidth allocation in a C-MIMO radar system is analyzed; by using a closed-loop cognitive tracking framework, first, an improved particle filter is used to obtain target state estimation information; then, the PC-CRLB is derived, which provides an accurate lower bound for the target state estimation error and is expressed as an optimal function; finally, a three-step solution method is adopted to solve the non-convex optimization problem; a large number of simulation results prove the effectiveness and robustness of the method.

Description

Technical Field

[0001] The present invention relates to the technical field of radar target tracking, and particularly to a beam-power-bandwidth joint allocation method in centralized MIMO radar multi-target tracking. Background Art

[0002] Centralized multiple-input multiple-output (C-MIMO) radar is a new type of radar system proposed in recent years, which has many advantages compared with standard phased array radars, such as simultaneous multi-beam (SM) mode, waveform diversity, structure diversity, etc. The C-MIMO radar system adopts the SM operating mode and can transmit multiple uncorrelated or orthogonal detection signals. In addition, due to the high degree of freedom in waveform design of C-MIMO radar, multiple tasks can be performed simultaneously, such as surveillance, multi-target tracking (MTT). However, in practical applications, the resources of the radar system are often limited. Therefore, in order to achieve better performance and give full play to the advantages of the C-MIMO radar system, it is necessary to effectively manage the limited resources.

[0003] Existing research on resource allocation problems based on C-MIMO radar systems mostly focuses on resource allocation problems in parameter estimation. Technically, these works can be divided into three categories: (1) Transmit parameter allocation, such as transmit power, effective bandwidth, effective time width; (2) System configuration optimization, such as the selection and arrangement of transmit and receive array elements; (3) The integration of the above two. Reference [1] also particularly focuses on introducing the power allocation problem of a single-station C-MIMO radar system using the SM operating mode, which provides a new solution to solve the resource allocation problem in the MTT scenario by transforming the MTT problem into a series of single-target tracking (STT) problems. In order to improve the speed and accuracy of target tracking, a joint power and time width allocation method was proposed in reference [3]. Since antenna configuration plays an important role in C-MIMO radar systems, an antenna selection method and an antenna arrangement method were proposed in references [2] and [4] respectively. A joint beam and power allocation scheme for a monostatic C-MIMO radar system was proposed in reference [5], and extended applications of centralized tracking and distributed tracking in C-MIMO radar network systems were proposed in references [6] and [7] respectively.

[0004] By allocating discrete bandwidth to each transmit beam, orthogonal beams can be achieved, and their performance is superior to other orthogonal beamforming techniques. In addition, in a real hostile environment, a radar needs to simultaneously perform multiple tasks such as communication, surveillance, and MTT, and each task requires a certain amount of bandwidth resources. Therefore, in order to meet the low intercept requirements of the C-MIMO radar system, the spectrum resources must be effectively managed. In addition, bandwidth allocation also has a good effect on improving the target tracking accuracy of distributed MIMO radar in the environment of reference [8]. In practice, there are three limited operating resources in the SM operating mode of the MTT task in the C-MIMO radar system: (1) the maximum number of beams; (2) the transmit power of multiple beams; (3) the discrete effective bandwidth of multiple beams. However, there is no research on the beam-power-bandwidth joint allocation problem for C-MIMO radar in the existing technology.

[0005] In addition, although the Cramér-Rao lower bound (CRLB) provides a lower bound for any unbiased estimate and has been used as a criterion to minimize the total system resources or state estimation error in many previous works, since the CRLB cannot be predicted, it is not suitable for the target tracking scenario. The posterior Cramér-Rao lower bound (PCRLB) has predictive ability and is not affected by the adopted filtering algorithm. Therefore, in many works, the PCRLB is used as the optimal criterion to achieve better tracking performance. However, the standard PCRLB is derived from the expectation of the target state and the measurement at the current time and does not fully utilize the measurement information, which does not meet the requirements of dynamic and real-time resource allocation. Summary of the Invention

[0006] In view of the above existing problems, based on the above research and combined with the cognitive tracking cycle, for the cognitive MTT in the C-MIMO radar system, the present invention proposes a beam-power-bandwidth joint allocation method for multi-target tracking in a centralized MIMO radar. The main technical idea of this method is: using the feedback information in the cognitive tracking cycle to achieve the optimal selection of beams, and then allocating the transmit power and bandwidth to each selected beam. Specifically, first, using a tracking filter, the target state estimate at the current time can be obtained. Then, the PC-CRLB is calculated using the estimation information and the measurement information and used as the optimal criterion to guide the next resource allocation. Finally, by forming a closed-loop cognitive tracking system, an adaptive resource allocation scheme is established by adaptively allocating power and bandwidth to the beams according to the PC-CRLB.

[0007] In order to achieve the above object, the technical solutions adopted by the present invention are as follows:

[0008] A beam-power-bandwidth joint allocation method for multi-target tracking in a centralized MIMO radar, characterized by including the following steps:

[0009] Step 1: Construct a system model of the centralized MIMO radar, where the system model includes a motion model, a signal model, and a measurement model;

[0010] Step 2: Use an anti-robust square root cubature particle filter to obtain target state estimation information;

[0011] Step 3: Calculate the PC-CRLB based on the target state estimation information and the measurement information obtained from the measurement model, and use this PC-CRLB as a benchmark for guiding the next resource allocation;

[0012] Step 4: According to the PC-CRLB, adaptively allocate the power and bandwidth of the beam, and establish a beam-power-bandwidth joint allocation optimization model;

[0013] Step 5: Solve the beam-power-bandwidth joint allocation optimization model and feedback the result to the centralized MIMO radar transmitter to obtain an adaptive resource allocation scheme;

[0014] Step 6: According to the adaptive resource allocation scheme, optimize and allocate the beam, power, and bandwidth resources limited by the system performance to each target, and estimate and track the target motion state at the next moment.

[0015] Furthermore, the specific steps of Step 2 include:

[0016] Step 21: Initialize random samples and obtain N particles through sampling Assign the same weight to each particle

[0017] Step 22: At time k, substitute the state and covariance set of each particle into the SCKF filtering algorithm, so as to obtain the predicted state of each particle at time k + 1 and its covariance After adding the measurement data, calculate the innovation covariance

[0018] Step 23: Calculate the residual of each particle at time k + 1 through Equation (13):

[0019]

[0020] Step 24: Calculate the adaptive factor:

[0021] Calculate the adaptive factor α:

[0022] From the particle residuals at time k + 1 and the innovation covariance The measurement model error discrimination statistic can be calculated

[0023]

[0024] To reduce the computational amount and improve the filtering rate, a two-segment functional form is selected to construct the adaptive factor:

[0025]

[0026]

[0027] where c is an empirical constant, usually taken as 1.0 < c < 2.5;

[0028] Step 25: Particle set update:

[0029] Substituting the above parameters into the SCKF framework, the following can be further obtained:

[0030]

[0031]

[0032]

[0033]

[0034] Step 26: Weight calculation and normalization:

[0035] Calculate the weights of each particle at time k + 1:

[0036]

[0037] Then normalize the weights of each particle:

[0038]

[0039] Step 27: Particle set resampling:

[0040] Judge whether the particle set meets the preset resampling condition. If it meets, update the particle set and its particle weights according to the resampling method to and If it does not meet, directly go to the next step;

[0041] Step 28: State update:

[0042] Based on the above calculations, the state and variance of the target at time k + 1 are estimated as follows:

[0043]

[0044] According to the obtained estimated value, sample according to and return the sampling result to step 2.

[0045] Furthermore, step 4 specifically includes the following content:

[0046] Step 41: After inverting the Bayesian matrix regarding the state x of the moving target k+1,q , the corresponding PC-CRLB matrix is obtained, and its definition is:

[0047] J(x k+1,q |z 1:k,q ) = J P (x k+1,q |z 1:k,q ) + J Z (x k+1,q |z 1:k,q ) (44)

[0048] where J P (x k+1,q |z 1:k,q ) and J Z (x k+1,q |z 1:k,q ) represent the prior information and data information respectively, and can be expressed as:

[0049]

[0050] Step 42: To improve the multi-target tracking accuracy, define the power allocation variable and bandwidth allocation variable, combine these two variables with the beam selection result u k to establish three vectors:

[0051]

[0052] Substitute the power and bandwidth allocation variables into Equation (44), and Equation (44) is rewritten as:

[0053]

[0054] Step 43: Take the tracking performance corresponding to the target with the worst tracking accuracy among all targets as the objective function:

[0055]

[0056] In the formula, tr(·) is the matrix tracking operator;

[0057] Step 44: According to the cost function, construct the optimization model as:

[0058]

[0059] where P total and β total represent the maximum power and bandwidth that the C-MIMO radar system can provide for each tracking sample; M represents the maximum number of simultaneously orthogonal beams, which is determined by the degrees of freedom in the system waveform design.

[0060] Furthermore, the beam-power-bandwidth joint allocation optimization model is solved based on Lemma 1. For the number of transmit beams m k and 1 ≤ m k ≤ M, there is Lemma 1:

[0061] Lemma 1: For a given situation, regardless of the power allocation and bandwidth allocation results, the optimal result of beam selection is uniquely determined.

[0062] Furthermore, the steps for solving the beam-power-bandwidth joint allocation optimization model in step 5 are as follows:

[0063] Step 51: Calculate the optimal number of beams m for target tracking k and according to Lemma 1, evenly allocate the power and bandwidth as and Transform equation (49) into:

[0064]

[0065] Step 52: Solve equation (51) to obtain the transmit beam allocation scheme Then substitute into equation (49), transform the original optimization problem into a joint allocation problem of power and bandwidth, and the optimal solutions for power and bandwidth allocation are:

[0066]

[0067] Step 53: Use a three-step solution method based on the CMA method to solve equation (52) to obtain the optimized power allocation result and the optimized bandwidth allocation result.

[0068] Furthermore, the three-step solution method based on the CMA method in step 53 includes the following steps,

[0069] Step 531: Set the initial value For a determined Combined with the SDP algorithm, transform equation (52) into equation (53) and use the Zoutendijk feasible direction method to solve equation (53) to obtain the transient power allocation result where equation (53) is:

[0070]

[0071] Wherein, M k,q is an auxiliary matrix that satisfies

[0072] Step 532: Substitute into Equation (52) to establish a convex optimization problem for solving transient bandwidth allocation:

[0073]

[0074] Wherein, both λ1 and λ2 are dynamic parameters;

[0075] Combined with the SDP algorithm, transform Equation (54) into Equation (55) and use the Zoutendijk feasible direction method to solve the transient bandwidth allocation result Where Equation (55) is:

[0076]

[0077] Wherein, N k,q is an auxiliary matrix that satisfies

[0078] Step 533: Return to Step 1 until the difference between the two tracking precisions is less than the preset threshold ε, then the calculation terminates, and output the final power optimization allocation result and the final bandwidth optimization allocation result

[0079] The beneficial effects of the present invention are as follows:

[0080] First, under the condition of limited system resources, the method of the present invention establishes an optimization model that combines PC-CRLB-based MTT joint beam selection with power and bandwidth allocation. An improved particle filter is used to obtain the target state estimation, and the corresponding PC-CRLB can be calculated, which has stronger robustness and accuracy than the standard PCRLB. Therefore, by minimizing the PC-CRLB of the target with the worst tracking effect, the beam, power, and bandwidth resources limited by the system performance can be optimally allocated to each target.

[0081] Second, combined with semi-definite programming (SDP), convex relaxation technology, and cyclic minimizer, an effective method for solving non-convex optimization problems is given. First, a local search method is used to obtain the optimal beam allocation result when the maximum number of beams M is known. After obtaining the beam selection result, for the non-convex problem of optimal power and bandwidth allocation for each given beam, by introducing convex relaxation technology and cyclic minimization method, the non-convex problem is transformed into a series of SDP problems and solved by the Zoutendijk feasible direction method. Description of the Drawings

[0082] Figure 1 This is the closed-loop feedback mechanism under the joint beam-power-bandwidth allocation proposed by the present invention;

[0083] Figure 2 This is a schematic diagram of simultaneous multi-beams in the SM working mode;

[0084] Figure 3 This is a schematic diagram of the working process of the beam selection mechanism;

[0085] Figure 4 This is the relationship between the radar position and the target movement trajectory;

[0086] Figure 5 This is the dynamic RCS model;

[0087] Figure 6 This is the comparison result of PC-CRLB under the distance influence scenario;

[0088] Figure 7 This is the comparison result of RMSE under the distance influence scenario;

[0089] Figure 8 This is the beam allocation result under the distance influence scenario;

[0090] Figure 9 This is the power allocation result under the distance influence scenario;

[0091] Figure 10 This is the bandwidth allocation result under the distance influence scenario;

[0092] Figure 11 This is the comparison result of PC-CRLB under the RCS influence scenario;

[0093] Figure 12 This is the comparison result of RMSE under the RCS influence scenario;

[0094] Figure 13 This is the beam allocation result under the RCS influence scenario;

[0095] Figure 14a This is the power allocation result under the RCS influence scenario, Figure 14b This is the bandwidth allocation result under the RCS influence scenario;

[0096] Figure 15 This is the average CPU running time of the proposed method. Specific implementation manner

[0097] In order to enable those of ordinary skill in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below in conjunction with the drawings and embodiments.

[0098] I. Construct a system model

[0099] Assume that the C-MIMO radar system is located in a two-dimensional space, and the geometric center of the radar is located at (x0, y0). In addition, there are widely distributed point targets in the radar detection area. The radar system adopts the SM operating mode and can generate multiple orthogonal transmit beams simultaneously for tracking different targets. In this way, the multi-target tracking problem is technically transformed into a series of single-target tracking problems. To simplify the complexity of the model, it is considered that there is no sensor error in the system. Therefore, the gain-phase error and mutual coupling are not considered. The schematic diagram of simultaneous multi-beams in the SM operating mode is as shown in Figure 2 Figure

[0100] (1) Signal model

[0101] Consider that the C-MIMO radar sends a signal to target q at time k. Due to the characteristics of orthogonal signals, the transmitted signal satisfies:

[0102]

[0103]

[0104]

[0105] where P k,q is the transmit power, and (·) H is the conjugate transpose operator;

[0106] In addition, assume that all transmitted signals are narrowband, and the effective bandwidth is:

[0107]

[0108] The effective time width is:

[0109]

[0110] After the received signal is processed by the matched filter, the baseband received signal of target q at time k is:

[0111]

[0112] In the formula: a k,q is the signal strength attenuation caused by the path loss effect, and the attenuation is inversely proportional to the square of the distance from the radar to target q at time k; h k,q is the target scattering cross-section area (RCS). For simplicity, it is modeled as a complex known variable; E k,q represents the normalized complex envelope of the transmitted signal to target q, where τ k,q , respectively represent the time delay and Doppler frequency; n k,q (t) represents a zero-mean, complex Gaussian noise, satisfying

[0113] (2) Motion model

[0114] Assume that Q independent targets move in a two-dimensional space. For simplicity, each target follows a constant acceleration (CA) model, then:

[0115] x k,q = F q x k-1,q + w k-1,q (6)

[0117] In the formula, is the motion state of target q at time k, (·) T is the matrix transpose operator; F q represents the state transition matrix of the CA model; w k-1,q represents the uncorrelated process noise sequence that conforms to, and satisfies w k-1,q (t) ~ N(0, Q k-1,q );

[0118] And the F q and Q k-1,q in the formula are:

[0119]

[0120]

[0121] In the formula, T s is the sampling time interval, I2 is the second-order identity matrix, m q is the process noise intensity of target q, and the mathematical symbol is the Kronecker product operator.

[0122] (3) Observation model

[0123] There is a large amount of target information in the radar received signal. The target information can be extracted by using a suitable signal processing method. In the present invention, we mainly focus on the range, Doppler frequency, and azimuth angle. At this time, combining binary variables, the non-linear measurement model is described as:

[0124]

[0125] In the formula, u k,q is the beam selection result of target q at time k, h(x k,q ) is the observation equation of target q at time k, v k,q h(·) is the non-linear measurement matrix:

[0126]

[0127] where λ is the carrier wavelength of the transmitted signal; R k,q , f k,q and θ k,q represent the radial distance between the target and the radar, the target Doppler frequency, and the target azimuth angle, respectively;

[0128] v in Equation (9) k,q is zero-mean Gaussian noise, satisfying v k,q ~N(0, R k,q ), and the covariance matrix of the Gaussian distribution is:

[0129]

[0130] where diag(·) is the diagonal matrix operator, representing the measurement error variances of range, Doppler frequency, and azimuth angle, respectively;

[0131] The CRLB of each diagonal element in Equation (11) can be expressed as:

[0132]

[0133] where α k,q represents the attenuation coefficient, P k,q represents the transmitted power, β k,q and T k,q represent the effective bandwidth and the effective time width, respectively, h k,q represents the complex number of the target radar cross section (RCS), and B w represents the width of the receiving beam; thus, a beam selection mechanism is established, and its working process is as shown in Appendix Figure 3 .

[0134] II. Construction of the resource optimization model

[0135] 1. Tracking filtering algorithm

[0136] Most of the existing Kalman series filtering algorithms are for Gaussian noise scenarios, while in the actual operation of radar, the noise often has non-Gaussian characteristics such as flicker noise and interference noise. Therefore, the Kalman series filtering algorithms based on Gaussian assumptions cannot well guide the resource allocation in the target tracking process. Although SPF breaks through the limitations of traditional Kalman filtering and can be applied to non-Gaussian noise scenarios, the way it obtains the importance density function is too simple, which will lead to particle degradation and even divergence.

[0137] In view of the above situation, the present invention adopts a robust square-root cubature particle filter (RSCPF). First, taking advantage of the simple structure and high precision of the SCKF, it can provide a basis for the selection of the importance function in the PF framework, thus constituting the square-root cubature particle filter (SCPF). Second, by using the characteristics of the robust adaptive filter (RAF) which can reduce the influence of model errors and improve the fault tolerance and filtering accuracy of the filtering algorithm, it is applied to the SCPF to improve the robustness and adaptive ability of the filtering algorithm. The RSCPF algorithm process is as follows:

[0138] Step 1: Initialize random samples;

[0139] Based on the prior information of the state mean and variance at the initial moment, establish the target state distribution function, and obtain N particles through sampling Assign the same weight to each particle

[0140] Step 2: Update the particle state and covariance matrix by SCKF;

[0141] At time k, collect the states and their covariances of each particle Substitute them into the SCKF filtering algorithm to obtain the predicted states of each particle at time k + 1 and their covariances After adding the measurement data, calculate the innovation covariance

[0142] Step 3: Calculate the residuals of each particle at time k + 1 through Equation (13):

[0143]

[0144] Step 4: Calculate the adaptive factor α:

[0145] From the particle residuals at time k + 1 and the innovation covariance calculate the model error discrimination statistic

[0146]

[0147] To reduce the computational load and improve the filtering rate, a two-segment functional form is selected to construct the adaptive factor:

[0148]

[0149] where c is an empirical constant, usually taken as 1.0 < c < 2.5;

[0150] Step 5: Particle set update:

[0151] Substitute the above parameters α, R k+1 into the SCKF framework, and further obtain:

[0152]

[0153]

[0154]

[0155]

[0156] It can be seen from Equation (19) that due to the introduction of the adaptive factor when the measurement model has abnormal disturbances, the adaptive factor becomes smaller, and the influence brought by the abnormal disturbances is weakened by reducing the state error covariance. Then the particle set at time k+1 can be updated according to the obtained parameters:

[0157]

[0158] Step 6: Weight calculation and normalization:

[0159] Calculate the weights of each particle at time k+1:

[0160]

[0161] Then normalize the weights of each particle:

[0162]

[0163] Step 7: Particle set resampling:

[0164] Judge whether the particle set meets the preset resampling condition. If it meets, update the particle set and its particle weights to and respectively according to the resampling method. If it does not meet, directly enter the next step;

[0165] Step 8: State update:

[0166] According to the above calculations, estimate the state and variance of the target at time k+1 as follows:

[0167]

[0168] According to the obtained estimated values, sample according to and return the sampling results to Step 2.

[0169] Furthermore, the specific calculation process of the SCKF is as follows:

[0170] S21: Time update:

[0171] Assume that the error covariance matrix P at time k k|k is known, and the posterior density function at time k satisfies Then we have:

[0172] S211: Decompose P k|k :

[0173] P k|k = S k|k (S k|k ) T (24)

[0174] S212: Calculate each cubature point and perform a one-step transfer prediction:

[0175]

[0176]

[0177] Among them, and represent the cubature point and the one-step transfer prediction cubature point respectively; m = 2n is the total number of cubature points, where n is the dimension of the state vector x; [1] represents a set composed of 2n n-dimensional unit vectors:

[0178]

[0179] S213: Calculate the state prediction value and the square root coefficient of its error covariance matrix:

[0180]

[0181]

[0182] Among them, Tria(·) represents the orthogonal triangular decomposition of the transposed form of the input matrix, and the resulting lower triangular matrix is used as the output; Chol(·) represents the Cholesky decomposition operator; the weighted matrix The calculation formula is:

[0183]

[0184] S22: Measurement update:

[0185] S221: Estimate each cubature point and convert it into the corresponding measurement information:

[0186]

[0187]

[0188] S222: Calculate the mean of the measurement information and the square root coefficient of the innovation covariance:

[0189]

[0190]

[0191] In the formula, R k+1 is the measurement covariance matrix. z k+1|k is the weighting matrix for the measurement information and can be calculated as:

[0192]

[0193] S223: Calculate the innovation covariance matrix and the cross-covariance matrix between the state and the measurement:

[0194]

[0195]

[0196] In the formula, x k+1|k is the weighting matrix for the state, and the calculation formula is as follows:

[0197]

[0198] S224: Update the filtering gain and calculate the posterior state estimate:

[0199]

[0200]

[0201] S225: Update the square root coefficient of the state error covariance matrix and return to S211. The update formula is;

[0202] S k+1|k+1 = Tria([x k+1|k - K k+1 z k+1|k , K k+1 Chol(R k+1 )]) (41)

[0203] It can be seen from the above calculation process that based on the idea of using the SCKF to provide the importance function reference for particle sampling. By combining the robust adaptive factor, the robust ability of the SCKF to model errors is improved, thereby improving the accuracy and stability of the particle filter.

[0204] (2) Tracking performance optimization criterion

[0205] Under high signal-to-noise ratio conditions, the CRLB provides a tight lower bound for unbiased estimators and has been shown to be very close to the target state estimation error. However, due to the lack of predictive ability of the CRLB, it cannot be applied to target tracking scenarios. At the same time, in many works, the posterior Cramér-Rao lower bound (PCRLB) with predictive ability is often used as the target tracking performance metric. However, the standard PCRLB does not fully utilize the actual measurement information and cannot meet the dynamic and real-time characteristics of resource allocation. Therefore, we adopt the PC-CRLB as the tracking performance criterion, which characterizes the performance of the tracker conditioned on the actual measurement information. As known from reference [9], the PC-CRLB can be written as:

[0206]

[0207] is the target state estimation; J(x k+1,q |z 1:k,q ) is the predicted conditional Fisher information matrix (PC-FIM), which is also the inverse matrix of the PC-CRLB and is defined as:

[0208]

[0209] where the mathematical symbol is the second-order partial derivative vector; the PC-CRLB is divided into two matrices:

[0210] J(x k+1,q |z 1:k,q ) = J P (x k+1,q |z 1:k,q ) + J Z (x k+1,q |z 1:k,q ) (44)

[0212] where J P (x k+1,q |z 1:k,q ) and J Z (x k+1,q |z 1:k,q ) represent the prior information and data information respectively and can be calculated as:

[0213]

[0214] In actual solution, it is difficult to obtain the analytical solution of Equation (45). The Monte Carlo method is often used to solve the numerical solution of (45) instead of calculating the mathematical expectation, but it may cause a heavy computational burden. In reference

[10] , a method for calculating PC-CRLB is proposed, which can be applied to the particle filtering framework to calculate the two partial matrices of PC-CRLB for the beam selection problem:

[0215]

[0216] where (·) -1 is the calculation of the inverse matrix; and respectively represent the Jacobian matrix and the measurement covariance matrix calculated by substituting ; P k+1,q and β k+1,q affect as parameters and ultimately affect J(x k+1,q |z 1:k,q ).

[0217] It can be seen from Equation (12) that the effective bandwidth only affects the position error and does not affect the velocity and acceleration. Therefore, we extract the position component of the PC-CRLB matrix and use the tracking operation as the cost function to avoid the heterogeneity among position, velocity, and acceleration. Therefore, unless otherwise specified, the PC-CRLB mentioned in the present invention refers to the PC-CRLB with respect to the target position.

[0218] (3) Establish an optimization model

[0219] To describe the problem of combining beam selection with power and bandwidth allocation, we further define power allocation variables and bandwidth allocation variables. Therefore, by combining these variables with the beam selection results, three vectors are established:

[0220]

[0221] where u k , P k and β k represent the beam selection result, power allocation result, and bandwidth allocation result at time k, respectively;

[0222] Combining Equations (44), (46), and (47) again, the PC-FIM can be expressed as:

[0223]

[0224] The complex problem of combining beam selection with power and bandwidth allocation can be transformed into an optimization problem subject to limited system resource budgets. Based on the above analysis and assumptions, the optimization model can be expressed as:

[0225]

[0226]

[0227]

[0228]

[0229]

[0230] q = 1, 2, ..., Q (49)

[0232] where P total and β total represent the maximum power and bandwidth that the C - MIMO radar system can provide for each tracking sample. M represents the maximum number of beams, which is determined by the degrees of freedom in the system waveform design. is the criterion for tracking performance in the worst - case scenario of tracking performance, and can be expressed as:

[0233]

[0234] where tr(·) is the matrix tracking operator;

[0235] Therefore, by solving (50) and feeding it back to the C - MIMO radar transmitter, an adaptive resource allocation scheme can be established, and its closed - loop framework is as shown in the appendix Figure 1 as shown.

[0236] III. Solving the Optimization Model

[0237] Considering that only the maximum number of transmitting beams is given in (49), and the specific number of transmitting beams m k still needs further discussion, where 1 ≤ m k ≤ M. Lemma 1 is given as follows:

[0238] Lemma 1: For a given situation, regardless of the power allocation and bandwidth allocation results, the optimal result of beam selection can be uniquely determined.

[0239] In each round of solution, first, the optimal number of beams m for target tracking needs to be calculated k , and secondly, according to Lemma 1, the power and bandwidth can be evenly distributed as and to facilitate obtaining the optimal beam allocation scheme through local search and the specific local search method for wave speed optimization selection is shown in Table 1. Therefore, (49) can be transformed into:

[0240]

[0241]

[0242]

[0243]

[0244] q = 1, 2, ..., Q (51)

[0246] Substitute the obtained transmit beam allocation scheme into equation (51). The original optimization problem can be transformed into a joint power and bandwidth allocation problem. Therefore, the optimal solution for power and bandwidth allocation is:

[0247]

[0248]

[0249]

[0250]

[0251] q = 1, 2, ..., Q (52)

[0253] Since the bandwidth exists in quadratic form in equation (52), the joint power and bandwidth allocation is a typical non-convex optimization problem. To solve this non-convex optimization problem, the present invention further proposes a three-step solution method based on the CMA method, specifically including:

[0254] Step 1: Calculate the transient power allocation result Set the initial value ( (indicating the uniform bandwidth allocation of the selected beam); for a given Equation (52) is actually a convex optimization problem. Combining with the SDP algorithm, equation (52) is transformed into:

[0255]

[0256]

[0257]

[0258]

[0259] q = 1, 2, ..., Q (53)

[0261] where M k,qis an auxiliary matrix that satisfies

[0262] Equation (53) can be solved using the Zoutendijk feasible direction method, as shown in Table 2, to obtain the transient power allocation result

[0263] Step 2: Solve for the transient bandwidth allocation result By substituting into (52) and introducing the convex relaxation technique, a convex optimization problem for solving the transient bandwidth allocation is established:

[0264]

[0265] where Both λ1 and λ2 are dynamic parameters that can be adjusted according to the simulation results;

[0266] Then, in combination with the SDP algorithm, (54) is further transformed into:

[0267]

[0268]

[0269]

[0270]

[0271]

[0272] q = 1, 2,..., Q (55)

[0274] In the formula, N k,q is an auxiliary matrix that satisfies

[0275] Using the Zoutendijk feasible direction method, solve equation (55) to further obtain the transient bandwidth allocation result The specific implementation steps of the Zoutendijk feasible direction method are shown in Table 2;

[0276] Step 3: Return to Step 1 until the difference in the two tracking accuracies is less than the preset threshold ε, terminate the calculation, and output the final power optimization allocation result and the final bandwidth optimization allocation result

[0277] Table 1 Local search methods for beam optimization selection

[0278]

[0279]

[0280] Table 2 Zoutendijk feasible direction method

[0281]

[0282]

[0283] Embodiment

[0284] To further verify the effectiveness of the algorithm proposed by the present invention, the proposed method is verified through simulation experiments. Assume that a single-base centralized MIMO radar is deployed at the origin of coordinates in the x-y plane, and Q = 6 targets performing CA motion are tracked. The initial motion parameters of each target are shown in Table 3. The sampling interval T s = 2 s, the number of tracking frames is Z t = 20, the number of Monte Carlo simulations is N sim = 100, and the target motion trajectories are as Figure 4 shown. Let the total transmission power P total = 25 kW, and the upper and lower bounds of the transmission power are P max = 0.8P total and P min = 0.1P total ; the carrier wavelength λ = 0.3 m; the number of particles is N p = 300; the maximum number of transmission beams M = 4.

[0285] Table 3 Initial motion parameters of each target

[0286]

[0287] In addition, to test the optimality of the proposed method in improving the target tracking accuracy, the root mean square error (RMSE) of the target with the worst position estimation accuracy at time k is proposed as:

[0288]

[0289] where is the position estimation value of target q at time k in experiment j;

[0290] To further reveal the influence of the target-to-radar distance and the target RCS on the resource allocation result, two RCS models are considered: in the first RCS model, the influence of the distance factor is mainly considered, so let h k,q = 1, q = 1, 2,..., 6; for the second RCS model, let the partial RCS of the target be h k,q = 1, q = 2, 4, 5, and the RCS of the remaining targets is as shown in Appendix Figure 5 shown.

[0291] To fully demonstrate the effectiveness of the proposed method, performance comparisons are carried out through four benchmarks:

[0292] Benchmark 1: The C-MIMO radar system adopts a resource allocation strategy of (u bench , p uni , β uni ). This represents that the C-MIMO radar system utilizes the beam allocation method mentioned in reference

[11] and limits the maximum number of transmitting beams M = 4 (a larger fixed number of beams will result in better tracking performance). After obtaining the beam allocation result, the corresponding power and bandwidth resources are evenly allocated to the selected beams.

[0293] Benchmark 2: The C-MIMO radar system adopts a resource allocation strategy of (u opt , p uni , β uni ), that is, the C-MIMO radar will allocate according to the allocation algorithm proposed in the present invention. After obtaining the beam allocation result, the power and bandwidth are then evenly allocated.

[0294] Benchmark 3: Joint beam and power optimization allocation is added to the resource allocation strategy, and the bandwidth is set to be evenly allocated, thus adopting a resource allocation strategy of (u opt , p opt , β uni ).

[0295] Benchmark 4: Joint beam and bandwidth optimization allocation is added to the resource allocation strategy, and the power is set to be evenly allocated, thus adopting (u opt , p uni , β opt ) in the resource allocation strategy.

[0296] Next, for different simulation scenarios, the above four benchmarks and the allocation method proposed in the present invention are compared in each simulation scenario, specifically including:

[0297] (1) Simulation scenario 1: Distance influence scenario

[0298] In this case, let the target RCS be a constant model, and the RCS of all targets is set to 1. Therefore, the distance factor becomes the main factor affecting the resource allocation problem. Figure 6 And Figure 7 respectively show the performance comparison of the above four benchmarks and the allocation method of the present invention from the perspectives of PC-CRLB and RMSE. From Figure 6 , 7It can be seen that the topmost line is reference 1, the second line is reference 2, the third line is reference 3, the fourth line is reference 4, and the bottommost line is the method proposed in the present invention. Thus, it can be seen that the allocation method proposed in the present invention has the best effect. In addition, it can also be seen from the figure that the line of reference 4 is below the line of reference 3. Therefore, it can be seen that bandwidth allocation has a better effect than power allocation. The beam selection method adopted by reference 1 is the beam selection method proposed in

[11] . Obviously, the beam selection method proposed in the present invention is superior to the beam selection method proposed in

[11] .

[0299] Appendix Figure 8 shows the beam selection results of the proposed algorithm in simulation scenario 1. The red circles indicate the beam allocation for the corresponding targets. It can be observed that targets 3 and 6 have significantly fewer allocated beams than other targets because they are the closest to the radar in scenario 1. In addition, the beam selection results show that it is better to use 4 beams in simulation scenario 1 (except when k = 2).

[0300] Appendix Figure 9-10 further shows the power and bandwidth allocation results based on the beam selection results in scenario 1, where the grid color represents the ratio of the allocated power and bandwidth to each tracking beam. The ratio of power to bandwidth is defined as:

[0301]

[0302] In Figure 9 and Figure 10 , black indicates that the ratio is zero, meaning that the corresponding target will not be allocated a transmit beam during this tracking interval. Obviously, targets 2 and 5 consume most of the power resources and bandwidth resources. In addition, as the distance between the target and the radar changes, the resources obtained by target 2 increase, while the resources obtained by target 5 decrease. Targets 3 and 6 have the least system resources because they are closer to the C-MIMO radar and have better angle spread. Generally, it can be seen that targets far from the C-MIMO radar tend to be allocated more power and bandwidth.

[0303] (2) Simulation scenario 2: RCS influence scenario

[0304] In this scenario, the influence of the RCS of the target on the resource allocation results will be further studied. Therefore, we consider a dynamic RCS model, as Figure 5 shown. Therefore, the resource allocation results are affected not only by the distance between the tracked target and the C-MIMO radar but also by the RCS of the target. Similarly, comparing the worst-case target tracking performance among all algorithms in simulation scenario 2, the results are as Figure 11 and Figure 12 shown.

[0305] Obviously, from AppendixFigure 11 and appendix Figure 12 It can be seen that the allocation method proposed in the present invention is the bottom line in the figure, that is, this method is still the best in performance among the five algorithms. This conclusion is consistent with the simulation results of the previous scenario. In addition, due to the weak RCS of Target 1, Target 3, and Target 6, the tracking performance in the worst case of the current scenario is worse than that of Simulation Scenario 1. In addition, the optimal bandwidth allocation is better than the optimal power allocation, and this result is consistent with Simulation Scenario 1.

[0306] In addition, Figure 13 The beam selection results in Scenario 2 are given. Obviously, due to the weak reflectivity of the targets, it can be seen that the number of allocated beams obtained by Target 3 and Target 6 has increased significantly. In addition, the beam selection results show that it is better to use 4 beams in Simulation Scenario 2 (except when k = 1), that is, at each moment (i.e., each column), four targets are allocated tracking beams.

[0307] The power allocation results are as Figure 14a shown, and the bandwidth allocation results are as Figure 14b shown. Compared with Scenario 1, Scenario 2 allocates more energy and bandwidth resources to the three targets with weak reflectivity (Target 1, Target 3, and Target 6), especially Target 3 and Target 6. In addition, from Figure 14a and Figure 14b results, it can also be seen that for targets with weak reflectivity, more resources tend to be allocated.

[0308] (3) Computational complexity and timeliness analysis

[0309] First, the computational complexity of the proposed algorithm is evaluated. For the Zoutendijk feasible direction method, it takes at most iterations to reach the given accuracy. For local search, it needs to iterate O(MQ) times in each round. Therefore, the overall complexity of the proposed algorithm is

[0310] Then, in order to test the timeliness of the algorithm, the CPU running time as shown in Figure 15 is obtained. The configuration for the simulation is: 3.7GHz CPU and 16GB RAM, MATLAB 2018a. The results in Figure 15 show that the step interval of the simulation experiment is less than 1.5s, which fully meets the real-time requirement. In addition, it is worth noting that the CPU time difference between the two methods is less than 5%, which further proves the robustness of the proposed method.

[0311] References:

[0312] Reference [1] J.K.Yan; B.Jiu; H.W.L; B.Chen; and Z.Bao. Prior knowledge-based simultaneous multibeam power allocation algorithm for cognitive multi-targets tracking in clutter. IEEE Trans. Signal Processing. 2015, vol.63, no.2, pp.512-527.

[0313] Reference [2] H.W.Zhang; J.P.Shi; Q.L.Zhang; et al. Antenna selection for target tracking in collocated MIMO radar[J]. IEEE Trans. Aerospace and Electronic Systems, to be published.

[0314] Reference [3] Z.J.Li; J.W.Xie; and H.W.Zhang. Joint power and time width allocation in collocated MIMO radar for multi-target tracking. IET Radar, Sonar & Navigation, 2020, vol.14, no.5, pp.686-693.

[0315] Reference [4] A.A.Gorji; T.Kirubarajan; and R.Tharmarasa. Optimal antenna allocation in MIMO radars with collocated antennas. IEEE Trans. Aerospace Electronic systems. 2014, vol.50, no.1, pp.542-557.

[0316] Reference [5] J.K. Yan; H.W. Liu; B. Jiu; and Z. Bao. Simultaneous multibeam resource allocation scheme for multiple target tracking. IEEE Trans. Signal Processing. 2015, vol. 63, no. 12, pp. 3110 - 3122.

[0317] Reference [6] J.K. Yan; H.W. Liu; W. Pu; S. Zhou; Z. Liu and Z. Bao. Joint beam selection and power allocation for multiple target tracking in netted colocated MIMO radar system. IEEE Trans. Signal Processing, 2016, vol. 64, no. 24, pp. 6417 - 6427.

[0318] Reference [7] W. Yi; Y. Yuan; R. Hoseinnezhad; and L.J. Kong. Resource scheduling for distributed multi - target tracking in netted colocated MIMO radar systems. IEEE Trans. Signal Processing. 2020, vol. 68, pp. 1602 - 1617.

[0319] Reference [8] H.W. Zhang; J.W. Xie; J.P. Shi; Z.Z. Zhang and X. Fu. Sensor scheduling and resource allocation in distributed MIMO radar for joint target tracking and detection. IEEE Access, 2019, vol. 7, pp. 62387 - 62400.

[0320] Reference [9] M.C. Xie; T. Kirubarajan; L.J. Kong. Joint node selection and power allocation strategy for multitarget tracking in decentralized radar networks. IEEE Trans. Signal Processing. 2018, vol. 66, no. 3, pp. 729 - 743.

[0321] Reference

[10] Y. Zheng; O. Ozdemir; R. Niu; et al. New conditional posterior Cramer - rao lower bounds for nonlinear sequential Bayesian estimation. IEEE Trans. Signal Processing, 2012, vol. 60, no. 10, pp. 5549 - 5556.

[0322] Reference

[11] H.W. Zhang; W.J.L; Z.Z. Zhang; et al. Joint target assignment and power allocation in multiple distributed MIMO radar networks. IEEE Systems Journal, 2020, published online, DOI: 10.1109 / JSYST.2020.2986020.

[0323] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above - mentioned embodiments. What is described in the above - mentioned embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A beam-power-bandwidth joint allocation method in centralized MIMO radar multi-target tracking, characterized in that It includes the following steps: Step 1: Construct a system model of a centralized MIMO radar, where the system model includes a motion model, a signal model, and a measurement model; Step 2: Use an anti-robust square root cubature particle filter to obtain target state estimation information; Step 3: Calculate the PC-CRLB based on the target state estimation information and the measurement information obtained from the measurement model, and use this PC-CRLB as a benchmark for guiding the next resource allocation; Step 4: Adaptively allocate the beams of power and bandwidth according to the PC-CRLB, and establish a beam-power-bandwidth joint allocation optimization model; Step 5: Solve the beam-power-bandwidth joint allocation optimization model and feedback the result to the centralized MIMO radar transmitter to obtain an adaptive resource allocation scheme; Step 6: According to the adaptive resource allocation scheme, optimally allocate the beam, power, and bandwidth resources limited by the system performance to each target, and estimate and track the target motion state at the next moment; Among them, Step 4 specifically includes: Step 41: After inverting the Bayesian matrix regarding the state x of the moving target k+1,q the corresponding PC-CRLB matrix is obtained, and its definition is: J(x k+1,q |z 1:k,q ) = J P (x k+1,q |z 1:k,q ) + J Z (x k+1,q |z 1:k,q ) (44) Among them, J P (x k+1,q |z 1:k,q ) and J Z (x k+1,q |z 1:k,q ) represent the prior information and the data information respectively, and can be expressed as: Step 42: To improve the multi-target tracking accuracy, define the power allocation variable and the bandwidth allocation variable, combine these two variables with the beam selection result u k and establish three vectors: Substitute the power and bandwidth allocation variables into Equation (44), and Equation (44) is rewritten as: Step 43: Use the tracking performance corresponding to the target with the worst tracking accuracy among all targets as the objective function: In the formula, tr(·) is the matrix tracking operator; Step 44: According to the cost function, construct the optimization model as: where P total and β total represent the maximum power and bandwidth that the C-MIMO radar system can provide for each tracking sample; M represents the maximum number of simultaneously orthogonal beams generated, which is determined by the degrees of freedom in the system waveform design.

2. The beam-power-bandwidth joint allocation method in centralized MIMO radar multi-target tracking according to claim 1, wherein, The specific steps of Step 2 include: Step 21: Initialize the random samples and obtain N particles through sampling Assign the same weight to each particle Step 22: At time k, the states and covariance sets of each particle are substituted into the SCKF filtering algorithm, and thus the predicted states of each particle at time k+1 and their covariances are obtained. After adding the measurement data, the innovation covariance is calculated Step 23: Calculate the residuals of each particle at time k+1 through Equation (13); Step 24: Calculate the adaptive factor: Calculate the adaptive factor α: From the particle residuals at time k+1 and the innovation covariance the measurement model error discrimination statistic can be calculated To reduce the computational amount and improve the filtering rate, a two-segment functional form is selected to construct the adaptive factor: Among them, c is an empirical constant, and usually 1.0 < c < 2.5; Step 25: Update the particle set: Substitute the above parameters into the SCKF framework, and further obtain: Step 26: Calculate and normalize the weights: Calculate the weights of each particle at time k+1: Then normalize the weights of each particle: Step 27: Resample the particle set: Determine whether the particle set meets the preset resampling condition. If it meets, update the particle set and its particle weights according to the resampling method to and If it does not meet, directly proceed to the next step; Step 28: Update the state: Based on the above calculations, estimate the state and variance of the target at time k+1 as follows: According to the obtained estimated value, sample according to and return the sampling result to step 2.

3. A beam-power-bandwidth joint allocation method in centralized MIMO radar multi-target tracking according to claim 1, characterized in that The joint beam-power-bandwidth allocation optimization model is solved based on Lemma 1. For the number of transmit beams \(m\) k and \(1\leq m\) k \(\leq M\), the following lemma holds: Lemma 1: For a given situation, regardless of the power allocation and bandwidth allocation results, the optimal result of beam selection is uniquely determined.

4. A beam-power-bandwidth joint allocation method in centralized MIMO radar multi-target tracking according to claim 3, characterized in that, The steps for solving the beam-power-bandwidth joint allocation optimization model in Step 5 are: Step 51: Calculate the optimal number of beams m for target tracking k And according to Lemma 1, evenly distribute the power and bandwidth as and Transform Equation (49) into: Step 52: Solve equation (51) to obtain the transmit beam allocation scheme Then substitute into equation (49) to transform the original optimization problem into a joint power and bandwidth allocation problem, and the optimal solutions for power and bandwidth allocation are as follows: Step 53: Use a three-step solution method based on the CMA method to solve Equation (52) to obtain the optimal power allocation result and the optimal bandwidth allocation result.

5. A beam-power-bandwidth joint allocation method in centralized MIMO radar multi-target tracking according to claim 4, characterized in that The three-step solution method based on the CMA method described in Step 53 includes the following steps, Step 531: Set the initial value For a definite Combined with the SDP algorithm, transform Equation (52) into Equation (53) and use the Zoutendijk feasible direction method to solve Equation (53) to obtain the transient power allocation result where Equation (53) is as follows: where, M k,q is the auxiliary matrix, satisfying Step 532: Substitute into Equation (52) to establish a convex optimization problem for solving transient bandwidth allocation: Among them, both λ1 and λ2 are dynamic parameters; Combined with the SDP algorithm, transform Equation (54) into Equation (55) and use the Zoutendijk feasible direction method to solve the transient bandwidth allocation result where Equation (55) is as follows: where N k,q is an auxiliary matrix that satisfies Step 533: Return to Step 1 until the difference between the two tracking precisions is less than the preset threshold ε, terminate the calculation, and output the final power optimization allocation result and the final bandwidth optimization allocation result

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