Adaptive resource management method for lpi-based cmimo target tracking

Abstract

The application belongs to the field of resource management of target tracking, and proposes an adaptive resource management method for CMIMO target tracking based on LPI. The relationship between the number of subarray division, radiation power and system interception probability in the tracking process of CMIMO radar is established, and is taken as a target function. The influence of resource allocation strategy change and various constraint conditions are comprehensively considered to form an optimization problem model. For this problem, the discrete particle swarm method is used for solution, the fitness of the particle is the radar interception probability, and the penalty term is introduced to reduce the influence of resource allocation action. According to the number of subarrays in the best particle, it is judged whether the particle swarm obtains the optimal solution, and finally the optimal resource allocation scheme at the next moment is obtained. The application can adaptively configure the number of subarray division and radiation power of CMIMO radar according to the change of the actual target tracking scene, and realize higher anti-interception performance under the constraint of limited radar resources.

Description

Technical Field

[0001] This invention belongs to the field of radar target tracking and low probability of intercept, specifically involving an adaptive resource management method for radar CMIMO (Centralized-Multiple-Input Multiple-Output) target tracking based on LPI (Low-Possibility-of-Intercept). Background Technology

[0002] MIMO radar is a new type of radar system that emerged in the early 21st century. Due to its performance advantages in target detection, parameter estimation, and target tracking, MIMO radar has become a hot topic in current research and development (Yang Su, Ting Cheng, and Zishu He. LPI-constrained Collaborative Transmit Beampattern Optimization and Resource Allocation for Maneuvering Targets Tracking in Colocated MIMO Radar Network. Signal Processing 207(2023):108935). Based on the spacing between the elements of the transmitting and receiving antennas, MIMO radar can be divided into two categories: distributed MIMO radar and centralized MIMO radar (Li Jian, and Stoica Peter. MIMO Radar Signal Processing. 1st ed. New York: John Wiley & Sons, 2008).

[0003] In distributed MIMO radar, the transmission antennas are far apart, which makes multi-station synchronization and channel matrix estimation difficult in practical applications (Xiaowei Tang, Jun Tang, Bo Tang, Zhaozhao Gao, Xin Bi, and Jinsong Du. "A New Electronic Reconnaissance Technology for MIMO Radar." Proceedings of 2011 IEEE CIE International Conference on Radar 1 (2011): 79-83). Centralized MIMO radar is an extension of traditional phased array radar, and its system structure is more practically valuable. In centralized MIMO radar, the transmitting and receiving antenna elements are closer together, and each antenna element has approximately the same viewing angle to the target. Moreover, each element can transmit mutually orthogonal signal waveforms, thereby obtaining waveform diversity and forming a wider, low-gain beam, unlike the narrow beam of traditional phased arrays. This effectively reduces the distribution of system radiated energy in a certain direction in the airspace, and has the potential to improve the system's anti-interception performance. Compared to traditional phased array radars, centralized MIMO radars offer greater flexibility in resource management. By controlling the number of subarrays, system resources can be effectively allocated in the airspace.

[0004] Radar resource management originated from phased array radar (Bi Zengjun, Lu Li, Xu Chenxi, Zhang Xianzhe. Research on the Development and Application of Phased Array Radar Resource Management Technology [J]. Modern Defense Technology, 2015, Vol. 43 (5): 116-123, 191). Its main purpose is to rationally allocate the radar's limited resources through adaptive operating parameters, thereby better improving the radar's overall performance. However, simply improving the radar's operating performance is not enough. In recent years, low probability of intercept (PLO) has become a key factor in resource management (Xiujuan Lu, Wei Yi, Yangming Lai, and Yang Su. "LPI-Based Joint Node Selection and Power Allocation Strategy for Target Tracking in Distributed MIMO Radar." 2022 25th International Conference on Information Fusion (FUSION) (2022): 1-7). When an enemy passive reconnaissance system intercepts a friendly radar signal, it can emit jamming signals to interfere with the radar, causing it to malfunction. Furthermore, after intercepting radar information, it may even launch a military strike, threatening the radar's survivability. Therefore, anti-interception performance is extremely important. Consequently, determining measures to ensure the normal operation of the radar while preventing its signal from being intercepted by intercepting aircraft has become a recent hot topic.

[0005] In CMIMO resource management, Li Qian et al. minimized the consumption of spatiotemporal resources while ensuring effective target detection and desired tracking accuracy. However, they did not directly optimize the system's anti-interception performance and lacked a reasonable method for characterizing anti-interception performance, which still has shortcomings (Li Qian. Research on Adaptive Resource Management Technology for MIMO Radar and Networked Radar [D]. University of Electronic Science and Technology of China, 2021). Based on this, Shi Chenguang et al. considered anti-interception performance, introduced the interception probability, and proposed a resource management scheme based on low interception probability. However, this scheme is for distributed networked MIMO radar (Lintao Ding, Chenguang Shi, Fei Wang, and Jianjiang Zhou. Low Probability of Intercept-based Cooperative Node Selection and Transmit Resource Allocation for Multi-target Tracking in Multiple Radars Architecture. IET Signal Processing). 16.5(2022):515-27); In addition to the interception probability, the interception factor (the ratio of the maximum detection range of the interceptor to the maximum detection range of the radar) also improves the radar's anti-interception performance in terms of range. However, this method only considers the anti-interception performance in space and does not reflect the advantage in probability (Liao Wenwen, Cheng Ting, He Zishu. Target tracking algorithm for optimizing the radio frequency stealth performance of MIMO radar [J]. Acta Aeronautica Sinica, 2014, (4):1134-1141).

[0006] To address the aforementioned issues, this invention uses signal-to-noise ratio analysis of CMIMO to obtain the interception probability of CMIMO. This probability is then used as the objective function for optimization, taking into account the impact of resource allocation action switching. The Discrete Particle Swarm Optimization (DPSO) algorithm is employed to solve the optimization problem, with a penalty factor applied to particles that do not meet the constraints. Ultimately, the optimal resource allocation scheme for the next time step is obtained. Summary of the Invention

[0007] To address the aforementioned problems or shortcomings, and in order to enable CMIMO radar resource management to achieve the desired tracking accuracy while effectively improving the system's anti-interception performance during target tracking, this invention provides an adaptive resource management method for CMIMO radar in target tracking.

[0008] Assuming the total number of array elements in a CMIMO radar is M, and the transmit and receive arrays are co-located, the number of possible subarrays is K. j =2 j-1 j = 1, 2, ..., (log2(K) max )+1), Kmax This represents the maximum number of subarrays that can be divided into. Assuming each element transmits the same signal power, and that multiple power levels are available, the total radar transmission power has a minimum value P. min It has a maximum value P max .

[0009] Assume the current time is k, and the positions of all particles in the local optimum particle swarm in the previous time are known: pBest(k) = [pBest1(k) ... pBest...]. N [(k)], where N is the population size of the particle swarm. Simultaneously, the radar obtains the predicted state at time k for time k+1 and its prediction error covariance matrix. Predicting states has a form

[0010]

[0011] The specific technical steps for obtaining time k+1 at time k are as follows:

[0012] Step 1: Initialize the particle swarm. Use the local optimal particle position pBest(k) at time k as the initial position information for the particle swarm, thereby generating a set of particle swarm S0(k+1) = [S 0,1 (k+1),…,S 0,N [(k+1)], assuming S n,j (k+1) represents the j-th particle in the n-th iteration of the particle swarm, where j∈[1,N] is an integer; each particle contains the particle's position information x. n,j (k+1) and velocity information v n,j (k+1). We have S n,j (k+1) is defined as follows:

[0013]

[0014] Where, x n,j (k+1)=[K n,j (k+1),P n,j [(k+1)],

[0015] Specifically, we have x 0,j (k+1)=pBest j (k).

[0016] The velocity information of the particle swarm is randomly generated within a range that satisfies certain constraints; that is, each particle must satisfy the following:

[0017]

[0018] Step 2: Calculate the signal-to-noise ratio of the predicted echo signal. Tracking accuracy The predicted standard deviation of the target in terms of distance and angle As given in steps 2.1 to 2.3.

[0019] Step 2.1: After the particle emits its waveform according to the pattern, the radar system obtains the signal-to-noise ratio of the predicted echo signal:

[0020]

[0021] Where, σ RCS It is the radar cross-section of the target; τ e This refers to the dwell time of the tracking mission. N1 is the power spectral density of zero-mean Gaussian white noise in the MIMO radar receiver channel; It is the predicted distance of the target from the center of the radar.

[0022] Step 2.2: Calculate the approximate estimated covariance matrix for all particles in each iteration.

[0023]

[0024] in, Let H be the Kalman gain of the j-th particle in the nth iteration, and let H be the transfer matrix, given by the following equations:

[0025]

[0026] Here is the covariance matrix of the approximate innovation process at time k+1:

[0027]

[0028] Among them, J Rtox (k+1|k) and These are the Jacobian matrix and the approximate measurement error covariance matrix of the particle at time k+1, representing the transformation from spherical to rectangular coordinates:

[0029]

[0030] Among them, the predicted azimuth angle This is the approximate Cramero lower bound for the particle at time k+1, where T is a constant matrix:

[0031]

[0032] in, It is a constant related to the CMIMO radar direction finding method, and is usually taken as... is the effective bandwidth of the signal; c is the speed of light.

[0033] Simultaneously calculate the radar system's tracking accuracy of the target.

[0034] Step 2.3: Extraction The variance in the variance is used to obtain the predicted position error covariance matrix. The predicted position covariance transition matrix in spherical coordinates

[0035]

[0036] Among them, J xtoR (k+1|k) is the Jacobian matrix from the Cartesian coordinate system to the spherical coordinate system, given by the following formula:

[0037]

[0038] Finally, the prediction standard deviations for distance and angle were calculated separately.

[0039]

[0040] Among them, A R =[1 0] T and These are the extraction matrices for distance and angle, respectively.

[0041] Step 3: To meet the tracking accuracy requirements, the following judgment needs to be made for all particles in this iteration:

[0042]

[0043] Where, μ 0.5α Let α be the two-sided quantile of the standard normal distribution N(0,1) with respect to α; Lg is the gate width of the MIMO radar transmitted signal; η is the angular one-way beamwidth at the pointing position of the transmitted beam; des It is the desired accuracy of target tracking; P fa It is the false alarm rate; It is the signal-to-noise ratio threshold.

[0044] If the j-th particle in the nth iteration does not satisfy equation (12), then let the objective function value F of that particle be... n,j =F false , of which F false It is a pre-defined constant; at the same time, directly execute step 5.

[0045] Step 4: Calculate the objective function value corresponding to the j-th particle in the n-th iteration:

[0046]

[0047] Where u(k) is a step function, which is 1 when k≥0 and 0 otherwise; k0 is a constant; K num It is the number of consecutive subarray divisions using the same number of subarrays. P f The frequency domain overlap probability is calculated by the following formula:

[0048]

[0049] Among them, T rdt It is the duration of the interceptor's stay in that frequency band, T scan It is the frequency band scanning period of the interceptor; It is the number of frequency bands required for the interceptor to search for all CMIMO radar transmission frequencies, f max It is the highest frequency that radar can transmit signals at, f min It is the lowest frequency that radar can transmit signals at, f scan It intercepts the bandwidth of each scan by the receiver. up It rounds the value inside the parentheses up to the nearest integer.

[0050] The detection probability of the interceptor is calculated by the following formula:

[0051]

[0052] The signal-to-noise ratio (SNR) received by the interceptor is calculated using the following formula:

[0053]

[0054] Among them, A I B is the effective area of ​​the reconnaissance antenna. I Let N0 be the effective receiving bandwidth of the interceptor, and let N0 be the power spectral density of zero-mean white Gaussian noise in the receiving channel of the interceptor, and let N0 = k0T0F. n Here, k0 = 1.38 × 10 -23 J / K is Boltzmann's constant; T0 is the reference temperature; F n G represents the receiver noise figure. IP It is the signal processing gain of the interceptor.

[0055] Step 5: Calculate the objective function value F for all particles in this iteration (the nth iteration). n,j Compared with historical local optima pbest n,j By comparison, if the current function value is smaller, then the historical local optimum is updated to the current objective function value, and the current position is taken as the local optimum. The minimum local optimum value among all particles in this iteration is selected as the global optimum, gbest. nAnd save the particle's position as the globally optimal particle position. Simultaneously update the positions of all particles:

[0056] x n+1,j (k+1)=x n,j (k+1)+v n,j (k+1), j=1,2,...,N (17)

[0057] Simultaneously, update the velocity v of all particles within the range that satisfies equation (2). n+1,j (k+1). If the number of subarray partitions at the current position of the particle is the same as the number of subarray partitions at time k, then let K num =K num +1; otherwise, set K. num =0.

[0058] Step 6: Repeat steps 2-5 until the number of iterations is G. k or meet gbest n -gbest n-1 <σ th The number of times is consecutively greater than k m If the number of subarray partitions in the previous time step is the same as the number of subarray partitions in the current globally optimal particle, then the update stops and the process exits. The position information of the globally optimal particle is used as the scheme at time step k+1. σ th and k m These are the particle position accuracy threshold and the iteration count threshold, respectively.

[0059] The globally optimal particle at this point contains the optimal scheme {K(k+1), P(k+1)}. Here, K(k+1) and P(k+1) are the number of subarray divisions and the total transmission power that the MIMO radar will use at time k+1, respectively.

[0060] Step 7: At time k+1, the radar system transmits a signal according to the optimal scheme obtained in Step 6 and receives the echo signal to obtain the measurement value. Based on the obtained measurement value, Kalman filtering is performed to obtain the predicted state and prediction error covariance matrix for the next time step.

[0061] Inventive Principles

[0062] The resource allocation problem studied in this invention is to adaptively change the subarray division and the total power of the transmitted signal under the conditions of meeting certain tracking accuracy requirements and limited resources, so as to reduce the interception probability.

[0063] Assume a CMIMO radar array contains M elements, which are divided into K subarrays, each containing L elements. The transmitted signal of the k-th subarray is represented as s. k(t), assuming the phase difference between the transmitted signals of adjacent array elements is φ, then the composite signal formed by the transmitted signal of the k-th subarray in a certain direction in the spatial domain can be expressed as:

[0064]

[0065] Assume the phase difference between each subarray is φ L The composite signal formed by the signals emitted by K subarrays in the spatial domain can be represented as:

[0066]

[0067] Assume the total radar transmit power is P t The Gaussian white noise power spectral density of the radar's transmitting and receiving channels is the same, N1, and both the transmitting and receiving bandwidths are B. r Then, the signal-to-noise ratio of the transmitted signal of the m-th array element.

[0068] After the synthesized signal is scattered by the target, the receiving array receives the echo signal. If the loss caused by transmission and target scattering is ignored, the signal received by the m-th array element can be expressed as:

[0069] y m (t)=x(t)e -j(m-1)φ +v m (t) (20)

[0070] Among them, v m (t) represents the noise of the m-th array element channel. Assume that all transmitted waveforms have the same energy, E. s The received signal of the m-th element of the MIMO radar is matched and filtered with the transmitted signal of the k-th subarray.

[0071]

[0072] Among them, v mk (t) is a power spectral density with a mean of 0 and an Et s N1 is Gaussian white noise. At time t, we sum the matched filtering results of the m-th element with respect to the K subarrays to obtain the equivalent transmitted beamforming:

[0073]

[0074] Therefore, the signal-to-noise ratio of the m-th receiving element of the MIMO radar is:

[0075]

[0076] Finally, receive beamforming is performed. The overall received signal-to-noise ratio is obtained as follows:

[0077]

[0078] It can be known that the total energy of the transmitted signal is the product of power and time. Therefore, the processing gain obtained after the radar signal undergoes matched filtering and equivalent transmitted beamforming is:

[0079]

[0080] Assume the transmit antenna gain is G t The distance from the target to the radar center is R, and the effective area of ​​the radar receiving array is A. e The received power can be calculated as follows:

[0081]

[0082] Based on the relationship between antenna receiving gain and effective area G r Where λ is the receiving antenna gain, λ is the dominant wavelength of the transmitted signal, and the received power can be further expressed as:

[0083]

[0084] Taking into account the gains from matched filtering and equivalent transmit beamforming, the final radar receive signal-to-noise ratio can be expressed as:

[0085]

[0086] To further simplify the expression, based on the characteristics of CMIMO radar, the transmit antenna gain... η e The aperture efficiency of the radar transmitting antenna is given by d, where d is the antenna spacing. Receive antenna gain η r Let N be the aperture efficiency of the radar receiving antenna. Assume it passes through N... p Accumulate pulses, while simultaneously letting τ e =τ B ·N p The following cumulative signal-to-noise ratio will be obtained:

[0087]

[0088] Typically η e =η r =0.5, then the signal-to-noise ratio can be simplified to:

[0089]

[0090] The above equation is equation (3) in step 2.2. Similarly, based on the characteristics of CMIMO, we assume that the effective area of ​​the reconnaissance antenna is A.I When the radar and the reconnaissance aircraft's antennas are aligned with each other by their main lobes, the signal power received by the intercept receiver from the m-th subarray is:

[0091]

[0092] Therefore, the signal-to-noise ratio received by the intercept receiver from the m-th subarray can be obtained as follows: Assume the receiving bandwidth of the intercepting receiver is B. I The signal processing gain of the interceptor is G. IP The signal-to-noise ratio of the interceptor receiving the CMIMO transmitted signal can be obtained as follows:

[0093]

[0094] To reflect the anti-interception performance of CMIMO radar, this invention introduces the concept of interception probability. Interception probability manifests in three aspects: time domain, spatial domain, and frequency domain. In the time domain, assuming the CMIMO radar detects the interceptor, the interceptor meets the conditions for signal interception in the time domain. When the radar system detects a target, the time-domain overlap probability is 1. In the frequency domain, a time window is used for analysis. Since the occurrence of the radar signal and its frequency band are completely unknown to the interceptor, and the interceptor's dwell time is the same in each frequency band, the frequency-domain overlap probability follows a Poisson distribution:

[0095]

[0096] Where P0 is the average overlap time and T0 is the average overlap period. According to The prediction time at time k+1 is t = (k+1)T s Then, based on the independent relationship between the window functions, equation (14) can be further obtained.

[0097] In the spatial domain, we use the detection probability to describe it, and its usual calculation method is given by equation (15).

[0098] Since this invention improves the system's anti-interception performance while ensuring the target's desired tracking accuracy, a function describing the system's anti-interception performance is first established and used as the optimization objective function as follows:

[0099]

[0100] Regarding the radar's anti-interception performance, we use the frequency domain overlap probability and the interceptor's detection probability to reflect it together. Therefore, the first term in (34) is in the form of the product of the two probabilities. In the actual operation of the system, in order to make the system's operating mode switch less frequent, a penalty term is set. Meanwhile, since the tracking accuracy at time k is related to the resource allocation scheme at previous times, this invention aims to avoid a situation where the performance suddenly improves at a certain time, causing a drastic change in the number of subarrays. It is more desirable for the radar system to change smoothly. When the target is first detected, since the estimation at this time is not accurate, we need to add the penalty factor after time k0.

[0101] The performance of target tracking is comprehensively described by the prediction estimation error covariance, the echo reception signal-to-noise ratio, and the illumination accuracy. These factors together constitute the constraints of the optimization model, as shown in Equation (12).

[0102] Constraints 1 and 2 are to ensure that the radar signal can successfully illuminate the target, because in order to obtain target measurements and update the target status, the target should be illuminated by the detection beam.

[0103] Constraint 3 is to ensure that the target can be successfully detected. The target's echo signal-to-noise ratio needs to be high enough to be detected. Therefore, it is a constraint on the detection probability of the target.

[0104] Constraint 4 is to ensure that the target can be successfully tracked. Only when the target tracking accuracy is high enough will the radar not lose track of the target. Therefore, the target tracking accuracy is constrained here.

[0105] To ensure successful target tracking and reduce the probability of friendly radar signals being intercepted, this invention establishes an optimization model:

[0106]

[0107]

[0108] As can be seen, when the radar system starts tracking the target, u(k-k0) = 0, and the optimization function becomes minP. f ·P d At this point, it only relates to anti-interception performance; the penalty function will have no effect, and the number of subarray partitions will change drastically. After stabilization, u(k-k0) = 1, and the optimization function becomes... When the number of subarray partitions begins to change, the subsequent penalty function will limit the number of subarray partitions from changing too drastically or frequently.

[0109] The problem constructed by equation (35) is a nonlinear and nonconvex problem. Therefore, this invention selects DPSO for adaptive resource management scheme selection, such as the initialization of particle swarm in step 1, the objective function in step 4, and the termination condition in step 6.

[0110] In summary, this invention comprehensively considers anti-interception performance and target tracking, adaptively selects subarray partitioning and power levels, and ultimately achieves efficient allocation of system resources during the tracking process while reducing the probability of signal interception. Attached Figure Description

[0111] Figure 1 This is a simulation scene diagram;

[0112] Figure 2 The actual target tracking accuracy obtained by using the method of this invention for CMIMO radar;

[0113] Figure 3 The number and power of subarrays in a single Monte Carlo simulation of CMIMO radar;

[0114] Figure 4 A comparison chart showing the probability of signal interception between CMIMO radar and traditional phased array radar;

[0115] Figure 5 A comparison chart of the probability of interception and the time consumption for CMIMO radar using the method of this invention and the exhaustive method; Detailed Implementation

[0116] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. Assuming a two-dimensional tracking scenario, the tracking accuracy is limited to 9m. 2 The radar transmits signals at a main frequency of 0.4 GHz, with an effective bandwidth of... The radar false alarm probability is P f =10 -4 The radar detection probability threshold is Pd th =0.9; Radar sampling interval T s =0.1s; τ e =1ms; the interceptor's interception frequency band is 40GHz; noise figure F n =2, reference temperature T0 = 290K; radar signal illumination target cross-sectional area σ RCS =1; The radar's transmitted power range is 10.24kW to 102.4kW, with power levels divided in 10.24kW increments. Related gain parameter G IP =2dB, G t =3dB, G I =3dB, maximum number of transmit array elements M=2048, maximum number of radar subarrays K max =64; The particle population size is set to N = 18; the maximum number of particle iterations is G. k =36,k m =9,F false =10.

[0117] Target motion scenario: Assuming the CMIMO radar is located at the origin, the target flies away from the radar center at time t=0 from [120km, 120km] with a speed of [100m / s, 100m / s].

[0118] An adaptive resource management method for CMIMO target tracking based on LPI, as proposed in this invention, was employed, and its performance was compared with that of the exhaustive search method. The following are the statistical results for 50 Monte Carlo runs.

[0119] Figure 1 The diagram shows the target's actual trajectory, the radar's measured trajectory, and the estimated trajectory obtained after Kalman filtering. It can be seen that the estimated trajectory is closer to the actual trajectory than the measured one.

[0120] Figure 2 This indicates the actual target tracking accuracy obtained by the CMIMO radar using this invention. It can be seen that the radar system, under this scheme, meets the desired target tracking accuracy requirements.

[0121] Figure 3 This figure illustrates the changes in the number of subarrays and power of a CMIMO radar over time. The result of a simulation shows that due to random noise and other factors, the CMIMO radar power and the number of subarrays experience abrupt changes at certain points in time to meet target tracking requirements. For example, when the number of subarrays decreases to 1, the transmit power reaches its maximum. When the number of subarrays stabilizes, the power gradually increases. When the number of subarrays abruptly decreases, the power abruptly decreases and then gradually increases, remaining positively correlated with time until the next abrupt change in the number of subarrays. Since the target moves away from the radar, the radar can increase the total transmit power or decrease the number of subarrays to keep up with the target, depending on factors such as the signal-to-noise ratio. From 0s to 110s, the figure shows that when the number of subarrays remains constant, the power gradually increases. At 110s, the decrease in the number of subarrays better meets the target tracking requirements; to improve anti-interception performance, the radar transmit power abruptly decreases to its minimum at this point. Between 110s and 360s, the number of subarrays remained largely constant at 32, while the radar's transmit power continuously increased to keep up with the target. The process after 360s was similar to the above description.

[0122] Figure 4 This demonstrates the advantages of CMIMO radar over traditional phased array radar in terms of anti-interception performance. Specifically, the CMIMO radar employs the method of this invention to implement an adaptive resource management scheme, while the phased array radar uses an exhaustive method for its adaptive resource management scheme. It can be observed that the CMIMO radar offers a significant improvement in anti-interception performance compared to traditional phased array radar.

[0123] Figure 5This demonstrates the advantages of the proposed method for CMIMO radar compared to the traditional exhaustive search method. It can be seen that this algorithm significantly reduces computation time while sacrificing a minimal probability of interception, allowing the solution to be adaptively derived within a single sampling period. In contrast, the exhaustive search method requires calculating all possibilities, consuming significantly more time than the available time. Comparing performance, the interception probabilities of the two algorithms are consistent, indicating that this invention can find the optimal solution much faster.

[0124] In summary, this invention provides a centralized MIMO radar adaptive resource management algorithm based on target tracking. This method first selects feasible subarray partitioning and total transmitted signal power based on target successful illumination constraints, effective target detection constraints, and effective target tracking constraints, adaptively allocating radar system resources. Furthermore, considering improved anti-interception performance, it selects the optimal combination of subarray partitioning and total transmitted power according to the objective function minimization principle, thereby significantly improving the radar's anti-interception performance while ensuring the desired target tracking performance.

Claims

1. An adaptive resource management method for CMIMO target tracking based on LPI, characterized in that... Includes the following steps: The total number of elements in the CMIMO radar is expressed as Furthermore, since it shares the same address for both transmission and reception, the number of its subarrays is in Selected from, This represents the maximum number of subarrays that can be divided into in a radar array; assuming that each element transmits the same signal power, and that there are multiple power levels to choose from, the total radar transmission power has a minimum value. It has a maximum value. ; Will The positions of all particles in a locally optimal particle swarm in time-resource management are represented as follows: , It is the population size of the particle swarm; at the same time, the radar obtained Always Predicted state at time 1 and its prediction error covariance matrix Predicting states has a form ; Step 1: Initialize the particle swarm, Local optimal particle position at time t As the initial position information of the particle swarm, a set of particle swarms is generated. ,assumed Represents the first particle in the swarm. The iteration of the ... One particle, The integers; each particle contains the particle's position information. and speed information We are Define: in, , ; in, ; The velocity information of the particle swarm is randomly generated within a range that satisfies certain constraints; that is, each particle must satisfy the following: Step 2: Calculate the signal-to-noise ratio of the predicted echo signal. Tracking accuracy The predicted standard deviation of the target in terms of distance and angle , As given in steps 2.1 to 2.3; Step 2.1: After the particle emits its waveform according to the pattern, the radar system obtains the signal-to-noise ratio of the predicted echo signal: in, It is the dominant wavelength of the transmitted signal. It is the radar cross-section of the target; It tracks the duration of task persistence; It is the power spectral density of zero-mean Gaussian white noise in the MIMO radar receiving channel; It is the predicted distance of the target from the radar center; Step 2.2: Calculate the approximate estimated covariance matrix for all particles in each iteration. : in, It is the first The particle in the first Kalman gain in the next iteration The transfer matrix is ​​given by the following formulas: yes The covariance matrix of the approximate innovation process at time: in, and These are the particles in The Jacobian matrix and approximate measurement error covariance matrix at time t: Among them, the predicted azimuth angle ; Is the particle in Approximate Cramerlow lower bound of time, It is a constant matrix: in, It is a constant related to the CMIMO radar direction finding method, and is taken as... ; , It is the effective bandwidth of the signal; It's the speed of light; Simultaneously calculate the radar system's tracking accuracy of the target. ; Step 2.3: Extraction The variance in the variance is used to obtain the predicted position error covariance matrix. The predicted position covariance transition matrix in spherical coordinates : in, The Jacobian matrix for transforming from Cartesian to spherical coordinates is given by the following formula: Finally, the prediction standard deviations for distance and angle were calculated separately. , : in, and These are the extraction matrices for distance and angle, respectively; Step 3: To meet the tracking accuracy requirements, the following judgment needs to be made for all particles in this iteration: in, It follows a standard normal distribution. about Two-tailed quantiles; It is the gate width of the MIMO radar transmitted signal; It is the one-way beamwidth at the angular pointing position of the transmitted beam; It is the desired accuracy of target tracking; It is the false alarm rate; It is the signal-to-noise ratio threshold; If in the 1st The th iteration in the If a particle does not satisfy equation (12), then let the objective function value of that particle be... ,in, It is a pre-defined constant; at the same time, directly execute step 5; Step 4: Calculate the first... The th iteration in the The objective function value corresponding to each particle: in, It is a step function, in When it is 1, it is 0; otherwise, it is 0. It is a constant; It is the number of times the same subarray is used consecutively; The frequency domain overlap probability is calculated by the following formula: in, It refers to the duration of the interceptor's stay in that frequency band. It is the frequency band scanning period of the interceptor; It is the number of frequency bands required for the interceptor to search for all CMIMO radar transmission frequencies. This is the highest frequency that radar can transmit signals at. It is the lowest frequency that radar can transmit signals at. It intercepts the bandwidth of each scan by the receiver. It rounds the value inside the parentheses up to the nearest integer. The detection probability of the interceptor is calculated by the following formula: The signal-to-noise ratio (SNR) received by the interceptor is calculated using the following formula: in, It is the effective area of ​​the reconnaissance antenna. To provide the interceptor's effective receiving bandwidth, It is the power spectral density of zero-mean Gaussian white noise in the interceptor's receiving channel, and it has ,here It is the Boltzmann constant; For reference temperature, take ; The receiver noise figure; It is the signal processing gain of the interceptor; Step 5: Set the objective function value of each particle in this iteration. Compared with historical local optima By comparison, if the current function value is smaller, then the historical local optimum is updated to the current objective function value, and the current position is taken as the local optimum position; the minimum value among all local optima of all particles in this iteration is selected as the global optimum. And save the particle's position as the globally optimal particle position; at the same time update the positions of all particles: Simultaneously, update the velocity of all particles within the range that satisfies equation (2). If the number of subarray divisions at the current position of the particle is the same as the current... If the number of subarrays at time points is the same, then let Otherwise, place ; Step 6: Repeat steps 2-5 until the number of iterations is reached. or satisfy The number of times is consecutively greater than If the number of subarray partitions in the previous time step is the same as the number of subarray partitions in the current global best particle, then stop updating and exit; use the position information of the global best particle as... The timing plan; and These are the particle position accuracy threshold and the iteration count threshold, respectively. At this point, the globally optimal particle contains the optimal solution. ;in, and The MIMO radar will be used in... The number of subarrays and the total transmission power used at each moment; Step 7: In At time 1, the radar system transmits a signal according to the optimal scheme obtained in step 6 and receives the echo signal to obtain the measurement value; based on the obtained measurement value, Kalman filtering is performed to obtain the predicted state and prediction error covariance matrix for the next time step.

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