Self-adaptive channel allocation method for maneuvering multi-target tracking of external radiation source radar

Abstract

The invention belongs to the field of electronic system resource management and control, and particularly relates to a heuristic self-adaptive channel allocation method for maneuvering multi-target tracking of an external radiation source radar for solving the problem of external radiation source channel allocation of maneuvering multi-targets. In this heuristic approach, channel selection is made as a function of the state of the target and error covariance. And the Cramer-Rao lower bound of the prediction condition is taken as a tracking performance index of a target. Through selecting a channel which enables the joint tracking precision of the maneuvering target to be optimal each time, the tracking performance of each target can be optimal under the condition that the requirement of an external radiation source radar system is satisfied.

Description

Technical Field

[0001] The invention belongs to the field of electronic system resource management and control, and proposes an adaptive channel allocation method for mobile multi-target tracking of an external radiation source radar. Background Art

[0002] In recent years, multi-base exo-radiator radar systems with multiple opportunity radiators and multiple receivers have attracted widespread attention. Compared with active radar systems, exo-radiator systems have the following advantages: the opportunity radiator can use existing signal sources in the environment as the transmitting source, and the radar system can detect and locate the target by receiving, processing and analyzing these reflected signals. Since the signal is not actively transmitted outward, the exo-radiator radar system has the advantages of low implementation cost and zero intercept probability. The radiator radar system can isolate the reference signal and the echo signal reflected by the target, which can be achieved by pointing the directional antenna to the opportunity radiator and the monitoring area respectively or by performing digital beamforming in a multi-channel receiver equipped with an array antenna. The cross-ambiguity function between the signals is calculated for target detection, and the measurement results are associated with the channel for positioning or tracking.

[0003] In the target tracking process, the number of dual-base channels used and their geometric distance to the target play an important role in improving system performance. Physically, the more channels are used, the better the tracking performance is. When the number of channels is limited, how to adaptively select channels that are conducive to target tracking from all channels is of great research significance for fully utilizing channel performance under resource-constrained conditions.

[0004] Channel allocation is a sub-problem of radar resource allocation. There are already a lot of research foundations for the resource allocation problem of radar systems. The literature (Xie, MC (Xie, Mingchi); Yi, W (Yi, Wei); Kong, LJ (Kong, Lingjiang); Kirubarajan, T (Kirubarajan, Thia). Receive-Beam Resource Allocation for Multiple Target Tracking With Distributed MIMO Radars [J]. IEEE Transactions on Aerospace and Electronic Systems, 2018, Vol. 54 (5): 2421-2436) proposed a receive beam resource allocation strategy for distributed multiple-input multiple-output (MIMO) radar systems. Its key mechanism is to achieve the optimal allocation between the receive beam and the target based on the feedback information in the tracking recursive loop to improve the worst tracking accuracy of multiple targets. Since the a posteriori Cramer-Rao lower bound (PCRLB) provides a lower bound on the accuracy of target state estimation, it is derived and adopted as the optimization criterion. The optimal resource allocation model established is an NP-hard multidimensional non-convex allocation problem, and an effective convex relaxation optimization is proposed to solve it. The literature (Zhang, Haowei; Liu, Weijian; Zong, Binfeng; Shi, Junpeng; Xie, Junwei. An Efficient Power Allocation Strategy for Maneuvering Target Tracking in Cognitive MIMO Radar[J]. IEEE Transactions on Signal Processing, 2021, Vol. 69: 1591-1602) developed an efficient power allocation (PA) strategy for maneuvering target tracking (MTT) in co-sited MIMO radar. The strategy mechanism is to achieve optimal power allocation based on the prior target maneuvering information during the tracking process. By utilizing the monotonically decreasing characteristic of the objective function, an efficient sequential relaxation-based solver is proposed to determine the minimum allocated power for each target through an iterative loop.The paper (Jinhui Dai; Junkun Yan; Wenqiang Pu; Hongwei Liu; Maria Sabrina Greco. Adaptive Channel Assignment for Maneuvering Target Tracking in Multistatic Passive Radar [J]. IEEE Transactions on Aerospace and Electronic Systems, 2023, Vol. 59 (3): 2780-2793) proposed two adaptive channel assignment (CA) schemes for maneuvering target tracking (MTT) in multistatic passive radars, derived the predicted conditional Cramer-Rao lower bound to evaluate the impact of CA on MTT performance, and formulated the CA scheme as a convex integer programming problem, where the first problem is to optimize the target tracking accuracy under resource constraints, and the second problem is to minimize the number of channels under the condition of satisfying the target tracking accuracy. The paper proposes the methods of applying alternating multipliers and linear correction functions to solve these two problems respectively. Although the work in this paper comprehensively considers the two channel allocation methods, they are both designed for a single target.

[0005] The above work has achieved many research results, but there is no external radiation source channel allocation method for maneuvering multiple targets. To solve this problem, the present invention proposes a heuristic external radiation source maneuvering multiple target channel allocation method, which optimizes the comprehensive tracking performance of multiple targets by adaptively allocating channels. Summary of the invention

[0006] In the external radiation source cluster, consider a radar system with M opportunity radiation sources and N receiving nodes. Assume that there are a total of Q targets to be tracked in the monitoring area. At discrete time t k (t k =t k-1 +T0), the state of the target can be expressed as For a receiving node, the maximum number of beams available to the receiving node is The maximum number of nodes used for each target is expressed as For the target q, its channel node selection vector can be expressed as in is a binary variable, i.e. It means that the channel (m,n) composed of the mth opportunity radiation source and the nth receiver tracks the target q, so the node selection matrix of the multi-target channel can be expressed as The specific algorithm steps of an adaptive channel allocation method for mobile multi-target tracking of external radiation source radar at the kth frame are as follows:

[0007] Step 1: For target q, initialize its node selection matrix That is, the node selection matrix U k is a matrix of all 0s. The corresponding mapping relationship between the elements in and the receiver is: the 1st to Mth elements represent the channels formed by each radiation source and receiver 1, and so on. The (N-1)M+1th to M×Nth elements represent the channels formed by each radiation source and receiver N. If the corresponding position element is set to 1, it means that the corresponding channel is activated. Used to record the index of the channel analyzed by target q. The index value is the same as The element number in corresponds to the initial value of empty, and the number of channels selected by the target q is initialized. is 0.

[0008] Step 2: Select channels for all targets in turn. The channel selection process for target q is as follows:

[0009] Step 2.1: It is used to represent the joint tracking accuracy of target q in the channel selection process. It is an M×N dimensional vector. The smaller its value is, the higher the tracking accuracy is, that is, the better the tracking effect of the corresponding channel is. The values ​​in are initialized to infinity.

[0010] Step 2.2: For all available M×N channels of target q, select the channels that are not in the index number. To ensure that the channel will not be selected repeatedly, select one channel each time. Assume that the channel selected by the target q is

[0011] Step 2.3: Calculate the value of the objective function, the Fisher information matrix J of the target q q (x k |Z 1:k-1 ) consists of three parts Number Index The selected channel in The sum of the channels selected in 2.1 Calculate the joint tracking accuracy of target q Where Ψ is a normalized matrix, which can be expressed as (13)

[0012] The value is updated after each channel selection.

[0013] Step 2.4: After the cycle of steps 2.2-2.3 is completed, the joint tracking accuracy vector of target q is calculated. The minimum value in and the channel index corresponding to the minimum value, the obtained tracking accuracy constitutes the minimum value vector γ min .

[0014] Step 2.5: In γ min Select the minimum value of the vector and find the corresponding target and the channel index used by it based on this minimum value.

[0015] Step 2.6: Determine the rationality of the selected channel based on the channel corresponding to the target selected in step 2.5. The judgment is based on two main criteria: first, the total number of channels used by the target corresponding to the channel does not exceed the maximum number of channels of the target after adding the channel; second, it meets the requirement of the maximum number of beams that the receiver can receive, that is, the sum of the number of channels used by the same receiving node n in each target is less than the maximum number of available beams of the receiving node. If the selected channel meets the above two requirements, then The corresponding position is set to 1, and the corresponding U k The channel index number is also updated and added to middle, Add 1 and go to step 3. If the selected target channel does not meet any requirement, the target corresponding γ min Set to infinity and add the channel index number to In the process, ensure that the channel will not be selected again, and judge γ min Are all elements infinite? If so, go to step 3; otherwise, return to step 2.5.

[0016] Step 3: Repeat the channel selection process in step 2 until the maximum channel usage of all targets reaches the maximum number of channels of the target, or the maximum number of beams that the receiver can receive is reached, then exit the loop and obtain the node allocation matrix U k .

[0017] Step 4: Analyze and index the nodes of each target Set to empty, the number of channels that target q has selected Set to 0 to select the channel for the next frame.

[0018] Principle of the Invention

[0019] In the external radiation source cluster, consider a radar system with M opportunity radiation sources (Illuminators OfOpportunity, IO) and N receiving nodes. The opportunity radiation sources can use the existing signal sources in the environment as the transmission source, and the radar system can achieve target detection and positioning by receiving, processing and analyzing these reflected signals. Each receiving node is equipped with an antenna array. The position of the mth IO can be expressed as (x Tm ,y Tm ),m∈{1,2,...,M}, the position of the nth receiving node can be represented by (x Rn ,y Rn ),n∈{1,2,...,N}. And make the following assumptions:

[0020] 1. Multiple IOs occupy non-overlapping spectrum so that there is no interference between all receivers.

[0021] 2. All radar receivers are synchronized and T0 is defined as the sampling time interval.

[0022] 3. There is a known maneuvering target in the surveillance area where there is no clutter, and the measurements are correctly associated with the corresponding bistatic channels.

[0023] Considering that the motion process of each target is a maneuvering process, a limited number of S models are used to describe its possible motion patterns. The model variable r k It is controlled by a discrete random process and takes one of a finite number of S possible models. Then, the dynamics of the target q is modeled as follows:

[0024]

[0025] Among them, r k Indicates t k-1 to k The model variables that work within the time interval, It is model r k The state transfer matrix in The covariance matrix is Zero-mean Gaussian white process noise.

[0026] Assume that the receiving node n∈{1,2,...,N} can generate multiple receiving beams simultaneously. Each of these beams is dedicated to an IO or a target. Define the propagation path from the mth IO to the target and from the target to the nth receiving node as a bistatic channel (m,n), then the measurement equation of the channel (m,n) for target measurement can be expressed as follows:

[0027]

[0028] Among them, u m,n,k is a Boolean variable, u m,n,k =1 means that channel (m,n) is activated, the beam of the nth receiving node points to the target and the mth IO respectively, and the target's measurement can be received. U k That is the node selection matrix, and then the corresponding measurement value can be obtained according to the node selection matrix

[0029]

[0030] in, Represents the measurement function as shown below:

[0031]

[0032] in, is the two-way distance, is the distance from the mth IO to the target q, is the distance from the nth receiving node to the target q, is the azimuth of target q relative to the nth receiving node. To obey the covariance The measurement noise is a zero-mean Gaussian distribution.

[0033]

[0034] in, is the variance of the distance and angle measurement error, which can be approximately obtained by the following formula:

[0035]

[0036] Where c is the speed of light, λ is the beam wavelength, and γ is the antenna aperture. is the 3dB receiving beam width, B m,n,k is the effective signal bandwidth, SNR m,n,k It is the signal-to-noise ratio of the channel (m,n) composed of the mth IO and the nth receiving node acting on the target q.

[0037] The purpose of optimizing the allocation of external radiation source cluster reconnaissance tasks is to achieve the best tracking performance of the system when the number of receivers is fixed. Since the distance and angle of each sensor relative to the target are different, the tracking accuracy of the target is also different. Assume that the node selection matrix U at the previous moment is k-1 It is known that U k-1 is a matrix of Q columns and M×N rows, and assume that U k-1 The number of elements in the qth column that are 1 is L q , that is, the channels selected by target q have a total of L qAt time k-1, the system obtains the measurement value of the target q Considering the maneuvering characteristics of the target, the interactive multi-mode (IMM) method will be used to track the maneuvering target. At the same time, since the relationship between the state and the measurement is nonlinear, the EKF method is used for filtering. The channels do not interfere with each other, so the tracking of the target by each channel is independent of each other. The filtering results obtained by each local filter are filtered and fused. The fusion can be performed according to the following formula to obtain the fusion path filtering state at time k-1: and the error covariance matrix

[0038]

[0039] in, is the local target state estimation result of target q obtained by the selected lth channel after EKF filtering at time k-1, is the local target error covariance estimation result obtained for the selected lth channel. is the global target state estimation result at time k-1, is the global error covariance estimation result at time k-1. The global estimation result is used as the local filter feedback input at the next moment. The path selection based on the fusion situation is performed according to the state and error covariance after path fusion.

[0040] The tracking performance of the target q can be expressed by the predicted conditional Cramér-Rao lower bound (PC-CRLB), whose inverse is the predicted conditional Fisher information matrix (PC-FIM). Assuming that the process noise of the system is small and the predicted probability density function of the state can be approximated as a Gaussian distribution, the PC-FIM can be approximately expressed by the following formula:

[0041]

[0042] in, is the Jacobian matrix of the measurement function of the target q corresponding to the channel (m,n), is the measurement noise of channel (m,n) for target q,

[0043] From the above formula, we can get the PC-CRLB of target q at time k:

[0044]

[0045] The goal is to maximize the system tracking accuracy, and the normalized PC-CRLB trace is used as the objective function to optimize the channel selection method. The objective function at time k can be expressed as:

[0046]

[0047] Among them, Ψ is a normalized matrix, which can be expressed as:

[0048]

[0049] in, is the Kronecker product, and I2 is the second-order identity matrix. k To match the relationship matrix, it is defined as follows:

[0050]

[0051] Among them, U k Can be written as

[0052] The purpose of channel allocation for the reconnaissance mission of the external radiation source cluster with the best reconnaissance performance is to optimize the target tracking performance by controlling the matching relationship between multiple information channels and multiple targets, with a certain number of channels and a certain number of beams received by each receiving node. The optimization model of this problem can be expressed as follows:

[0053]

[0054] in, The maximum number of beams received by the nth receiving node, is the maximum number of channels that the target q can select. Physically speaking, the more measurement information is obtained, the better the tracking performance will be. Therefore, in order to achieve the best tracking performance, the original inequality constraint is changed into an equality constraint during the solution process.

[0055] The problem described by the above optimization model is a mixed integer nonlinear programming problem, in which the elements in the node selection vector are all binary variables, and there are also constraints between the node selection vectors of different targets. Therefore, the above problem is an NP-hard problem. In order to solve this problem, a heuristic method is proposed. It is described as follows: Considering that the objective function is to improve the comprehensive tracking accuracy of multiple targets, and the number of channels and the maximum number of beams of the receiving node are limited, the selected channels and the corresponding detection targets should be able to improve the target tracking accuracy to the greatest extent. Based on this, as shown in step 1, a vector is used to represent the tracking accuracy of each target using each channel, and the value in the vector is initialized to infinity, and the situation of the nodes used by each target is recorded at the same time. For each target, the unanalyzed channel is selected, and the joint tracking accuracy after adding the channel is calculated, as shown in step 2.2. Select the channel that can improve the tracking performance of the target the most. The joint tracking accuracy consists of three parts: the error covariance matrix of the target, the measurement information matrix of the selected channel, and the measurement information matrix of the selected channel, as shown in step 2.3. Find the minimum value in the joint tracking accuracy vector of each target obtained, and form a vector, select the minimum value and find the corresponding target and the channel index used by it according to this minimum value, as shown in steps 2.4-2.5. Due to the limitations of the radar system conditions, in step 2.6, the rationality of the selected channel is judged. The basis for the judgment is that the total number of channels used by the target does not exceed the maximum number of channels of the target, and the second is to meet the requirements of the maximum number of beams that the receiver can receive. If the above two conditions are met, the channel is selected. Repeat the above channel selection process until the maximum number of channels used by each target reaches the maximum number of channels of the target, or the maximum number of beams that the receiver can receive is reached, then exit the loop, as shown in step 3. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 .External radiation source system simulation scene diagram

[0057] Figure 2 .Node selection of heuristic method

[0058] Figure 3 . Schematic diagram of target tracking effect

[0059] Figure 4 Comparison of the square root of the objective function of the heuristic method, the exhaustive method, and the fixed channel method

[0060] Figure 5 .Comparison of the total tracking accuracy of the target with the heuristic method and the fixed channel method

[0061] Figure 6 .Estimation error of actual measurement, fixed channel and fusion path position filtering results DETAILED DESCRIPTION

[0062] Consider a problem of maneuvering target tracking. The system consists of 4 opportunity illumination sources IO and 3 receivers. The distribution of opportunity illumination sources and receivers and the movement of the target are as follows: Figure 1 For simplicity, the transmit power and effective bandwidth of each IO are set to p m,k =1kW,B m,n,k =0.1MHz, the dwell time and 3dB receiving beam width are T d =1s, The maximum number of beams received by each receiving node is set to For each channel (m,n), κ m,n,k =1m 2 In this case, the signal-to-noise ratio (SNR) is only related to the geometric factors. If the product of the distance from the IO to the target and the distance from the receiving node to the target satisfies R m,k ×R n,k =3500km 2 , then the reference signal-to-noise ratio is 10dB. The sampling time interval is set to T0 = 3s. Consider a motion model with a time length of 40 frames. The initial state of target 1 is set to x1 = [25000m; 300m / s; 0; 98000m; -80m / s; 0], and the initial state of target 2 is set to x2 = [30000m; -200m / s; 0; 90000m; 50m / s; 0]. The target motion consists of uniform motion and uniform turning motion. Assume that the model variable sequences of the two targets are set to r1,...,r 15 =CV,r 16 ,…,r 25 =CT,r 26 ,…,r 40 =CV, turning rate Ω = -3° / s, and the initial model probabilities are all set to [0.7; 0.1; 0.2].

[0063] Figure 2 The channel allocation results of the proposed heuristic method are given. Since M = 4 and N = 3, a total of 12 channels can be formed by IO and receiving nodes. Figure 3The channels represented by the vertical axes 1 to 12 are (m=1, n=1), (m=2, n=1), … (m=4, n=3). It can be seen from the figure that during the movement, IO2 and IO4 are selected because IO2 and IO4 are closer to the target than IO1 and IO3. Channel 2 and channel 12 are always selected because the two-way distance product of channel 12 and channel 2 composed of (m=4, n=3) and (m=2, n=1) is the smallest during the movement of the last twenty frames. At the same time, the selection of channels is also related to the degree of angular expansion and the combined gain composed of multiple channels, rather than just the two-way distance product. In addition, due to the limitations of the radar system, at the same time, receiving node 1 can receive up to 3 transmission beams from IO, receiving node 2 can receive up to 2 transmission beams from IO, and receiving node 3 can receive up to 3 transmission beams from IO. The maximum number of channels that can be activated is 4. Similarly, the node selection for target 2 is similar to the selection mechanism for target 1. Figure 2 The channel allocation relationship shown also reflects the limitation of the maximum number of beams of the receiving node on the system.

[0064] Figure 3 A schematic diagram of the tracking effect of two targets is given. It can be seen from the figure that the tracking effect after channel selection and then fusion filtering is closer to the actual trajectory of the target than the measured point traces, which illustrates the effectiveness of this method.

[0065] In order to verify the effectiveness of the adaptive channel allocation algorithm, the results obtained by the algorithm are compared with the fixed channel selection method and the exhaustive method. Figure 4 As shown. In the exhaustive method, all possible channel selection strategies are listed at a certain moment, and the channel with the smallest function value is selected from all channel selection strategies. In the above simulation scenario, there are 13392 channel selection strategies that meet the requirements of the receiver node and the total number of channels. These 13392 channel selection strategies are calculated at each tracking moment, and the one that minimizes the square root value of the objective function, that is, the tracking error, is selected as the optimal channel selection. The square root value of the objective function is compared with the square root values ​​of the objective function obtained by the other two methods. It can be seen that the values ​​obtained by the exhaustive method and the heuristic method are comparable, and are obviously smaller than the values ​​obtained by the fixed channel, that is, the tracking error is smaller. Figure 5 is the sum of the square root values ​​of the total objective function compared with the heuristic method and the fixed channel method. Figure 5It can be seen that the value of the square root of the objective function obtained by the heuristic method is very close to the value obtained by the exhaustive method, but smaller than the value obtained by the fixed channel allocation method, which shows the effectiveness of the heuristic method. In the above simulation, the exhaustive method takes about 0.313s to calculate one frame, while the heuristic method takes about 0.08s to calculate one frame, which shows that the heuristic method can significantly reduce the complexity of the operation. Figure 6 The estimated errors of the actual measurement, fixed channel and the fusion path position filtering results obtained by the heuristic method are given. Figure 6 It can be seen that both the proposed heuristic method and the fixed channel method can improve the position estimation error, and the improvement degree of the heuristic method is smaller than that of the fixed channel method.

[0066] The heuristic method proposed in the present invention is an effective solution to the channel allocation problem of mobile multi-targets in an external radiation source system, and can effectively improve the performance of multi-target tracking through real-time adaptive channel selection.

Claims

1. An adaptive channel allocation method for mobile multi-target tracking of external radiation source radar, the specific technical scheme at the kth frame is as follows: Step 1: For target q, initialize its node selection matrix That is, the node selection matrix U k is a matrix of all 0s. The corresponding mapping relationship between the elements in and the receiver is: the 1st to Mth elements represent the channels formed by each radiation source and receiver 1, and so on. The (N-1)M+1th to M×Nth elements represent the channels formed by each radiation source and receiver N. If the corresponding position element is set to 1, it means that the corresponding channel is activated. Used to record the index of the channel analyzed by target q. The index value is the same as The element number in corresponds to the initial value of empty, and the number of channels selected by the target q is initialized. is 0. Step 2: Select channels for all targets in turn. The channel selection process for target q is as follows: Step 2.1: It is used to represent the joint tracking accuracy of target q in the channel selection process. It is an M×N dimensional vector. The smaller its value is, the higher the tracking accuracy is, that is, the better the tracking effect of the corresponding channel is. The values ​​in are initialized to infinity. Step 2.2: For all available M×N channels of target q, select the channels that are not in the index number. To ensure that the channel will not be selected repeatedly, select one channel each time. Assume that the channel selected by the target q is Step 2.3: Calculate the value of the objective function, the Fisher information matrix J of the target q q (x k |Z 1:k-1 ) consists of three parts Number Index The selected channel in The sum of the channels selected in 2.1 Calculate the joint tracking accuracy of target q Where Ψ is a normalized matrix, which can be expressed as (13) The value is updated after each channel selection. Step 2.4: After the cycle of steps 2.2-2.3 is completed, the joint tracking accuracy vector of target q is calculated. The minimum value in and the channel index corresponding to the minimum value, the obtained tracking accuracy constitutes the minimum value vector γ min . Step 2.5: In γmin Select the minimum value of the vector and find the corresponding target and the channel index used by it based on this minimum value. Step 2.6: Determine the rationality of the selected channel based on the channel corresponding to the target selected in step 2.

5. The judgment is based on two main criteria: first, the total number of channels used by the target corresponding to the channel does not exceed the maximum number of channels of the target after adding the channel; second, it meets the requirement of the maximum number of beams that the receiver can receive, that is, the sum of the number of channels used by the same receiving node n in each target is less than the maximum number of available beams of the receiving node. If the selected channel meets the above two requirements, then The corresponding position is set to 1, and the corresponding U k The channel index number is also updated and added to middle, Add 1 and go to step 3. If the selected target channel does not meet any requirement, the target corresponding γ min Set to infinity and add the channel index number to In the process, ensure that the channel will not be selected again, and judge γ min Are all elements infinite? If so, go to step 3; otherwise, return to step 2.

5. Step 3: Repeat the channel selection process in step 2 until the maximum channel usage of all targets reaches the maximum number of channels of the target, or the maximum number of beams that the receiver can receive is reached, then exit the loop and obtain the node allocation matrix U k . Step 4: Analyze and index the nodes of each target Set to empty, the number of channels that target q has selected Set to 0 to select the channel for the next frame.

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