Rapid external radiation source radar maneuvering multi-target tracking channel distribution method

Abstract

The invention belongs to the field of electronic system resource management and control, and particularly relates to a rapid external radiation source radar maneuvering multi-target tracking channel allocation method for solving the problem of external radiation source channel allocation of maneuvering multi-targets. In the method, channel selection is carried out according to the state of a target and an 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 a maneuvering target to be optimal each time, the total tracking performance of each target can be optimal under the condition that the requirements of the beam number of an external radiation source radar system and the capability of a data processing unit are met.

Description

Technical Field

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

[0002] In recent years, multi-static external radiation source radar systems with multiple opportunity radiation sources and multiple receivers have received extensive attention. Compared with active radar systems, external radiation source systems have the following advantages: The opportunity illumination source can use existing signal sources in the environment as the transmission source, and the radar system realizes target detection and positioning by receiving, processing, and analyzing these reflected signals. Since it does not actively transmit signals outward, the external radiation source radar system has the advantages of low implementation cost and zero intercept probability. The radiation source radar system can simultaneously receive the reference signal and the echo signal reflected by the target, which can be achieved by respectively pointing the directional antenna at the opportunity illumination source and the surveillance area or by performing digital beamforming in a multi-channel receiver equipped with an array antenna. The cross ambiguity function between signals is calculated for target detection, and the measurement results are associated with the channels for positioning or tracking.

[0003] During the target tracking process, the number of bistatic channels used and the geometric relationship between the channels and the target will affect the system performance. Physically speaking, the more channels are used, the better the tracking performance obtained. When the number of given channel sets is limited, how to adaptively select channels that are conducive to target tracking from all channels is of great research significance for giving full play to the channel performance under resource constraints.

[0004] Channel allocation is a sub-problem of radar resource allocation. There has been a lot of research foundation 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 MultipleTarget Tracking With Distributed MIMO Radars[J]. IEEE Transactions onAerospace 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 according to the feedback information in the tracking recursive loop to improve the worst tracking accuracy of multiple targets. Since the posterior Cramér-Rao lower bound (PCRLB) provides the lower bound of the target state estimation accuracy, it was derived and adopted as the optimization criterion. The established optimal resource allocation model is an NP-hard multi-dimensional non-convex allocation problem, and an effective convex relaxation optimization was proposed in the paper to solve the task allocation. The literature (Yan J, Liu H, Jiu B, et al. Simultaneous multibeamresource allocation scheme for multiple target tracking[J]. IEEE Transactionson Signal Processing, 2015, 63(12):3110-3122) proposed a resource allocation strategy for multi-target tracking tasks in the multi-beam working mode. The number and direction of the beams and the transmit power of each beam are adjusted through feedback to improve the worst tracking performance among multiple targets. The optimal solution is obtained by reformulating the resulting non-convex resource optimization problem as a series of convex problems to determine the resource allocation scheme.The literature (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 radar, derived the predicted conditional Cramér-Rao lower bound to evaluate the impact of CA on MTT performance, and formulated the CA scheme as a convex integer programming problem. Among them, 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 meeting the target tracking accuracy. In this paper, methods applying alternating multipliers and linear correction functions are proposed to solve these two problems respectively. Although the work in this paper comprehensively considers two channel assignment methods, they are all designed for single targets. In the multi-target scenario, it is not a simple extension of the single-target scenario, and the optimization problem model and algorithm need to be readjusted.

[0005] The above work has achieved many research results, but no external radiation source channel assignment method for maneuvering multi-targets has been seen. To address this problem, the present invention proposes a fast external radiation source maneuvering multi-target channel assignment method to optimize the multi-target comprehensive tracking performance through adaptive channel assignment. Summary of the Invention

[0006] In an external radiation source cluster, consider a radar system with M opportunistic radiation sources and N receiving nodes. Assume that there are a total of Q targets to be tracked in the surveillance area. At discrete time t k (t k =t k-1 +T0), the state of the target can be expressed as For the receiving node, the maximum number of available beams of the receiving node is Due to the limited information processing capacity of the information interaction unit, the maximum number of node usages for each target is expressed as For target q, its channel node selection vector can be expressed as Where is a binary variable, that is Indicates that the channel (m,n) composed of the m-th opportunistic radiation source and the n-th receiver acts on target q. Therefore, the node selection matrix of the channels for multi-targets can be expressed as The specific algorithm steps of an adaptive channel allocation method for maneuvering multi-target tracking in an external radiation source radar at the k-th frame are as follows:

[0007] Step 1: Initialize the node selection matrix U k as a matrix of all zeros. The variable χ index is used to record the index numbers of the channels that have been analyzed for all targets. This index value corresponds to the sequence number of each column element in U k and is initially empty. η channel is used to represent the joint tracking accuracy in the channel selection process and is an MN×Q-dimensional matrix. η_q is used to represent the joint tracking accuracy of target q in the channel selection process and is an M×N-dimensional vector. The smaller its value, the higher the tracking accuracy, that is, the better the tracking effect of adding the corresponding channel. The contribution matrix C is an MN×Q-dimensional matrix, and its values are initially set to infinity.

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

[0009] Step 2.1: For all available M×N channels of target q, select the channels that are not in the index numbers in turn to ensure that the channels are not selected repeatedly. Each time a channel is selected. Assume the channel selected by target q is

[0010] Step 2.2: Calculate the value of the objective function. The Fisher information matrix J q (X k |Z 1:k-1 ) of target q consists of three parts, including the sum of the information amounts of the channels that have been selected in the index numbers plus the Fisher information amount of the channel selected in 2.1 Calculate the joint tracking accuracy of target q At the same time, record the tracking accuracy composed of the first two parts when the channel selected in 2.1 is not selected The value will be updated after each channel selection.

[0011] Step 2.3: After the loop in Steps 2.1 - 2.2 ends, calculate the tracking accuracy contribution matrix C = η channel - η' channel .

[0012] Step 2.4: Select the minimum value in the contribution matrix C and find the corresponding target q and the channel index used according to this minimum value. And set this minimum value to infinity to ensure that the target channel combinations that do not meet the requirements will not be analyzed repeatedly.

[0013] Step 2.5: Determine the rationality of the selected channel corresponding to the target q according to Step 2.4. There are mainly two bases for the determination: one is that after adding the channel corresponding to the target, the total number of channels used by each target, that is, the number of elements in does not exceed the maximum number of channels of the target The second is to meet the requirement of the maximum number of beams that the receiver can receive, that is, the sum of the number of channels used by each target corresponding to the same receiving node n plus the number of external radiation sources used is not greater than the maximum number of available beams of the receiving node If the selected channel meets the above two requirements, then at the corresponding U k Disposal 1, and add the channel index number to and enter Step 3. If the selected target channel does not meet any of the requirements, return to Step 2.4.

[0014] Step 3: Repeat the channel selection process in Step 2 until the maximum number of channels used by all targets reaches the maximum number of channels of the target, or until the maximum number of beams that the receiver can receive is reached, then exit the loop to obtain the node allocation matrix U k .

[0015] Step 4: Set the node analysis index χ of each target index to be empty, and perform channel selection for the next frame.

[0016] Principle of the invention

[0017] In an external radiation source cluster, consider a radar system with M opportunity radiation sources (Illuminators Of Opportunity, IO) and N receiving nodes. The opportunity radiation sources can use the existing signal sources in the environment as transmitters, and the radar system realizes 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 m-th IO can be expressed as (x Tm , y Tm ), m ∈ {1, 2,..., M}, and the position of the n-th receiving node can be expressed as (x Rn , y Rn ), n ∈ {1, 2,..., N}. And the following assumptions are made:

[0018] 1. Multiple IOs occupy non-overlapping spectra, so that there is no interference between all receivers.

[0019] 2. All radar receivers are synchronized, and T0 is defined as the sampling time interval.

[0020] 3. There is a known maneuvering target in the surveillance area without clutter, and the measurement results are correctly associated with the corresponding bistatic channels.

[0021] Assume that the receiving node \(n\in\{1,2,\ldots,N\}\) can generate multiple receiving beams simultaneously. Each of these beams is dedicated to an IO or a target. Define the propagation paths from the \(m\)-th IO to the target and from the target to the \(n\)-th receiving node as the bistatic channel \((m,n)\). Then, the measurement equation of the channel \((m,n)\) with respect to the target measurement can be expressed as follows:

[0022]

[0023] where, \(u\) m,n,k is a Boolean variable, \(u\) m,n,k \( = 1\) indicates that the channel \((m,n)\) is activated, the beams of the \(n\)-th receiving node are respectively directed to the target and the \(m\)-th IO, and the measurement of the target can be received. The matrix \(U\) k is the node selection matrix, and then the corresponding measurement value can be obtained according to the node selection matrix

[0024]

[0025] where, represents the measurement function, as shown in the following formula:

[0026]

[0027] where, is the two-way distance, is the distance from the \(m\)-th IO to the target \(q\), is the distance from the \(n\)-th receiving node to the target \(q\), is the azimuth angle of the target \(q\) relative to the \(n\)-th receiving node. is the measurement noise that follows a zero-mean Gaussian distribution with covariance .

[0028]

[0029] where, is the variance of the distance and angle measurement errors, which can be approximately obtained by the following formula:

[0030]

[0031] where, \(c\) is the speed of light, \(\lambda\) is the beam wavelength, \(\gamma\) is the antenna aperture, is the 3dB receiving beam width, \(B\) m,n,k is the effective signal bandwidth, SNR m,n,kis the signal-to-noise ratio when the channel (m,n) composed of the m-th IO and the n-th receiving node acts on the target q. SNR m,n,k can be obtained by the following formula:

[0032]

[0033] where, T d is the dwell time, T r is the pulse repetition interval, p m,k is the transmit power of the m-th IO, G t is the transmitting antenna gain of the external radiation source, Gr is the radar receiving antenna gain, κ m,n,k is the radar cross section (RCS) of the target relative to the channel (m,n). G RP is the processing gain, k0 is the Boltzmann constant, T0 is the noise temperature, β m,k is the effective bandwidth of the matched filter, F r is the noise factor, is the 3dB receiving beamwidth. Note that the parameters p m,k , β m,k , κ m,n,k , G t are related to the types of IO and the target, and are beyond the control range of the external radiation source radar.

[0034] The purpose of the optimal allocation of the external radiation source cluster reconnaissance mission is to make the system tracking performance reach the optimal when the number of receivers is certain. Since the distances and angles of each sensor relative to the target are different, the tracking accuracy of the target is also different. It can be seen from equations (5) and (6) that the selection of the channel affects the signal-to-noise ratio by affecting the product of the round-trip distances, thereby affecting the measurement error and then the tracking accuracy.

[0035] The centralized interacting multiple model method is adopted in the tracking process. The tracking performance of the target q can be represented by the predicted conditional Cramér-Rao lower bound (PC-CRLB), and its 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, then PC-FIM can be approximately represented by the following formula:

[0036]

[0037]

[0038] where, is the predicted error covariance matrix, is the Jacobian matrix of the measurement function for the target q corresponding to the channel (m, n). is the measurement noise of the channel (m, n) for the target q. are the prediction probabilities of different models. is the state transition function of different models.

[0039] From the above formula, the PC-CRLB of the target q at time k can be obtained:

[0040]

[0041] With the goal of maximizing the system tracking accuracy and using the trace of the normalized PC-CRLB as the objective function, the channel selection method is optimized. The objective function at time k can be expressed as:

[0042]

[0043] where Ψ is the normalization matrix and can be expressed as:

[0044]

[0045] where is the Kronecker product, and I2 is the second-order identity matrix. U k is the matching relationship matrix, defined as follows:

[0046]

[0047] where U k can be written as

[0048] The purpose of the channel allocation for the external radiation source cluster reconnaissance mission based on the optimal reconnaissance performance is to optimize the tracking performance of the target 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 by the following formula:

[0049]

[0050] where is the maximum number of beams of the nth receiver. The indicator function I(·) can be expressed as:

[0051]

[0052] It can be seen that represents the number of IO signals that the nth receiver needs to receive, It represents the number of target echoes received by the nth receiver. Physically speaking, if more measurement information is obtained, the tracking performance will be better. Therefore, to achieve the best tracking performance, the original inequality constraint is changed to an equality constraint during the solution process.

[0053] The problem described by the above optimization model is a mixed-integer non-linear programming problem. The elements in the node selection vector are all binary variables, and there are also constraint relationships between the node selection vectors of different targets. Therefore, the above problem is an NP-hard problem. To solve this problem, a fast channel allocation method for maneuvering multi-target tracking of passive bistatic radar is proposed, which is described as follows: Considering that the objective function is to improve the comprehensive tracking accuracy of multi-targets, and the number of channels and the maximum beam number of receiving nodes are limited. Therefore, the selected channels and the corresponding detected targets should be able to improve the target tracking accuracy to the greatest extent. Based on this, in step 1, a matrix is used to represent the contribution degree of each channel to the improvement of the tracking accuracy of different targets. The values in the matrix are initialized to infinity, and at the same time, the situation of the nodes used by each target is recorded. For each target, the unanalyzed channels are selected, and the joint tracking accuracy after adding the channels is calculated, as shown in step 2.2. The joint tracking accuracy consists of three parts: the error covariance matrix of the target, the measurement information matrix of the selected channels, and the measurement information matrix of the selected channels, as shown in step 2.3. Subtract the joint tracking accuracy of the target before the unselected channels from the joint tracking accuracy of the target after the selected channels, select the minimum value among them, 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 channels is judged. The judgment basis is that the total number of channels used by the target does not exceed the maximum number of channels of the target, and the requirement of the maximum number of beams that the receiver can receive is met. 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, and then exit the loop, as shown in step 3. Brief Description of the Drawings

[0054] Figure 1 . Simulation scenario diagram of the passive bistatic system

[0055] Figure 2 . Channel selection situation of the proposed method

[0056] Figure 3 . Comparison of objective functions of the proposed method, exhaustive method, random channel and fixed channel methods

[0057] Figure 4 . Change of the switching probability of the target motion model

[0058] Figure 5. RMSE Comparison of the Method Proposed for Target 1, Exhaustive Search Method, Random Channel and Fixed Channel Methods

[0059] Figure 6 . RMSE Comparison of the Method Proposed for Target 2, Exhaustive Search Method, Random Channel and Fixed Channel Methods Detailed Implementation Manner

[0060] Consider a problem of maneuvering target tracking. The system consists of 4 opportunistic illuminators (IOs) and 3 receivers. The distribution of the opportunistic illuminators and receivers and the movement of the target are as Figure 1 shown. For simplicity, set the transmit power and effective bandwidth of each IO to p m,k = 1 kW, B m,n,k = 0.1 MHz, the dwell time and 3 dB receive beamwidth are T d = 1 s, The maximum number of receive beams received by each receiving node is set to For each channel (m,n), κ m,n,k = 1 m 2 , in this case, the signal-to-noise ratio (SNR) is only related to 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 = 3500 km 2 , then the reference SNR is 10 dB. The sampling time interval is set to T0 = 1 s. Consider a motion model with a time length of 100 frames. Assume that there are two targets moving in the surveillance area, and the target can be affected by at most channels. Set the initial state of Target 1 to x1 = [35000 m; 200 m / s; 0; 98000 m; -80 m / s; 0], and the initial state of Target 2 to x2 = [35000 m; -200 m / s; 0; 60000 m; -100 m / s; 0]. The target motion consists of uniform motion and uniform turning motion. Assume that the model variable sequences of the two targets are both set to r1,...,r 39 = CV, r 40 ,..., r 60 = CT, r 61 ,..., r 100 = CV, the turning rate Ω = -6° / s, and the initial model probabilities are both set to [0.8; 0.2].

[0061] Figure 2 The channel allocation results of the proposed fast method are given. Since M = 4 and N = 3, a total of 12 channels can be formed by the IOs and receiving nodes. In 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, for target 1, the mainly selected channels are channels 2, 6, 8, and 12, and the corresponding IOs are IO2 and IO4. This is because compared with IO1 and IO3, the round-trip distance product of the channels formed by IO2 and IO4 and the receiver is the smallest, and at the same time, the angular expansion degree is relatively good. In addition, due to the limitations of the radar system, at the same time, receiving node 1 can receive at most 4 beams, receiving node 2 can receive at most 3 beams, and receiving node 3 can receive at most 3 beams. Similarly, for target 2, the above node selection situation is similar to the selection mechanism of target 1. Each target can be affected by at most 4 channels at the same time, and the mainly selected channels for target 2 are channels 1, 2, 11, and 12, and the corresponding IOs are IO1 and IO2. It is also because the channels formed by IO1 and IO2 have better tracking accuracy improvement. Figure 2 The shown channel allocation relationship reflects both the maximum beam number limit of the receiving nodes and the maximum number of channels that can act on the target.

[0062] To verify the effectiveness of the adaptive channel allocation algorithm, the results obtained by this algorithm are compared with the fixed channel selection method, random channel allocation, and exhaustive method. The obtained results are as Figure 3 shown. In the exhaustive method, by listing all possible channel selection strategies at a certain moment, the channel that makes the function value the smallest is selected from all the channel selection strategies. In the above simulation scenario, there are a total of 74088 channel selection strategies that meet the requirements of the receiver nodes and the total number of channels. At each tracking moment, these 74088 channel selection strategies are calculated, and the one that makes the square root value of the objective function, that is, the tracking error, the smallest is selected as the optimal channel selection, and its square root value of the objective function is compared with that obtained by other methods. It can be seen that the values obtained by the exhaustive method and the proposed fast method are relatively close, and are significantly smaller than those of the fixed channel allocation and random channel allocation. And in the above simulation, the exhaustive method takes about 5.14 s to calculate one frame, while the proposed method takes about 0.004 s to calculate one frame, indicating that the proposed fast channel allocation method for maneuvering multi-target tracking of external radiation source radar is effective and feasible.

[0063] Figure 4 It is the model switching probability diagram during the movement process. It can be seen that the interacting multiple model algorithm based on centralized fusion can identify the switching of the target movement mode. Figure 5 、 Figure 6 The estimation errors of the filtering results of the proposed method and the comparison algorithm are given. From Figure 5 、 Figure 6It can be seen that the changing trend of the actual RMSE conforms to that of the objective function, indicating that it is reasonable to use PCRLB as the prediction index for characterizing the change of tracking accuracy in the radar system resource allocation process. Moreover, the proposed method has improved the tracking accuracy compared with both the fixed-channel and random-channel methods.

[0064] The proposed fast channel allocation method for maneuvering multi-target tracking in passive bistatic radar of the present invention is an effective solution, which can effectively improve the performance of multi-target tracking through real-time adaptive channel selection.

Claims

1. A channel allocation method for rapid maneuvering multi-target tracking of external illuminator radar. The specific technical solution at the k-th frame is as follows: Step 1: Initialize the node selection matrix U k as a matrix of all zeros. The variable χ index is used to record the number indices of the channels for which all targets have been analyzed. This index value corresponds to the serial number of each column element in U k and is initially empty. η channel is used to represent the joint tracking accuracy during the channel selection process and is a matrix of dimensions MN×Q. is used to represent the joint tracking accuracy of target q during the channel selection process and is a vector of dimensions M×N. The smaller its value, the higher the tracking accuracy, that is, the better the tracking effect of adding the corresponding channel. The contribution matrix C is a matrix of dimensions MN×Q, and the values in it are initially set to infinity. Step 2: Sequentially perform channel selection for all targets. The channel selection process for target q is as follows: Step 2.1: For all the available M×N channels of target q, select the channels that are not in the numbered index in turn, ensuring that the channels are not selected repeatedly. Select one channel each time. Assume the channel selected for target q is Step 2.2: Calculate the value of the objective function, the Fisher information matrix J of target q q (X k |Z 1:k-1 ) consists of three parts, including the sum of the information amounts of the already selected channels in the number index plus the Fisher information amount of the channels selected in 2.1 calculate the joint tracking accuracy of target q At the same time, record the tracking accuracy composed of the first two parts when the channels selected in 2.1 are not selected The value will be updated after each channel selection. Step 2.3: After the loop in Steps 2.1 - 2.2 ends, calculate the tracking accuracy contribution matrix C = η channel - η' channel . Step 2.4: Select the minimum value in the contribution matrix C and find the corresponding target q and its used channel index according to this minimum value. And set this minimum value to infinity to ensure that the target channel combinations that do not meet the requirements will not be repeatedly analyzed. Step 2.5: Judge the rationality of the selected channel according to the channel corresponding to the target q selected in Step 2.

4. There are mainly two bases for the judgment: one is that after adding the channel corresponding to the target, the total number of channels used by each target, that is the number of elements in does not exceed the maximum number of channels of the target The second is to meet the requirement of the maximum number of beams that the receiver can receive, that is, the sum of the number of channels used by each target corresponding to the same receiving node n plus the number of used external radiation sources is not greater than the maximum available beam number of the receiving node If the selected channel meets the above two requirements, then at the corresponding U k Disposal 1, and add the channel index number to and enter Step 3. If the selected target channel does not meet any of the requirements, return to Step 2.

4. Step 3: Repeat the channel selection process in Step 2 until the maximum channel usage of all targets reaches the maximum channel number of the target or the maximum number of beams that the receiver can receive, and then exit the loop to obtain the node allocation matrix U k . Step 4: Set the node analysis index χ of each target index to be empty and perform channel selection for the next frame.

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