An adaptive channel allocation method for motional multi-target tracking of an external radiation source radar

Abstract

The present application belongs to the field of electronic system resource management and control, and particularly relates to a channel allocation problem of a motorized multi-target external radiation source, and proposes a heuristic adaptive channel allocation method for motorized multi-target tracking of an external radiation source radar. In the heuristic method, the channel is selected according to the state and error covariance of the target. The tracking performance index is the predicted conditional Cramer-Rao lower bound. By selecting the channel that can make the joint tracking accuracy of the motorized target optimal each time, the tracking performance of each target can be optimized under the requirements of the external radiation source radar system.

Description

Technical Field

[0001] This invention belongs to the field of electronic system resource management and proposes an adaptive channel allocation method for tracking maneuvering multi-target radar with external radiation sources. Background Technology

[0002] In recent years, multistatic exostatic radar systems with multiple opportunistic irradiation sources and multiple receivers have attracted widespread attention. Compared with active radar systems, exostatic systems offer the following advantages: opportunistic irradiation sources can utilize existing signal sources in the environment as emission sources, and the radar system achieves target detection and localization by receiving, processing, and analyzing these reflected signals. Because they do not actively emit signals, exostatic radar systems offer advantages such as low implementation cost and zero probability of intercept. Isolation systems can separate reference signals from echo signals reflected from targets. This can be achieved by pointing directional antennas at the opportunistic irradiation source and the monitored area respectively, or by performing digital beamforming in a multi-channel receiver equipped with an array antenna. Target detection is achieved by calculating cross-ambiguity functions between signals, and measurement results are correlated with channels for localization or tracking.

[0003] In target tracking, the number of bistatic channels used and their geometric distance from the target play a crucial role in improving system performance. Physically, the more channels used, the better the tracking performance. When the number of channels is limited, how to adaptively select the channels that are beneficial for target tracking from all channels is of great research significance for fully utilizing channel performance under resource constraints.

[0004] Channel allocation is a subproblem of radar resource allocation, and there is already a great deal of research on resource allocation for 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) proposes 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, thereby improving the worst-case tracking accuracy for multiple targets. Since the posterior Cramer-Rao lower bound (PCRLB) provides a lower bound for the accuracy of target state estimation, it is derived and adopted as the optimization criterion. The established optimal resource allocation model is an NP-hard multidimensional non-convex allocation problem, which is solved by an efficient convex relaxation optimization method. The paper (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) develops an efficient power allocation (PA) strategy for maneuvering target tracking (MTT) in co-located MIMO radar. The strategy mechanism achieves optimal power allocation based on 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, which determines the minimum allocated power for each target through iterative loops.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) proposes two adaptive channel assignment (CA) schemes for maneuvering target tracking (MTT) in multistatic passive radar. It derives a predicted conditional Cramer-Rao lower bound to evaluate the impact of CA on MTT performance and formulates the CA scheme as a convex integer programming problem. The first problem optimizes target tracking accuracy under resource constraints, while the second problem minimizes the number of channels while satisfying target tracking accuracy. The paper proposes methods using alternating multipliers and linear correction functions to solve these two problems respectively. Although the work comprehensively considers both channel assignment methods, both are designed for single targets.

[0005] While the aforementioned work has yielded numerous research results, a method for allocating external radiation source channels for maneuvering multi-target targets has yet to be found. To address this issue, this invention proposes a heuristic method for allocating external radiation source channels for maneuvering multi-target targets, optimizing the overall tracking performance of multiple targets through adaptive channel allocation. Summary of the Invention

[0006] Suppose there exists a... An opportunity for radiation sources, A radar system with [number] receiving nodes, assuming there are a total of [number] nodes within the monitored area. Each target needs to be tracked. At discrete times... At that time, the state of the target can be represented as For the receiving node, the maximum number of beams available to the receiving node is: The maximum number of nodes for each target is represented by the number of nodes. For the target Its channel node selection vector can be represented as ,in It is a binary variable. Indicates by the first The first opportunity radiation source and the first A channel consisting of receivers For the target Tracking is performed. An adaptive channel allocation method for tracking maneuvering multi-target radar with an external radiation source is proposed. The specific steps during frame time are as follows:

[0007] Step 1: Initialize the target Number of channels already selected Set the value to 0 to initialize the node selection matrix. It is a matrix of all zeros, therefore the target Node selection vector . The mapping relationship between the elements in the array and the receiver is as follows: Each element represents a channel formed by the radiation source and receiver 1, and so on, until the 1st element... Each element represents a radiation source and a receiver. The constructed channels, if the corresponding element is set to 1, indicate that the corresponding channel is active. Variables Used to record targets The analyzed channel number index, the index value is... The element index corresponds to the element index, and is initially set to empty.

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

[0009] Step 2.1: Used to represent the target during the channel selection process The joint tracking accuracy is a A vector of dimension 1, where a smaller value indicates higher tracking accuracy, meaning that adding the corresponding channel results in better tracking performance. The value in is initialized to infinity.

[0010] Step 2.2: For the target All available Each channel, sequentially select those not listed by index number. The channels are selected one at a time to ensure that no channel is selected repeatedly, assuming the target... The selected channel is .

[0011] Step 2.3: Calculate the target Fisher Information Matrix :

[0012]

[0013] in, The goal The error covariance matrix, The goal Corresponding channel The Jacobian matrix of the measurement function, For channel For the goal Measurement noise, It is a numbered index The measurement information matrix of the selected channels in the matrix. It is the channel selected in step 2.2. The measurement information matrix.

[0014] Target The joint tracking accuracy is expressed as:

[0015]

[0016] in, It is a normalized matrix, which can be represented as:

[0017]

[0018] in, For Kronecker product, It is a second-order identity matrix. It is the sampling time interval. The value will be updated each time a channel is selected.

[0019] Step 2.4: After the loop in steps 2.2-2.3 is completed, calculate the target value. Joint tracking accuracy vector The minimum value in the vector, along with the channel index corresponding to the minimum value, forms the minimum value vector by combining the obtained tracking accuracy. .

[0020] Step 2.5: In The minimum value of the vector is selected, and the corresponding target and its channel index are found based on this minimum value.

[0021] Step 2.6: Determine the rationality of the selected channel based on the corresponding target channel selected in Step 2.5. The determination is based on two criteria: first, the total number of channels used by all targets after adding this channel does not exceed the target's maximum number of channels; second, it meets the requirement of the receiver's maximum receivable beam count, meaning that each target corresponds to the same receiving node. The sum of the number of channels used is less than the maximum number of available beams at the receiving node. If the selected channel meets the above two requirements, then in the corresponding... The corresponding position is set to 1, the corresponding It is also updated accordingly, and the channel index number is added. middle, Add 1, proceed to step 3; if the selected target channel does not meet any of the requirements, then change the target to the corresponding... Set to infinity and add the channel index number to In the middle, ensure that the channel will not be selected again, and at the same time judge If all elements are infinite, proceed to step 3; otherwise, return to step 2.5.

[0022] 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 for 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. .

[0023] Step 4: Analyze and index the nodes of each target. Set to empty, target Number of channels already selected Set it to 0 to select the channel for the next frame.

[0024] Inventive Principles

[0025] In an external radiation source cluster, consider a cluster with... Illuminators of Opportunity (IO) A radar system with multiple receiving nodes utilizes existing signal sources in the environment as emission sources. The radar system detects and locates targets by receiving, processing, and analyzing these reflected signals. Each receiving node is equipped with an antenna array. The location of an I / O can be represented as , No. The location of each receiving node can be represented as And we make the following assumptions:

[0026] 1. Multiple I / Os occupy non-overlapping spectrum, ensuring no interference between all receivers.

[0027] 2. All radar receivers complete synchronization and definition. This represents the sampling time interval.

[0028] 3. A known moving target exists in the surveillance area where there is no clutter, and the measurement results are correctly correlated with the corresponding bistatic channel.

[0029] Considering that the motion of each target is a maneuvering process, therefore, using a finite Several models are used to describe its possible motion patterns, and model variables are... Controlled by a discrete stochastic process, and taking a finite number of... One of the possible models. Then, for the target. The dynamic model is as follows:

[0030]

[0031] in, express arrive Model variables that are effective within the time interval. It is a model The state transition matrix in The covariance matrix is ​​represented as Zero-mean Gaussian white process noise.

[0032] Assuming the receiving node Multiple receive beams can be generated simultaneously. Each of these beams is dedicated to a single I / O or a single target. The definition starts from the first... IO to target and from target to the target The propagation path of each receiving node is a dual-base channel. Then the channel The measurement equation for the target measurement can be expressed by the following formula:

[0033]

[0034] in, It is a Boolean variable. Indicates channel Activated, number The beams of the receiving nodes are respectively pointed to the target and the first receiving node. Each I / O can receive measurements of the target. Matrix , This is the node selection matrix, and the corresponding measurement values ​​can be obtained based on the node selection matrix. .

[0035]

[0036] in, The measurement function is represented as shown in the following equation:

[0037]

[0038] in, For two-way distance, It is the first One IO to target distance, It is the first Each receiving node to the target distance, For the goal Compared to the first The azimuth angle of each receiving node. To conform to the covariance Measurement noise with a zero-mean Gaussian distribution.

[0039]

[0040] in, , The variance of the distance and angle measurement errors can be approximated by the following formula:

[0041]

[0042] in, At the speed of light, For the beam wavelength, For antenna aperture, The receiving beamwidth is 3 dB. For the effective bandwidth of the signal, It is the first The first IO and the first A channel consisting of receiving nodes Acting on the target Signal-to-noise ratio at that time.

[0043] The goal of optimizing the allocation of reconnaissance missions for external radiation sources is to achieve the best system tracking performance with a fixed number of receivers. Since each sensor has a different distance and angle relative to the target, the tracking accuracy will also vary. Assume the node selection matrix at the previous time step... It is known that It is List, A matrix of rows, and assume The Middle The number of elements in the column with a value of 1 is , that is, the goal The selected channels have a total of One, in At that moment, the system obtains the target. Measured values Considering the target's maneuvering characteristics, an Interactive Multimode (IMM) approach will be used for maneuvering target tracking. Simultaneously, since the relationship between state and measurement is non-linear, an Extensive Kinematic Filter (EKF) method will be employed for filtering. Since channels do not interfere with each other, the target tracking of each channel is independent. The filtering results obtained from each local filter will be fused using the following formula: Fusion path filtering state at time step And error covariance matrix :

[0044]

[0045]

[0046] in, for The selected time after EKF filtering The target obtained by each channel Local target state estimation results, For the selected number The local target error covariance estimation results obtained from each channel. for The global target state estimation results at any given time. for The global error covariance estimation result at time step 1 is used as the local filter feedback input at the next time step. Based on the state after path fusion and the error covariance, path selection is then performed based on the fusion condition.

[0047] Target The tracking performance can be represented by the predicted conditional Cramér-Rao lower bound (PC-CRLB), whose inverse is the predicted conditional Fisher information matrix (PC-FIM). Assuming that the system has low process noise and the predicted probability density function of the state can be approximated as a Gaussian distribution, the PC-FIM can be approximated by the following equation:

[0048]

[0049]

[0050] in, It can be represented as: .

[0051] The target can be obtained from the above formula. exist PC-CRLB at any given moment:

[0052]

[0053] With the goal of maximizing system tracking accuracy, and using the normalized PC-CRLB trace as the objective function, the channel selection method is optimized. The objective function at time step can be expressed as:

[0054]

[0055] The matching relation matrix is ​​defined as follows:

[0056]

[0057] in, It can be written as .

[0058] The purpose of channel allocation in reconnaissance missions based on optimal reconnaissance performance of external radiation source clusters is to optimize target tracking performance by controlling the matching relationship between multiple information channels and multiple targets, given a fixed number of channels and a fixed number of beams received by each receiving node. The optimization model for this problem can be expressed by the following equation:

[0059]

[0060] in, No. The maximum number of beams received by each receiving node. The goal The maximum number of channels that can be selected. Physically speaking, the more measurement information acquired, the better the tracking performance. Therefore, to achieve the best tracking performance, the original inequality constraints are transformed into equality constraints during the solution process.

[0061] The problem described by the above optimization model is a mixed-integer nonlinear programming problem, where 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 NP-hard. To solve this problem, a heuristic method is proposed. The method is described as follows: Considering that the objective function is to improve the integrated tracking accuracy of multiple targets, and the number of channels and the maximum number of beams of receiving nodes are limited, the selected channels and corresponding detection targets should maximize the improvement of target tracking accuracy. Based on this, as in step 1, a vector is used to represent the tracking accuracy of each target using each channel. The values ​​in the vector are initialized to infinity, and the node information used by each target is recorded. For each target, unanalyzed channels are selected, and the joint tracking accuracy after adding channels is calculated, as shown in step 2.2. The channel that maximizes the target's tracking performance is selected. The joint tracking accuracy consists of three parts: the target's error covariance matrix, the measurement information matrix of the selected channels, and the measurement information matrix of the selected channels, as shown in step 2.3. Find the minimum value among the joint tracking accuracy vectors of all targets and construct a vector. Select the minimum value and find the corresponding target and its channel index based on this minimum value, as shown in steps 2.4-2.5. Due to the limitations of the radar system, in step 2.6, determine the rationality of the selected channel. The criteria for determination are: first, the total number of channels used by the target does not exceed the target's maximum number of channels; and second, it meets the requirement of the receiver's maximum receivable beam count. If both 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 target's maximum number of channels, or reaches the receiver's maximum receivable beam count, at which point the loop exits, as shown in step 3. Attached Figure Description

[0062] Figure 1 Simulation scenario diagram of external radiation source system.

[0063] Figure 2 Node selection in heuristic methods

[0064] Figure 3 . Schematic diagram of target tracking effect

[0065] Figure 4 Comparison of the square root values ​​of the objective function of heuristic methods, exhaustive methods, and fixed-channel methods.

[0066] Figure 5 A comparison of the total target tracking accuracy with heuristic and fixed-channel methods.

[0067] Figure 6 Estimation errors of actual measurements, fixed channels, and fused path position filtering results. Detailed Implementation

[0068] Consider a maneuvering target tracking problem. The system consists of four opportunistic illumination sources (IOs) and three receivers. The distribution of the opportunistic illumination sources and receivers and the target's motion are as follows: Figure 1 As shown. For simplicity, the transmit power and effective bandwidth of each IO are set to... The dwell time and the 3 dB receiving beamwidth are The maximum number of beams that each receiving node can receive is set to... For each channel , In this case, the signal-to-noise ratio (SNR) depends only on 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... The reference signal-to-noise ratio is then 10 dB. The sampling time interval is set to... Consider a motion model with a duration of 40 frames. Set the initial state of target 1 as follows: The initial state of objective 2 is set as The target motion consists of uniform motion and uniform turning motion. Assume that the model variable sequences for both targets are set as follows: Steering rate The initial model probabilities are all set to .

[0069] Figure 2 The channel allocation results of the proposed heuristic method are presented. , Therefore, a total of 12 channels can be formed by the IO and the receiving node. Figure 3 The channels represented by the vertical axes 1 to 12 are respectively As can be seen from the graph, IO2 and IO4 are selected during the motion because they are closer to the target than IO1 and IO3. Channels 2 and 12 are consistently selected because during the motion of the last twenty frames, [the following text appears to be unrelated and possibly machine-generated: "by..."] The product of the two-way ranges of channels 12 and 2 is minimized. Furthermore, channel selection is related to the angular spread and the combined gain of multiple channels, not just the two-way range product. Additionally, due to limitations of the radar system, at any given time, receiving node 1 can receive a maximum of 3 transmitted beams from IO, receiving node 2 can receive a maximum of 2 transmitted beams from IO, and receiving node 3 can receive a maximum of 3 transmitted beams from IO. The maximum number of channels that can be activated is 4. Similarly, the node selection mechanism for target 2 is similar to that 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.

[0070] Figure 3 A schematic diagram of the tracking effect of two targets is given. As can be seen from the figure, the tracking effect after channel selection and fusion filtering is closer to the true trajectory of the target than the measured point trace, which demonstrates the effectiveness of the method.

[0071] To verify the effectiveness of the adaptive channel allocation algorithm, the results obtained by the algorithm are compared with those of the fixed channel selection method and the exhaustive method. The results are as follows: Figure 4 As shown, the exhaustive method enumerates all possible channel selection strategies at a given time and selects the channel that minimizes the function value from all strategies. In the simulation scenario above, 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 time, and the one that minimizes the square root of the objective function (i.e., the tracking error) is selected as the optimal channel selection. The square root of the objective function obtained by this method is compared with the square root 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 significantly smaller than the values ​​obtained by the fixed channel method, i.e., the tracking error is smaller. Figure 5 This is a comparison between the sum of the square roots of the overall objective function and heuristic and fixed-channel methods, from... Figure 5 As can be seen, the square root of the objective function obtained by this 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. This demonstrates the effectiveness of the heuristic method. Furthermore, in the above simulation, the exhaustive method requires approximately [missing information - likely a number of frames] to compute. The heuristic method requires approximately [a certain amount of computation time] per frame. This demonstrates that the heuristic method can significantly reduce computational complexity. Figure 6 The estimation errors of the fused path position filtering results obtained from actual measurements, fixed channels, and this heuristic method are presented. 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 of the heuristic method is smaller than that of the fixed-channel method.

[0072] The heuristic method proposed in this invention is an effective solution to the channel allocation problem of maneuvering multiple targets in external radiation source systems, and can effectively improve the performance of multi-target tracking through real-time adaptive channel selection.

Claims

1. An adaptive channel allocation method for tracking maneuvering multi-target radar with an external radiation source, in the first... The specific steps during frame time are as follows: Step 1: Initialize the target Number of channels already selected Set the value to 0 to initialize the node selection matrix. It is a matrix of all zeros, therefore the target Node selection vector ; The mapping relationship between the elements in the array and the receiver is as follows: Each element represents a channel formed by the radiation source and receiver 1, and so on, until the 1st element... Each element represents a radiation source and a receiver. The constructed channel, if the corresponding element is set to 1, indicates that the corresponding channel is active; variables Used to record targets The analyzed channel number index, the index value is... The element indices correspond to the element indices, and are initially set to empty; Step 2: Select channels for all targets in sequence. The channel selection process is as follows: Step 2.1: Used to represent the target during the channel selection process The joint tracking accuracy is a A vector of dimension 1, where a smaller value indicates higher tracking accuracy, meaning that adding the corresponding channel results in better tracking performance. The value in is initialized to infinity; Step 2.2: For the target All available Each channel, sequentially select those not listed by index number. The channels are selected one at a time to ensure that no channel is selected repeatedly, assuming the target... The selected channel is ; Step 2.3: Calculate the target Fisher Information Matrix : in, The goal The error covariance matrix, The goal Corresponding channel The Jacobian matrix of the measurement function, For channel For the goal Measurement noise, It is a numbered index The measurement information matrix of the selected channels in the matrix. It is the channel selected in step 2.

2. Measurement information matrix; Target The joint tracking accuracy is expressed as: in, It is a normalized matrix, represented as: in, For Kronecker product, It is a second-order identity matrix. It is the sampling time interval. The value will be updated accordingly each time a channel is selected; Step 2.4: After the loop in steps 2.2-2.3 is completed, calculate the target value. Joint tracking accuracy vector The minimum value in the vector, along with the channel index corresponding to the minimum value, forms the minimum value vector by combining the obtained tracking accuracy. ; Step 2.5: In Select the minimum value of the vector and find its corresponding target and the channel index it uses based on this minimum value; Step 2.6: Determine the rationality of the selected channel based on the corresponding target channel selected in Step 2.

5. The determination is based on two criteria: first, the total number of channels used by all targets after adding this channel does not exceed the target's maximum number of channels; second, it meets the requirement of the receiver's maximum receivable beam count, meaning that each target corresponds to the same receiving node. The sum of the number of channels used is less than the maximum number of available beams at the receiving node. If the selected channel meets the above two requirements, then in the corresponding The corresponding position is set to 1, the corresponding It is also updated accordingly, and the channel index number is added. middle, Add 1, proceed to step 3; if the selected target channel does not meet any of the requirements, then change the target to the corresponding... Set to infinity and add the channel index number to In the middle, ensure that the channel will not be selected again, and at the same time judge If all elements are infinite, proceed to step 3; otherwise, return to step 2.

5. 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 the maximum number of beams that the receiver can receive is reached. Then exit the loop and obtain the node selection matrix. ; Step 4: Analyze and index the nodes of each target. Set to empty, target Number of channels already selected Set it to 0 to select the channel for the next frame.

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