CN114779232A - Real-time simultaneous multi-beam CMIMO radar networking resource management algorithm - Google Patents

Real-time simultaneous multi-beam CMIMO radar networking resource management algorithm Download PDF

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CN114779232A
CN114779232A CN202210466614.3A CN202210466614A CN114779232A CN 114779232 A CN114779232 A CN 114779232A CN 202210466614 A CN202210466614 A CN 202210466614A CN 114779232 A CN114779232 A CN 114779232A
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程婷
侯子林
李中柱
王元卿
恒思宇
付小川
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University of Electronic Science and Technology of China
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Abstract

The method belongs to the field of radar resource management, and provides a real-time simultaneous multi-beam CMIMO radar networking resource management algorithm. The method preferentially allocates resources to the target with larger difference between the tracking accuracy and the expected value, and during resource allocation, the transmitting energy required to be provided by each radar and the corresponding tracking accuracy are calculated firstly, and the radar which can provide beams and enables the tracking accuracy to reach the expected value or the transmitting energy to be increased minimally is selected. When judging whether the radar can provide the wave beam, judging whether the node can provide enough signal-to-noise ratio when no target exists in the radar task set; when a plurality of targets are included in the radar task set, the subarray division needs to be increased, whether enough signal-to-noise ratio can be provided or not is judged, and redundant beams are used for reducing radar transmission energy. The method can adaptively select the network nodes and adjust the subarray division, the emission energy and the beam distribution of the working nodes, and the total emission energy of the system is saved while the target tracking precision meets the expected value.

Description

Real-time simultaneous multi-beam CMIMO radar networking resource management algorithm
Technical Field
The method belongs to the field of radar resource management, and provides a real-time simultaneous multi-beam CMIMO radar networking resource management algorithm.
Background
A co-located Multiple Input and Multiple Output (CMIMO) radar is a radar (Jianan L, Stoica P.MIMO radio with a coordinated antenna [ J ]. IEEE Signal Process Mag,2007,24(5): 106-. However, the single CMIMO radar still has the limitations of relatively less available resources and relatively smaller monitoring range, and cannot meet the increasingly complex multi-target tracking scene. The radar networking concept overcomes the defects of a single CMIMO radar, and provides more possibilities for CMIMO radar target tracking. In a CMIMO radar network, data among radars are transmitted through a computer network, the positions of a plurality of radars are widely distributed, the whole networking system can cover a larger monitoring area, and different radar nodes can detect targets from different angles of space by using different parameters, so that the information of the detection area can be more comprehensively obtained.
In a multi-target tracking scene, how to reasonably distribute limited radar node resources of a system and energy resources of each radar node is a problem to be solved by resource management of a CMIMO radar networking system. For this problem, there are two main criteria: the first is to consume all system resources of the radar network, so that the accuracy of multi-target tracking is improved. For example, Yi et al propose a Joint Beam and Power Scheduling (JBPS) method for a CMIMO Radar network, solve an optimization problem through an iterative descent method based on rewards, and improve global Tracking accuracy of a Target under the constraint conditions of limited Beam number and Radar transmission Power (w.yi, y.yuan, r.hoselinezhad and l.kong, Resource Scheduling for Distributed Multi-Target Tracking in networked MIMO system rads, IEEE Transactions on Signal Processing,2020,68:1602 @). Yan et al propose a Joint Beam Selection and Power Allocation (JBSPA) method for CMIMO radar network multi-target tracking, control the Beam number and Beam Power resources of the radar network, and optimize the worst target tracking precision (J.Yan, H.Liu, W.Pu, S.ZHou, Z.Liu and Z.Bao, Joint Beam Selection and Power Allocation for multiple target tracking in networked coded MIMO radar system, IEEE Transactions on Signal Processing,2016,64(24):6417 and 6427.) by a two-stage method; the document (J.Yan, B.Jiu, H.Liu, B.Chen and Z.Bao.primer-based multiple beam power allocation for cognitive multiple targets tracking in the client [ J ], IEEE Transactions on Signal Processing,2014,63(2):512-527.) considers the false alarm in the tracking scene, reflects the influence of the false alarm by introducing an information attenuation factor, solves the optimization problem by an improved gradient projection method, and achieves the effect of improving the multi-target worst tracking precision. The second is to reduce the system resource consumed by the radar network under the condition of meeting the expected accuracy of multi-target tracking. Among them, Yan et al propose a Simultaneous multi-beam Resource management (SMRA) Method for multi-target tracking, which solves the problem by an approximately Alternating Direction multiplier (ADMM) Method by relaxing a non-convex optimization problem into a set of convex optimization problems, and efficiently allocates radar-limited power resources to different beams so that the tracking accuracy of the worst target is close to a desired value, and increases target capacity (j.yan, h.liu, b.jiu, b.chen, z.liu and z.bao, and simultane multi-beam Allocation scheme for multi-target tracking [ J ], IEEE Transactions on Signal Processing, 63(12): 3110.). Lu et al establish a sparse optimization problem based on a fully distributed target tracking framework with a Posterior Cramer frame-Rao Lower Bound (PCRLB) as a performance index, and can automatically relax the target tracking accuracy requirement at the lowest cost and determine the target to be tracked according to the priority, thereby forming a combined Radar scheduling and power distribution method (y.lu, c.han, z.he, s.liu and y.wang.adaptive JSPA in distributed coordinated MIMO radio Radar network for multiple targets tracking, IET radio, source & Navigation,2019,13(3):410 + 419.).
In fact, in a target tracking scenario, there is generally an expected value requirement for the tracking accuracy of a target, and when the tracking accuracy of the target just meets the expected value, which is the most reasonable result, an excessively high tracking accuracy may increase resource consumption of the radar network on one hand, and increase the probability that the radar network is discovered on the other hand. Therefore, the radar networking resource management method using the second rule has more practical significance. However, the CMIMO radar networking resource management method in the above research does not consider the problem of beam width; meanwhile, the solving algorithm used by the method has higher complexity, and the real-time requirement of the CMIMO radar networking resource management method is not considered.
Aiming at the problems, the invention provides a real-time simultaneous multi-beam CMIMO radar networking resource management algorithm which can realize real-time resource management when the multi-target expected tracking precision is given, and reduce the consumption of system energy resources under the condition of ensuring that the target tracking precision meets the requirement of the expected value.
Disclosure of Invention
Considering that a CMIMO radar networking system tracks Q targets, N CMIMO radars coexist in the network, and the sequence is compiled into N-1, … and N. The number of array elements of the nth part of radar is mnN is 1, …, N, and the sub-array division is selected from the group
Figure BDA0003618762120000021
The emission energy can be selected within a range of
Figure BDA0003618762120000022
Suppose that at time k, the state estimation results for Q targets are
Figure BDA0003618762120000023
The Bayesian information matrix of the target is { J1(tk，1)，…，Jq(tk，q)，，…，JQ(tk，Q)}。
The algorithm comprises the following steps:
step 1: target information set initialization of radar needing to execute tracking task
Figure BDA0003618762120000031
The target set represents a target set of the radar n which needs to execute a target tracking task; Φ represents an empty set.
Dividing parameter vector K (t) of radar subarrayk+1) Is initialized to
Figure BDA0003618762120000032
Radar transmission energy parameter vector E (t)k+1) Is initialized to
Figure BDA0003618762120000033
Radar beam allocation parameter matrix D (t)k+1) Is initialized to
Figure BDA0003618762120000034
Wherein 0 represents a zero vector; d is a radical ofn(tk+1) The number of beams of the radar n pointing to each target is represented, and the condition is satisfied
dn(tk+1)＝[d1,n(tk+1) … dq,n(tk+1) … dQ,n(tk+1)]T (5)
wherein ,
Figure BDA0003618762120000035
the number of orthogonal beams of the radar n pointing to the target q is represented, and the condition is satisfied
Figure BDA0003618762120000036
Target and radar detection relation matrix U (t)k+1) Initialization
Figure BDA0003618762120000037
wherein ,un(tk+1) Indicates whether radar n detects each target or not
un(tk+1)＝[u1,n(tk+1) … uq,n(tk+1) … uQ,n(tk+1)]T (8)
wherein ,uq,n(tk+1) Indicates whether the radar n detects the target q or not, and satisfies
Figure BDA0003618762120000038
And 2, step: the predicted state of the target is
Figure BDA0003618762120000039
wherein ,FqIs the state transition matrix of the target.
The prediction information matrix of the target is
Jq(tk+1|k)＝(FqJq(tk,q)(Fq)T+Qq)-1 (11)
And step 3: and calculating the predicted tracking precision of the target according to the predicted information matrix of the target, and calculating the difference between the predicted tracking precision of the target and the tracking precision of the target.
Figure BDA0003618762120000041
Wherein Λ represents an information extraction matrix satisfying
Figure BDA0003618762120000042
And 4, step 4: defining the difference of the predicted tracking accuracy of each target as the difference between the predicted tracking accuracy of the target and the expected value, calculating the result and arranging the result in descending order
Figure BDA0003618762120000043
Figure BDA0003618762120000044
wherein ,
Figure BDA0003618762120000045
and a sequence number indicating the target with the predicted target tracking accuracy ranked at the q-th position.
Initialization
Figure BDA0003618762120000046
And go to step 5.
And 5: if Q ≦ Q and target
Figure BDA0003618762120000047
Predicted tracking accuracy difference of (2)
Figure BDA0003618762120000048
Go to step 6; if Q is less than or equal to Q and
Figure BDA0003618762120000049
turning q to q +1 in step 5; otherwise, outputting the subarray division K (t)k+1) Emission energy E (t)k+1) Beam allocation D (t)k+1) State update relationship U (t)k+1)。
Step 6: establishing a set of hypothetical allocations
Figure BDA00036187621200000410
Store all possible hypothesesAssigning a radar label and control parameter of the situation, let n*Go to step 7, 1.
And 7: if n is*N go to step 10, else if radar N*Task set of
Figure BDA00036187621200000411
Go to step 8, if radar n*Task set of
Figure BDA00036187621200000412
Go to step 9.
And step 8: the radar subarray division hypothesis is set to
Figure BDA00036187621200000413
Beam allocation vector
Figure BDA00036187621200000414
Is assumed to be set to
Figure BDA00036187621200000415
At this time, the signal-to-noise ratio required to be provided by the radar is calculated according to the formula (17)
Figure BDA00036187621200000416
wherein ,
Figure BDA0003618762120000051
representing a desired tracking accuracy of the target;
Figure BDA0003618762120000052
representing the signal-to-noise ratio required for the target tracking accuracy to reach a desired value; beta is aiRepresentation matrix
Figure BDA0003618762120000053
The ith diagonal element of (1); piiRepresentation matrixThe ith diagonal element of Π. Wherein the matrix W and the matrix pi satisfy the eigenvalue decomposition process
Figure BDA0003618762120000054
Figure BDA0003618762120000055
Representing an object q*Existing prediction condition information matrix
Figure BDA0003618762120000056
Figure BDA0003618762120000057
Representing radar n*Is a target q*The measurement information matrix provided removes the measurement signal-to-noise ratio portion
Figure BDA0003618762120000058
wherein ,
Figure BDA0003618762120000059
a measurement noise covariance matrix representing the target, satisfied when the target measurements obtained by the radar are the range and azimuth of the target
Figure BDA00036187621200000510
Figure BDA00036187621200000511
The expansion result of the Jacobian matrix representing the measurement function to the target state at the prediction state of the target satisfies
Figure BDA00036187621200000512
wherein ,
Figure BDA00036187621200000513
respectively representing the distance resolution and the receiving beam width of the radar n;
Figure BDA00036187621200000514
Figure BDA00036187621200000515
respectively represent the target q*The result of the one-step prediction of the state is the X coordinate and the Y coordinate of the radar n in a Cartesian coordinate system.
Meanwhile, the signal-to-noise ratio required by successful detection of the target is calculated according to a formula
Figure BDA00036187621200000516
wherein ,
Figure BDA00036187621200000517
representing a detection probability threshold; pfRepresenting the false alarm probability.
Respectively calculating the signal-to-noise ratio of target detection according to a formula
Figure BDA0003618762120000061
Tracking signal-to-noise ratio
Figure BDA0003618762120000062
Corresponding detected energy
Figure BDA0003618762120000063
Tracking energy
Figure BDA0003618762120000064
Figure BDA0003618762120000065
wherein ,
Figure BDA0003618762120000066
representing radar n*The number of array elements;
Figure BDA0003618762120000067
to represent
Figure BDA0003618762120000068
Or
Figure BDA0003618762120000069
Figure BDA00036187621200000610
Representing radar n*Effective antenna area fraction of (a);
Figure BDA00036187621200000611
representing an object q*For radar n*The predicted cross-sectional area of (a);
Figure BDA00036187621200000612
represents the operating wavelength of the radar;
Figure BDA00036187621200000613
representing radar n*With a target q*The predicted distance therebetween; k0Represents the boltzmann constant; t is a unit of0Representing the noise temperature;
Figure BDA00036187621200000614
representing radar n*The operating bandwidth of the receiver.
If the required energy is detected
Figure BDA00036187621200000615
When the maximum value of the transmitting energy which can be provided by the radar is exceeded, the radar cannot provide measurement for the state updating of the target, and n is enabled*＝n*+1 and go to step 7; otherwise, the emission energy of the radar is measured
Figure BDA00036187621200000616
Assume setting as
Figure BDA00036187621200000617
Recording hypothesis subarray division, emission energy and beam distribution hypothesis distribution results, and storing measurement information of the target and signal-to-noise ratio corresponding to required radar emission energy into a tracking task target set
Figure BDA00036187621200000618
In (2), recording radar to hypothesis allocation set
Figure BDA00036187621200000619
In (1). At the same time, let n*＝n*+1 and go to step 7.
And step 9: if radar n*Comprises a target q in a tracking task set*Let n be*＝n*+1 go to step 7; else radar n*New number of hypothesis sub-array partitions
Figure BDA00036187621200000620
The corresponding number of simultaneous beams should cover at least the targets in the tracking task target set and the target q*I.e. by
Figure BDA00036187621200000621
wherein ,
Figure BDA00036187621200000622
representing a set of trace task objects
Figure BDA00036187621200000623
The number of targets in (1);
Figure BDA00036187621200000624
indicating rounding up.
New hypothetical beam allocation
Figure BDA00036187621200000625
Should be determined as
Figure BDA00036187621200000626
Figure BDA00036187621200000627
At this time, the targets in the task target set and the target q are tracked*Using radar n*Is/are as follows
Figure BDA0003618762120000071
The beams are illuminated separately, and the width of each beam can be calculated as
Figure BDA0003618762120000072
The target q is also calculated according to the formula*Required tracking signal-to-noise ratio, detection signal-to-noise ratio, tracking energy and detection energy
Figure BDA0003618762120000073
Figure BDA0003618762120000074
Figure BDA0003618762120000075
Simultaneously calculating the current assumed subarray division of each target in the target tracking set under the condition of new beam allocationThe number of sub-beams and the radar n required for the case of only one beam*Provided emission energy
Figure BDA0003618762120000076
wherein ,
Figure BDA0003618762120000077
indicating radar n in the previous allocation*The transmitting energy, the dividing number of the subarrays and the number of beams pointing to a target i;
Figure BDA0003618762120000078
indicating that target q is to be updated in the current allocation*Radar n*To ensure that the update of the target i in the original set requires the delivered emission energy.
At this time, there will be two remaining beam resources
Figure BDA0003618762120000079
Wherein the first part
Figure BDA00036187621200000710
The multiple characteristic of the sub-array division number leads to extra beam resources, and the number is
Figure BDA00036187621200000711
The second part
Figure BDA00036187621200000712
Due to simultaneous detection of single beam caused by width of orthogonal beam, it is initialized to
Figure BDA00036187621200000713
Tracking the target in the task set and the target q*Are arranged in order
Figure BDA00036187621200000714
Sequentially calling the smaller predicted azimuth angle as a main azimuth angle, circularly searching from the next predicted azimuth angle of the main azimuth angle to the larger predicted azimuth angle until the main azimuth angle is searched, and if the included angle between the two predicted azimuth angles does not exceed the orthogonal beam width of the radar
Figure BDA0003618762120000081
wherein ,θmainPredicted azimuth information representing a principal azimuth; θ represents predicted azimuth information of the determination azimuth. Then the two targets can be regarded as a composite target, and the next prediction azimuth angle is continuously judged; if the included angle between the two predicted azimuth angles exceeds the orthogonal beam width of the radar, the two targets cannot be regarded as a composite target, and composite target searching of the next main azimuth angle is needed.
Computing a number of beams saved for formation of a composite target
Figure BDA0003618762120000082
wherein ,
Figure BDA0003618762120000083
representing the number of composite targets;
Figure BDA0003618762120000084
indicating the number of single objects.
Selecting the target with the maximum required emission energy
Figure BDA0003618762120000085
For and with this objectAnd adding a subarray wave beam to the target under the wave beam coverage, and reducing the required transmitting energy until the saved wave beam number is completely used.
Figure BDA0003618762120000086
Figure BDA0003618762120000087
wherein ,
Figure BDA0003618762120000088
representation and target qmaxTargets under the same beam coverage.
At this time, if the maximum value e of the radar transmission energy required by the target in the original setmaxExceeds the maximum transmitted energy that the radar can provide, let n*＝n*+1 go to step 7; otherwise if q is*Detecting the required energy
Figure BDA0003618762120000089
The maximum value of the transmitting energy which can be provided by the radar is not exceeded, then the transmitting energy of the radar is assumed to be set to
Figure BDA00036187621200000810
Recording the sub-array division, emission energy and wave beam distribution hypothesis distribution results, and storing the measurement information of the target and the signal-to-noise ratio corresponding to the required radar emission energy into a tracking task target set
Figure BDA00036187621200000811
In (1), using the radar n*And its recording of hypothetical control parameters to a hypothetical allocation set
Figure BDA00036187621200000812
In, let n*＝n*+1 go to step7。
If q is*Detecting the required energy
Figure BDA00036187621200000813
Beyond the maximum amount of transmitted energy that the radar can provide, the transmitted energy of the radar is assumed to be set to
Figure BDA0003618762120000091
At the same time order n*＝n*+1 goes to step 7.
Step 10: computing collections
Figure BDA0003618762120000092
In each radar to provide an increased value of resource consumption
Figure BDA0003618762120000093
wherein ,
Figure BDA0003618762120000094
representing an object q*Selecting the transmitting energy which needs to be provided by the radar n when the radar n is selected;
Figure BDA0003618762120000095
representing an object q*The transmitted energy that radar n needs to provide when radar n is not selected.
Utilizing collections
Figure BDA0003618762120000096
In the assumed control parameter calculation target q of each radar*Hypothesis use sets
Figure BDA0003618762120000097
Obtained tracking accuracy after updating of each radar
Figure BDA0003618762120000098
wherein ,
Figure BDA0003618762120000099
representing an object q*Suppose that the obtained information matrix after updating using radar n
Figure BDA00036187621200000910
Step 11: selecting the CMIMO radar n with the minimum resource consumption increase value from the condition that the target tracking precision reaches the expected valueoptimal
Figure BDA00036187621200000911
If the target tracking accuracy does not reach the expected value, selecting the CMIMO radar n with the best target tracking accuracyoptimal
Figure BDA00036187621200000912
Parameters such as subarray division, emission energy, beam distribution and state updating relation of the selected radar are updated, and meanwhile, an information matrix of the target is updated
Figure BDA00036187621200000913
Figure BDA00036187621200000914
Figure BDA00036187621200000915
Figure BDA00036187621200000916
Figure BDA00036187621200000917
wherein ,
Figure BDA00036187621200000918
indicating radar n under the current allocationoptimalThe provided measurement signal-to-noise ratio satisfies
Figure BDA0003618762120000101
The target q is*The information of the predicted distance and azimuth angle and the information of the required transmitting energy are stored in the radar noptimalTarget tracking task set of
Figure BDA0003618762120000102
Centering and calculating the tracking accuracy of the target
Figure BDA0003618762120000103
And if the tracking accuracy of the target reaches the expected value, making q equal to q +1 and turning to the step 5, otherwise, turning to the step 6.
Principle of the invention
Assuming that N CMIMO radars exist in one simultaneous multi-beam CMIMO radar network, tracking Q targets by using the radar network, wherein each CMIMO radar works in the simultaneous multi-beam mode as shown in fig. 1, array elements of the CMIMO radars can be uniformly divided into different sub-arrays, each sub-array transmits signals which are orthogonal to each other to form a plurality of low-gain wide beams, and a plurality of narrow beams are formed by adopting a digital beam forming method during receiving to cover a detection area of the transmitted beams.
At tkAfter the target state is updated all the time, a target state estimation set is obtained
Figure BDA0003618762120000104
Bayesian information matrix set { J1(tk,1),…,Jq(tk,q),…,JQ(tk,Q)}. The resource management algorithm of the CMIMO radar networking system is controlled t through optimizationk+1Whether each CMIMO radar works at any moment, and parameters such as the transmitting energy, the sub-array division number, the transmitting energy and the like of the radar, so that the target meets the requirement of expected tracking precision
Figure BDA0003618762120000105
And minimizes the resource consumption of the networking system.
The controllable parameters are respectively represented by the following symbols:
K(tk+1)＝[k1(tk+1) … kn(tk+1) … kN(tk+1)] (55)
E(tk+1)＝[e1(tk+1) … en(tk+1) … eN(tk+1)] (56)
Figure BDA0003618762120000106
Figure BDA0003618762120000111
wherein ,kn(tk+1) Representing the number of sub-array partitions of radar n, from which only a set can be partitioned when the sub-array is uniformly partitioned
Figure BDA0003618762120000112
In which m isnExpressing the number of array elements of the radar; e.g. of the typen(tk+1) Representing the transmitted energy of radar n as a positive real variable with an upper bound, i.e.
Figure BDA0003618762120000113
Figure BDA0003618762120000114
wherein ,
Figure BDA0003618762120000115
represents a positive real number; d is a radical ofq,n(tk+1) Representing the number of beams of radar n directed at target q, obviously smaller than the number of sub-arrays of radar n, i.e.
Figure BDA0003618762120000116
In addition, since the beam of each subarray is orthogonal, even if a plurality of subarrays irradiate the same target together, the respective measurement can be extracted by matched filtering, so that
Figure BDA0003618762120000117
wherein
Figure BDA0003618762120000118
Represents a natural number; u. uq,n(tk+1) Representing the state updating relation between the radar n and the target q, and being a variable from 0 to 1 when uq,n(tk+1) When the target q is 1, the measurement obtained by the radar n is used, otherwise, the target q is not used.
In order to obtain measurements for the updated target, it should first be ensured that the updated target is illuminated, i.e. its azimuth angle is within the beam coverage of the radar
Figure BDA0003618762120000119
wherein ,bn(tk+1) A certain beam pointing direction representing radar n; theta.theta.q,n(tk+1) Representing the azimuth of the target q relative to the radar n;
Figure BDA00036187621200001110
represents the transmission beam width of the radar n, and satisfies
Figure BDA00036187621200001111
In addition to this, it should also be ensured that the updated target is detected, i.e. that a successful detection condition is fulfilled
Figure BDA00036187621200001112
wherein ,
Figure BDA00036187621200001113
representing a detection probability;
Figure BDA00036187621200001114
representing a detection probability threshold. Wherein the detection probability is related to the signal-to-noise ratio of the target, and satisfies
Figure BDA00036187621200001115
wherein ,SNRq,nSignal-to-noise ratio representing the target, dependent on the control parameter, is satisfied
Figure BDA0003618762120000121
wherein ,mnRepresenting the number of array elements of the radar n; dn(tk+1) Representing the number of simultaneous co-directional beams of the radar n pointing to the target q; etanRepresenting the effective antenna area occupation ratio of the radar n; alpha is alphaq,n(tk+1) Represents the cross-sectional area of the target q for the radar n; zetanRepresents the operating wavelength of the radar; r isq,n(tk+1) Representing the distance between the radar n and the target q; k0Represents the boltzmann constant; t is0Representing the noise temperature; bnRepresenting the radar n receiver operating bandwidth.
On the basis of meeting the irradiation and detection conditions, the expected tracking accuracy of a given target
Figure BDA0003618762120000122
At t, atkThe time of day should be such that tk+1Target tracking accuracy η at timeq(tk+1|k) Satisfy the desired value, i.e.
Figure BDA0003618762120000123
wherein ηq(tk+1|k) Relating to the prediction condition of the target, namely the lower boundary of Cramellor, and satisfying
Figure BDA0003618762120000124
wherein ,Jq(tk+1|k) Bayesian information matrix representing prediction conditions of objects
Figure BDA0003618762120000125
wherein ,
Figure BDA0003618762120000126
representing a predicted Bayesian information matrix, represented by a Bayesian information matrix J at a previous timeq(tk,q) Predicting to obtain;
Figure BDA0003618762120000127
representing a measurement information matrix provided by a radar n; fq(tk+1) A state transition matrix representing a target q; qq(tk+1) A process noise covariance matrix representing the target q;
Figure BDA0003618762120000128
representing linearized metrology functions, i.e. jacobian matrices of the metrology function of the target for the target state
Figure BDA0003618762120000129
Rq,n(tk+1|k) Watch (CN)A target-indicating measurement error covariance formula satisfying
Figure BDA0003618762120000131
The CMIMO radar networking resource management should consume as few system emission energy resources as possible under the constraint conditions, namely:
Figure BDA0003618762120000132
in order to solve the optimization problem (68), aiming at the constraint condition of the tracking precision, the prediction tracking precision obtained when all targets are not updated in state is calculated, and the resources are subsequently analyzed and distributed for the targets which do not meet the requirement of the expected tracking precision, as shown in steps 2, 3 and 4.
The actual tracking precision of the target is in direct proportion to the obtained measurement signal-to-noise ratio, and the requirements of the target on the accuracy and the signal-to-noise ratio are met
Figure BDA0003618762120000133
wherein ,Vq,n(tk+1|k) The part of the measurement information provided by the radar n for the target q after the signal to noise ratio is removed is shown to meet the requirement
Figure BDA0003618762120000134
From equation (69), the actual tracking accuracy of the target is proportional to the amount of resources it obtains, and in order to minimize the objective function, the amount of resources the target is allocated to should be just enough to achieve the desired tracking accuracy, i.e., the target is assigned to the amount of resources
Figure BDA0003618762120000141
In order to further minimize the target function, a heuristic solving method is adopted for radar selection, a radar providing a large amount of information should be preferentially used, when a radar n is added as a state updating basis of a target q, the radar n actually provides additional information for the target q, and the process can be expressed as
Jq(tk+1|k)＝Uq(tk+1|k)+SNRq,n(tk+1|k)Vq,n(tk+1|k) (72)
wherein ,Uq(tk+1|k) Indicating the bayesian information that the target q has obtained.
At this time, the relationship between the tracking accuracy of the target q and the signal-to-noise ratio provided by the radar n satisfies
Figure BDA0003618762120000142
wherein ,βiRepresentation matrix
Figure BDA0003618762120000143
The ith diagonal element of (1); piiThe ith diagonal element of the matrix is represented. Eigenvalue decomposition process for matrix W and matrix pi satisfying matrix
Figure BDA0003618762120000144
When the radar n meets the irradiation condition of the target q, the amount of resources to which the target should be allocated can be accurately obtained by solving the equation, as shown in steps 8 and 9.
Considering that the beam width of each CMIMO radar node is wider than that of the traditional phased array radar, one beam can be used for detecting multiple targets, thereby further reducing the consumption of system resources. In order to determine whether a plurality of targets can be detected by one beam, the beam width of the radar is first calculated, and the azimuth angle deviation between the direction of the radar and all targets in charge of updating should be less than half of the beam width of the radar, the predicted angles of the targets are subtracted, and if the deviation is less than the beam width, the targets can be detected by the same beam, as shown in formula (37). At this point, some beams may be saved.
Since the transmission energy resource required by the radar n is the maximum value of the transmission energy required by all targets which are responsible for updating, the measured signal-to-noise ratio of the target is proportional to the number of beams of the radar n pointing to the target q, as shown in formula (63). For the redundant beams, a method of loop iteration is adopted to sequentially allocate the targets with the maximum energy requirement, as shown in step 9, so as to further reduce the transmitting energy of the radar node, as shown in formula (40).
Drawings
Figure 1 is a beam schematic of a simultaneous multi-beam CMIMO radar;
FIG. 2 is a diagram of the actual movement trajectory of multiple targets and the relative position relationship between the targets and the radar;
FIG. 3 is a diagram showing the change of the detection relationship between each radar and the target in a single Monte Carlo operation;
FIG. 4 shows the variation of the transmitted energy of each radar during a single Monte Carlo operation;
FIG. 5 shows the sub-array division variation of each radar during a single Monte Carlo operation;
FIG. 6 is a graph of actual tracking accuracy for a single Monte Carlo run target 1, 2, 3, 4;
FIG. 7 is a graph of the actual tracking accuracy of a single Monte Carlo run of targets 5,6, 7, 8;
FIG. 8 is a statistical average comparison of target tracking accuracy deviation sums for different algorithms;
FIG. 9 is a statistical average comparison of resource consumption sums for different algorithms;
FIG. 10 is a running time statistical average of the resource management algorithm of the invented algorithm.
Detailed Description
The CMIMO radar network has 4 CMIMO radars, and continuously tracks 8 dot-shaped targets Q in a two-dimensional monitoring area by 100 frames, wherein the number of array elements of each radar is
Figure BDA0003618762120000151
Can provide emission energy of
Figure BDA0003618762120000152
The detection probability threshold of the target is
Figure BDA0003618762120000153
False alarm probability of Pf＝10-5The sampling interval is 2s, the motion state of each target is approximately uniform linear (NCV) motion, and the specific multi-target track and the mutual position relationship between the target and the radar network are shown in fig. 2.
Fig. 3, fig. 4, and fig. 5 respectively show the target state update relationship, the transmission energy, and the subarray division change condition of each radar in the single monte carlo operation radar network. Fig. 6 and 7 show target tracking accuracy changes corresponding to parameter outputs.
It can be seen from the target state update change situation and the subarray division change situation that each radar forms a plurality of beams to simultaneously track a plurality of targets. In the tracking process, the radar 1 bears the tracking tasks of the targets because the targets are closer to the targets 2, 3, 4, 5,6 and 7 at the later stage; the radars 2 and 4 respectively undertake the tracking tasks of the targets 1 and 2 at a later stage. And as can be seen from the variation of the transmitting energy, the transmitting energy consumption of each radar is less, and when the division of the target subarray is larger, the transmitting energy consumption of the radar is larger.
As can be seen from the change situation of the target tracking accuracy, under the parameter output conditions corresponding to fig. 3, 4, and 5, the tracking accuracy of each target can reach the requirement of the expected value, but because the transmission energy of the radar in the simultaneous multi-beam mode is determined as the maximum value of the transmission energy required by all the updated targets, the tracking accuracy of some targets is far better than the expected value in each tracking interval.
Finally, in order to verify the superiority of the algorithm disclosed by the invention, the algorithm is compared with two algorithms with fixed parameters, wherein the subarrays of each radar in the comparison method 1 are divided and fixed into 2, and point to fixed targets, wherein the radar 1 always updates the targets 1 and 8, the radar 2 always updates the targets 2 and 3, the radar 3 always updates the targets 4 and 5, the radar 4 always updates the targets 6 and 7, and the transmitted energy is controlled in a self-adaptive manner; in the comparison method 2, the number of sub-array partitions of each radar is fixed to 1, and the transmission energy is adaptively controlled and can be approximately regarded as a phased array working mode.
FIGS. 8 and 9 show the statistical average results of the target tracking accuracy deviation sum and the resource consumption sum of the three algorithms, i.e. the objective function in the established dual-objective function optimization problem, where the statistical average results of the target tracking accuracy deviation sum and the resource consumption sum are defined as the target function in the dual-objective function optimization problem, respectively
Figure BDA0003618762120000161
Figure BDA0003618762120000162
Wherein, M represents the number of Monte Carlo random experiments; etaq(tk|k-1) Denotes the m-th Monte Carlo experiment target q at tkTracking accuracy of time; e.g. of the typen(tk) The transmitted energy of the mth monte carlo experiment radar n is shown.
Firstly, it can be seen that the statistical average result of the sum of deviation of target tracking accuracy of the algorithm disclosed herein is basically maintained near a value of 0, which indicates that the algorithm disclosed herein can ensure that the tracking accuracy of each target meets the requirement of an expected value; however, the target tracking accuracy deviation of the other two comparison algorithms is always large, which indicates that the target tracking accuracy does not meet the requirement of an expected value. Next, from the statistical average of the resource consumption sums, the algorithm invented herein consumed the emission energy resource sum at each tracking interval closer to the comparison method 2, much lower than the comparison method 1, while the overall level is stable and also much lower than the peak consumption of the comparison method 2 at the early and late stages of tracking.
Therefore, the algorithm provided by the invention can preferentially ensure the tracking accuracy of multiple targets to be close to respective expected values, and can save the emission energy resources consumed by the radar network.
Fig. 10 shows the running time statistical average result of the algorithm of the present invention when resource management parameter determination is performed on each frame, and the single-step running time is basically maintained at about 3.5ms, which is much smaller than the sampling interval 2s of target tracking.
In summary, the algorithm provided by the invention ranks the prediction tracking accuracy of the target, preferentially allocates resources to the target with poor tracking accuracy, calculates the transmission energy required to be provided for the target by the radar capable of successfully irradiating the target, and preferentially selects the radar with the minimum transmission energy consumption. The algorithm can preferentially ensure that the tracking precision of the target meets the requirement of an expected value, and consumes less total transmitting energy consumed by the radar network; meanwhile, the resource management control parameter acquisition time of the algorithm is short, the real-time requirement of radar network cognitive multi-target tracking can be met, and the algorithm has practicability.

Claims (1)

1. A real-time simultaneous multi-beam CMIMO radar networking resource management algorithm specifically comprises the following steps:
considering that a CMIMO radar networking system tracks Q targets, N CMIMO radars coexist in the network, the sequence is compiled into N equal to 1, … and N, the number of array elements of the N-th radar is mnN is 1, …, N, and the sub-array division is selected from the group
Figure FDA0003618762110000011
The emission energy can be selected within a range of
Figure FDA0003618762110000012
Suppose that at time k, the state estimation results for Q targets are
Figure FDA0003618762110000013
The Bayesian information matrix of the target is { J1(tk,1),…,Jq(tk,q),,…,JQ(tk,Q) And then the algorithm comprises the following steps:
step 1: initialization of target information set of radar needing to execute tracking task
Figure FDA0003618762110000014
The target set represents a target set of the radar n which needs to execute a target tracking task; phi denotes empty set
Dividing parameter vector K (t) of radar subarrayk+1) Is initialized to
Figure FDA0003618762110000015
Radar emission energy parameter vector E (t)k+1) Is initialized to
Figure FDA0003618762110000016
Radar beam allocation parameter matrix D (t)k+1) Is initialized to
Figure FDA0003618762110000017
Wherein 0 represents a zero vector; d is a radical ofn(tk+1) The number of beams of the radar n pointing to each target is represented, and the requirements are met
dn(tk+1)＝[d1,n(tk+1)…dq,n(tk+1)…dQ,n(tk+1)]T (5)
wherein ,
Figure FDA0003618762110000018
the number of orthogonal beams of the radar n pointing to the target q is represented, and the condition is satisfied
Figure FDA0003618762110000019
Detection relation matrix U (t) of target and radark+1) Initialization
Figure FDA00036187621100000110
wherein ,un(tk+1) Indicates whether radar n detects each target or not
un(tk+1)＝[u1,n(tk+1)…uq,n(tk+1)…uQ,n(tk+1)]T (8)
wherein ,uq,n(tk+1) Indicates whether the radar n detects the target q or not, and satisfies
Figure FDA0003618762110000021
And 2, step: the predicted state of the target is
Figure FDA0003618762110000022
wherein ,FqTargeted state transition matrix
The prediction information matrix of the target is
Jq(tk+1|k)＝(FqJq(tk,q)(Fq)T+Qq)-1 (11)
And step 3: calculating the predicted tracking precision of the target according to the predicted information matrix of the target, and calculating the difference between the predicted tracking precision of the target and the tracking precision of the target
Figure FDA0003618762110000023
Wherein Λ represents an information extraction matrix satisfying
Figure FDA0003618762110000024
And 4, step 4: defining the difference value of the predicted tracking precision of each target as the difference value between the predicted tracking precision and the expected value of the target, calculating the result and sequencing the result in descending order
Figure FDA0003618762110000025
Figure FDA0003618762110000026
wherein ,
Figure FDA0003618762110000027
a sequence number indicating a target with a predicted target tracking accuracy ranked at the q-th position;
initialization
Figure FDA0003618762110000028
And go to step 5;
and 5: if Q ≦ Q and target
Figure FDA0003618762110000029
Predicted tracking accuracy difference of
Figure FDA00036187621100000210
Go to step 6; if Q is less than or equal to Q and
Figure FDA00036187621100000211
making q equal to q +1 go to step 5; otherwise, outputting the subarray division K (t)k+1) Emission energy E (t)k+1) Beam allocation D (t)k+1) State update relationship U (t)k+1)；
Step 6: establishing a hypothesis scoreAssembly set
Figure FDA00036187621100000212
Storing the radar labels and control parameters for all possible hypothetical allocations, let n*Go to step 7 when equal to 1;
and 7: if n is*N go to step 10, else if radar N*Task set of
Figure FDA00036187621100000213
Go to step 8, if radar n*Task set of (2)
Figure FDA00036187621100000214
Go to step 9;
and step 8: the radar subarray division hypothesis is set to
Figure FDA0003618762110000031
Beam allocation vector
Figure FDA0003618762110000032
Is assumed to be set to
Figure FDA0003618762110000033
At this time, the signal-to-noise ratio required to be provided by the radar is calculated according to the formula (17)
Figure FDA0003618762110000034
wherein ,
Figure FDA0003618762110000035
representing a desired tracking accuracy of the target;
Figure FDA0003618762110000036
the signal-to-noise ratio required for the target tracking accuracy to reach the expected value is represented; beta is aiRepresentation matrix
Figure FDA0003618762110000037
The ith diagonal element of (1); piiRepresenting the ith diagonal element of the matrix Π, wherein the matrix W and the matrix Π satisfy an eigenvalue decomposition process
Figure FDA0003618762110000038
Figure FDA0003618762110000039
Representing an object q*Existing prediction condition information matrix
Figure FDA00036187621100000310
Figure FDA00036187621100000311
Representing radar n*Is a target q*The measurement information matrix provided removes the measurement signal-to-noise ratio portion
Figure FDA00036187621100000312
wherein ,
Figure FDA00036187621100000313
a measurement noise covariance matrix representing the target, satisfied when the target measurements obtained by the radar are the range and azimuth of the target
Figure FDA00036187621100000314
Figure FDA00036187621100000315
The expansion result of the Jacobian matrix representing the measurement function to the target state at the prediction state of the target satisfies
Figure FDA00036187621100000316
wherein ,
Figure FDA00036187621100000317
respectively representing the distance resolution and the receiving beam width of the radar n;
Figure FDA00036187621100000318
Figure FDA0003618762110000041
respectively represent the targets q*The one-step prediction result of the state is the X coordinate and the Y coordinate of the radar n in a Cartesian coordinate system;
meanwhile, the signal-to-noise ratio required by successful target detection is calculated according to a formula
Figure FDA0003618762110000042
wherein ,
Figure FDA0003618762110000043
representing a detection probability threshold; pfRepresenting a false alarm probability;
according to the formula
Figure FDA0003618762110000044
Respectively calculating the signal-to-noise ratio of target detection
Figure FDA0003618762110000045
Tracking signal-to-noise ratio
Figure FDA0003618762110000046
Corresponding detected energy
Figure FDA0003618762110000047
Tracking energy
Figure FDA0003618762110000048
wherein ,
Figure FDA0003618762110000049
representing radar n*The number of array elements;
Figure FDA00036187621100000410
represent
Figure FDA00036187621100000411
Or
Figure FDA00036187621100000412
Figure FDA00036187621100000413
Representing radar n*Effective antenna area fraction of (a);
Figure FDA00036187621100000414
representing an object q*For radar n*The predicted cross-sectional area of (a);
Figure FDA00036187621100000415
represents the operating wavelength of the radar;
Figure FDA00036187621100000416
representing radar n*With a target q*The predicted distance therebetween; k is0Represents the boltzmann constant; t is0Representing the noise temperature;
Figure FDA00036187621100000417
representing radar n*Receiver operating bandwidth;
if the required energy is detected
Figure FDA00036187621100000418
When the maximum value of the transmitting energy which can be provided by the radar is exceeded, the radar cannot provide measurement for the state updating of the target, so that n*＝n*+1 and go to step 7; otherwise, the emission energy of the radar is measured
Figure FDA00036187621100000419
Assume setting as
Figure FDA00036187621100000420
Recording hypothesis subarray division, emission energy and beam distribution hypothesis distribution results, and storing measurement information of the target and signal-to-noise ratio corresponding to required radar emission energy into a tracking task target set
Figure FDA00036187621100000421
In (2), recording radar to hypothesis allocation set
Figure FDA00036187621100000422
In, simultaneously make n*＝n*+1 and go to step 7;
and step 9: if radar n*Comprises a target q in a tracking task set*Let n be*＝n*+1 go to step 7; else radar n*New number of hypothesis sub-array partitions
Figure FDA00036187621100000423
The corresponding number of simultaneous beams should cover at least the targets in the tracking task target set and the target q*I.e. by
Figure FDA00036187621100000424
wherein ,
Figure FDA0003618762110000051
representing a set of trace task objects
Figure FDA0003618762110000052
The number of targets in (1);
Figure FDA0003618762110000053
represents rounding up;
new hypothetical beam allocation
Figure FDA0003618762110000054
Should be determined as
Figure FDA0003618762110000055
Figure FDA0003618762110000056
At this time, the targets in the task target set and the target q are tracked*Using radar n*Is
Figure FDA0003618762110000057
The beams are illuminated separately, and the width of each beam can be calculated as
Figure FDA0003618762110000058
The target q is also calculated according to the formula*Required tracking signal-to-noise ratio, detection signal-to-noise ratio,Tracking energy, detecting energy
Figure FDA0003618762110000059
Figure FDA00036187621100000510
Figure FDA00036187621100000511
Simultaneously calculating the number of the current assumed subarray division of each target in the target tracking set under the condition of new beam allocation and the required radar n under the condition of only allocating one beam*Provided emission energy
Figure FDA00036187621100000512
wherein ,
Figure FDA00036187621100000513
indicating radar n in the previous allocation*The transmitting energy, the dividing number of the subarrays and the number of beams pointing to a target i;
Figure FDA00036187621100000514
indicating that target q is to be updated in the current allocation*Radar n*The transmitted energy required to be provided for ensuring the update of the target i in the original set;
at this time, there will be two remaining beam resources
Figure FDA00036187621100000515
Wherein the first part
Figure FDA00036187621100000516
Is a multiple of the sub-array division number characteristic, resulting in additional beam resources of the number
Figure FDA0003618762110000061
The second part
Figure FDA0003618762110000062
Due to simultaneous detection of single beam caused by width of orthogonal beam, it is initialized to
Figure FDA0003618762110000063
Tracking the target in the task set and the target q*In order of predicted azimuth information
Figure FDA0003618762110000064
Sequentially calling the smaller predicted azimuth angle as a main azimuth angle, circularly searching from the next predicted azimuth angle of the main azimuth angle to the larger predicted azimuth angle until the main azimuth angle is searched, and if the included angle between the two predicted azimuth angles does not exceed the orthogonal beam width of the radar
Figure FDA0003618762110000065
Then the two targets can be regarded as a composite target, and the next prediction azimuth angle is continuously judged; if the included angle between the two predicted azimuth angles exceeds the orthogonal beam width of the radar, the two targets cannot be regarded as a composite target, and the composite target of the next main azimuth angle needs to be searched, wherein thetamainPredicted azimuth information representing a principal azimuth; theta represents a determination partyPredicted azimuth information of the azimuth;
computing a number of beams saved from formation of a composite target
Figure FDA0003618762110000066
wherein ,
Figure FDA0003618762110000067
representing the number of composite targets;
Figure FDA0003618762110000068
representing the number of single targets;
selecting the target with the largest required emission energy
Figure FDA0003618762110000069
Adding a sub-array beam to the target and the target under the same beam coverage with the target, reducing the required transmitting energy until the saved beam number is completely used
Figure FDA00036187621100000610
Figure FDA00036187621100000611
wherein ,
Figure FDA00036187621100000612
representation and target qmaxTargets under the same beam coverage;
at this time, if the maximum value e of the radar transmission energy required by the target in the original setmaxExceeds the maximum transmitting energy that the radar can provide, let n*＝n*+1 go to step 7; otherwise if q is*Detecting the required energy
Figure FDA00036187621100000613
The maximum value of the transmitting energy which can be provided by the radar is not exceeded, and the transmitting energy of the radar is assumed to be set
Figure FDA00036187621100000614
Recording the sub-array division, emission energy and beam distribution hypothesis distribution results, and storing the measurement information of the target and the signal-to-noise ratio corresponding to the required radar emission energy into a tracking task target set
Figure FDA0003618762110000071
In (1), using the radar n*And its recording of hypothetical control parameters to a hypothetical allocation set
Figure FDA0003618762110000072
In, let n*＝n*+1 go to step 7;
if q is*Detecting the required energy
Figure FDA0003618762110000073
The maximum value of the transmitting energy which can be provided by the radar is exceeded, the transmitting energy of the radar is supposed to be set to be
Figure FDA0003618762110000074
At the same time order n*＝n*+1 go to step 7;
step 10: computing collections
Figure FDA0003618762110000075
In each radar provides an increased value of resource consumption
Figure FDA0003618762110000076
wherein ,
Figure FDA0003618762110000077
representing an object q*Selecting the transmitting energy which needs to be provided by the radar n when the radar n is selected;
Figure FDA0003618762110000078
representing an object q*The transmitting energy required to be provided by the radar n when the radar n is not selected;
utilizing collections
Figure FDA0003618762110000079
Target q is calculated by assuming control parameters of each radar*Hypothesis use sets
Figure FDA00036187621100000710
Updated acquired tracking accuracy of each radar
Figure FDA00036187621100000711
wherein ,
Figure FDA00036187621100000712
representing an object q*Suppose that the obtained information matrix after updating using radar n
Figure FDA00036187621100000713
Step 11: selecting the CMIMO radar n with the minimum resource consumption increase value from the condition that the target tracking precision reaches the expected valueoptimal
Figure FDA00036187621100000714
If the target tracking accuracy does not reach the expected value, selecting the CMIMO radar n with the best target tracking accuracyoptimal
Figure FDA00036187621100000715
Parameters such as subarray division, emission energy, beam distribution, state updating relation and the like of the selected radar are updated, and meanwhile, an information matrix of the target is updated
Figure FDA00036187621100000716
Figure FDA00036187621100000717
Figure FDA0003618762110000081
Figure FDA0003618762110000082
Figure FDA0003618762110000083
wherein ,
Figure FDA0003618762110000084
indicating radar n under the current allocationoptimalThe provided measurement signal-to-noise ratio satisfies
Figure FDA0003618762110000085
The target q is*The information of the predicted distance and azimuth angle and the information of the required transmitting energy are stored in the radar noptimalTarget tracking task set of
Figure FDA0003618762110000086
Centering and calculating the tracking accuracy of the target
Figure FDA0003618762110000087
And if the tracking accuracy of the target reaches the expected value, enabling q to be q +1 and going to step 5, and otherwise going to step 6.
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