CN107192985B - Resource joint optimization method for multi-target speed estimation of distributed MIMO radar system - Google Patents

Resource joint optimization method for multi-target speed estimation of distributed MIMO radar system Download PDF

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CN107192985B
CN107192985B CN201710530452.4A CN201710530452A CN107192985B CN 107192985 B CN107192985 B CN 107192985B CN 201710530452 A CN201710530452 A CN 201710530452A CN 107192985 B CN107192985 B CN 107192985B
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receiving
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CN107192985A (en
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郑娜娥
宋喜玉
任修坤
陈松
吕品品
田英华
柏婷
张龙
张靖志
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PLA Information Engineering University
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Abstract

The invention relates to a resource joint optimization method for multi-target speed estimation of a distributed MIMO radar system, which comprises the following steps: a target is specified, and a resource joint optimization model comprising four optimization variables of a transmitting array element, a receiving array element, transmitting power and signal duration is established by taking the minimum key target speed estimation error as a target function; converting the optimization problem into a second-order cone programming problem, and solving the four optimization variables in sequence by adopting a circular minimization algorithm; and after the algorithm is converged, terminating the cycle, binarizing array element selection variables, selecting the optimal array element, and distributing the transmitting power and the signal duration again to obtain a result of resource joint distribution. The method has great flexibility on the number of the tracked targets, can select the least transmitting array elements under the condition of meeting the requirements of multi-target different speed estimation, improves the key target tracking performance, achieves the effect of minimizing the error of the multi-target overall tracking precision, and has good application value.

Description

Resource joint optimization method for multi-target speed estimation of distributed MIMO radar system
Technical Field
The invention belongs to the technical field of MIMO radars, and particularly relates to a resource joint optimization method for multi-target speed estimation of a distributed MIMO radar system.
Background
The distributed MIMO radar has the advantages of large element spacing and good space diversity gain, overcomes the flicker of the target RCS, and accords with the development trend of the detection and multi-target processing of stealth targets by modern radars, thereby receiving more and more extensive attention. However, as radar functionality becomes more sophisticated, the problem of resource management of radar systems is becoming an important component in military applications. Especially for airborne, vehicular and shipborne radars, the transmitting power of the system is usually limited, when the working time is long, the problem of resource shortage is obvious, and simultaneously, under the multi-task mode, the resource scheduling and the signal bandwidth and time distribution under different tasks influence the task execution effect, so that different data transmission amount and calculation complexity are brought to data fusion. In order to improve the detection and tracking capacity of the radar system on the target, system resources are reasonably distributed to meet the multi-task requirement of the system, and the method becomes a problem to be solved urgently under the multi-target tracking task of the distributed MIMO radar system. In consideration of the fact that the target speed is complex and changeable in the actual environment, mastering of the speed change of the target is beneficial to better mastering of the change trend, different tracking levels can be divided according to different properties of multiple targets, and the multi-target speed estimation capability is improved by adopting a distributed MIMO radar multi-resource joint distribution method.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a resource joint optimization method for multi-target speed estimation of a distributed MIMO radar system, which combines the target task properties, puts forward different tracking requirements on multiple targets, fully schedules radar system resources and effectively improves the overall speed tracking precision of the multiple targets.
According to the design scheme provided by the invention, the resource joint optimization method for multi-target speed estimation of the distributed MIMO radar system comprises the following steps:
step 1, selecting a target q*Determining a target speed estimation precision expression and a resource optimization model objective function;
step 2, under the constraint of the upper limit of the transmitting power and the signal duration of the single radar, establishing a transmitting array element ftReceiving array element frA resource joint optimization model of four optimization variables of transmitting power p and signal duration t; f. ofr *
Step 3, transmitting array element ftAnd a receiving array element frRelaxation is continuous variable, the optimization problem is converted into a second-order cone programming (SOCP) problem, and a cyclic minimization algorithm is adopted to sequentially carry out transmission array elements ft *Receiving array element, transmitting power p*Sum signal duration t*Solving the four optimization variables;
step 4, selecting the array elements into dualization according to the solving result, selecting the optimal array elements, and redistributing the transmitting power and the signal duration to obtain a resource joint allocation result f of the MIMO radar systemt opt、fr opt、poptAnd topt。
As described above, step 1 includes the following steps: and taking Bayes Clarithrome as a measurement criterion of the target speed estimation error to obtain a Bayes Clarithrome boundary of the q-th target speed estimation error, determining a target speed estimation accuracy function, and converting the constraint problem of the target speed estimation accuracy into a second-order cone problem.
The resource joint optimization model of the four optimization variables in step 2 is expressed as follows:
Figure BDA0001336379880000021
Figure BDA0001336379880000022
wherein, in the step (A),
Figure BDA0001336379880000023
is a target q*The speed estimation accuracy of (2); ptotalAnd TtotalRespectively the total transmission power and the signal duration of the system; kt and Kr are respectively the maximum allowable number of transmitting array elements and receiving array elements; p is a radical ofmaxAnd tmaxRespectively allocating the upper limits of the transmitting power and the signal duration of the single radar; MSEqAn upper error bound is estimated for the speed tracked by the system for the qth target,
Figure BDA0001336379880000024
is an auxiliary variable; m, N are the numbers of transmitting radars and receiving radars in the distributed MIMO radar system.
In step 3, the four optimization variables are solved in sequence by using a cyclic minimization algorithm, includingThe following contents: under the framework of the circular minimization algorithm, a) fixing the receiving array element fr *A transmission power p*Sum signal duration t*Under the condition of (1), solving the transmitting array element ft *Selecting a result; b) at fixed transmitting array element ft *A transmission power p*Sum signal duration t*Under the condition of (1), solving the receiving array element fr *Selecting a result; c) at fixed transmitting array element ft *Receiving array element fr *Under the condition of (1), solving the transmission power p*Sum signal duration t*The result of the allocation of (c); d) and after convergence, terminating the loop iteration.
Preferably, the transmit array element f is solvedt *The selection result comprises the following contents: fixed receiving array element fr *A transmission power p*Sum signal duration t*To solve the transmitting array element ft *And selecting, and adjusting the optimization model as follows:
Figure BDA0001336379880000025
Figure BDA0001336379880000026
wherein A isq＝[Cq,Sq,0]T，
Figure BDA0001336379880000027
F in objective function and constraint variabletAnd
Figure BDA0001336379880000028
are all linear functions, and the selection result f of the transmitting array elements is obtained by solvingt *。
Preferably, the receiving array element f is solvedr *The selecting result of (1) comprises: at fixed transmitting array element ft *A transmission power p*Sum signal duration t*Under the condition of (2), for the receiving array element fr *And solving, and adjusting the optimization model as follows:
Figure BDA0001336379880000031
Figure BDA0001336379880000032
wherein, in the step (A),
Figure BDA0001336379880000033
solving to obtain a receiving array element selection result fr *And corresponding
Figure BDA0001336379880000034
Preferably, the transmit power p is solved*Sum signal duration t*The allocation result of (1), comprising: at fixed transmitting array element ft *Receiving array element fr *For transmission power p*Sum signal duration t*And solving, and adjusting the optimization model as follows:
Figure BDA0001336379880000035
Figure BDA0001336379880000036
wherein, in the step (A),
Figure BDA0001336379880000037
solving to obtain a transmission power distribution result p*Sum signal duration assignment result t*。
Preferably, in step 4, the array element selection is binarized, the optimal array element is selected, and the transmission power and the signal duration are redistributed, including the following contents: array element selection result ft *And fr *Dualization, wherein the larger values of Kt and Kr are respectively taken as 1, the smaller values of the others are taken as 0, and the optimal array element selection result f is obtainedt opt、fr opt(ii) a Repeating the step c to obtain the optimal power distribution poptAnd optimal duration allocation topt(ii) a According to poptAnd toptResult f of selecting transmitting array element according to value of each componentt optAnd correcting to obtain the MIMO radar resource joint distribution result.
The invention has the beneficial effects that:
the method takes a minimized key target speed estimation error as a target function, establishes a resource joint optimization model containing four optimization variables of a transmitting array element, a receiving array element, transmitting power and signal duration under the conditions of limited system resources and given multi-target speed estimation requirements, converts the optimization problem into a second-order cone programming (SOCP) problem, adopts a cycle minimization algorithm to sequentially solve the four optimization variables, terminates the cycle after the algorithm converges, selects variable dualization for the array element, selects an optimal array element, and distributes the transmitting power and the signal duration again to obtain a result of resource joint distribution; the method can improve the key target tracking performance and meet the performance requirements of other target speed estimation at the same time, realizes the joint distribution of four resources of transmitting array elements, receiving array elements, transmitting power and signal duration, and can effectively improve the overall multi-target speed tracking precision compared with other distribution algorithms; the number of the tracked targets can be flexibly controlled by controlling the target speed tracking precision requirement; the speed tracking capability of multiple targets in a given experimental scene is evaluated through a random array arrangement experiment, less transmitting array elements can be selected and the requirement of the overall estimation error of a radar system can be met under the condition of meeting the estimation requirement, and the method has good practical application value.
Description of the drawings:
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic flow chart of a resource joint allocation algorithm in the embodiment;
FIG. 3 is a diagram illustrating a positional relationship between a radar and a target in a fixed arrangement scene in the embodiment;
fig. 4 shows MSE [ inf, inf ] in the fixed array scenario in the embodiment]m2Time-of-day different distributionComparing the algorithm distribution result;
fig. 5 shows MSE [10 ] in the fixed array scenario in the embodiment2,inf]m2Comparing distribution results of different distribution algorithms;
fig. 6 shows that MSE is 20 in the fixed array scenario in the embodiment2,202]m2Comparing distribution results of different distribution algorithms;
FIG. 7 shows the results of the speed estimation accuracy and the number of array elements selected in the random array layout in the embodiment.
The specific implementation mode is as follows:
the present invention will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to adapt to the development trend of detecting stealth targets and processing multiple targets by modern radars, considering that the target speed is complex and changeable in the actual environment and the change of the target speed is favorable for mastering the change trend, aiming at the problem, different tracking grades are divided according to different properties of multiple targets, and a method for joint distribution of multiple resources of a distributed MIMO radar is adopted to improve the estimation capability of the multiple targets, in the first embodiment, as shown in FIG. 1, the embodiment provides a resource joint optimization method for the multiple target speed estimation of a distributed MIMO radar system, and the resource joint optimization method comprises the following steps:
101. selecting a target q*Determining a target speed estimation precision expression and a resource optimization model objective function;
102. under the constraint of the upper limit of the transmitting power and the signal duration of a single radar, a transmitting array element f is establishedtReceiving array element frA resource joint optimization model of four optimization variables of transmitting power p and signal duration t;
103. transmitting array element ftAnd a receiving array element frRelaxation is a continuous variable, the optimization problem is converted into a second-order cone programming SOCP problem, and the SOCP problem is acquiredUsing cyclic minimization algorithm to sequentially pair transmitting array elements ft *Receiving array element fr *A transmission power p*Sum signal duration t*Solving the four optimization variables;
104. according to the solution result, the array element selection is dualized, the optimal array element is selected, the transmitting power and the signal duration are redistributed, and the resource joint distribution result f of the MIMO radar system is obtainedt opt、fr opt、poptAnd topt。
Taking a minimized key target speed estimation error as a target function, establishing a resource joint optimization model containing four optimization variables of a transmitting array element, a receiving array element, transmitting power and signal duration under the conditions of limited system resources and given multi-target speed estimation requirements, converting the optimization problem into a second-order cone programming SOCP problem, adopting a cycle minimization algorithm to sequentially solve the four optimization variables, terminating the cycle after the algorithm is converged, selecting a variable dualization for the array element, selecting an optimal array element, and allocating the transmitting power and the signal duration again to obtain a resource joint allocation result; the performance requirements of speed estimation of other targets can be met while the tracking performance of key targets is improved.
In a second embodiment, referring to fig. 2, a resource joint allocation method for multi-target speed estimation of a distributed MIMO radar system specifically includes the following steps:
step 1: selecting a certain key target q*And calculating a target speed estimation precision expression, and taking the target speed estimation precision expression as an objective function of the resource optimization model.
The distributed MIMO radar system comprises M parts of transmitting radars and N parts of receiving radars, wherein the radar interval is large enough to track Q moving targets. In a two-dimensional plane, the coordinates of the transmitting radar are
Figure BDA0001336379880000051
Receive radar coordinates of
Figure BDA0001336379880000052
The target position state is (x)q,yq) Q1.. Q, speed state is
Figure BDA0001336379880000053
Suppose that each part of the radar transmits an orthogonal signal sm(t), M ═ 1.. M, satisfying
Figure BDA0001336379880000054
TmIn order to be the duration of the signal,
Figure BDA0001336379880000055
τ0is the signal delay. Defining the transmitting power vector of radar as p ═ p1,p2,...,pM]TThe signal duration vector is t ═ t1,t2,...,tM]T. Because the radar array element spacing is relatively large, MN channel signals generated by each target are mutually independent. For the convenience of research, assuming that the receiving end of the distributed MIMO radar has satisfied the time synchronization characteristic, the low-pass equivalent signal received by the nth receiving radar may be represented as
Figure BDA0001336379880000056
Wherein, αmqnRepresents a path loss factor, is related to the target-to-radar distance,
Figure BDA0001336379880000057
Figure BDA0001336379880000058
and
Figure BDA0001336379880000059
ξ distance of target to transmitting and receiving radar, respectivelymqnRepresenting the radar complex scattering coefficient of the target to form a radar scattering cross-sectional area (RCS) model; tau ismqnRepresents signal time delay and satisfies
Figure BDA00013363798800000510
c is the speed of light; w is amqnIndicating the Doppler frequency shift of the target motion, and satisfying
Figure BDA00013363798800000511
λ is the signal wavelength;
Figure BDA00013363798800000512
and
Figure BDA00013363798800000513
and observing angles of the m-th transmitting radar and the n-th receiving radar to the target q respectively. w is an(t) represents white Gaussian noise having an autocorrelation function of
Figure BDA00013363798800000514
Defining a state vector of target q at time k as
Figure BDA00013363798800000515
The motion model of the object can be described as
Where F is the state transition matrix.
Figure BDA00013363798800000516
Is a zero mean, white Gaussian process noise sequence with a covariance matrix of Qk. When tracking a uniform moving object
Figure BDA00013363798800000517
Figure BDA00013363798800000518
Where Δ t denotes the sampling interval, q0Representing the intensity of process noise, I2A 2 x 2 unit array is represented,
Figure BDA00013363798800000519
is a matrix direct product operator.
The fusion center at each moment tracks the target according to the distance and Doppler information of the received data, and the observation model can be described as
Figure BDA0001336379880000061
Wherein f (-) represents the observation process,
Figure BDA0001336379880000062
is observed gaussian noise. For the uniform motion target, f (-) is a linear observation process, and a Kalman filter can be adopted for target tracking.
Considering that at high signal-to-noise ratio, the BCRB can be a lower bound for the motion target parameter estimation error. Defining a velocity estimator for a target
Figure BDA0001336379880000063
The Bayesian information matrix of the target tracking is
Figure BDA0001336379880000064
Wherein Q isk-1Covariance matrix of process noise, F is state transition matrix of target,
Figure BDA0001336379880000065
is that
Figure BDA0001336379880000066
The fischer matrix of (a), can be calculated by a probability density function,
Figure BDA0001336379880000067
since the above equation requires expectations, it needs to be calculated by the method of Monte Carlo
Figure BDA0001336379880000068
The first term of (2) is only related to the last moment and the motion form of the target, and can be regarded as a constant, so that the Bayesian information matrix of the target at the current moment is onlyBy
Figure BDA0001336379880000069
The second item of (1). Definition CqA BCRB matrix for velocity error estimation whose diagonal elements are the lower bound of the velocity estimation component satisfies
Figure BDA00013363798800000610
Tr (-) represents matrix tracing.
The BCRB for the qth target speed estimation error may be approximately expressed as
Figure BDA00013363798800000611
Wherein, gq,zq,hqRespectively expressed as:
Figure BDA00013363798800000612
wherein, in the step (A),
Figure BDA00013363798800000613
respectively, the selection variables of the mth transmitting array element and the nth receiving array element are 0 for abandoning and 1 for selecting, and then the selection vectors of the transmitting array element and the receiving array element are respectively
Figure BDA00013363798800000614
Figure BDA00013363798800000615
Therefore, the speed estimation accuracy of the target is influenced by the transmitting array element, the receiving array element, the transmitting power and the signal duration. Definition of
Figure BDA00013363798800000616
The BCRB of the target speed estimate may be converted into:
Figure BDA00013363798800000617
wherein, in the step (A),
Figure BDA0001336379880000071
1 is an mx 1-dimensional column vector;
Figure BDA0001336379880000072
diag {. } represents matrix diagonalization;
Figure BDA0001336379880000073
∑qin the form of a symmetrical matrix, the matrix is,
Figure BDA0001336379880000074
is a diagonal matrix with a rank less than 3,
Figure BDA0001336379880000075
in the same way, the method for preparing the composite material,
Figure BDA0001336379880000076
Figure BDA0001336379880000077
step 2: comprehensively considering the requirements of limited system resources and multi-target speed estimation, and establishing a transmitting array element f under the constraints of single radar transmitting power and signal duration upper limittReceiving array element frThe resource joint optimization model of the four optimization variables of the transmitting power p and the signal duration t is as follows:
Figure BDA0001336379880000078
Figure BDA0001336379880000079
wherein, in the step (A),
Figure BDA00013363798800000710
is a target q*The speed estimation accuracy of (2); ptotalAnd TtotalRespectively the total transmission power and the signal duration of the system; kt and Kr are eachThe maximum number of transmitting array elements and receiving array elements is allowed; p is a radical ofmaxAnd tmaxRespectively allocating the upper limits of the transmitting power and the signal duration of the single radar; MSEqAn upper error bound is estimated for the speed tracked by the system for the qth target.
Introducing auxiliary variables
Figure BDA00013363798800000711
The optimization problem of the above formula is rewritten as:
Figure BDA00013363798800000712
Figure BDA00013363798800000713
the objective function of the above formula is a non-linear function,
Figure BDA00013363798800000714
can be equivalent to
Figure BDA00013363798800000715
For the convenience of analysis, the method can be further converted into the following steps:
Figure BDA0001336379880000081
Figure BDA0001336379880000082
according to theorem 1, the optimal signal duration allocation result can be determined from the optimal power allocation result
Figure BDA0001336379880000083
Therefore, the optimization problem can be decomposed into sub-problems containing three optimization variables for study. The objective function of the above-described optimization model is linear, but the 8 th constraint is a non-linear function. According to the existing research, after the array element selection variable is relaxed into a continuous variable, the formulaFor convex optimization model, and ∑qIs a low rank matrix, so the problem can be translated into the SOCP problem for research.
Binary variable for selecting array elements
Figure BDA0001336379880000084
Relaxation being a continuous variable
Figure BDA0001336379880000085
The initial transmitting power and the signal duration are uniformly distributed to p*＝Ptotal/M·1,t*＝Ttotal1/M. Assuming that all receiving array elements are selected
Figure BDA0001336379880000086
And step 3: fixed receiving array element fr *A transmission power p*Sum signal duration t*To solve the transmitting array element ft *And selecting, wherein the optimization model is changed into:
Figure BDA0001336379880000087
Figure BDA0001336379880000088
wherein A isq＝[Cq,Sq,0]T，
Figure BDA0001336379880000089
Objective function in formula and f in constraint variabletAnd
Figure BDA00013363798800000810
are all linear functions. Therefore, the selection result f of the transmitting array element of the optimization problem can be obtainedt *。
And 4, step 4: at fixed transmitting array element ft *A transmission power p*Sum signal duration t*Under the condition of (2), for the receiving array element fr *And solving, converting the optimization model into:
Figure BDA0001336379880000091
Figure BDA0001336379880000092
wherein, in the step (A),
Figure BDA0001336379880000093
in the same way, a receiving array element selection result f can be obtainedr *And corresponding Fr *。
And 5: at fixed transmitting array element ft *Receiving array element fr *For transmission power p*Sum signal duration t*And solving, converting the optimization model into:
Figure BDA0001336379880000094
Figure BDA0001336379880000095
wherein, in the step (A),
Figure BDA0001336379880000096
the same method can obtain the transmission power distribution result p*Signal duration assignment result t*。
Step 6: and 3, skipping to the step 3, and terminating the loop iteration after the algorithm is converged. Array element selection result ft *And fr *Dualization, wherein the larger values of Kt and Kr are respectively taken as 1, the smaller values of the others are taken as 0, and the optimal array element selection result f is obtainedt opt、fr opt. Repeating the step 5 to obtain the optimal power distribution poptAnd optimal duration allocation topt. Finally, according to poptAnd toptValue size of each component to transmitting arrayMeta selection result ft optFurther correcting to obtain a joint distribution result f of the MIMO radar resourcest opt、fr opt、poptAnd topt。
To further verify the effectiveness of the present invention, referring to fig. 3 to 7, the present invention is further explained by the following specific example of the third embodiment:
example three:
1) simulation conditions are as follows:
considering a distributed MIMO radar platform with M6 and N6, in a 20 × 20km experimental scenario, velocity estimates of 3 moving objects with Q are analyzed. The radar system allows the number of the maximum transmitting and receiving array elements to be selected as Kt 4 and Kr 4 respectively. Total power of system transmission is Ptotal6kw, the upper limit of the transmitting power of the single radar is pmax4kw, the total duration of the signal is Ttotal0.6s, the upper limit of the time length of the signal transmitted by the single radar is tmax0.4 s. Assuming that target 1 is always the key target in the objective function, MSE is the speed estimation requirement of the system for target 2 and target 3. Four resource allocation algorithms are considered to estimate the target speed, namely, receiving and transmitting array element selection, array element selection and transmitting power joint allocation, array element selection and signal duration joint allocation, and array element selection and transmitting power and signal duration joint allocation. In order to better analyze the influence of the radar array arrangement form on the distribution result, the experiment divides the array arrangement relation of the radar and the target into a fixed array arrangement part and a random array arrangement part.
2) Simulation experiment:
referring to fig. 3, a spatial position relationship between the radar and the target at a certain time is given; referring to fig. 4, MSE ═ inf, inf is given]m2Corresponding speed estimation results and resource allocation results. I.e. only the velocity estimate of the counterweight target 1 is optimized. In fig. 4(a), an estimated value and a true value are mentioned, where the estimated value refers to a resource allocation result and a target speed estimation accuracy obtained by using a SOCP direct optimization calculation, and since an optimization problem in the present application is converted into a SOCP problem as an approximate representation, a target speed estimation is recalculated according to the resource allocation resultThe gauge accuracy, defined as the true velocity estimation accuracy. As can be seen from fig. 4(a), the more the types of resources participating in allocation, i.e. the larger the regulation range of the system for resource allocation, the better the estimation performance of the key target is, wherein the estimation performance of the array element selection and the joint allocation of the transmission power and the signal duration is the best. The effect of the signal duration allocation on the improvement of the estimation performance is more significant than the power allocation, because the target speed estimation accuracy is related to the square of the signal duration, and therefore the signal duration has a greater influence on the estimation result. And comparing the speed precision estimated value obtained by optimizing each target by adopting the SOCP problem and the real value corresponding to the resource allocation result, so that the difference between the estimated value and the real value can be seen. This is mainly because an approximation method is used in the process of converting the problem of resource allocation into the SOCP problem, and therefore, an error exists between the estimated value and the true value of the target speed accuracy. Fig. 4(b) shows the resource allocation results corresponding to different allocation algorithms, and it can be seen that, in order to improve the estimation accuracy of the target 1, system resources are mainly allocated to the transmission array elements T2 and T5, which indicates that the closer the radar is to the target, the more obvious the tracking effect is.
In consideration of the fact that the radar system needs to put forward different tracking precision requirements for different targets according to target properties in the actual working process. Fig. 5 and 6 analyze MSE [10 ], respectively2,inf]m2And MSE ═ 202,202]m2Resource allocation case of time. Fig. 5 proposes an estimation requirement for the target 2 and optimizes the estimation result of the target 1, and it can be seen that the latter two allocation algorithms achieve the estimation requirement, system resources are mainly allocated to the T3 and T5 transmit array elements closest to the target 2, and to simultaneously reduce the estimation performance of the target 1, the T5 closer to the target 1 is allocated to more resources. The first two allocation algorithms have limited resource regulation and control space and cannot meet the task requirements. Fig. 6 improves the estimation performance of the target 1 on the premise of ensuring the tracking requirements of the target 2 and the target 3. Comparing fig. 4, fig. 6 mainly needs to optimize the estimation accuracy of the target 3, and it can be seen that in order to optimize the estimation accuracy of the target 3, the system allocates a part of the transmission power and signal duration resources to the T3 array element close to the target 3, but at the same time, the purpose is also createdMark 1 increases in tracking error.
Through analysis, array elements close to the tracking target are allocated to more system resources, wherein T5 is closer to the key target, so that T5 is divided into more resources on the premise of meeting the estimation accuracy requirement. Along with the increase of the number of the tracking targets, the estimation performance of the system on the gravity targets is increasingly poor. The estimation error of the resource allocation algorithm related to the transmission parameter is different from the real error of the resource allocation result, thereby indicating that the resource allocation result optimized based on the SOCP problem needs to further calculate the real target speed estimation precision.
In order to better analyze the influence of the position relationship between the radar and the target on the distribution algorithm, in the existing experimental scene with the same size, the radar and the target at a certain moment are randomly arranged, and the minimum distance between array elements or targets is 2 km. Random arraying experiment: the average of 500 random arraying results was used for the experiments. The experiment only considers the true accuracy of the target velocity estimate.
Considering that the maximum value Kr of the receiving array element is always 4, fig. 7 shows the ratio of the target speed estimation accuracy result to the number of the transmitting array elements selected under the above three MSE performance requirements. The system in fig. 7(a) only tracks the target 1, and it can be seen that the estimation accuracy of the target 1 is significantly higher than that of the other two targets, and since the system does not set specific tracking requirements for the other two targets, the statistical errors of the estimation accuracy are approximately equal. Fig. 7(c) improves the tracking performance of the target 1 while tracking the target 2, and for the first three allocation algorithms, the estimation accuracies of the target 1 and the target 3 are substantially the same, and the estimation accuracy of the target 2 is higher than the MSE upper limit, which indicates that the system resources are mainly used for tracking the target 2 at this time. For the last optimization algorithm, the estimation accuracy of the target 2 meets the requirement of the MSE upper limit, the estimation performance of the target 1 is superior to that of the target 3, and the estimation requirement of the key target 1 is optimized on the premise that the estimation requirement of the target 2 can be realized through resource joint allocation. FIG. 7(e) tracks three targets simultaneously, and four distribution algorithms can achieve velocity tracking of three targets within an error of 20 m/s. Fig. 7(b), (d), and (f) count the ratio of the number of selected array elements under different MSE requirements, and the result shows that the resource allocation algorithm combining the array element selection and the transmission parameter can reduce the number of the selected array elements, wherein the number of the array elements selected by the resource allocation algorithm combining the array element selection, the transmission power, and the signal duration is the least. As the number of the system attention targets increases, the number of the transmitting array elements selected by various distribution algorithms gradually increases.
Through analysis, the resource allocation algorithm combining the array element selection and the transmission parameters is superior to a single array element selection algorithm in the aspects of meeting the system estimation performance requirement and selecting the number of the transmission array elements, wherein the overall system estimation error of the allocation algorithm combining the array element selection and the transmission power is the largest, and the resource allocation algorithm combining the array element selection, the transmission power and the signal duration can select the least transmission array elements and achieve the minimum overall system estimation error under the condition of meeting the estimation requirement.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (7)

1. A resource joint optimization method for multi-target speed estimation of a distributed MIMO radar system is characterized by comprising the following steps:
step 1, selecting a target q*Determining a target speed estimation precision expression and a resource optimization model objective function;
step 2, under the constraint of the upper limit of the transmitting power and the signal duration of the single radar, establishing a transmitting array element ftReceiving array element frA resource joint optimization model of four optimization variables of transmitting power p and signal duration t;
step 3, transmitting array element ftAnd a receiving array element frRelax to continuous variable, optimize toConverting the problem into a second-order cone programming SOCP problem, and sequentially carrying out alignment on transmitting array elements f by adopting a circular minimization algorithmt *Receiving array element fr *A transmission power p*Sum signal duration t*Solving the four optimization variables;
step 4, selecting the array elements into dualization according to the solving result, selecting the optimal array elements, and redistributing the transmitting power and the signal duration to obtain a resource joint allocation result f of the MIMO radar systemt opt、fr opt、poptAnd topt；
The resource joint optimization model of the four optimization variables in the step 2 is expressed as follows:
Figure FDA0002188141780000011
Figure FDA0002188141780000012
，
wherein the content of the first and second substances,
Figure FDA0002188141780000013
is a target q*The speed estimation accuracy of (2); ptotalAnd TtotalRespectively the total transmission power and the signal duration of the system; kt and Kr are respectively the maximum allowable number of transmitting array elements and receiving array elements; p is a radical ofmaxAnd tmaxRespectively allocating the upper limits of the transmitting power and the signal duration of the single radar; MSEqAn upper error bound is estimated for the speed tracked by the system for the qth target,
Figure FDA0002188141780000014
is an auxiliary variable; m, N are the numbers of transmitting radars and receiving radars in the distributed MIMO radar system.
2. The method for resource joint optimization for multi-objective speed estimation of a distributed MIMO radar system as claimed in claim 1, wherein step 1 comprises the following steps: and taking the Bayes Clarithrome bound as a measurement criterion of the target speed estimation error to obtain the Bayes Clarithrome bound of the q-th target speed estimation error, determining a target speed estimation precision function, and converting the constraint problem of the target speed estimation precision into a second-order cone problem.
3. The resource joint optimization method for multi-objective speed estimation of the distributed MIMO radar system as claimed in claim 1, wherein in step 3, a cyclic minimization algorithm is adopted to sequentially solve four optimization variables, which comprises the following contents: under the framework of the circular minimization algorithm, a) fixing the receiving array element fr *A transmission power p*Sum signal duration t*Under the condition of (1), solving the transmitting array element ft *Selecting a result; b) at fixed transmitting array element ft *A transmission power p*Sum signal duration t*Under the condition of (1), solving the receiving array element fr *Selecting a result; c) at fixed transmitting array element ft *Receiving array element fr *Under the condition of (1), solving the transmission power p*Sum signal duration t*The result of the allocation of (c); d) and after convergence, terminating the loop iteration.
4. The resource joint optimization method for multi-objective speed estimation of the distributed MIMO radar system as claimed in claim 3, wherein the solution of the transmitting array element ft *The selection result comprises the following contents: fixed receiving array element fr *A transmission power p*Sum signal duration t*To solve the transmitting array element ft *And selecting, and adjusting the optimization model as follows:
Figure FDA0002188141780000021
Figure FDA0002188141780000022
，
wherein A isq＝[Cq,Sq,0]T，
Figure FDA0002188141780000023
F in objective function and constraint variabletAnd
Figure FDA0002188141780000024
are all linear functions, and the selection result f of the transmitting array elements is obtained by solvingt *，
Figure FDA0002188141780000025
1 is an mx 1-dimensional column vector;
Figure FDA0002188141780000026
Figure FDA0002188141780000027
diag {. denotes matrix diagonalization, v ═ p ⊙ t2⊙ft；
Figure FDA0002188141780000028
Figure FDA0002188141780000029
Figure FDA00021881417800000210
Wherein, the transmitting array element, the receiving real element, the transmitting power and the signal duration are respectively expressed as ft、frP and t, ξmqnThe complex scattering coefficient of radar of the target is shown, M, N shows the number of radar emitting and receiving radars, q shows the target,
Figure FDA00021881417800000211
and
Figure FDA00021881417800000212
observation angles of target q for m-th transmitting radar and n-th receiving radar respectivelyAnd (4) degree.
5. The resource joint optimization method for multi-objective speed estimation of the distributed MIMO radar system as claimed in claim 3, wherein the receiving array element f is solvedr *The selecting result of (1) comprises: at fixed transmitting array element ft *A transmission power p*Sum signal duration t*Under the condition of (2), for the receiving array element fr *And solving, and adjusting the optimization model as follows:
Figure FDA0002188141780000031
Figure FDA0002188141780000032
wherein the content of the first and second substances,
Figure FDA0002188141780000033
solving to obtain a receiving array element selection result fr *And corresponding Fr *1 is an mx 1-dimensional column vector;
Figure FDA0002188141780000034
diag {. denotes matrix diagonalization, v ═ p ⊙ t2⊙ft；
Figure FDA0002188141780000035
Figure FDA0002188141780000036
Aq＝[Cq,Sq,0]TThe transmitting array element, the receiving real element, the transmitting power and the signal duration are respectively expressed as ft、frP and t, ξmqnThe complex scattering coefficient of radar of the target is shown, M, N shows the number of radar emitting and receiving radars, q shows the target,
Figure FDA0002188141780000037
and
Figure FDA0002188141780000038
and observing angles of the m-th transmitting radar and the n-th receiving radar to the target q respectively.
6. The resource joint optimization method for multi-objective speed estimation of the distributed MIMO radar system as claimed in claim 3, wherein the solution of the transmitting power p*Sum signal duration t*The allocation result of (1), comprising: at fixed transmitting array element ft *Receiving array element fr *For transmission power p*Sum signal duration t*And solving, and adjusting the optimization model as follows:
Figure FDA0002188141780000039
Figure FDA00021881417800000310
wherein the content of the first and second substances,
Figure FDA00021881417800000311
solving to obtain a transmission power distribution result p*Sum signal duration assignment result t*，
Figure FDA00021881417800000312
1 is an mx 1-dimensional column vector;
Figure FDA00021881417800000313
diag {. denotes matrix diagonalization, v ═ p ⊙ t2⊙ft；
Figure FDA0002188141780000041
Figure FDA0002188141780000042
Aq＝[Cq,Sq,0]TWherein, the transmitting array element, the receiving real element, the transmitting power and the signal duration are respectively expressed as ft、frP and t, ξmqnThe complex scattering coefficient of radar of the target is shown, M, N shows the number of radar emitting and receiving radars, q shows the target,
Figure FDA0002188141780000043
and
Figure FDA0002188141780000044
and observing angles of the m-th transmitting radar and the n-th receiving radar to the target q respectively.
7. The resource joint optimization method for multi-objective speed estimation of the distributed MIMO radar system as claimed in claim 3, wherein in step 4, the array element selection is binarized, the optimal array element is selected, and the transmission power and the signal duration are redistributed, comprising the following steps: array element selection result ft *And fr *Dualization, wherein the larger values of Kt and Kr are respectively taken as 1, the smaller values of the others are taken as 0, and the optimal array element selection result f is obtainedt opt、fr opt(ii) a Repeating the step c to obtain the optimal power distribution poptAnd optimal duration allocation topt(ii) a According to poptAnd toptResult f of selecting transmitting array element according to value of each componentt optAnd correcting to obtain the MIMO radar resource joint distribution result.
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