CN107340515B - Target positioning resource allocation method based on distributed networking radar system - Google Patents

Target positioning resource allocation method based on distributed networking radar system Download PDF

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CN107340515B
CN107340515B CN201710452474.3A CN201710452474A CN107340515B CN 107340515 B CN107340515 B CN 107340515B CN 201710452474 A CN201710452474 A CN 201710452474A CN 107340515 B CN107340515 B CN 107340515B
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radar system
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CN107340515A (en
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严俊坤
冯涵哲
刘宏伟
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Xi'an Interwiser Electronic Technology Co ltd
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Xidian University
Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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Abstract

The invention belongs to the technical field of radars, and discloses a target positioning resource allocation method based on a distributed networking radar system, which comprises the following steps: determining a lower Clarithromone boundary of an error when the distributed networking radar system positions a target; setting an initial power distribution optimization model of the distributed networking radar system for target positioning according to the lower Clarmetro boundary of the error of the distributed networking radar system for target positioning; carrying out convex relaxation on the initial power distribution optimization model for target positioning by the distributed networking radar system to obtain a convex relaxed power distribution optimization model; solving the power optimization model after convex relaxation to obtain a power distribution result of the distributed networking radar system for target positioning; the method can quickly acquire better target positioning performance under the constraints of limited power and the like according to the transmitting parameters of each radar of the distributed networking radar system.

Description

Target positioning resource allocation method based on distributed networking radar system
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a target positioning resource allocation method based on a distributed networking radar system, which is suitable for a single-target tracking method under the condition of no false alarm and no detection omission and a power allocation method under a multi-station distributed working mode, and can quickly improve the positioning precision of a single target under a complex environment.
Background
Quick resource allocation aiming at target positioning in a complex environment is a technical problem to be solved urgently by a distributed networking radar system. Through a distributed working mode, the multi-station distributed networking radar can quickly complete a resource allocation result, namely, the position information of a target can be better acquired. In this mode of operation, each radar independently adjusts its respective transmit power. Compared with the traditional single-station positioning mode, the method can greatly improve the power utilization rate of the networking radar in the target positioning process, so that the positioning accuracy is improved, and the intercepted probability is reduced.
Theoretically, the larger the transmitting power of each radar station of the networking radar is, the better the positioning precision of the target is. However, as power increases, the probability of radar system exposure increases dramatically. In order to enable the networking radar to stably work for a long time, the total transmission power of each networking radar needs to be limited. At this time, it is important how to effectively utilize limited power resources and obtain better positioning performance.
The traditional method for distributing power of networking radars is to distribute power to all radars evenly. Although this method is relatively simple and easy to implement in engineering, it does not achieve the desired target location effect. For example, when the distance difference between the target and each radar is large, the positioning information acquired by the radar close to the target is highly accurate, and the positioning information acquired by the radar far from the target is poor. Aiming at the problem, the prior art provides a method for quickly and dynamically allocating transmitting power based on networking radar single-target positioning. The method dynamically adjusts the transmitting power of each transmitting station according to the perception information of a receiver to the environment, forms a cognitive single-target positioning method, and is mainly used for solving the problem that the calculation time is too slow when the conventional networking radar carries out target positioning.
Although the existing method has achieved the goal of saving the transmission power and optimizing the positioning effect, the whole method is based on the following two assumptions: (1) target radar cross-sectional scattering area (RCS) information is known a priori; (2) in the whole processing process, the detection probability of each target at each moment is implicitly assumed to be 1, and the ideal condition of false alarm does not exist. On one hand, in actual tracking, the RCS of the target needs to be estimated in real time, and the system cannot obtain the prior information of the target before measurement; on the other hand, under the (2) th assumption, the system can only obtain one measurement point for each target within the relevant wave gate of the target at each time. However, such ideal detection conditions are not satisfied in practice. At each moment, there may be many excessive detection threshold points in the relevant wave gate of each target, and how to realize multi-target cognitive tracking in such a cluttered environment is an urgent problem to be solved.
Disclosure of Invention
In view of the problems in the prior art, an object of the present invention is to provide a target positioning resource allocation method based on a distributed networking radar system, which can quickly obtain better target positioning performance under the constraints of limited power and the like according to the transmission parameters of each radar of the distributed networking radar system.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
A target positioning resource allocation method based on a distributed networking radar system comprises the following steps:
step 1, determining a Cramer-Rao lower bound CRLB (p) of an error when a distributed networking radar system positions a target:
Figure BDA0001322846290000021
wherein CRLB (-) represents the lower cramer bound, CRLB (-) is a function of a power distribution vector p for a distributed networked radar system, p ═ p1，...，pm，...，pM]And p denotes a power allocation vector of the distributed networking radar system, pmRepresenting the transmitting power of the mth radar transmitting station; u denotes the target position to be located, J (u) denotes the Fisher information matrix of the target position u to be located, Tr (-) denotes the trace of the matrix, (.)-1Represents the inversion operation, b represents the trace of the adjoint matrix of J (u), A represents the determinant of J (u);
step 2, setting an initial power distribution optimization model of the distributed networking radar system for target positioning according to the lower Clarithromol limit of the error of the distributed networking radar system for target positioning;
Figure BDA0001322846290000031
Figure BDA0001322846290000032
s.t.Pmin≤pm≤Pmax，m＝1，...，M
wherein the content of the first and second substances,
Figure BDA0001322846290000033
all 1 vectors, P, representing dimension M × 1maxRepresenting the maximum rated power, P, of each radar transmitting stationminRepresenting the minimum standby power, P, of each radar transmitting stationtotalThe sum of the transmitting power of all radar transmitting stations in the distributed networking radar system is represented;
step 3, performing convex relaxation on the initial power distribution optimization model of target positioning by the distributed networking radar system to obtain a convex relaxed power distribution optimization model:
min bTp-η(pTAp)
Figure BDA0001322846290000034
s.t.Pmin≤pm≤Pmax，m＝1，...，M
and 4, solving the power optimization model after the convex relaxation to obtain a power distribution result of the distributed networking radar system for positioning the target.
The technical scheme of the invention has the characteristics and further improvements that:
(1) the step 1 specifically comprises the following substeps:
(1a) the distributed networking radar system is arranged under a unified rectangular coordinate system and comprises M radar transmitting stations, N radar receiving stations and a target to be positioned, and the coordinate of the mth radar transmitting station is recorded as
Figure BDA0001322846290000041
The coordinates of the nth radar receiving station are recorded as
Figure BDA0001322846290000042
The target position to be positioned is recorded as u ═ x, y;
the distance from the mth radar transmitting station to the target is recorded as
Figure BDA0001322846290000043
The distance from the nth radar receiving station to the target is recorded as
Figure BDA0001322846290000044
The azimuth angle between the mth radar transmitting station and the target is recorded as
Figure BDA0001322846290000045
The azimuth angle between the nth radar receiving station and the target is recorded as
Figure BDA0001322846290000046
(1b) Recording an error prior conditional probability density function for the target position u to be located as:
Figure BDA0001322846290000047
wherein σωRepresenting the variance of noise inside the distributed networking radar system, and a received signal matrix r ═ r1，1，r1，2，...rm，n，...，rM，N]，rm，nIndicating the signal of the mth radar transmitting station after the reflection of the target received by the nth radar receiving station, αm，nIs a decay factor, and
Figure BDA0001322846290000048
pmrepresenting the transmission power, h, of the mth radar transmitting stationm，nRepresenting the radar scattering cross section when the nth radar receiving station receives the signal of the mth radar transmitting station from the target;
(1c) obtaining a Fisher information matrix J (u) of the target position u to be positioned according to the error prior conditional probability density function of the target position u to be positioned:
Figure BDA0001322846290000049
wherein E {. is } represents an expectation operation,
Figure BDA00013228462900000410
representing a derivative operation, ln representing a logarithmic operation;
(1d) determining a Cramer-Rao lower bound CRLB (p) of the error of the distributed networking radar system in the target positioning according to the Fisher information matrix J (u) of the target position u to be positioned:
Figure BDA00013228462900000411
wherein, b ═ d + e, A ═ deT-qqTThe first intermediate variable d ═ d1，...，dm，...dM]TThe second intermediate variable e ═ e1，...em，...，eM]TThe third intermediate variable q ═ q1，...qm，...，，qM]TAnd, and:
Figure BDA0001322846290000051
Figure BDA0001322846290000052
Figure BDA0001322846290000053
wherein d ismM-th element, e, representing a first intermediate variable dmE m-th element, q, representing a second intermediate variablemThe m-th element representing the third intermediate variable q, ξnIs a constant value and is a constant value,
Figure BDA0001322846290000054
wherein, βmThe bandwidth of the signal transmitted by the mth radar transmitting station is shown, and c represents the speed of light.
(2) The step 4 specifically comprises the following substeps:
(4a) given parameter Ptotal、Pmax、PminA value of (d); and setting an initial value of a power distribution vector p of the distributed networking radar system
Figure BDA0001322846290000055
Setting the value of the estimated parameter η;
(4b) solving the power distribution optimization model after convex relaxation:
min bTp-η(pTAp)
Figure BDA0001322846290000056
s.t.Pmin≤pm≤Pmax，m＝1，...，M
obtaining an output result p of a power distribution vector p of the distributed networking radar systemoutAccording to said output result poutCalculating correction parameters η1The value of (c):
Figure BDA0001322846290000057
(4c) setting the convergence parameter ε if | η1If the value of- η | ≦ epsilon, stopping iteration, and adding poutAs a power distribution result of the distributed networking radar system for positioning the target;
otherwise, let η be η1Returning to substep (4b), the correction parameters are recalculated η1Until the correction parameter η is reached1Satisfies the condition | η1η | ≦ ε, and p calculated at the last iterationoutAs a result of power allocation to target positioning by the distributed networking radar system.
The technical scheme of the invention provides a target positioning resource allocation method based on a distributed networking radar system under a multi-station distributed radar system. The method can quickly acquire better positioning performance under the constraints of limited power and the like according to the transmitting parameters of each radar of the distributed networking radar system. In particular, at each instant, power is allocated to the dominant radar as much as possible to better locate the existing target. Compared with the traditional power allocation algorithm, the method of the invention has the following advantages: (1) the CVX optimization software package can be used for solving, so that software programming and actual engineering operation are facilitated; (2) the convex relaxation parameters are corrected through feedback, so that extra errors introduced by convex relaxation are effectively reduced, and the optimized result is close to the optimal result.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flowchart of a target positioning resource allocation method based on a distributed networking radar system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the distribution of each radar and target provided in the simulation experiment of the present invention;
FIG. 3 is a schematic diagram showing the comparison of positioning performance and the comparison of operation time of different algorithms in a simulation experiment of the present invention;
FIG. 4 is a schematic diagram showing the comparison of the effect of each algorithm under different initial parameters in the simulation experiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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.
The embodiment of the invention provides a target positioning resource allocation method based on a distributed networking radar system, which comprises the following steps of:
step 1, setting radar system parameters.
The distributed networking radar system is assumed to have M radar transmitting stations and N radar receiving stations, and the coordinates of the radar transmitting stations in the distributed networking radar system are recorded as
Figure BDA0001322846290000071
The coordinates of the radar receiving station are noted
Figure BDA0001322846290000072
Modern radars can estimate distance information from the mth radar transmitting station to a target according to echo data received after transmission
Figure BDA0001322846290000073
And information on the distance of the target to the nth receiving station
Figure BDA0001322846290000074
And the azimuth information of the target relative to the mth radar transmitting station under the unified coordinate system
Figure BDA0001322846290000075
The azimuth information of the target relative to the nth receiving station
Figure BDA0001322846290000076
(the azimuth information respectively represents a direction vector under a rectangular coordinate system, the starting point is a radar transmitting station or a radar receiving station, and the end point is a target).
According to the measurement information (specifically, the measurement information may include information such as time delay, azimuth, distance, and the like) acquired by each radar receiving station, the distributed networking radar system may achieve more accurate positioning of a target under the condition of limited power, that is, obtain a better estimate of the target position u ═ x, y.
If the internal noise of the distributed networking radar system is the variance of sigmaωThe gaussians are independently distributed in the same way, then the error prior conditional probability density function of the variable u to be estimated can be written as
Figure BDA0001322846290000077
Wherein σωRepresenting the variance of noise inside the distributed networking radar system, and a received signal matrix r ═ r1，1，r1，2，...rm，n，...，rM，N]，rm，nIndicating the signal of the mth radar transmitting station after the reflection of the target received by the nth radar receiving station, αm，nThe attenuation factor represents that the signal strength is inversely proportional to the square of the transmission distance, gradually attenuates, and
Figure BDA0001322846290000081
pmrepresenting the transmission power, h, of the mth radar transmitting stationm，nAnd represents a radar scattering cross-sectional area when the nth radar receiving station receives a signal of the mth radar transmitting station from a target.
(1) The equation can also be called a Fisher information matrix of the variable u to be estimated, and the Fisher information matrix is taken as a covariance matrix of the likelihood function gradient of the variable u to be estimated, and can be expressed as follows:
Figure BDA0001322846290000082
the above equation represents the covariance matrix of the likelihood function gradient, E {. is the expectation operation,
Figure BDA0001322846290000083
is a derivation operation. The cramer-Rao Lower Bound (CRLB for short) of the estimation error of the variable u to be estimated can be derived:
Figure BDA0001322846290000084
adjustable variable is transmission power p of each transmitting station of multi-station distributed radar systemmTheir constituent vector is p ═ p1，...pM]. Since the lower cramer-mero boundary represents the lower boundary of the target positioning accuracy, it is suitable as a measure of the target positioning accuracy. Therefore, the current work mostly uses the cramer-circle lower bound as a cost function for power allocation. The lower boundary of the Kramer Rao of errors when the multi-station distributed radar positions the target is closely related to the Fisher information matrix, and can be represented as follows:
Figure BDA0001322846290000085
wherein J (u) is a Fisher information matrix of the variable u to be estimated, and Tr (·) is a tracing operation of the matrix. In formula (3), b is (d + e) and a is deTqqT. Wherein d ═ d1，...，dm，...，dM]T，e＝[e1，...em，...，eM]TAnd q ═ q1，...qm，...，，qM]T(ii) a Wherein the content of the first and second substances,
Figure BDA0001322846290000086
Figure BDA0001322846290000087
Figure BDA0001322846290000091
in formulae (4) to (6), hm，nDenotes a radar scattering cross-sectional area (RCS) constant when the nth radar receiving station receives a signal of the mth radar transmitting station from the target
Figure BDA0001322846290000092
βmIs the mth radar transmitting station transmitting signal bandwidth, and c represents the speed of light. To is coming toConvenient calculation, using equivalent transformation
Figure BDA0001322846290000093
The matrix A can be converted into a symmetric quadratic form by equivalent transformation
Figure BDA0001322846290000094
And 2, setting a target optimization model and deducing a convex relaxation model.
The optimization model of power allocation can be expressed as
Figure BDA0001322846290000095
Wherein the content of the first and second substances,
Figure BDA0001322846290000096
all 1 vectors, P, representing dimension M × 1maxRepresenting the maximum rated power, P, of each radar transmitting stationminRepresenting the minimum standby power, P, of each radar transmitting stationtotalRepresenting the sum of the transmitting power of all radar transmitting stations in the distributed networking radar system.
The constraint in equation (7) above is convex but the objective function is a non-convex nonlinear function. The convex relaxation of the proportional cost function into an additive cost function can make it a convex function. After convex relaxation, the original optimization model becomes:
Figure BDA0001322846290000097
η is a preset self-correcting parameter value, which is a typical convex quadratic programming, and is convenient to solve by adopting a CVX optimization software package.
Step 3, adopting a classic CVX optimization software package to carry out optimization solution on the convex relaxed model (8) to obtain an output result P of a power distribution vector P of the distributed networking radar systemout。
Step 4, optimizing the output result p of the step 3outThe cost function is introduced into the non-convex relaxation model (7) to solveObtaining the correction parameter
Figure BDA0001322846290000101
Step 5, setting a convergence parameter epsilon, if | η1If the value of- η | ≦ epsilon, stopping iteration, and adding poutAs a power distribution result of the distributed networking radar system for positioning the target;
otherwise, let η be η1And repeatedly executing the step 3 and the step 4 until the correction parameter η1Satisfies the condition | η1- η | ≦ ε, and P calculated at last iterationoutAs a result of power allocation to target positioning by the distributed networking radar system.
The convergence parameter is 10-8。
The effect of the invention is further illustrated by the following simulation comparison experiment:
1. an experimental scene is as follows:
in order to verify that the method can effectively and quickly correct the extra error caused by convex relaxation under the background that the multi-base radar positions the target, and approaches the optimal power distribution. The embodiment of the present invention performs the following simulation.
As shown in fig. 2, a target positioning simulation scenario is designed for a multi-station distributed radar system, and the validity of the modified convex relaxation method is verified by comparing the convex relaxation method with the conventional convex relaxation algorithm and the DDM algorithm. In order to simplify the simulation, the radar transmission parameters of all parts are assumed to be the same in the experiment. Maximum working power P of transmitting radarmaxIs 100kW, and minimum standby power P of transmitting radarminThe carrier frequency of the radar emission signal is 1 kW. The target dynamic model noise and the observation noise are both Gaussian white noise.
2. Simulation content:
and under a set scene, positioning a target and distributing power, and comparing the time required by positioning accuracy and optimization under the power average distribution scheme and a plurality of optimization distribution schemes.
3. And (3) simulation result analysis:
it can be seen from fig. 3(a) that the DDM algorithm can obtain the optimal positioning accuracy; the traditional convex relaxation method only obtains poor positioning precision due to the introduction of extra errors; the convex relaxation correction algorithm can effectively correct errors caused by the traditional convex relaxation. Notably, in most cases, the first correction significantly reduces the extra error; the correction after this is not significant in reducing the extra error. Figure 3(b) shows the time required for several optimization algorithm optimization processes.
FIG. 4 compares the loss caused by the performance of the conventional convex relaxation algorithm and the effect after correction, in which, in the condition that the initial value of η is 10 in FIG. 4(a), the optimization results obtained by the conventional convex relaxation algorithm, the DDM algorithm and the modified convex relaxation algorithm are respectively adopted, in the condition that the initial value of η is 1 in FIG. 4(b), the optimization results obtained by the conventional convex relaxation algorithm, the DDM algorithm and the modified convex relaxation algorithm are respectively adopted, and in comparison, the performance loss of the conventional convex relaxation algorithm under the condition that the parameter is 1 is far greater than that of the conventional convex relaxation algorithm under the condition that the parameter is 10 in FIG. 4(b), accordingly, the correction improvement effect is more obvious under the condition that the parameter is 1.
Those of ordinary skill in the art will understand that: all or part of the steps for realizing the method embodiments can be completed by hardware related to program instructions, the program can be stored in a computer readable storage medium, and the program executes the steps comprising the method embodiments when executed; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (2)

1. A target positioning resource allocation method based on a distributed networking radar system is characterized by comprising the following steps:
step 1, determining a Cramer-Rao lower bound CRLB (p) of an error when a distributed networking radar system positions a target:
Figure FDA0002396214580000011
wherein CRLB (-) represents the lower cramer bound, CRLB (-) is a function of a power distribution vector p for a distributed networked radar system, p ═ p1,…,pm,...,pM]And p denotes a power allocation vector of the distributed networking radar system, pmThe method comprises the steps of representing the transmitting power of an mth radar transmitting station, wherein M is 1,2, and M represents the total number of radar transmitting stations contained in a distributed radar networking system; u denotes the target position to be located, J (u) denotes the Fisher information matrix of the target position u to be located, Tr (-) denotes the trace of the matrix, (.)-1Represents the inversion operation, b represents the trace of the adjoint matrix of J (u), A represents the determinant of J (u);
step 2, setting an initial power distribution optimization model of the distributed networking radar system for target positioning according to the lower Clarithromol limit of the error of the distributed networking radar system for target positioning;
Figure FDA0002396214580000012
Figure FDA0002396214580000013
s.t.Pmin≤pm≤Pmax,m＝1,…,M
wherein the content of the first and second substances,
Figure FDA0002396214580000014
all 1 vectors, P, representing dimension M × 1maxIndicating maximum rating of each radar transmitting stationPower, PminRepresenting the minimum standby power, P, of each radar transmitting stationtotalThe sum of the transmitting power of all radar transmitting stations in the distributed networking radar system is represented;
step 3, performing convex relaxation on the initial power distribution optimization model of target positioning by the distributed networking radar system to obtain a convex relaxed power distribution optimization model:
min bTp-η(pTAp)
Figure FDA0002396214580000021
s.t.Pmin≤pm≤Pmax,m＝1,…,M
wherein the self-correcting parameter value is represented; s.t denotes constraints;
step 4, solving the power optimization model after convex relaxation to obtain a power distribution result of the distributed networking radar system for positioning the target;
the method specifically comprises the following substeps:
(4a) given parameter Ptotal、Pmax、PminA value of (d); and setting an initial value of a power distribution vector p of the distributed networking radar system
Figure FDA0002396214580000022
Setting the value of the estimated parameter η;
(4b) solving the power distribution optimization model after convex relaxation:
min bTp-η(pTAp)
Figure FDA0002396214580000023
s.t.Pmin≤pm≤Pmax,m＝1,…,M
obtaining an output result p of a power distribution vector p of the distributed networking radar systemoutAccording to said output result poutCalculating correction parameters η1The value of (c):
Figure FDA0002396214580000024
(4c) setting the convergence parameter ε if | η1If the value of- η | ≦ epsilon, stopping iteration, and adding poutAs a power distribution result of the distributed networking radar system for positioning the target;
otherwise, let η be η1Returning to substep (4b), the correction parameters are recalculated η1Until the correction parameter η is reached1Satisfies the condition | η1η | ≦ ε, and p calculated at the last iterationoutAs a result of power allocation to target positioning by the distributed networking radar system.
2. The method for allocating target positioning resources based on the distributed networking radar system according to claim 1, wherein step 1 specifically comprises the following sub-steps:
(1a) the distributed networking radar system is arranged under a unified rectangular coordinate system and comprises M radar transmitting stations, N radar receiving stations and a target to be positioned, and the coordinate of the mth radar transmitting station is recorded as
Figure FDA0002396214580000031
The coordinates of the nth radar receiving station are recorded as
Figure FDA0002396214580000032
The target position to be positioned is recorded as u ═ x, y;
the distance from the mth radar transmitting station to the target is recorded as
Figure FDA0002396214580000033
The distance from the nth radar receiving station to the target is recorded as
Figure FDA0002396214580000034
The azimuth angle between the mth radar transmitting station and the target is recorded as
Figure FDA0002396214580000035
The azimuth angle between the nth radar receiving station and the target is recorded as
Figure FDA0002396214580000036
(1b) Recording an error prior conditional probability density function for the target position u to be located as:
Figure FDA0002396214580000037
wherein σωRepresenting the variance of noise inside the distributed networking radar system, and a received signal matrix r ═ r1,1,r1,2,…rm,n,...,rM,N]，rm,nIndicating the signal of the mth radar transmitting station after the reflection of the target received by the nth radar receiving station, αm,nIs a decay factor, and
Figure FDA0002396214580000038
pmrepresenting the transmission power, h, of the mth radar transmitting stationm,nRepresenting the radar scattering cross section when the nth radar receiving station receives the signal of the mth radar transmitting station from the target;
(1c) obtaining a Fisher information matrix J (u) of the target position u to be positioned according to the error prior conditional probability density function of the target position u to be positioned;
Figure FDA0002396214580000039
wherein E {. is } represents an expectation operation,
Figure FDA00023962145800000310
representing a derivative operation, ln representing a logarithmic operation;
(1d) determining a Cramer-Rao lower bound CRLB (p) of the error of the distributed networking radar system in the target positioning according to the Fisher information matrix J (u) of the target position u to be positioned:
Figure FDA00023962145800000311
wherein, b ═ d + e, A ═ deT-qqTThe first intermediate variable d ═ d1,…,dm,...,dM]TThe second intermediate variable e ═ e1,…em,...,eM]TThe third intermediate variable q ═ q1,…qm,...,,qM]TAnd, and:
Figure FDA0002396214580000041
Figure FDA0002396214580000042
Figure FDA0002396214580000043
wherein d ismM-th element, e, representing a first intermediate variable dmE m-th element, q, representing a second intermediate variablemThe m-th element representing the third intermediate variable q, ξmIs a constant value and is a constant value,
Figure FDA0002396214580000044
wherein, βmThe bandwidth of the signal transmitted by the mth radar transmitting station is shown, and c represents the speed of light.
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