CN108802720B - Cooperative detection and power distribution method for target tracking in multi-radar system - Google Patents

Cooperative detection and power distribution method for target tracking in multi-radar system Download PDF

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CN108802720B
CN108802720B CN201810395710.7A CN201810395710A CN108802720B CN 108802720 B CN108802720 B CN 108802720B CN 201810395710 A CN201810395710 A CN 201810395710A CN 108802720 B CN108802720 B CN 108802720B
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kth
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CN108802720A (en
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严俊坤
马时飞
刘宏伟
周生华
纠博
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Xidian University
Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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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
    • 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
    • G01S13/70—Radar-tracking systems; Analogous systems for range tracking only

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Abstract

The invention relates to a cooperative detection and power distribution method for target tracking in a multi-radar system, which comprises the following steps: establishing a multi-radar system; a motion model; observing the model; and detecting the model; transmitting the transmission power distribution result to a transmitter, calculating effective measurement values of each radar station according to the false alarm rate, and calculating interconnection probability according to the effective measurement values so as to update a target state; the distribution of the transmitting power and the selection of the false alarm rate are determined by a final optimization model obtained by replacing a Bayesian information matrix obtained by relaxed information reduction factors with a defined detection model; and minimizing the final optimization model to obtain the optimized transmitting power and the optimized false alarm rate. The invention aims at the target tracking closed-loop perception in a multi-radar system, properly selects the false alarm rate of each radar for a detector according to the computing capacity of a fusion center of each tracking frame, and correctly allocates a transmitting power resource with a preset power budget at each tracking frame for a transmitter.

Description

Cooperative detection and power distribution method for target tracking in multi-radar system
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a cooperative detection and power distribution method for target tracking in a multi-radar system.
Background
Most tracking systems in recent years have relied on multiple cooperating radars. Information from multiple radars can be efficiently fused, thus allowing for increased area coverage, detection probability, positioning and tracking performance. Due to these advantages, multi-radar systems are receiving increasing attention in various application areas, wherein one of the main applications is the detection and tracking of defense targets.
For practical applications, the radars in a multi-radar system operate in an active manner and should maximize their transmit power to achieve better target tracking performance. However, on board a ship, due to its limited energy, if the radar is constantly transmitting maximum power, its energy will be quickly depleted. Therefore, the concept of Power Allocation (PA) design is crucial to extend network lifetime. Furthermore, power distribution is an important component of military operations in harsh environments, and multi-radar systems may be required to achieve low interception probabilities. Therefore, power amplifier design, which aims to maximize tracking accuracy at a given power budget, is an important point for applying target tracking in multi-radar systems. Meanwhile, for target tracking in a multi-radar system, each radar sets a threshold value for data received by the radar according to a predetermined False Alarm Rate (FAR), and then transmits the data to a Fusion Center (FC) for data fusion. In practice, the data computation power of a fusion center is usually limited, which means that it cannot process all data from multiple radars simultaneously. Therefore, the false alarm value of each radar station must be selected to determine the amount of data transmitted from the local radar to the fusion center based on the limited computing power of the fusion center. It is noteworthy that selecting the false alarm rate may have a significant impact on target tracking performance, as radar data with a greater signal-to-noise ratio (SNR) or/and better angle of observation will contribute more to target tracking performance.
In the traditional multi-base tracking framework, information flows from only one direction: from the local radar station to the fusion center. In such an open-loop framework, any a priori information from previous tracking frames is not fed back and used to select the false alarm rate and power allocation, and therefore this information neither considers the properties of the detector nor the transmitter. For convenience, the limited power budget of a multi-radar system is evenly distributed to multiple radars and the false alarm rate is set according to the constraints of the fusion center while ensuring that the data traffic from different radars to the fusion center is the same. In practice, a priori information may be obtained from previous tracking frames, e.g., predicted target states and target radar cross-sectional scattering areas (RCS). Target tracking performance can be significantly improved if information can be fed back and used appropriately for the detector selecting the false alarm rate and the transmitter of the power allocation. In this case, a reasonable and challenging problem is how to coordinate setting the false alarm rates of multiple radars to achieve better target tracking performance while satisfying the constraints of the fusion center.
Disclosure of Invention
In order to solve the technical defects in the prior art, the invention provides a display screen energy-saving algorithm.
Specifically, an embodiment of the present invention provides a cooperative detection and power allocation method for target tracking in a multi-radar system, including:
step 1, establishing a multi-radar system, wherein the multi-radar system comprises N radar stations, initial transmitting power and initial false alarm rate which are distributed to the N radar stations of the multi-radar system are set, the multi-radar system is initialized, K represents kth tracking time, the initial value of K is 1, K is larger than or equal to 1 and smaller than or equal to K, and K is the preset maximum tracking time;
step 2, obtaining a motion model at the kth moment through the transfer matrix, the target state at the kth-1 moment and zero-mean Gaussian process noise, and determining the target state at the kth moment according to the motion model;
step 3, obtaining an observation model at the kth moment according to the target state at the kth moment;
step 4, obtaining a detection model at the kth moment by using a Neyman-Pearson theory according to the relation among the detection probability, the transmitting power and the false alarm rate;
step 5, sending an initial transmitting power distribution result of the multi-radar system to a transmitter, calculating an effective measurement value of each radar station according to the initial false alarm rate, calculating interconnection probability according to the effective measurement values, and obtaining an updated target state according to the interconnection probability;
step 6, according to the updated target state, carrying out reduction and relaxation on the Bayesian information matrix according to an information reduction factor, and then replacing the information reduction factor by a detection model to obtain a final optimization model;
and 7, minimizing the final optimization model to obtain optimized transmitting power and optimized false alarm rate, and substituting the optimized transmitting power and the optimized false alarm rate into the step 5 until the target states of the multi-radar system at all times are updated.
In an embodiment of the present invention, before step 5, further comprising:
and obtaining a predicted target state and a predicted covariance matrix of the ith radar through the motion model according to the target state at the k-1 th moment and the covariance at the k-1 th moment, wherein i is more than or equal to 1 and less than or equal to N.
In one embodiment of the present invention, the step 2 comprises:
establishing an initial motion model according to the transfer matrix, the target state at the k-1 moment and the zero mean Gaussian process noise;
and carrying out dimension expansion processing on the initial motion model according to the radar scattering cross section to obtain a motion model at the k-th moment.
In one embodiment of the present invention, the motion model is:
ξk＝Fξξk-1+ηk-1
wherein ξkIs a target state vector xi after dimensionality expansion at the k momentk-1Is a dimension-expanded target state vector at the k-1 th moment, FξFor the whole transfer matrix after dimension expansion, etak-1And the zero mean Gaussian process noise after the dimensionality expansion at the k-1 moment is generated.
In one embodiment of the present invention, the step 3 comprises:
obtaining an observation function according to the predicted target state at the kth moment, and establishing an observation model according to the observation function and the measurement noise, wherein the observation model is as follows:
Figure GDA0001728970950000041
wherein, the
Figure GDA0001728970950000042
For the j-th measured value, g, of the i-th radar station at the k-th timei(ξk) Observation function of the ith radar station at the kth time, wi,kFor the measurement noise of the ith radar station at the kth time, vi,kIs the zero mean gaussian process noise of the ith radar station at the kth time.
In one embodiment of the present invention, step 4 comprises:
obtaining the detection probability according to the transmitting power and the false alarm rate;
processing the detection probability by utilizing a Nelman-Pearson theory to obtain the detection model, wherein the detection model is as follows:
Figure GDA0001728970950000043
wherein the content of the first and second substances,
Figure GDA0001728970950000044
Figure GDA0001728970950000045
the detection probability of the ith radar station at the kth time,
Figure GDA0001728970950000046
is the false alarm rate, mu, of the ith radar station at time ki,k(ξk) The signal-to-noise ratio of the ith radar station at the target at the kth time.
In one embodiment of the present invention, the step 5 comprises:
sending the initial transmit power allocation results for the multi-radar system to the transmitter and calculating a valid measurement for each of the radar stations based on the initial false alarm rate;
obtaining interconnection probabilities of all the radar stations in the multi-radar system according to the effective measured values, wherein the interconnection probabilities are as follows:
Figure GDA0001728970950000047
wherein the content of the first and second substances,
Figure GDA0001728970950000048
the interconnection probability of the jth valid measurement at the kth time,
Figure GDA0001728970950000049
j (i) th valid measurement value of ith radar station at k time measures correct event, Zi,kIs the valid measurement value of the ith radar station at the kth moment;
obtaining the update target state according to the interconnection probability, wherein the update target state is as follows:
Figure GDA0001728970950000051
wherein ξJ,k|kThe updated state of the jth event condition at time kth,
Figure GDA0001728970950000052
interconnection probability, ξ, of the J-th valid measurement at time kk|kIs the update target state at the k-th time.
In one embodiment of the present invention, step 6 comprises:
establishing a Bayesian information matrix for target tracking of the multi-radar system;
utilizing an information reduction factor to reduce and relax the Bayesian information matrix to obtain a reduced Bayesian information matrix;
and replacing the information reduction factor in the reduced Bayesian information matrix with the detection model to obtain the final optimization model.
In one embodiment of the present invention, the final optimization model is:
Figure GDA0001728970950000053
wherein Tr is J-1(uk) Trace of, J (u)k) For the relaxed predicted bayesian information matrix at time k,
Figure GDA0001728970950000054
probability of detection of predicted target state for ith radar station at time k-1 after relaxation, Pi,kFor the transmission power of the ith radar station at the kth time, A ═ Qk-1+FJ-1(ξk-1)FT]-1，
Figure GDA0001728970950000055
Qk-1Is the covariance of the motion noise at time k-1, F is the overall transfer matrix, J (ξ)k-1) Is a Bayesian information matrix at time k-1, Hi,kIs the Jacobian matrix of the ith radar station at the kth time, T is the transpose, Yi,kAnd the matrix is formed by the product of the covariance of the observed noise of the ith radar station at the kth moment and the transmission power.
In one embodiment of the present invention, the step 7 comprises:
obtaining the final optimization model minimization by introducing a monotone auxiliary variable;
obtaining the optimized transmitting power and the optimized false alarm rate of the multi-radar system according to the minimized final optimization model;
and substituting the optimized transmitting power and the optimized false alarm rate into the step 5 to update the target state of the multi-radar system until the target state of the multi-radar system at all times is updated.
Other aspects and features of the present invention will become apparent from the following detailed description, which proceeds with reference to the accompanying drawings. It is to be understood, however, that the drawings are designed solely for purposes of illustration and not as a definition of the limits of the invention, for which reference should be made to the appended claims. It should be further understood that the drawings are not necessarily drawn to scale and that, unless otherwise indicated, they are merely intended to conceptually illustrate the structures and procedures described herein.
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The following detailed description of embodiments of the invention will be made with reference to the accompanying drawings.
Fig. 1 is a schematic flow chart of a cooperative detection and power allocation method for target tracking in a multi-radar system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of cooperative detection and power allocation for target tracking in a multi-radar system according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating an internal relationship between a system parameter and a tracking accuracy according to an embodiment of the present invention;
fig. 4 is a schematic diagram of radar network deployment under different target radar scattering cross-sectional area models according to an embodiment of the present invention;
5 a-5 b are schematic diagrams of a relationship between a Bayesian-Lame lower bound and a root mean square error tracked under different target radar scattering cross-sectional area models according to an embodiment of the present invention;
6 a-6 b are schematic diagrams illustrating power distribution results of different target radar scattering cross-sectional area models according to an embodiment of the present invention;
7 a-7 b are schematic diagrams of detection and power distribution schemes of a radar scattering cross-sectional area model system for different targets according to an embodiment of the present invention;
fig. 8 a-8 b are schematic diagrams illustrating selection of false alarm rates of different target radar scattering cross-sectional area models according to an embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
Example one
Referring to fig. 1 to 8, fig. 1 is a schematic flow chart of a cooperative detection and power distribution method for target tracking in a multi-radar system according to an embodiment of the present invention, fig. 2 is a schematic flow chart of cooperative detection and power distribution for target tracking in a multi-radar system according to an embodiment of the present invention, fig. 3 is a schematic diagram of an internal relationship between a system parameter and tracking accuracy according to an embodiment of the present invention, fig. 4 is a schematic diagram of radar network deployment under different target radar cross-sectional area models according to an embodiment of the present invention, fig. 5a to 5b are schematic diagrams of a relationship between a bayesian-rao lower bound and a root mean square error tracked under different target radar cross-sectional area models according to an embodiment of the present invention, fig. 6a to 6b are schematic diagrams of power distribution results of different target radar cross-sectional area models according to an embodiment of the present invention, fig. 7a to 7b are schematic diagrams of system detection and power distribution schemes of radar scattering cross-sectional area models of different targets according to embodiments of the present invention, and fig. 8a to 8b are schematic diagrams of false alarm rate selection of radar scattering cross-sectional area models of different targets according to embodiments of the present invention. The cooperative detection and power distribution method for target tracking in the multi-radar system of the embodiment comprises the following steps:
step 1, establishing a multi-radar system, wherein the multi-radar system comprises N radar stations, initial transmitting power and initial false alarm rate which are distributed to the N radar stations of the multi-radar system are set, the multi-radar system is initialized, K represents kth tracking time, the initial value of K is 1, K is larger than or equal to 1 and smaller than or equal to K, and K is the preset maximum tracking time;
step 2, obtaining a motion model at the kth moment through the transfer matrix, the target state at the kth-1 moment and zero-mean Gaussian process noise, and determining the target state at the kth moment according to the motion model;
step 3, obtaining an observation model at the kth moment according to the target state at the kth moment;
step 4, obtaining a detection model at the kth moment by using a Neyman-Pearson theory according to the relation among the detection probability, the transmitting power and the false alarm rate;
step 5, sending an initial transmitting power distribution result of the multi-radar system to a transmitter, calculating an effective measurement value of each radar station according to the initial false alarm rate, calculating interconnection probability according to the effective measurement values, and obtaining an updated target state according to the interconnection probability;
step 6, according to the updated target state, carrying out reduction and relaxation on the Bayesian information matrix according to an information reduction factor, and then replacing the information reduction factor by a detection model to obtain a final optimization model;
and 7, minimizing the final optimization model to obtain optimized transmitting power and optimized false alarm rate, and substituting the optimized transmitting power and the optimized false alarm rate into the step 5 until the target states of the multi-radar system at all times are updated.
In the embodiment, a motion model, an observation model and a detection model of a multi-radar system are established, and a fusion center can predict a target state and a covariance matrix through the motion model to obtain a predicted measurement value and an innovation covariance matrix. For the detector, we choose the false alarm rate of each radar appropriately based on the computation power of the fusion center of each tracking frame. For the transmitter, we correctly allocate a transmission power resource with a predetermined power budget at each tracking frame. And calculating effective measurement values of each radar according to the false alarm rate, and calculating interconnection probability. And finally, obtaining an updated state and covariance matrix. Thereby forming a closed loop cooperative detection power distribution framework to realize the tracking of the target state at each frame. In this case, the target tracking accuracy can be improved using feedback information at both the detector and the transmitting end.
Specifically, as shown in fig. 2, the present embodiment describes in detail a cooperative detection and power allocation method for target tracking in a multi-radar system:
step 1, establishing a multi-radar system, and initializing the multi-radar system;
the multi-radar system comprises N radar stations and a fusion center, wherein N is an integer larger than 1.
And setting the position of the target 0 as an origin o, the east-west direction as an x axis and the south-north direction as a y axis, and establishing a plane rectangular coordinate system xoy.
The task of a multi-radar system is to track a target using measurements of multiple radars. Suppose that: (1) different radars transmit signals of different carrier frequencies; (2) the radar is equipped with only a matched filter associated with the signal itself being transmitted. Thus, any radar station can accept the signal of the radar itself, and the target echoes from other signals have an output at the matched filter close to zero, since any signal is uncorrelated with other signals. In this case, each radar is operated in a single channel mode and its valid measurement is sent to the fusion center.
Initializing a multi-radar system: the covariance matrix of the target state vector of the target at the time 0 is recorded as C0，C0To set up
Figure GDA0001728970950000091
The diagonal matrix of (a), wherein,
Figure GDA0001728970950000092
for the dimension of the target state vector at each time instant,
Figure GDA0001728970950000093
is a positive integer greater than 0; wherein the target state of the target at the k-th time is
Figure GDA0001728970950000094
Figure GDA0001728970950000095
Wherein x iskCoordinate values representing the target in the x-axis direction at the k-th time,
Figure GDA0001728970950000096
represents the speed of the target in the x-axis direction at the k-th time, ykA coordinate value indicating the y-axis direction of the target at the k-th time,
Figure GDA0001728970950000097
represents the speed of the target in the y-axis direction at the k-th time, hkRepresenting the channel state vector, k representing the kth time,the initial value of K is 1, K belongs to {1,2, …, K }, K is a preset maximum tracking time, and K is a positive integer greater than 0. The coordinate of the ith radar station in the multi-radar system is set to (x)i,yi) Wherein, 1,2, 1, N is more than or equal to 2, xiIndicating the position of the ith radar station in the x-axis direction, yiThe position of the ith radar station in the y-axis direction in the multi-radar system is shown.
Defining an initial transmit power and an initial false alarm rate, wherein the initial transmit power Pk,opt＝P0Initial false alarm rate Pfk,opt＝Pf0In which P is0Transmission power when k is 1, Pf0The false alarm rate when k is 1.
Step 2, setting a target in the multi-radar system to do uniform linear motion in a planar rectangular coordinate system xoy, wherein an initial motion model of the target is as follows:
xk＝Fxk-1+vk-1
wherein x iskIs the target state, x, of the target at the k-th moment before dimension expansionk-1Is the target state of the target at the k-1 th moment before dimension expansion, vk-1Zero mean Gaussian process noise for the target at time k-1 before dimension expansion, where vk-1Corresponding covariance of Qk-1And F is the whole transfer matrix before dimension expansion, wherein,
Figure GDA0001728970950000101
wherein, T0Is the time interval between successive time instants,
Figure GDA0001728970950000102
is an operator of the direct product of the matrices, I2An identity matrix of order 2 is represented.
Assuming that the conversion model of the radar scattering cross-sectional area between successive time instants is a first order markov process, the radar scattering cross-sectional area at the k-th time instant can be expressed as:
hk＝hk-1+μk-1
wherein h iskIs the radar scattering cross-sectional area, h, at time kk-1Is the radar scattering cross section at the k-1 time, muk-1Is of known covariance Qh,k-1Zero mean gaussian process noise (estimated from historical data in the maximum likelihood sense).
Wherein the content of the first and second substances,
Figure GDA0001728970950000103
wherein the content of the first and second substances,
Figure GDA0001728970950000104
hkrepresenting a channel state vector
Figure GDA0001728970950000105
Now, the target state vector and the channel state vector before dimension expansion are connected into a dimension Nx+2N of individual vectors to form a dimension-extended target state vector, which may be defined as
Figure GDA0001728970950000106
The motion model is then:
ξk＝Fξξk-1+ηk-1
wherein, Fξ＝blkdiag{F,I2N} (blkdiag stands for diagonal matrix), FξIs an integral transfer matrix after dimension expansion, etak-1Is the zero mean Gaussian process noise, η, of the k-1 th moment after dimension expansionk-1Corresponding covariance of Qξ,k-1＝blkdiag{Qk-1,Qh,k-1}，ξkAnd the target state vector is subjected to dimension expansion.
Step 3, setting an observation model of the multi-radar system, and collecting the measurement results of the effective measurement values of the ith radar station as:
Figure GDA0001728970950000111
wherein m isi,kIndicating the number of echoes received by the ith radar station at the kth time,
Figure GDA0001728970950000112
denotes the j-th measured value, Z, of the ith radar at the k-th timei,kA set of measurements representing valid measurements for the ith radar station at time k, wherein the observation model is:
Figure GDA0001728970950000113
wherein, the
Figure GDA0001728970950000114
For the j-th measured value, g, of the i-th radar station at the k-th timei(ξk) For the observation function of the ith radar station at the kth time, wi,kFor the measurement noise of the ith radar station at the kth time, vi,kIs the zero mean Gaussian process noise of the ith radar station at the kth time, where vi,kThe corresponding covariance is:
Figure GDA0001728970950000115
wherein
Figure GDA00017289709500001111
And
Figure GDA0001728970950000117
is the bayesian krame-luo lower bound on the estimated Mean Square Error (MSE) of the target distance and bearing information, where,
Figure GDA0001728970950000118
μi,kis zero mean Gaussian process noise, ξkIs a target state vector beta after dimensionality expansion at the kth momenti,kIs the k-th timeEffective bandwidth of signal of ith radar station, Bi,NNIs the half-power beamwidth of the receiver antenna.
Observation noise covariance ∑i,kThe expression of (c) can be abbreviated as:
Figure GDA0001728970950000119
wherein the content of the first and second substances,
Figure GDA00017289709500001110
is the power of-1, Y of the transmission power of the ith radar station at the kth timei,kIs a matrix of the remaining parameters.
At the tracking frame at the k-th time, the multi-radar system estimates the target state at the k-th time by using valid measurement values collected from a plurality of radars.
Step 4, the update target state at the k-1 time is xik-1|k-1With a corresponding covariance of Ck-1|k-1The fusion center predicts the predicted target state through the motion model and obtains a covariance matrix corresponding to the predicted target state, wherein,
Figure GDA0001728970950000121
ξk|k-1predicted target State for time k-1, FξIntegral transfer matrix xi after dimension expansionk-1|k-1The state is the updated target state at the k-1 moment; ck|k-1The prediction covariance matrix at the k-1 moment is obtained; ck-1|k-1For the updated covariance matrix at time k-1,
Figure GDA0001728970950000122
for transposition of the overall transfer matrix after dimension expansion, Qξ,k-1Is etak-1The corresponding covariance.
In addition, the predicted measurement value and the innovation covariance matrix of the ith radar station can be obtained,
Figure GDA0001728970950000123
wherein Z isi,k|k-1For the predicted measurement of the i-th radar station at the time of the (k-1) th time, gi(ξk|k-1) As an observation function of the ith radar station, Si,kAn innovation covariance matrix, C, for the ith radar station at time kk|k-1The prediction covariance matrix at time k-1,
Figure GDA0001728970950000124
as a transpose of the Jacobian matrix, sigmai,kIn order to observe the covariance of the noise,
Figure GDA0001728970950000125
Hi,kis Nz×(Nx+2N), wherein,
Figure GDA0001728970950000126
wherein, giIs an observation function of the ith radar station, and
Figure GDA0001728970950000131
wherein (x)i,yi) Coordinates of the radar station at the ith time point, (x)Tk,yTk) The coordinates of the tth radar station at the kth time instant are indicated,
Figure GDA00017289709500001311
corresponding to the distance-measuring part,
Figure GDA00017289709500001312
corresponding to the azimuth angle measurement section. Thus, the dimension of the measurement vector is nz＝2。
Suppose that the ith radar station uses the echo of the target in the rectangular wave gate to determine whether the target isPresence, verifying that the centre of the door is Zi,k|k-1Then the gate volume of the ith radar station is
Figure GDA0001728970950000132
Where g is a constant controlling the size of the verification region and nz＝2，Si,kIs an innovation covariance matrix. Let mi,kIndicating the number of echoes received by the ith radar station at the kth time. These mi,kCan be a false alarm or the presence of a true detection target (with detection probability)
Figure GDA0001728970950000133
)(mi,k1) may not even be observed (m)i,k＝0)。
Mathematically, the transmission power p of the ith radar station at time ki,kDetection probability of ith radar station at kth time
Figure GDA0001728970950000134
And false alarm rate of ith radar station at time k
Figure GDA0001728970950000135
The relationship between them is:
Figure GDA0001728970950000136
detecting a target of a Swerling I or II (a Swerling model is a model for describing the scattering cross-sectional area of a target radar) fluctuation model by using Neumann-Pearson theory, wherein the detection model is as follows:
Figure GDA0001728970950000137
wherein the content of the first and second substances,
Figure GDA0001728970950000138
Figure GDA0001728970950000139
the detection probability of the ith radar station at the kth time,
Figure GDA00017289709500001310
is the false alarm rate, mu, of the ith radar station at time ki,k(ξk) The signal-to-noise ratio of the ith radar station at the target at the kth time.
Wherein, mui,k(ξk) Is the signal-to-noise ratio of the ith radar station at the target at time k.
Figure GDA0001728970950000141
LiIs the number of coherent pulses, P, of the ith radar stationi,kIs the transmission power, gamma, of the ith radar station at time ki,kIs a system-dependent constant, gRi,kIs the distance, ξ, between the ith radar station and the target at the time of kthkIs a target state vector h after dimension expansion at the kth momenti,kIs the radar scattering cross-sectional area of the ith radar station at the kth time, then it can be set
Figure GDA0001728970950000142
Therefore, the detection model of Swerling type I or II model can be rewritten as
Figure GDA0001728970950000143
False alarms are modeled as being independent and evenly distributed over the validation gate with a Probability Density Function (PDF) of 1/Vi,k. The number distribution of false alarms is assumed to be a Poisson distribution with an average value of Ki,k＝λi,kVi,kWherein λ isi,kIs the spatial density of false alarms, the probability density p of false alarmsfa(mi,k) Is composed of
Figure GDA0001728970950000144
Wherein, the total number of samples in the wave gate is set as Numi,kThe spatial density of false alarms can be calculated as
Figure GDA0001728970950000145
In this case, there is mi,kThe probability of an individual observation is given by:
Figure GDA0001728970950000146
wherein, gamma (m)i,k) Is an index function, and Γ (m)i,k) Is defined as
Figure GDA0001728970950000147
Given mi,kOf the measurements, the probability that one of the measurements is generated for the target is:
Figure GDA0001728970950000151
step 5, estimating the target state, and distributing the initial transmitting power distribution result P at the kth moment under the condition that the transmitting power and the false alarm rate of each radar station are selected and the targets from a plurality of radar stations are detected for a plurality of times and fall into a wave gatek,optSent to the transmitter according to the initial false alarm rate Pfk,optThe effective measurement values of each radar station are calculated, and then the effective measurement values collected from different radar stations can be represented as
Figure GDA0001728970950000152
Suppose that
Figure GDA0001728970950000153
Is a 'join' event which is a unique permutation of measurements corresponding to measurements from different radar stations. For the J-th correlation event, the interconnection probability is
Figure GDA0001728970950000154
Wherein the content of the first and second substances,
Figure GDA0001728970950000155
for interconnection probability, p is assigned
Figure GDA0001728970950000156
The probability of (c).
Since the measurement errors of different radar stations are independent of each other, the interconnection probability can be calculated as
Figure GDA0001728970950000157
Wherein the content of the first and second substances,
Figure GDA0001728970950000158
and (4) an event that the J (i) th measurement value of the ith radar station is correct is shown. J (i) ═ 0 indicates an event in which the measurement results of the i-th radar station are all incorrect,
Figure GDA0001728970950000159
is the probability of interconnection of a single radar.
Updating the target state to obtain an updated target state, i.e.
Figure GDA00017289709500001510
Wherein ξk|kIs the update target state, ξ, at the k-th timeJ,k|kIs the update target state of the J-th event at the k-th time, and the number of the associated events is
Figure GDA00017289709500001511
Wherein the content of the first and second substances,
Figure GDA0001728970950000161
wherein the content of the first and second substances,
Figure GDA0001728970950000162
is the innovation of the J-th event corresponding to the ith radar station at the k-th time,
Figure GDA0001728970950000163
is the gain matrix, ξ, of the J-th event corresponding to the ith radar station at the kth timeJ,k|k-1Is the predicted target state for the jth event at time k-1.
The covariance Ck|kAnd updating to obtain:
Figure GDA0001728970950000164
wherein C isJ,k|kIs corresponding to xiJ,k|kT denotes the transposition.
Step 6, constructing an optimization standard, and expressing a Bayesian Information Matrix (BIM) for multi-radar system target tracking as
Figure GDA0001728970950000165
Wherein, J (xi)k) Is the Bayesian information matrix, Q, at time kk-1For motion noise covariance, F is the overall transfer matrix, FTIs a transpose of the overall transfer matrix,
Figure GDA00017289709500001614
for function expectation in brackets, Ti,k(ξk) Reducing a factor for information
Figure GDA0001728970950000167
Is a Jacobian matrix, Yi,kIs a matrix formed by the product of the observed covariance and the transmission power of the ith radar station at the kth time, Pi,kIs the transmission power of the ith radar station at time k, J (ξ)k-1) Is the bayesian information matrix at time k-1.
Figure GDA0001728970950000168
Wherein, Ti,k(ξk) Is an information reduction factor. By definition
Figure GDA0001728970950000169
Wherein the content of the first and second substances,
Figure GDA00017289709500001610
is the l component of the j event normalized measurement,
Figure GDA00017289709500001611
is the j-th measured value, h, of the i-th radar station at the k-th timei(ξk) Is the measured value (noiseless), σ, of the ith radar station at time klIs that
Figure GDA00017289709500001612
And
Figure GDA00017289709500001613
the standard deviation of the corresponding component in (a), wherein,
Figure GDA0001728970950000171
Figure GDA0001728970950000172
wherein the content of the first and second substances,
Figure GDA0001728970950000173
is composed of
Figure GDA0001728970950000174
According to the above equation, an Information Reduction Factor (IRF) T can be derivedi,k(ξk) Dependent on the target state xikOfi,k、
Figure GDA0001728970950000175
Sum observed noise covariance ∑i,k. It may not be able to convert Ti,k(ξk) Expressed as a constant information reduction factor, then a monte carlo integration has to be performed, which involves jointly sampling the target state evolution and measurement sequence, and is computationally expensive.
Applying cooperative detection and power allocation techniques to real-time systems requires fast and efficient computation of information reduction factors. Therefore, the predicted target state ξ at the k-1 th predicted time is utilizedk|k-1The origin uncertainty (from T) will be measuredi,k(ξk) Quantization) and target state uncertainty (by)
Figure GDA00017289709500001710
Given). In this case, the decoupling information reduction factor may be determined prior to cooperative detection and power allocation
Figure GDA00017289709500001711
And xik-1The relationship between them is taken as reference.
Figure GDA0001728970950000177
Then, a target J ([ xi ]) at the k-1 th time is givenk) Updated bayesian information matrix and candidates ukFurther estimating the predicted Bayesian information matrix at time k by discarding the desired operator
Figure GDA0001728970950000178
Wherein, J (u)k) Is a Bayesian information matrix, Qk-1Is the covariance of the motion noise at time k-1, F is the overall transfer matrix, J (ξ)k-1) For the predicted Bayesian information matrix at time k, pi,kThe transmission power of the ith radar station at the kth time,
Figure GDA0001728970950000179
as an information reduction factor, Hi,kIs a Jacobian matrix, Yi,kAnd forming a matrix by the product of the observed noise covariance and the transmission power of the ith radar station at the kth moment. In the above formula, the Jacobian matrix and the observation noise covariance can both be represented by xik|k-1And (4) calculating. The predicted Bayesian-Lame lower bound of the target is defined as the inverse of the predicted Bayesian information matrix, and then the optimization model can be written as
Figure GDA0001728970950000181
Wherein Tr represents obtaining J-1(uk) The trace of (c).
And Pi,kAnd
Figure GDA0001728970950000182
nonlinear non-coupled information reduction factor
Figure GDA0001728970950000183
Cannot be expressed in an analytical form. Thus, conventional gradient-based methods may not be directly applicable to this problem. To facilitate optimization, a relaxed bayesian krame-roval lower bound is defined by using proposition 1, which is then used as a cost function for the cooperative detection and power allocation scheme.
Proposition 1: order to
Figure GDA0001728970950000184
Wherein the content of the first and second substances,
Figure GDA0001728970950000185
is xik|k-1The detection probability of the ith radar station in the state, and the information reduction factor is satisfied
Figure GDA0001728970950000186
If no false alarm occurs, the equation holds.
Remarking: if the signal-to-noise ratio is relatively large, one can be found
Figure GDA0001728970950000187
To make
Figure GDA0001728970950000188
This is true.
In this case, mi,kCan only be 1 or 0, with a probability of respectively
Figure GDA0001728970950000189
And
Figure GDA00017289709500001810
thus, make
Figure GDA00017289709500001811
And
Figure GDA00017289709500001812
then
Figure GDA00017289709500001813
In radar applications, the false alarm rate is very small and thus can be known
Figure GDA00017289709500001814
The final optimization model is therefore:
Figure GDA00017289709500001815
wherein Tr is J-1(uk) Trace of, J (u)k) For the predicted bayesian information matrix at time k,
Figure GDA00017289709500001816
probability of detection of predicted target state for ith radar station at time k-1, Pi,kFor the transmission power of the ith radar station at the kth time, A ═ Qk-1+FJ-1(ξk-1)FT]-1，
Figure GDA00017289709500001817
Is the covariance of the motion noise at time k-1, F is the overall transfer matrix, J (ξ)k-1) For the predicted Bayesian information matrix at time k, Hi,kIs the Jacobian matrix of the ith radar station at the kth time, T is the transpose, Yi,kAnd forming a matrix by the product of the observed noise covariance and the transmission power of the ith radar station at the kth moment.
A good approximation can be provided for the bayesian krame-luo lower bound to measure the tracking estimate mean square error. In this case, G (u) is usedk) As a reasonable cost function of the cooperative detection and power allocation scheme. In the above formula, A ═ Qk-1+FJ-1(ξk-1)FT]-1，
Figure GDA0001728970950000191
And
Figure GDA0001728970950000192
is defined in proposition 1.
Step 7, minimizing the final optimization model;
the first optimization problem generated at the kth time may be constructed as follows:
Figure GDA0001728970950000193
Figure GDA0001728970950000194
wherein s.t. represents a constraint condition of
Figure GDA0001728970950000195
min represents taking the minimum value, i.e.
Figure GDA0001728970950000196
Taking the minimum value.
Wherein the content of the first and second substances,
Figure GDA0001728970950000197
is a closed convex set, and the convex set is a closed convex set,
Figure GDA0001728970950000198
Figure GDA0001728970950000199
wherein p iskIs the transmitted power vector at the k-th time instant, pfkFor the false alarm rate vector at time k, pkThe first constraint of (a) means that the transmit power of each radar is non-negative, while the second constraint means that the total transmit power of the radar network is limited. For pfkIndicates that the false alarm rate of the ith radar station belongs to [0,1 ]]While the second constraint indicates that the computational power of the fusion center is limited. In the above formula, MiIs the number of resolution units in the verification gate of the ith radar station, expression
Figure GDA00017289709500001910
Representing the average amount of data, P, that needs to be transmitted from the ith radar station to the fusion centertotalIs the total transmit power.
It is clear that the first optimization problem comprises two adaptation vectors, respectively transmit power vector pkSum false alarm rate vector pfk. It is difficult to find an optimal solution due to the following facts: (1) two types of adaptive parameters are coupled in a cost function; (2) cost function for ukNon-linear and non-convex. To solve this problem, first a series of sequences t is definedkMonotonic auxiliary variable of a representation
Figure GDA0001728970950000201
The first optimization problem can then be reformulated as a second optimization problem, the second optimization problem being:
Figure GDA0001728970950000202
Figure GDA0001728970950000203
Figure GDA00017289709500002012
to solve this problem, a two-step solution is proposed to solve the above optimization problem.
The method comprises the following steps: the first optimization problem is relaxed appropriately. By definition, it can know
Figure GDA00017289709500002011
Wherein the content of the first and second substances,
Figure GDA0001728970950000204
is xik|k-1Probability of detection of i-th radar station in state, Pi,kIs the transmit power of the ith radar station at time k.
Thus, aggregate
Figure GDA0001728970950000205
Can be taken as tkAnother closed convex set of
Figure GDA0001728970950000206
Is relaxed
Figure GDA0001728970950000207
Then, if feasible t is further relaxed by eliminating non-linear equality constraintskAggregate, then the relaxation problem is of the form:
Figure GDA0001728970950000208
Figure GDA0001728970950000209
the above equation is actually a convex optimization problem with optimal results tk,optCan be easily obtained by using a male toolbox.
Step two: an optimal solution t to the relaxation problem has been obtained by step onek,optThe question left is then how to do
Figure GDA00017289709500002010
Effectively from tk,optTo obtain the optimum transmitting power Pk,optAnd optimizing false alarm rate Pfk,opt. The resulting problem can be equated with:
Figure GDA0001728970950000211
Figure GDA0001728970950000212
wherein
Figure GDA0001728970950000213
To represent
Figure GDA0001728970950000214
The complex function of (2). Due to the fact that
Figure GDA0001728970950000215
Non-convex, complex function gi(uk) Is non-convex. To solve this non-convex but separable problem and to ensure convergence, we turn to a flexible alternative direction multiplier algorithm developed.
First, a new set of vectors is introduced
Figure GDA0001728970950000216
0.. N, and equivalently converts the problem of the above equation to the following linear constraint problem:
Figure GDA0001728970950000217
Figure GDA0001728970950000218
Figure GDA0001728970950000219
after reconfiguration, due to the introduction of auxiliary vectors
Figure GDA00017289709500002110
N, the problem dimension is increased by N. However, one major benefit to the solution is to allow each radar to process a single local vector
Figure GDA00017289709500002111
And a local function gl(uk)。
For the linear constraint problem, the augmented Lagrangian function is given by
Figure GDA00017289709500002112
In this function, a set of different dual vectors y is usedlAnd a penalty parameter [ rho ]lFor multiple equality constraints
Figure GDA00017289709500002113
1., N. The detailed steps of the flexible alternative direction multiplier algorithm, based on which the steady state point of the problem of guaranteeing convergence can be obtained, are summarized below.
Let t equal to 0 and set the termination threshold e equal to 10-3And a penalty parameter ρl＝100；
(II) every iteration t +1, calculate
Figure GDA00017289709500002114
(III) the variable l is selected from one of {0, 1.. eta., (N) }, and if l is equal to {1, 2.. eta., (N) }, the variable l is calculated by solving the following formula
Figure GDA0001728970950000221
Figure GDA0001728970950000222
Updating dual vectors
Figure GDA0001728970950000223
Otherwise set up
Figure GDA0001728970950000224
And (y)l)t+1＝(yl)t，l＝1,...,N；
If (IV) is
Figure GDA0001728970950000225
Let t be t +1, continue step (one), otherwise stop and let
Figure GDA0001728970950000226
In the algorithm, block variables
Figure GDA0001728970950000227
Is updated in each iteration, and
Figure GDA0001728970950000228
is governed by block selection rules. In step (three), the linear constraint problem is to
Figure GDA0001728970950000229
Rather than to
Figure GDA00017289709500002210
To ensure convergence. Furthermore, since the above equation is an unconstrained convex quadratic optimization problem, a closed form in each iteration can be obtained:
Figure GDA00017289709500002211
wherein the content of the first and second substances,
Figure GDA00017289709500002212
auxiliary vector, l ═ 0.,. N, ylIs the Langerhans multiplier, plIs a penalty parameter.
Obtaining an optimized transmitting power and an optimized false alarm rate by minimizing the final optimization model, wherein the optimized transmitting power and the optimized false alarm rate are respectively as follows:
Figure GDA00017289709500002213
wherein, Pk,optTo optimize the transmission power, Pfk,optTo optimize the false alarm rate.
And substituting the optimized transmitting power and the optimized false alarm rate into the step 5 until the target states of the multi-radar system at all times are updated.
The effect of the present invention is further verified and explained by the following simulation experiment.
Simulation conditions:
the simulation running system is an INtel (R) core (TM) i7-4790CPU @3.60GHz 64-bit WiNdows7 operating system, and MATLAB (R2016b) is adopted as simulation software.
(II) simulation content and result analysis:
the simulation experiment of the invention sets the deployment situation of a multi-radar system with reference to fig. 4, the total number N of radar stations contained in the multi-radar system is 6, the initial position of a target is (0,0) km, and the target moves at a constant speed with the speed of (200,0) m/s; the simulation sequence data is 60 frames, the effective bandwidth of a signal transmitted by each radar station is 2MHz, and the wavelength of the signal transmitted by each radar station is lambdac1 m; each radar station antenna aperture D10 λc(ii) a The correlation gate coefficient g is 4; noise intensity q of object motion process 0100; the sampling period of each radar station is 4s, the target distance is 100km, the signal-to-noise ratio (SNR) is set to 10dB when the reflection coefficient is 1, the reflection coefficient is set to 1 in the simulation, and two RCS models (h) are considered in the simulation1,h2). In both models, the RCS average values corresponding to different radars are assumed to fluctuate according to the Swerling I model
Figure GDA0001728970950000231
i is 1,2, N is different. First RCS model h1The cooperative detection and power allocation strategy of the target RCS may be evaluated. In the second RCS model h2RCS average value for radar 3
Figure GDA0001728970950000233
Larger, while other RCS averages remain with h1The same is true. The following table details the operating parameters of each radar under test.
Figure GDA0001728970950000232
Bayesian Claamer-Rove lower bound and tracking RMS error in tracking experiments under different RCS models, defined as position tracking RMS error, are given with reference to FIGS. 5a and 5b
Figure GDA0001728970950000241
Wherein N isMCIs the number of monte carlo tests,
Figure GDA0001728970950000242
is the target state estimate in the j-th trial.
The first reference represents the case with fixed false alarm rate and equal power allocation, the second reference is that the limited power resources of the multi-radar system are properly allocated as reference, and the false alarm rate of each radar is set to be the same as reference 1. The results in fig. 5a and 5b show that reference 1 exhibits a higher root mean square error compared to the optimized false alarm rate selection and transmit power allocation. For different RCS models, the tracking accuracy in experiment 1 can be improved by more than 40% by the process of cooperative detection and power allocation, and the enhancement brought by the power allocation scheme is much greater than that of the cooperative detection scheme.
Fig. 6a and 6b depict power allocation results averaged over thousands of monte carlo trials. The results show that power resources are allocated to a limited number of radars. In FIG. 6a, the radar 6 starts tracking a target with k ≧ 43 in conjunction with the radar 4 instead of the radar 2, because the target is moving toward it. A similar conclusion can be drawn in fig. 6 b. In the second RCS model h2In this case, radar 4, although benefiting from better observation conditions (closer target radar distance), is assigned to tracking the target in radar 2(k < 44) or radar 5(k ≧ 44) tracking, based on the fact that radar 3 has a better propagation path.
Notably, radars 2 with relatively large signal bandwidths are used in both RCS models with k < 43. The intuitive explanation is that a larger signal bandwidth will result in a smaller distance estimation error, and a smaller tracking bayesian-larval lower bound. However, in h2No radar 6 with a relatively small half-power beamwidth (small azimuth estimation error) is used. To clarify this, FIGS. 7a and 7b are presented to usSome physical explanations are provided. Taking k 30 as an example, the different sectors in fig. 7a and 7b approximate the spatial variance distribution of the target distance and azimuth angle measurement error, where ρ 20 is a constant used to enlarge the uncertainty region, so that an unambiguous physical interpretation can be presented. Then, in the range rings of different radars intersected in fig. 7a and fig. 7b, we can obtain the uncertainty region of the target position of the k-th frame (see the subgraphs in fig. 7a and fig. 7 b). Note that the target radar range is very large (e.g., 100 kilometers), and the azimuth information contributes much less to the tracking performance than the range information. Therefore, not at h2Instead of using radar 6, radar 5 with a relatively good angular spread is selected and radar 3 tracks the target. Overall, the above results imply that radars with a large contribution to the tracking accuracy, such as larger signal bandwidth, higher target reflectivity and better observation conditions, will be allocated more power resources.
Fig. 8a and 8b show the average false alarm rate assignment results per frame. According to the power distribution result, the radar which greatly contributes to the tracking accuracy sends data thereof to the fusion center according to the optimized false alarm rate so as to track the target. While no other radar is selected to track the target, so other radars may be dispatched to perform other tasks. In these selected radars, nodes with larger signal bandwidths and half-power receiver beamwidths (which themselves verify more resolution cells in the gate) will employ smaller false alarm rates, see for example radar 2 and radar 6 results.
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the method.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (6)

1. A cooperative detection and power distribution method for target tracking in a multi-radar system is characterized by comprising the following steps:
step 1, establishing a multi-radar system, wherein the multi-radar system comprises N radar stations, initial transmitting power and initial false alarm rate which are distributed to the N radar stations of the multi-radar system are set, the multi-radar system is initialized, K represents kth tracking time, the initial value of K is 1, K is larger than or equal to 1 and smaller than or equal to K, and K is the preset maximum tracking time;
step 2, obtaining a motion model at the kth moment through the transfer matrix, the target state at the kth-1 moment and zero-mean Gaussian process noise, and determining the target state at the kth moment according to the motion model;
step 3, obtaining an observation model at the kth moment according to the target state at the kth moment;
step 4, obtaining a detection model at the kth moment by using a Neyman-Pearson theory according to the relation among the detection probability, the transmitting power and the false alarm rate;
step 5, sending an initial transmitting power distribution result of the multi-radar system to a transmitter, calculating an effective measurement value of each radar station according to the initial false alarm rate, calculating interconnection probability according to the effective measurement values, and obtaining an updated target state according to the interconnection probability;
step 6, according to the updated target state, carrying out reduction and relaxation on the Bayesian information matrix according to an information reduction factor, and then replacing the information reduction factor by a detection model to obtain a final optimization model;
step 7, minimizing the final optimization model to obtain optimized transmitting power and optimized false alarm rate, and substituting the optimized transmitting power and the optimized false alarm rate into the step 5 until the target states of the multi-radar system at all times are updated;
the step 4 comprises the following steps:
obtaining the detection probability according to the transmitting power and the false alarm rate;
processing the detection probability by utilizing a Nelman-Pearson theory to obtain the detection model, wherein the detection model is as follows:
Figure FDA0003309238520000021
wherein the content of the first and second substances,
Figure FDA0003309238520000022
Figure FDA0003309238520000023
the detection probability of the ith radar station at the kth time,
Figure FDA0003309238520000024
is the false alarm rate, mu, of the ith radar station at time ki,k(ξk) The signal-to-noise ratio of the ith radar station at the target at the kth moment;
the step 5 comprises the following steps:
sending the initial transmit power allocation results for the multi-radar system to the transmitter and calculating a valid measurement for each of the radar stations based on the initial false alarm rate;
obtaining interconnection probabilities of all the radar stations in the multi-radar system according to the effective measured values, wherein the interconnection probabilities are as follows:
Figure FDA0003309238520000025
wherein the content of the first and second substances,
Figure FDA0003309238520000026
the interconnection probability of the jth valid measurement at the kth time,
Figure FDA0003309238520000027
j (i) th valid measurement value of ith radar station at k time measures correct event, Zi,kIs the valid measurement value of the ith radar station at the kth moment;
obtaining the update target state according to the interconnection probability, wherein the update target state is as follows:
Figure FDA0003309238520000028
wherein ξJ,k|kThe updated state of the jth event condition at time kth,
Figure FDA0003309238520000029
interconnection probability, ξ, of the J-th valid measurement at time kk|kThe updated target state at the kth moment;
the step 6 comprises the following steps:
establishing a Bayesian information matrix for target tracking of the multi-radar system;
utilizing an information reduction factor to reduce and relax the Bayesian information matrix to obtain a reduced Bayesian information matrix;
and replacing the information reduction factor in the reduced Bayesian information matrix with the detection model to obtain the final optimization model.
2. The method of claim 1, wherein the step 2 comprises:
establishing an initial motion model according to the transfer matrix, the target state at the k-1 moment and the zero mean Gaussian process noise;
and carrying out dimension expansion processing on the initial motion model according to the radar scattering cross section to obtain a motion model at the k-th moment.
3. The method of claim 2, wherein the motion model is:
ξk＝Fξξk-1+ηk-1
wherein ξkIs a target state vector xi after dimension expansion at the kth momentk-1Is a dimension-expanded target state vector at the k-1 th moment, FξFor the whole transfer matrix after dimension expansion, etak-1And the zero mean Gaussian process noise after the dimensionality expansion at the k-1 moment is generated.
4. The method of claim 1, wherein step 3 comprises:
obtaining an observation function according to the target state at the kth moment, and establishing an observation model according to the observation function and the measurement noise, wherein the observation model is as follows:
Figure FDA0003309238520000031
wherein, the
Figure FDA0003309238520000032
For the j-th measured value, g, of the i-th radar station at the k-th timei(ξk) For the observation function of the ith radar station at the kth time, wi,kFor the measurement noise of the ith radar station at the kth time, vi,kIs the zero mean gaussian process noise of the ith radar station at the kth time.
5. The method of claim 1, wherein the final optimization model is:
Figure FDA0003309238520000033
wherein Tr is J-1(uk) Trace of, J (u)k) For the relaxed predicted bayesian information matrix at time k,
Figure FDA0003309238520000034
probability of detection of predicted target state for ith radar station at time k-1 after relaxation, Pi,kFor the transmission power of the ith radar station at the kth time, A ═ Qk-1+FJ-1(ξk-1)FT]-1，
Figure FDA0003309238520000035
Qk-1Is the covariance of the motion noise at time k-1, F is the overall transfer matrix, J (ξ)k-1) Is a Bayesian information matrix at time k-1, Hi,kIs the Jacobian matrix of the ith radar station at the kth time, T is the transpose, Yi,kAnd the matrix is formed by the product of the covariance of the observed noise of the ith radar station at the kth moment and the transmission power.
6. The method of claim 1, wherein the step 7 comprises:
establishing a first optimization problem, and enabling the first optimization problem to be equivalent to a second optimization problem by introducing a monotone auxiliary variable;
minimizing the final optimization model according to a second optimization problem;
obtaining the optimized transmitting power and the optimized false alarm rate of the multi-radar system according to the minimized final optimization model;
and substituting the optimized transmitting power and the optimized false alarm rate into the step 5 to update the target state of the multi-radar system until the target state of the multi-radar system at all times is updated.
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