CN106990399A - Radar network system power and bandwidth combined distributing method for target following - Google Patents

Abstract

The invention discloses a kind of radar network system power and bandwidth combined distributing method for target following, its main thought is：Radar network system is set up, the radar network system, which is included in fusion center and N number of radar station, the search coverage of N number of radar station, has target；K, k ∈ { 1,2 ..., K } are initialized, the sampled echo data of N number of radar station in k moment radar network systems are calculated, and send to fusion center；Fusion center receives N number of radar station in k moment radar network systems and receives the vectorial estimate of dbjective state calculated after the echo data waveform that target is reflected to the k moment, so calculate k+1 moment radar network system resource allocations on P_k+1And β_k+1Cost function, and then respectively calculate k+1 moment N number of radar station transmission signal power output value and k+1 moment radar network systems transmitted signal bandwidth output valve；Until obtain K moment N number of radar station transmission signal power output value and K moment radar network systems transmitted signal bandwidth output valve when stop tracking to target.

Description

Radar network system power and bandwidth combined distributing method for target following

Technical field

The invention belongs to Radar Signal Processing Technology field, more particularly to a kind of radar network system for target following Power and bandwidth combined distributing method, it is adaptable to effectively lift carrier-borne or In-vehicle networking radar platform limited emission resource profit With efficiency, and the tracking accuracy to target can be lifted.

Background technology

In recent years, with the development of science and technology and weaponry, single radar station has been difficult to tackle what is become increasingly complex Operational environment, can effectively make up deficiency of the single radar station to target detection tracing using traditional radar network system, be based on The target positioning of radar network system and the transmission signal power of tracking accuracy and the quantity of radar station and each radar station etc. are permitted Multifactor relevant, when radar station quantity is more, transmission signal power is higher, the positioning of target and tracking accuracy are higher.But For some specific application scenarios, (the limited radar network grid of such as gross energy carries out target following, or military Demand of low intercepting and capturing etc. in), it is necessary to limit the total emission power of radar network system.Therefore in the constraint of resource-constrained Under, the transmission signal power of each radar station in dynamic coordinate radar network system enables to radar network system to have more Good performance of target tracking.

Simultaneously for the radar network system under central fusion framework, the measurement data of all radar stations is required for passing Center processor is sent to be handled and merged；However, the processing capability in real time of center processor is limited, each moment passes The defeated data total amount to center processor must be limited.In the case of given over-sampling coefficient, signal bandwidth is wider, adopts Sample frequency is higher, and the data volume that correspondence radar station is transmitted to center processor is bigger.Therefore, when the real-time processing of center processor , it is necessary to control the data volume that each radar station is transmitted when limited in one's ability, and the bandwidth resources of dynamically distributes radar network system.

Alfred O.Hero and Douglas Cochran are in paper " Hero A O, the Cochran D.Sensor delivered management:Past,present,and future[J].IEEE Sensors Journal,2011,11(12):3064- A kind of cognitive tracking based on radar netting is proposed in 3075. ", the CRLB of target location error is regard as power distribution Cost function, it is therefore an objective to the power resource that reasonable distribution system is fixed, make the CRLB of target location error minimum.However, should Paper regards power distribution as a non-convex optimization problem, and is solved with greedy algorithm, and greedy algorithm amount of calculation compared with Greatly, it is also possible to cannot get optimal solution.

The patent that Xian Electronics Science and Technology University applies at it " is used for the Multi-beam transmitting power dynamic that Radar Multi Target is tracked Distribution method " (number of patent application：201110260636.6, publication No.：Disclose a kind of many for radar in 102426358A) The Multi-beam transmitting power dynamic allocation method of target following, solves tracking performance when single radar station carries out multiple target tracking Poor the problem of, but this method can not be applied in traditional radar network system.

The content of the invention

The deficiency existed for above-mentioned prior art, it is an object of the invention to propose a kind of networking for target following Radar system power and bandwidth combined distributing method, this kind are used for the radar network system power and bandwidth joint point of target following Method of completing the square can strengthen detecting and tracking performance of the radar network system to target under conditions of system resource constraint.

The basic ideas of the present invention：The motion model and radar network system of target are initially set up, to minimize target Tracking error is cost, designs cost function, sets up the mathematic optimal model of resource allocation；With reference to mathematical optimization tools, solve The model, obtains the optimization emission parameter of networking radar system, and then in radar network system total emission power and real-time place Under conditions of reason is limited in one's ability, the tracking performance to target is lifted.

To reach above-mentioned technical purpose, the present invention, which is adopted the following technical scheme that, to be achieved.

A kind of radar network system power and bandwidth combined distributing method for target following, comprises the following steps：

Step 1, radar network system is set up, the radar network system includes fusion center and N number of radar station, N number of thunder There is target up in the search coverage at station；Objective emission signal of N number of radar station into its search coverage simultaneously receives echo data； The echo data received is sent to fusion center and carries out fusion treatment by N number of radar station, and fusion center is according to the number of echoes Estimate according to dbjective state, and then obtain transmission signal power output value and any time of any time N number of radar station The transmitted signal bandwidth output valve of radar network system；N is the positive integer more than 0；

Initialization：K is made to represent k moment, k ∈ { 1,2 ..., K }, maximum at the time of K is setting；K values in the present embodiment It is 1 for 23, k initial value；The Bayesian Information matrix of the dbjective state vector at 0 moment is designated as J respectively₀, J₀For 0 moment Dbjective state vector forecasting covariance matrix C₀Inverse, the dbjective state vector forecasting covariance matrix C at 0 moment₀For setting Tie up diagonal matrix,For the dbjective state vector dimension at each moment；Wherein dbjective state refers to seat of any time target in y directions Scale value and the speed in y directions, and any time target is in the coordinate value in x directions and the speed in x directions；

Step 2, the target motion in setting radar network system is linear uniform motion, and sets the target-like at k moment State is x_k；

Step 3, N number of radar station is measured to target respectively in radar network system, obtains k moment radar network systems In N number of radar station sampled echo data, and by k moment radar network systems N number of radar station sampled echo data send To fusion center；

Step 4, fusion center receives the sampled echo data of N number of radar station in k moment radar network systems, and calculates To measurement vector theta of the k moment radar network systems to target_k；

Step 5, fusion center is according to measurement vector theta of the k moment radar network systems to target_kDbjective state is carried out Estimation, obtains the vectorial estimate x of dbjective state at k moment_k|k；

Step 6, k+1 moment N number of radar station is measured to the Jacobian matrix of the single order local derviation of prediction to dbjective state vector It is defined as G (x_k+1), and according to the vectorial estimate x of dbjective state at k moment_k|k, the dbjective state vector at k+1 moment is calculated successively x_k+1Bayesian Information matrix J (x_k+1) and the k+1 moment dbjective state vector x_k+1Carat Metro lower bound Matrix C (x_k+1)；

Step 7, according to the dbjective state vector x at k+1 moment_k+1Carat Metro lower bound Matrix C (x_k+1), calculating obtains k+ 1 moment radar network system resource allocation on P_k+1And β_k+1Cost function F (P_k+1,β_k+1)|x_k+1, P_k+1When representing k+1 Carve the set of N number of radar station transmission signal power in radar network system, β_k+1Represent N number of thunder in k+1 moment radar network systems Up to the set of station transmitted signal bandwidth, x_k+1Represent the dbjective state vector at k+1 moment；

Step 8, according to the set P of N number of radar station transmission signal power in k+1 moment radar network systems_k+1During with k+1 Carve the set β of N number of radar station transmitted signal bandwidth in radar network system_k+1, calculate obtain k+1 moment N number of radar station respectively Transmission signal power output valueWith the transmitted signal bandwidth output valve of k+1 moment radar network systems

Step 9, k is made plus 1, return to step 2, the transmission signal power output value until obtaining K moment N number of radar stationWith The transmitted signal bandwidth output valve of K moment radar network systemsWhen stop tracking to target.

The present invention has the following advantages that compared with prior art：

First, due to the Bayes carat Metro lower bound that the present invention is tracked by optimization aim, adjust radar network system In each radar station transmission signal power and transmitted signal bandwidth so that the inventive method can improve radar network system pair The tracking accuracy of target.

Second, because the present invention to cost function during solving, use circulation minimum method to solve and cause generation The bivariate optimization problem of the minimum transmission signal power of valency function and transmitted signal bandwidth, and to the optimization problem of each variable Solved using Projected Gradient so that cost function can obtain optimal solution, while the inventive method operand is relatively low, can Meet the demand of real-time.

Brief description of the drawings

The present invention is described in further detail with reference to the accompanying drawings and detailed description.

Fig. 1 is a kind of radar network system power and bandwidth combined distributing method flow for target following of the invention Figure；

Fig. 2 (a) is the spatial distribution of each radar station and target in radar network system in the case of the first Method in Positioning of Radar Figure；Wherein the first Method in Positioning of Radar situation is target in radar network system region internal motion；

Fig. 2 (b) is the spatial distribution of each radar station and target in radar network system in the case of second Method in Positioning of Radar Figure；Wherein second Method in Positioning of Radar situation is target in radar network system region external movement；

Fig. 3 (a) shows for the root-mean-square error of Target state estimator in radar network system in the case of the first Method in Positioning of Radar It is intended to；

Fig. 3 (b) is the root-mean-square error in Target state estimator in radar network system in the case of second of Method in Positioning of Radar Schematic diagram；

Fig. 4 (a) divides each radar station transmission signal power for radar network system in the case of the first Method in Positioning of Radar With result figure；

Fig. 4 (b) divides each radar station transmitted signal bandwidth for radar network system in the case of the first Method in Positioning of Radar With result figure；

Fig. 4 (c) divides each radar station transmission signal power for radar network system in the case of second of Method in Positioning of Radar With result figure；

Fig. 4 (d) divides each radar station transmitted signal bandwidth for radar network system in the case of second of Method in Positioning of Radar With result figure.

Embodiment

Reference picture 1, is a kind of radar network system power and bandwidth co-allocation side for target following of the present invention Method flow chart；Wherein described radar network system power and bandwidth combined distributing method for target following, including following step Suddenly：

Step 1, radar network system is set up, the radar network system includes fusion center and N number of radar station, N number of thunder There is target up in the search coverage at station；Objective emission signal of N number of radar station into its search coverage simultaneously receives echo data, The echo data includes radial distance of the target relative to each radar station, and target relative to each radar station Doppler frequency shift；The echo data received is sent to fusion center and carries out fusion treatment, fusion center root by N number of radar station Dbjective state is estimated according to the echo data, and then obtains the transmission signal power output of any time N number of radar station The transmitted signal bandwidth output valve of value and any time radar network system；N is the positive integer more than 0.

Initialization：K is made to represent k moment, k ∈ { 1,2 ..., K }, maximum at the time of K is setting；K values in the present embodiment It is 1 for 23, k initial value；The Bayesian Information matrix J of the dbjective state vector at 0 moment₀For the dbjective state vector at 0 moment Predict covariance matrix C₀Inverse, the dbjective state vector forecasting covariance matrix C at 0 moment₀For settingTie up diagonal matrix,For The dbjective state vector dimension at each moment；In the present embodimentTake 4, and

Step 2, the target motion in setting radar network system is linear uniform motion, and sets the target-like at k moment State is x_k, its expression formula is：

x_k=Fx_k-1+u_k-1

Wherein, x_kThe dbjective state vector at k moment is represented, F represents dbjective state vector in the case of linear uniform motion Transfer matrix, x_k-1Represent the dbjective state vector at k-1 moment, u_k-1It is that zero, covariance is Q to represent that the k-1 moment obeys average_k-1 Gaussian Profile motion process noise, Q_k-1For the motion process noise covariance matrix of k-1 moment targets；Wherein target-like State refers to any time target in the coordinate value in y directions and the speed in y directions, and any time target is in the coordinate value in x directions With the speed in x directions.

Target movement model is configured to linear uniform motion, therefore calculating obtains target-like in the case of linear uniform motion State vector transfer matrix F be：

Wherein,Expression asks direct product to operate, T₀Represent that each radar station detects the time interval of target.

The Q_k-1For the motion process noise covariance matrix of k-1 moment targets, its expression formula is：

Wherein, q₁Represent the process noise intensity of control targe dynamic model.

Step 3, N number of radar station is measured to target respectively in radar network system, obtains k moment radar network systems In N number of radar station sampled echo data, and by k moment radar network systems N number of radar station sampled echo data send To fusion center.

The transmission signal power output value of k moment N number of radar station is designated as respectivelyBy k moment radar network systems Transmitted signal bandwidth output valve is designated as Represent in k moment radar network systems The transmission signal power output value of i-th of radar station； Represent k moment networking thunders The transmitted signal bandwidth output valve of i-th of radar station up in system；Then radar network system is according to k moment N number of radar station Transmission signal power output valueWith the transmitted signal bandwidth output valve of k moment radar network systemsTarget is measured, Obtain the sampled echo data of N number of radar station in k moment radar network systems.

(3a) according to the following formula, calculating obtains i-th of radar station in k moment radar network systems and receives target reflecting Echo data be r_i,k(t), its expression formula:

Wherein, h_i,kRepresent the scattering resonance state of i-th of radar station measurement target in k moment radar network systems, this implementation H in example_i,kValue is 1；α_i,kThe attenuation coefficient of i-th of radar station measurement target in k moment radar network systems is represented,∝ represents to be proportional to；R_i,kRepresent radial direction of i-th of radar station relative to target in k moment radar network systems Distance,x_kRepresent k moment target in the coordinate value in x directions, x_iRepresent radar network system I-th of radar station is in the coordinate value in x directions, y in system_kRepresent k moment target in the coordinate value in y directions, y_iRepresent radar network system Coordinate value of i-th of radar station in y directions in system；s_i,kRepresent i-th of radar station transmission signal in k moment radar network systems Complex envelope；α represents the light velocity, is 3 × 10⁸m/s；J represents imaginary unit, f_i,kRepresent k moment target relative to radar network system The Doppler frequency shift of i-th of radar station in system,λ_i,kRepresent k moment radar networks The transmission signal wavelength of i-th of radar station in system,Speed of the k moment target in x directions is represented,Represent that k moment targets exist The speed in y directions, v_i,k(t) the measurement noise of i-th of radar station in k moment radar network systems is represented, is that one-sided power spectrum is close Spend and beZero mean Gaussian white noise, t represents time variable.

(3b) receives the echo data r that target is reflected to i-th of radar station in k moment radar network systems_i,k (t) sampled with over-sampling coefficient ρ, ρ >=1, in the present embodiment, over-sampling coefficient value is 1；And then obtain k moment networkings The sampled echo data that i-th of radar station is received in radar system, are designated as i-th of radar station in k moment radar network systems Sampled echo data r_i,k, then by the sampled echo data r of i-th of radar station in k moment radar network systems_i,kSend extremely Fusion center.

(3c) according to the following formula, calculating obtains what k moment fusion center i-th of radar station from radar network system was received Sampled echo data volume M_i,k,ρ represents over-sampling coefficient, β_i,kRepresent the in k moment radar network systems The transmitted signal bandwidth of i radar station, α represents the light velocity, V_i,kRepresent that i-th of radar station is to target in k moment radar network systems Observation area area, L represents L values in the coherent pulse string number of K moment N number of radar station transmission signal, the present embodiment For 128.

(3d) makes i take 1 respectively to N, is repeated in performing (3a) to (3c), and then respectively obtain k moment radar networks system The sampled echo data r of 1st radar station in system_1,kThe sampled echo number of n-th radar station into k moment radar network systems According to r_N,k, and the k moment fusion center sampled echo data volume M that the 1st radar station is received from radar network system_1,kExtremely The sampled echo data volume M that k moment fusion center n-th radar station from radar network system is received_N,k, when being designated as k respectively Carve sampled echo data and k moment fusion center N number of radar from radar network system of N number of radar station in radar network system The sampled echo data volume that what station was received receive.

Step 4, fusion center receives the sampled echo data of N number of radar station in k moment radar network systems, and calculates To measurement vector theta of the k moment radar network systems to target_k。

The sub-step of step 4 is：

(4a) fusion center is according to the sampled echo data r of i-th of radar station in k moment radar network systems_i,k, use Train of pulse location algorithm, which is calculated, obtains radial distance measurement of i-th of radar station to target in k moment radar network systems

(4b) according to the following formula, fusion center, which is calculated, obtains in k moment radar network systems i-th of radar station to target radial The measurement variance of distance

Wherein,Represent the measurement noise v of i-th of radar station in k moment radar network systems_i,k(t) one-sided power spectrum Density, α_i,kRepresent the attenuation coefficient of i-th of radar station measurement target in k moment radar network systems, P_i,kRepresent k moment networkings The transmission signal power of i-th of radar station in radar system, L represents the coherent pulse string of K moment N number of radar station transmission signal Number, T_i,kRepresent T in the transmission signal pulse width of i-th of radar station in k moment radar network systems, the present embodiment_i,kTake It is worth for 90 μ s；h_i,kRepresent the scattering resonance state of i-th of radar station measurement target in k moment radar network systems, β_i,kWhen representing k Carve the transmitted signal bandwidth of i-th of radar station in radar network system.

(4c) fusion center is according to the sampled echo data r of i-th of radar station in k moment radar network systems_i,k, use Fast Fourier Transform (FFT) method, which is calculated, obtains Doppler frequency shift measurement of i-th of radar station to target in k moment radar network systems

(4d) according to the following formula, it is how general to target that fusion center calculating obtains i-th of radar station in k moment radar network systems Strangle the measurement variance of frequency displacement

Wherein,Represent the measurement noise v of i-th of radar station in k moment radar network systems_i,k(t) one-sided power spectrum Density, α_i,kRepresent the attenuation coefficient of i-th of radar station measurement target in k moment radar network systems, P_i,kRepresent k moment networkings The transmission signal power of i-th of radar station in radar system, L represents the coherent pulse string of K moment N number of radar station transmission signal Number, T_i,kRepresent the transmission signal pulse width of i-th of radar station in k moment radar network systems, h_i,kRepresent k moment networkings I-th of radar station measures the scattering resonance state of target in radar system,Represent i-th of radar in k moment radar network systems In the length for transmission signal of standing, the present embodimentValue is 329ms.

(4e) is measured according to i-th of radar station in k moment radar network systems to the radial distance of targetWith the k moment I-th of radar station is measured to the Doppler frequency shift of target in radar network systemObtain i-th in k moment radar network systems Measurement vector theta of the individual radar station to target_i,k,[]^TExpression asks transposition to operate.

(4f) makes i take 1 respectively to N, is repeated in performing (4a)-(4e), and then obtain k moment radar network systems to mesh Target measures vector theta_k,

Step 5, according to measurement vector theta of the k moment radar network systems to target_k, fusion center is using particle filter calculation Method is estimated dbjective state, obtains the vectorial estimate x of dbjective state at k moment_k|k。

(5a) is initialized：U is made to represent u-th of particle, u ∈ { 1,2 ..., U }, U is the particle total number of setting, this implementation U values are 10000 in example, and particle is used for representing the state of target；The initial time state of u-th of particle is designated as The normalization weights of 0 moment, u-th of particle are represented, The state vector of 0 moment, u-th of particle is represented,x₀Represent the original state of the dbjective state at 0 moment, i.e. target；Chol () is represented Cholesky is decomposed, C₀Represent the dbjective state vector forecasting covariance matrix at 0 moment, Rand represent one between 0 and 1 with Machine number,Dimension it is identical with the dbjective state vector dimension at each moment.

(5b) according to the following formula, fusion center calculates the state vector for obtaining u-th of particle of k moment

Wherein,The state vector of u-th of particle of k-1 moment is represented, F represents target-like in the case of linear uniform motion The transfer matrix of state vector, u_k-1It is that zero, covariance is Q to represent that the k-1 moment obeys average_k-1The motion process of Gaussian Profile make an uproar Sound, Q_k-1For the motion process noise covariance matrix of k-1 moment targets；The state vector of wherein particle refers to any time particle Coordinate value and the speed in x directions in x directions, and any time target is in the coordinate value in y directions and the speed in y directions.

(5c) is initialized：γ is made to represent the γ times iteration, { 1,2 ..., K'}, γ initial value are that 1, K' represents to set to γ ∈ Fixed iterations maximum, and K' is identical with N values；Set the 0th iteration of k moment after u-th of particle particle state to Measure and be With the state vector of u-th of particle of k momentValue is identical.

(5d) according to the following formula, fusion center, which is calculated, obtains after the γ times iteration of k moment u-th of particle relative to radar network The measurement vector of i-th of radar station in system

Wherein,Represent that u-th of particle is relative to i-th of radar in radar network system after the γ times iteration of k moment The radial distance stood,Represent that u-th of particle is relative to i-th of radar in radar network system after the γ times iteration of k moment The Doppler frequency shift stood, []^TExpression asks transposition to operate.

(5e) according to the following formula, fusion center, which is calculated, obtains after the γ times iteration of k moment u-th of particle relative to radar network The weights of i-th of radar station in system

Wherein,Represent that u-th of particle is relative to i-th of radar in radar network system after the γ times iteration of k moment The radial distance stood,Represent that i-th of radar station is measured to the radial distance of target in k moment radar network systems,Table Show the measurement variance of i-th of radar station in k moment radar network systems to target radial distance,The expression k moment the γ times After iteration u-th of particle relative to i-th of radar station in radar network system Doppler frequency shift,Represent k moment networking thunders I-th of radar station is measured to the Doppler frequency shift of target up in system,Represent i-th of radar in k moment radar network systems The measurement variance stood to target Doppler frequency displacement, exp represents that exponential function is operated.

Weights by u-th of particle after the γ times iteration of k moment relative to i-th of radar station in radar network systemIt is used as the weights of u-th of particle after the γ times iteration of k moment

(5f) makes u take 1 respectively to U, repeats step (5e), and then respectively obtain after the γ times iteration of k moment the 1st The weights of particleThe weights of the U particle after to the γ times iteration of k moment

(5g) according to the following formula, fusion center calculates the normalization weights for obtaining u-th of particle after the γ times iteration of k moment

(5h) makes u take 1 respectively to U, repeats step (5g), and then respectively obtain after the γ times iteration of k moment the 1st The normalization weights of particleThe normalization weights of the U particle after to the γ times iteration of k momentIt is designated as k moment γ The normalization weights of U particle after secondary iteration

(5i) uses the resampling methods of particle filter, and is weighed according to the normalization of U particle after the γ times iteration of k moment ValueThe particle of low weights is removed to U particle, and replicates the particle of high weight, is obtained after the γ times iteration of k moment The state vector of U particle

Represent the particle state of u-th of particle after the γ times iteration of k moment Vector.

(5j) makes γ plus 1, returns to sub-step (5d), the state vector until obtaining U particle after the K' times iteration of k momentAnd by the state vector of U particle after the K' times iteration of k momentIt is designated as the end-state vector of U particle of k momentThe end-state vector of wherein u-th of particle of k moment isGo to step (5k).

(5k) calculates the vectorial estimate x of dbjective state for obtaining the k moment according to the following formula_k|k：

Step 6, k+1 moment N number of radar station is measured to the Jacobian matrix of the single order local derviation of prediction to dbjective state vector It is defined as G (x_k+1), and according to the vectorial estimate x of dbjective state at k moment_k|k, the dbjective state vector at k+1 moment is calculated successively x_k+1Bayesian Information matrix J (x_k+1) and the k+1 moment dbjective state vector x_k+1Carat Metro lower bound Matrix C (x_k+1)。

The sub-step of step 6 is：

The Jacobian matrix for the single order local derviation that k+1 moment N number of radar station is measured prediction by (6a) to dbjective state vector is determined Justice is G (x_k+1), and according to the vectorial estimate x of dbjective state at k moment_k|k, calculate the dbjective state vector for obtaining the k+1 moment x_k+1Bayesian Information matrix J (x_k+1)：

Wherein, x_k+1The dbjective state vector at k+1 moment is represented, E { } represents to ask expectation to calculate, X is sought in expression_k+1Single order local derviation,Expression is askedSingle order local derviation, p (x_k+1) represent k+ The dbjective state vector x at 1 moment_k+1Probability density function, z_k+1Represent the measurement set that k+1 moment fusion centers are received, p (z_k+1|x_k+1) represent the likelihood function that the dbjective state vector at k+1 moment is measured on target, Q_k-1Represent k-1 moment targets Motion process noise covariance matrix, F represents the transfer matrix of dbjective state vector in the case of linear uniform motion, J^-1(x_k-1) Represent the dbjective state vector x at k-1 moment_k-1Bayesian Information inverse of a matrix, G (x_k+1) represent k+1 moment N number of radar station pair Dbjective state vector measures the Jacobian matrix of the single order local derviation of prediction, and diag () represents to ask diagonal matrix to operate, x_k+1|kRepresent k The predicted state vector of+1 moment target,X in expression_k+1Value be x_k+1|k；Represent k+1 moment networking thunders I-th of radar station be to the estimation error variance of the observation of target Doppler frequency displacement up in system,Represent k+1 moment networkings I-th of radar station be to the measurement variance of target radial distance in radar system,Represent the in k+1 moment radar network systems Measurement variance of the i radar station to target Doppler frequency displacement.

(6b) is according to the dbjective state vector x at k+1 moment_k+1Bayesian Information matrix J (x_k+1), calculate the k+1 moment Dbjective state vector x_k+1Carat Metro lower bound Matrix C (x_k+1), its expression formula is：

C(x_k+1)=J^-1(x_k+1)

Wherein, ()^-1Represent inversion operation.

Step 7, by the dbjective state vector x at k+1 moment_k+1Carat Metro lower bound Matrix C (x_k+1) it is used as cost function And set up model.

(7a) is according to the dbjective state vector x at k+1 moment_k+1Carat Metro lower bound Matrix C (x_k+1), calculating obtains k+1 Moment radar network system resource allocation on P_k+1And β_k+1Cost function F (P_k+1,β_k+1)|x_k+1：

F(P_k+1,β_k+1)|x_k+1=Trace (C (x_k+1))

Wherein, P_k+1Represent the set of N number of radar station transmission signal power in k+1 moment radar network systems, P_k+1= [P_1,k+1,P_2,k+1,...,P_i,k+1,...,P_N,k+1]^T, P_i,k+1Represent the hair of i-th of radar station in k+1 moment radar network systems Penetrate signal power；β_k+1Represent the set of N number of radar station transmitted signal bandwidth in k+1 moment radar network systems, β_k+1= [β_1,k+1,β_2,k+1,...,β_i,k+1,...,β_N,k+1]^T, β_i,k+1Represent the hair of i-th of radar station in k+1 moment radar network systems Penetrate signal bandwidth；C(x_k+1) represent the k+1 moment dbjective state vector x_k+1Carat Metro lower bound matrix, x_k+1When representing k+1 The dbjective state vector at quarter, Trace () represents to ask mark computing.

(7b) is according to k+1 moment radar network system resource allocations on P_k+1And β_k+1Cost function F (P_k+1,β_k+1) |x_k+1, set Optimized model：

Wherein,So thatValue distinguishes corresponding when minimum P_i,k+1Value and β_i,k+1Value, P_i,k+1The transmission signal power of i-th of radar station in k+1 moment radar network systems is represented, β_i,k+1The transmitted signal bandwidth of i-th of radar station in k+1 moment radar network systems is represented,Represent in radar network system The lower limit of i-th of radar station transmission signal power,Represent i-th radar station transmission signal power in radar network system The upper limit,The lower band of i-th of radar station transmission signal in radar network system is represented,Represent radar network system In i-th of radar station transmission signal the bandwidth upper limit, N represents the radar station total number included in radar network system, 1^T=[1, 1,...,1]_1×N, P_totalRepresent the transmission signal general power of N number of radar station in each moment radar network system, M_totalRepresent The maximum amount of data that each moment corresponding fusion center can be received, V_k+1 ^T=[V_1,k+1,V_2,k+1,...,V_i,k+1,..., V_N,k+1]_1×N, V_i,k+1The observation area area of i-th of radar station in k+1 moment radar network systems is represented, s.t. represents constraint Condition.

Step 8, circulation minimum method is used to solve the transmission signal power and transmission signal for make it that cost function is minimum The bivariate optimization problem of bandwidth.

(8a) is set at the beginning of one to the transmitted signal bandwidth of each radar station in k+1 moment radar network systems Initial value, wherein the transmitted signal bandwidth initial value of i-th of radar station in k+1 moment radar network systems is designated as β_k+1,i,opt, It is the bandwidth value evenly distributed for the transmitted signal bandwidth of each radar station, andM_totalRepresent corresponding fusion center of each moment The maximum amount of data that can be received, V_i,k+1The observation area area of i-th of radar station in k+1 moment radar network systems is represented,Represent the observation area area sum of k+1 moment N number of radar station.

C is made to represent the c times iteration, c initial value is 0；Setting terminates thresholding E, E ∈ (0,0.1)；E takes in the present embodiment It is worth for 0.01；Set the transmitted signal bandwidth β of radar network system after the 0th iteration of k+1 moment_k+1,0,optFor [β_k+1,1,opt, β_k+1,2,opt,...,β_k+1,i,opt,...,β_k+1,N,opt]^T, β_k+1,i,optRepresent i-th of radar station in k+1 moment radar network systems Transmitted signal bandwidth initial value.

The transmitted signal bandwidth β of radar network system after the c times iteration of (8b) fixed k+1 moment_k+1,c,optIt is constant, and then Obtaining the object function after the c times iteration of k+1 moment is：

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1And β_k+1,c,optCost function, P_i,k+1Represent the transmission signal work(of i-th of radar station in k+1 moment radar network systems Rate, s.t. represents constraints, P_k+1The set of N number of radar station transmission signal power in k+1 moment radar network systems is represented, x_k+1Represent the dbjective state vector at k+1 moment.

(8c) solves the object function after the c times iteration of k+1 moment using Projected Gradient:By k+1 moment networking thunders The transmission signal power initial value of N number of radar station is designated as P up in system_k+1,0, P_k+1,0=P_total/ N, P_totalRepresent each moment The transmission signal general power of N number of radar station in radar network system, N represents that the radar station included in radar network system is always individual Number；And making l be the l times Projected Gradient iteration, l initial value is 0；It is △ p and Projected to set step-size in search respectively The termination thresholding of algorithm is ε, and △ p are the positive integer of setting, and ε is the positive number less than 1；△ p values are that 100, ε takes in the present embodiment It is worth for 0.01.

(8d) carries out piecemeal to the object function after the c times iteration of k+1 moment, respectively obtains the l times Projected of expression The first block units matrix A after algorithm iteration_1l, the second block units matrix A after the l times Projected Gradient iteration_2l、 The first piecemeal column vector b after the l times Projected Gradient iteration_1lWith the second piecemeal after the l times Projected Gradient iteration Column vector b_2l。

Specifically, the object function after the c times iteration of k+1 moment is rewritten into following formula：

Wherein,Expression is equivalent to, and A represents 2N × N-dimensional unit matrix,P_k+1,lWhen representing k+1 Value of the transmission signal power of N number of radar station in radar network system in the l times Projected Gradient iteration is carved,P_i,k+1,lRepresent the transmission signal power of i-th of radar station in k+1 moment radar network systems at the l times Value during Projected Gradient iteration；B represents N-dimensional column vector, The lower limit of i-th of radar station transmission signal power in radar network system is represented,Represent i-th in radar network system The upper limit of individual radar station transmission signal power, subscript T represents that transposition is operated.

Piecemeal is carried out respectively to 2N × N-dimensional unit matrix A and N-dimensional column vector b so that A_1lP_k,l=b_1l, A_2lP_k,l>b_2l, A_1lRepresent the first block units matrix after the l times Projected Gradient iteration, A_2lRepresent the The second block units matrix after l Projected Gradient iteration, b_1lRepresent first point after the l times Projected Gradient iteration Block column vector, b_2lRepresent the second piecemeal column vector after the l times Projected Gradient iteration, P_k,lRepresent k moment radar networks system Value of the transmission signal power of N number of radar station in the l times Projected Gradient iteration in system.

(8e) according to the following formula, calculates the projection matrix after the l times Projected Gradient iteration

(8f) according to the following formula, calculates the transmission signal of N number of radar station after the l+1 times Projected Gradient iteration of k+1 moment Power P_k+1,l+1：

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation onAnd β_k+1,c,optCost function,Represent the Q of N number of radar station after the l times Projected Gradient iteration of k+1 moment Dimensional vector transmission signal power, Represent q for 1, its Remaining position is all 0 Q dimensional vectors；Q is equal with N values；The possible value of subscript+expression, represents dot product,Table It is shown as corresponding P during minimum value_k+1,lValue, P_k+1,lRepresent N number of radar station after the l times Projected Gradient iteration of k+1 moment Transmission signal power.

(8g) ifThen by the l+1 times throwing of k+1 moment The transmission signal power P of N number of radar station after shadow gradient algorithm iteration_k+1,l+1It is used as N number of radar station after the c times iteration of k+1 moment Transmission signal power output value P_k+1,c,opt, go to sub-step (8h)；Otherwise, make l plus 1, return to sub-step (8d).

Wherein,Represent the pass of radar network system resource allocation after the c times iteration of k+1 moment In P_k+1,l+1And β_k+1,c,optCost function,Represent radar network system after the c times iteration of k+1 moment Unite resource allocation on P_k+1,lAnd β_k+1,c,optCost function, P_k+1,l+1Represent the l+1 times Projected Gradient of k+1 moment The transmission signal power of N number of radar station, β after iteration_k+1,c,optRepresent the transmitting of radar network system after the c times iteration of k+1 moment Signal bandwidth, P_k+1,lRepresent the transmission signal power of N number of radar station after the l times Projected Gradient iteration of k+1 moment.

(8h) is by the transmission signal power output value P of N number of radar station after the c times iteration of k+1 moment_k+1,c,optDuring as k+1 Carve N number of radar station transmission signal power in radar network system；And then calculating obtains the target letter after the c times iteration of k+1 moment Number：

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1,c,optAnd β_k+1Cost function, β_k+1Represent the collection of N number of radar station transmitted signal bandwidth in k+1 moment radar network systems Close, V_k+1 ^T=[V_1,k+1,V_2,k+1,...,V_i,k+1,...,V_N,k+1]_1×N, V_i,k+1Represent in k+1 moment radar network systems i-th The observation area area of radar station, s.t. represents constraints.

(8i) solves the object function after the c times iteration of k+1 moment using Projected Gradient:By k+1 moment networking thunders The transmitted signal bandwidth initial value of N number of radar station is designated as β up in system_k+1,0,

M_totalRepresent each moment pair The maximum amount of data that the fusion center answered can be received, V_i,k+1Represent the sight of i-th of radar station in k+1 moment radar network systems Survey region area,Represent the observation area area sum of k+1 moment N number of radar station；And make l' be the l' times projection ladder Algorithm iteration is spent, l' initial value is 0；Setting step-size in search is △ p' respectively and the termination thresholding of Projected Gradient is ε ', △ p' are the positive integer of setting, and ε ' is the positive number less than 1；△ p' values are that 100, ε ' values are 0.01 in the present embodiment；(·)^T Represent transposition operation.

(8j) carries out piecemeal to the object function after the c times iteration of k+1 moment, respectively obtains the l' times Projected of expression The first block units matrix A after algorithm iteration_1l', the second block units matrix after the l' times Projected Gradient iteration A_2l', the first piecemeal column vector b after the l' times Projected Gradient iteration_1l'With after the l' times Projected Gradient iteration Two piecemeal column vector b_2l'。

Specifically, the object function after the c times iteration of k+1 moment is rewritten into following formula：

Wherein,Expression is equivalent to, and A' represents 2N × N-dimensional unit matrix of setting,β_k+1,l' Represent the transmitted signal bandwidth of N number of radar station in k+1 moment radar network systems in the l' times Projected Gradient iteration Value,β_i,k+1,l'Represent the transmitting of i-th of radar station in k+1 moment radar network systems Value of the signal bandwidth in the l' times Projected Gradient iteration；B' represents the N-dimensional column vector of setting, Represent in radar network system i-th The lower limit of radar station transmitted signal bandwidth,The upper limit of i-th of radar station transmitted signal bandwidth in radar network system is represented, (·)^TRepresent transposition operation.

The N-dimensional column vector b' of 2N × N-dimensional unit matrix A' and setting to setting carry out piecemeal respectively so thatA_1l'β_k,l'=b_1l', A_2l'β_k,l'>b_2l', A_1l'Represent after the l' times Projected Gradient iteration The first block units matrix, A_2l'Represent the second block units matrix after the l' times Projected Gradient iteration, b_1l'Represent The first piecemeal column vector after the l' times Projected Gradient iteration, b_2l'Represent after the l' times Projected Gradient iteration Two piecemeal column vectors, β_k,l'Represent the transmitted signal bandwidth of N number of radar station in k moment radar network systems in the l' times projection ladder Spend value during algorithm iteration.

(8k) according to the following formula, calculates the projection matrix after the l' times Projected Gradient iteration

V_i,k+1Represent the observation area area of i-th of radar station in k+1 moment radar network systems.

(8l) according to the following formula, calculates the transmission signal of N number of radar station after the l'+1 times Projected Gradient iteration of k+1 moment Power β_k+1,l'+1：

Wherein,Represent radar network system resource allocation after the c times iteration of k+1 moment On P_k+1,c,optWithCost function, P_k+1,c,optRepresent the transmitting letter of N number of radar station after the c times iteration of k+1 moment Number power output value,Represent the Q dimensional vectors transmitting of N number of radar station after the l' times Projected Gradient iteration of k+1 moment Signal bandwidth, Represent q be 1, remaining be all 0 Q dimensional vectors；Q is equal with N values；The possible value of subscript+expression, represents dot product,When being expressed as minimum value Corresponding β_k+1,l'Value, β_k+1,l'Represent the transmission signal band of N number of radar station after the l' times Projected Gradient iteration of k+1 moment It is wide.

(8m) ifThen by k+1 moment the l'+1 times The transmitted signal bandwidth β of N number of radar station after Projected Gradient iteration_k+1,l'+1It is used as N number of radar after the c times iteration of k+1 moment The transmitted signal bandwidth output valve β stood_k+1,c,opt；Otherwise, make l' plus 1, return to sub-step (8j).

Wherein, F (P_k+1,c,opt,β_k+1,l'+1) represent the c times iteration of k+1 moment after radar network system resource allocation pass In P_k+1,c,optAnd β_k+1,l'+1Cost function, P_k+1,c,optRepresent the transmission signal of N number of radar station after the c times iteration of k+1 moment Power output value, β_k+1,l'+1Represent the transmission signal band of N number of radar station after the l'+1 times Projected Gradient iteration of k+1 moment Width,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1,c,optWith β_k+1,l'Cost function, β_k+1,l'Represent the transmission signal band of N number of radar station after the l' times Projected Gradient iteration of k+1 moment It is wide.

UntilIteration stopping, now distinguishes The transmission signal power output value P of N number of radar station after the c times iteration of k+1 moment obtained during by iteration stopping_k+1,c,optIt is used as k The transmission signal power output value of+1 moment N number of radar stationBy the hair of radar network system after the c times iteration of k+1 moment Penetrate signal bandwidth β_k+1,c,optIt is used as the transmitted signal bandwidth output valve of k+1 moment radar network systems

Wherein,Represent radar network system resource allocation after the c times iteration of k+1 moment On P_k+1,c,optAnd β_k+1,c,optCost function, P_k+1,c,optRepresent the transmitting letter of N number of radar station after the c times iteration of k+1 moment Number power output value, β_k+1,c,optThe transmitted signal bandwidth of radar network system after the c times iteration of k+1 moment is represented,Represent the c-1 times iteration of k+1 moment after radar network system resource allocation on P_k+1,c-1,optAnd β_k+1,c-1,optCost function, P_k+1,c-1,optRepresent the transmitting of N number of radar station after the c-1 times iteration of k+1 moment Signal power output valve, β_k+1,c-1,optRepresent the transmitted signal bandwidth of radar network system after the c-1 times iteration of k+1 moment.

Step 9, k is made plus 1, return to step 2 continues transmission signal of the subsequent time radar network system on N number of radar station The resource allocation of power and transmitted signal bandwidth, the transmission signal power output value until obtaining K moment N number of radar stationAnd K The transmitted signal bandwidth output valve of moment radar network systemWhen stop to target following.

Further checking explanation is made to effect of the present invention by following emulation experiment.

(1) simulated conditions：

The simulated running system of the present invention is Intel (R) Core (TM) i5-4590CPU@3.30GHz, 64 Windows7 Operating system, simulation software uses MATLAB (R2014b).

(2) emulation content and interpretation of result：

The emulation experiment of reference picture 2 (a) and Fig. 2 (b) present invention situation of structuring the formation that to set two kinds different, two kinds of situations In, the radar station total number N=4 that radar network system is included, target initial position all in (12.75,3) km, and using speed as (100,0) m/s moves with uniform velocity, and simulation sequence data are 23 frames, and each radar station detects the time interval T of target₀=10s, The lower limit of i-th of radar station transmission signal power in radar network systemI-th in radar network system The upper limit of radar station transmission signal powerThe data of i-th of radar station transmission signal in radar network system Measure lower limitThe bandwidth upper limit of i-th of radar station transmission signal in radar network systemM_to_talRepresent the maximum amount of data that corresponding fusion center of each moment can be received, V_i,k+1 Represent the observation area area of i-th of radar station in k+1 moment radar network systems, i ∈ { 1,2 ..., N }, the RCS moulds of target Type is set as non-fluctuating；Radar 1, radar 2, radar 3 and radar 4 in Fig. 2 (a) and Fig. 2 (b) are respectively the 1st radar station, the 2 radar stations, the 3rd radar station and the 4th radar station.

Reference picture 3 (a) and Fig. 3 (b), Fig. 3 (a) are dbjective state in radar network system in the case of the first Method in Positioning of Radar The root-mean-square error schematic diagram of estimation, Fig. 3 (b) is Target state estimator in radar network system in the case of second of Method in Positioning of Radar In root-mean-square error schematic diagram；Wherein, the ordinate in Fig. 3 (a) and Fig. 3 (b) represents root-mean-square error, the equal table of abscissa At the time of showing to target following, the curve indicated with pecked line represents that radar network system is estimated to dbjective state after power distribution The carat Metro lower limit of meter, represents that radar network system is to target after power bandwidth co-allocation with the curve that long dotted line is indicated The carat Metro lower limit of state estimation, the curve indicated with chain-dotted line represents that system resource evenly distributes radar network system pair The carat Metro lower limit of Target state estimator, radar network system after power distribution is represented with the curve that solid line and circle are indicated To the root-mean-square error of Target state estimator, networking after power bandwidth co-allocation is represented with the curve that solid line and multiplication sign are indicated Radar system represents that system resource is uniformly divided to the root-mean-square error of Target state estimator with the curve that solid line and plus sige are indicated With root-mean-square error of the networking radar system to Target state estimator.

Each curve compared in Fig. 3 (a) and Fig. 3 (b) be can see, and tracking accuracy is lifted about 15% by power distribution, And power bandwidth co-allocation then can be by performance boost 30% or so.

Reference picture 4 (a) and Fig. 4 (b), Fig. 4 (a) are radar network system in the case of the first Method in Positioning of Radar to each radar The allocation result figure of transmission signal of standing power, Fig. 4 (b) is radar network system in the case of the first Method in Positioning of Radar to each radar The allocation result figure for transmitted signal bandwidth of standing, Fig. 4 (c) is radar network system in the case of second of Method in Positioning of Radar to each radar The allocation result figure of transmission signal of standing power, Fig. 4 (d) is radar network system in the case of second of Method in Positioning of Radar to each radar The allocation result figure for transmitted signal bandwidth of standing；

Wherein, ordinates of the Fig. 4 (a) into Fig. 4 (d) represents that each radar station power or bandwidth account for total resources respectively Ratio, at the time of abscissa is represented to target following, what is represented with square frame is the 1st radar station institute in radar network system Account for the ratio of resource, with plus sige represent be the 2nd resource shared by radar station in radar network system ratio, with rhombus table What is shown is the ratio of the 3rd resource shared by radar station in radar network system, and what is represented with multiplication sign is radar network system In the 4th resource shared by radar ratio.

Power and bandwidth allocation result figure shown in reference picture 4 (a) to Fig. 4 (d), it can be seen that as k >=11, due to mesh 4th radar station flight of the mark away from the 3rd radar sum, therefore the 1st radar station and the 2nd radar station replace the 3rd radar 4th radar station of sum is tracked to target, these results indicate that power and bandwidth resources are tended to distribute to distance objective Nearer radar.

In summary, emulation experiment demonstrates the correctness of the present invention, validity and reliability.

Obviously, those skilled in the art can carry out the essence of various changes and modification without departing from the present invention to the present invention God and scope；So, if these modifications and variations of the present invention belong to the scope of the claims in the present invention and its equivalent technologies Within, then the present invention is also intended to comprising including these changes and modification.

Claims (10)

1. a kind of radar network system power and bandwidth combined distributing method for target following, it is characterised in that including with Lower step：

Step 1, radar network system is set up, the radar network system includes fusion center and N number of radar station, N number of radar station Search coverage in there is target；Objective emission signal of N number of radar station into its search coverage simultaneously receives echo data；It is N number of The echo data received is sent to fusion center and carries out fusion treatment by radar station, and fusion center is according to the echo data pair Dbjective state is estimated, and then obtains transmission signal power output value and any time networking of any time N number of radar station The transmitted signal bandwidth output valve of radar system；N is the positive integer more than 0；

Initialization：K is made to represent k moment, k ∈ { 1,2 ..., K }, K is maximum at the time of setting, and k initial value is 1；Wherein mesh Mark state refers to any time target in the coordinate value in y directions and the speed in y directions, and any time target is in the seat in x directions Scale value and the speed in x directions；

Step 2, the target motion in setting radar network system is linear uniform motion, and set the dbjective state at k moment as x_k；

Step 3, N number of radar station is measured to target respectively in radar network system, obtains N in k moment radar network systems The sampled echo data of individual radar station, and the sampled echo data of N number of radar station in k moment radar network systems are sent to melting Conjunction center；

Step 4, fusion center receives the sampled echo data of N number of radar station in k moment radar network systems, and calculating obtains k Measurement vector theta of the moment radar network system to target_k；

Step 5, fusion center is according to measurement vector theta of the k moment radar network systems to target_kDbjective state is estimated, Obtain the vectorial estimate x of dbjective state at k moment_k|k；

Step 6, the Jacobian matrix that k+1 moment N number of radar station is measured to the single order local derviation of prediction to dbjective state vector is defined For G (x_k+1), and according to the vectorial estimate x of dbjective state at k moment_k|k, the dbjective state vector x at k+1 moment is calculated successively_k+1 Bayesian Information matrix J (x_k+1) and the k+1 moment dbjective state vector x_k+1Carat Metro lower bound Matrix C (x_k+1)；

Step 7, according to the dbjective state vector x at k+1 moment_k+1Carat Metro lower bound Matrix C (x_k+1), when calculating obtains k+1 Carve radar network system resource allocation on P_k+1And β_k+1Cost function F (P_k+1,β_k+1)|x_k+1, P_k+1Represent k+1 moment groups The set of N number of radar station transmission signal power, β in net radar system_k+1Represent N number of radar station in k+1 moment radar network systems The set of transmitted signal bandwidth, x_k+1Represent the dbjective state vector at k+1 moment；

Step 8, according to the set P of N number of radar station transmission signal power in k+1 moment radar network systems_k+1With k+1 moment groups The set β of N number of radar station transmitted signal bandwidth in net radar system_k+1, the transmitting for obtaining k+1 moment N number of radar station is calculated respectively Signal power output valveWith the transmitted signal bandwidth output valve of k+1 moment radar network systems

Step 9, k is made plus 1, return to step 2, the transmission signal power output value until obtaining K moment N number of radar stationDuring with K Carve the transmitted signal bandwidth output valve of radar network systemWhen stop tracking to target.

2. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 1, Characterized in that, in step 2, the dbjective state at the k moment is x_k, its expression formula is：

x_k=Fx_k-1+u_k-1

Wherein, x_kThe dbjective state vector at k moment is represented, F represents the transfer square of dbjective state vector in the case of linear uniform motion Battle array, Expression asks direct product to operate, T₀Represent that each radar station detects the time interval of target, x_k-1Table Show the dbjective state vector at k-1 moment, u_k-1It is that zero, covariance is Q to represent that the k-1 moment obeys average_k-1Gaussian Profile fortune Dynamic process noise；Q_k-1For the motion process noise covariance matrix of k-1 moment targets,q₁Represent the process noise intensity of control targe dynamic model.

3. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 2, Characterized in that, in step 3, the sampled echo data of N number of radar station in the k moment radar network system, it was obtained Cheng Wei：

(3a) calculate obtain i-th of radar station in k moment radar network systems and receive the echo data that target reflects be r_i,k(t), its expression formula is：

$r_{i,k}\left(t\right)=h_{i,k}\sqrt{{\mathrm{\α}}_{i,k}}{s}_{i,k}(t-\frac{2R_{i,k}}{\mathrm{\α}})\exp \left(j2{\mathrm{\πf}}_{i,k}t\right)+v_{i,k}\left(t\right)$

Wherein, h_i,kRepresent the scattering resonance state of i-th of radar station measurement target in k moment radar network systems, α_i,kWhen representing k The attenuation coefficient that i-th of radar station in radar network system measures target is carved,∝ represents to be proportional to；R_i,kRepresent k In moment radar network system i-th of radar station relative to target radial distance,

x_kRepresent k moment target in the coordinate value in x directions, x_iRepresent radar network system In i-th of radar station in the coordinate value in x directions, y_kRepresent k moment target in the coordinate value in y directions, y_iRepresent radar network system In i-th of radar station y directions coordinate value；s_i,kRepresent i-th radar station transmission signal in k moment radar network systems Complex envelope；α represents the light velocity, and j represents imaginary unit, f_i,kRepresent k moment target relative to i-th of radar in radar network system The Doppler frequency shift stood,λ_i,kRepresent i-th of thunder in k moment radar network systems Up to the transmission signal wavelength at station,Speed of the k moment target in x directions is represented,Speed of the k moment target in y directions is represented, v_i,k(t) the measurement noise of i-th of radar station in k moment radar network systems is represented, t represents time variable；

(3b) receives the echo data r that target is reflected to i-th of radar station in k moment radar network systems_i,k(t) with Over-sampling coefficient ρ is sampled, ρ >=1；And then obtain the sampling time that i-th of radar station is received in k moment radar network systems Wave number evidence, is designated as the sampled echo data r of i-th of radar station in k moment radar network systems_i,k, then by k moment networking thunders The sampled echo data r of i-th of radar station up in system_i,kSend to fusion center；

(3c) makes i take 1 respectively to N, is repeated in performing (3a) to (3b), and then respectively obtain in k moment radar network systems The sampled echo data r of 1st radar station_1,kThe sampled echo data of n-th radar station into k moment radar network systems r_N,k, it is designated as the sampled echo data of N number of radar station in k moment radar network systems.

4. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 3, Characterized in that, the sub-step of step 4 is：

(4a) fusion center is according to the sampled echo data r of i-th of radar station in k moment radar network systems_i,k, using pulse String location algorithm, which is calculated, obtains radial distance measurement of i-th of radar station to target in k moment radar network systems

(4b) fusion center calculates and obtains measurement side of i-th of radar station to target radial distance in k moment radar network systems Difference Represent the measurement of i-th of radar station in k moment radar network systems Noise v_i,k(t) one-sided power spectrum density, α_i,kRepresent that i-th of radar station measures declining for target in k moment radar network systems Subtract coefficient, P_i,kThe transmission signal power of i-th of radar station in k moment radar network systems is represented, L represents K moment N number of thunder Up to the coherent pulse string number of station transmission signal, T_i,kRepresent the transmission signal of i-th of radar station in k moment radar network systems Pulse width, h_i,kRepresent the scattering resonance state of i-th of radar station measurement target in k moment radar network systems, β_i,kWhen representing k Carve the transmitted signal bandwidth of i-th of radar station in radar network system；

(4c) fusion center is according to the sampled echo data r of i-th of radar station in k moment radar network systems_i,k, using quick Fourier transform method, which is calculated, obtains Doppler frequency shift measurement of i-th of radar station to target in k moment radar network systems

(4d) fusion center calculates and obtains measurement of i-th of radar station to target Doppler frequency displacement in k moment radar network systems Variance Represent the amount of i-th of radar station in k moment radar network systems Survey noise v_i,k(t) one-sided power spectrum density, α_i,kRepresent that i-th of radar station measures target in k moment radar network systems Attenuation coefficient, P_i,kThe transmission signal power of i-th of radar station in k moment radar network systems is represented,Represent k moment networkings The length of i-th of radar station transmission signal in radar system；

(4e) is measured according to i-th of radar station in k moment radar network systems to the radial distance of targetWith k moment networking thunders I-th of radar station is measured to the Doppler frequency shift of target up in systemObtain i-th of radar in k moment radar network systems The measurement vector theta stood to target_i,k,[ ]^TExpression asks transposition to operate；

(4f) makes i take 1 respectively to N, is repeated in performing (4a)-(4e), and then obtain k moment radar network systems to target Measure vector theta_k,

5. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 4, Characterized in that, the sub-step of step 5 is：

(5a) is initialized：U is made to represent u-th of particle, u ∈ { 1,2 ..., U }, u initial value is that the particle that 1, U is setting is always individual Number, particle is used for representing the state of target；The initial time state of u-th of particle is designated as Represent 0 moment U particle relative to i-th of radar station in radar network system normalization weights, Represent u-th of 0 moment The state vector of particle,x₀The dbjective state at 0 moment is represented, chol () represents Cholesky Decompose, C₀The dbjective state vector forecasting covariance matrix at 0 moment is represented, Rand represents a random number between 0 and 1；

(5b) fusion center calculates the state vector for obtaining u-th of particle of k moment Represent k-1 The state vector of u-th of particle of moment, F represents the transfer matrix of dbjective state vector in the case of linear uniform motion, u_k-1Represent It is that zero, covariance is Q that the k-1 moment, which obeys average,_k-1Gaussian Profile motion process noise, Q_k-1For the fortune of k-1 moment targets Dynamic process noise covariance matrix；The state vector of wherein particle refers to coordinate value and x direction of any time particle in x directions Speed, and any time target is in the coordinate value in y directions and the speed in y directions；

(5c) is initialized：γ is made to represent the γ times iteration, { 1,2 ..., K'}, γ initial value are that 1, K' represents setting to γ ∈ Iterations maximum, and K' is identical with N values；The particle state vector of u-th of particle is after setting the 0th iteration of k moment With the state vector of u-th of particle of k momentValue is identical；

(5d) fusion center, which is calculated, obtains after the γ times iteration of k moment u-th of particle relative to i-th of thunder in radar network system Up to the measurement vector at station

$G_{\mathrm{\γ},i,k}^u={\[{\mathrm{Rg}}_{\mathrm{\γ},i,k}^u,{\mathrm{fg}}_{\mathrm{\γ},i,k}^u\]}^T$

Wherein,Represent that u-th of particle is relative to i-th radar station in radar network system after the γ times iteration of k moment Radial distance,Represent that u-th of particle is relative to i-th radar station in radar network system after the γ times iteration of k moment Doppler frequency shift, []^TExpression asks transposition to operate；

(5e) fusion center, which is calculated, obtains after the γ times iteration of k moment u-th of particle relative to i-th of thunder in radar network system Up to the weights at station Represent the k moment the After γ iteration u-th of particle relative to i-th of radar station in radar network system radial distance,Represent k moment networkings I-th of radar station is measured to the radial distance of target in radar system,Represent i-th of radar in k moment radar network systems The measurement variance stood to target radial distance,Represent that u-th of particle is relative to radar network system after the γ times iteration of k moment The Doppler frequency shift of i-th of radar station in system,Represent that i-th of radar station is to the how general of target in k moment radar network systems Frequency displacement is strangled to measure,Represent that i-th of radar station is to the measurement variance of target Doppler frequency displacement in k moment radar network systems, Exp represents that exponential function is operated；

Weights by u-th of particle after the γ times iteration of k moment relative to i-th of radar station in radar network systemAs The weights of u-th of particle after the γ times iteration of k moment

(5f) makes u take 1 respectively to U, repeats step (5e), and then respectively obtain the 1st particle after the γ times iteration of k moment WeightsThe weights of the U particle after to the γ times iteration of k moment

(5g) fusion center calculates the normalization weights for obtaining u-th of particle after the γ times iteration of k moment

(5h) makes u take 1 respectively to U, repeats step (5g), and then respectively obtain the 1st particle after the γ times iteration of k moment Normalization weightsThe normalization weights of the U particle after to the γ times iteration of k momentIt is designated as k moment the γ times repeatedly For the normalization weights of rear U particle

(5i) uses the resampling methods of particle filter, and according to the normalization weights of U particle after the γ times iteration of k momentThe particle of low weights is removed to U particle, and replicates the particle of high weight, U after the γ times iteration of k moment is obtained The state vector of individual particle

Represent the γ times iteration of k moment after u-th of particle particle state to Amount；

(5j) makes γ plus 1, returns to sub-step (5d), the state vector until obtaining U particle after the K' times iteration of k moment And by the state vector of U particle after the K' times iteration of k momentIt is designated as the end-state vector of U particle of k momentIts The end-state vector of middle u-th of particle of k moment isGo to step (5k)；

(5k) calculates the vectorial estimate x of dbjective state for obtaining the k moment according to the following formula_k|k：

$x_{k|k}=\underset{u=1}{\overset{U}{\mathrm{\Σ}}}{\tilde{g}}_k^u/U.$

6. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 5, Characterized in that, the sub-step of step 6 is：

The Jacobian matrix for the single order local derviation that k+1 moment N number of radar station is measured prediction by (6a) to dbjective state vector is defined as G (x_k+1), and according to the vectorial estimate x of dbjective state at k moment_k|k, calculate the dbjective state vector x for obtaining the k+1 moment_k+1Shellfish Leaf this information matrix J (x_k+1)：

$\begin{array}{c}J\left(x_{k+1}\right)=-E\{{\mathrm{\Δx}}_{x_{k+1}}^{x_{k+1}}\ln \[p\left(x_{k+1}\right)p\left(z_{k+1}\right|x_{k+1})\]\}\\ ={(Q_k+{\mathrm{FJ}}^{-1}(x_k\left)F^T\right)}^{-1}\\ +\left\{G^T\left(x_{k+1}\right){\[diag({\mathrm{\σ}}_{R_{1,k+1}}^2,{\mathrm{\σ}}_{R_{2,k+1}}^2,\mathrm{...},{\mathrm{\σ}}_{R_{N,k+1}}^2,{\mathrm{\σ}}_{f_{1,k+1}}^2,{\mathrm{\σ}}_{f_{2,k+1}}^2,\mathrm{...},{\mathrm{\σ}}_{f_{N,k+1}}^2)\]}^{-1}G\left(x_{k+1}\right)\right\}{|}_{x_{k+1|k}}\end{array}$

Wherein, x_k+1The dbjective state vector at k+1 moment is represented, E { } represents to ask expectation to calculate, △_xk+1X is sought in expression_k+1Single order local derviation,Expression is askedSingle order local derviation, p (x_k+1) represent the k+1 moment dbjective state Vector x_k+1Probability density function, z_k+1Represent the measurement set that k+1 moment fusion centers are received, p (z_k+1|x_k+1) represent k+ The likelihood function that the dbjective state vector at 1 moment is measured on target, Q_k-1Represent the motion process noise association of k-1 moment targets Variance matrix, F represents the transfer matrix of dbjective state vector in the case of linear uniform motion, J^-1(x_k-1) represent the k-1 moment mesh Mark state vector x_k-1Bayesian Information inverse of a matrix, G (x_k+1) represent k+1 moment N number of radar station to dbjective state vector quantity The Jacobian matrix of the single order local derviation of prediction is surveyed, diag () represents to ask diagonal matrix to operate, x_k+1|kRepresent the pre- of k+1 moment targets Survey state vector,X in expression_k+1Value be x_k+1|k；Represent i-th of thunder in k+1 moment radar network systems Up to estimation error variance of the station to the observation of target Doppler frequency displacement,Represent in k+1 moment radar network systems i-th Radar station to the measurement variance of target radial distance,Represent that i-th of radar station is to target in k+1 moment radar network systems The measurement variance of Doppler frequency shift；

(6b) is according to the dbjective state vector x at k+1 moment_k+1Bayesian Information matrix J (x_k+1), calculate the target at k+1 moment State vector x_k+1Carat Metro lower bound Matrix C (x_k+1), its expression formula is：

C(x_k+1)=J^-1(x_k+1)

Wherein, ()^-1Represent inversion operation.

7. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 6, Characterized in that, in step 7, the k+1 moment radar network system resource allocation on P_k+1And β_k+1Cost function F (P_k+1,β_k+1)|x_k+1, its expression formula is：

F(P_k+1,β_k+1)|x_k+1=Trace (C (x_k+1))

Wherein, P_k+1Represent the set of N number of radar station transmission signal power in k+1 moment radar network systems, P_k+1=[P_1,k+1, P_2,k+1,...,P_i,k+1,...,P_N,k+1]^T, P_i,k+1Represent the transmission signal of i-th of radar station in k+1 moment radar network systems Power；β_k+1Represent the set of N number of radar station transmitted signal bandwidth in k+1 moment radar network systems, β_k+1=[β_1,k+1, β_2,k+1,...,β_i,k+1,...,β_N,k+1]^T, β_i,k+1Represent the transmission signal of i-th of radar station in k+1 moment radar network systems Bandwidth；C(x_k+1) represent the k+1 moment dbjective state vector x_k+1Carat Metro lower bound matrix, x_k+1Represent the mesh at k+1 moment State vector is marked, Trace () represents to ask mark computing；

The k+1 moment radar network system resource allocation on P_k+1And β_k+1Cost function F (P_k+1,β_k+1)|x_k+1, also Including：According to k+1 moment radar network system resource allocations on P_k+1And β_k+1Cost function F (P_k+1,β_k+1)|x_k+1If, Determine Optimized model：

$\left.\begin{array}{c}\underset{P_{i,k+1},{\mathrm{\β}}_{i,k+1},i=1,\mathrm{...},N}{\min }\left(F\right(P_{k+1},{\mathrm{\β}}_{k+1}\left){|}_{x_{k+1}}\right)\\ \begin{array}{cc}s.t.& {\stackrel{\‾}{P}}_{i\min }\≤{\stackrel{\‾}{P}}_{i,k}\≤{\stackrel{\‾}{P}}_{i\max }\end{array}\\ {\stackrel{\‾}{\mathrm{\β}}}_{i\min }\≤{\stackrel{\‾}{\mathrm{\β}}}_{i,k}\≤{\stackrel{\‾}{\mathrm{\β}}}_{i\max },i=1,\mathrm{...},N\\ 1^T{P}_{k+1}=P_{total}\\ {V_{k+1}}^T{\mathrm{\β}}_{k+1}=M_{total}\end{array}\right\}$

Wherein,So thatValue distinguishes corresponding P when minimum_i,k+1 Value and β_i,k+1Value, P_i,k+1Represent the transmission signal power of i-th of radar station in k+1 moment radar network systems, β_i,k+1Table Show the transmitted signal bandwidth of i-th of radar station in k+1 moment radar network systems,Represent in radar network system i-th The lower limit of radar station transmission signal power,The upper limit of i-th of radar station transmission signal power in radar network system is represented,The lower band of i-th of radar station transmission signal in radar network system is represented,Represent i-th in radar network system The bandwidth upper limit of individual radar station transmission signal, N represents the radar station total number included in radar network system, 1^T=[1, 1,...,1]_1×N, P_totalRepresent the transmission signal general power of N number of radar station in each moment radar network system, β_totalRepresent The transmission signal total bandwidth of N number of radar station, V in each moment radar network system_k+1 ^T=[V_1,k+1,V_2,k+1,..., V_i,k+1,...,V_N,k+1]_1×N, V_i,k+1Represent the observation area area of i-th of radar station in k+1 moment radar network systems, s.t. Represent constraints, M_totalRepresent the acceptable maximum amount of data of corresponding fusion center of each moment.

8. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 7, Characterized in that, the sub-step of step 8 is：

The transmitted signal bandwidth initial value of i-th of radar station in k+1 moment radar network systems is designated as β by (8a)_k+1,i,opt, For the transmitted signal bandwidth of each radar station, and M_totalRepresent the maximum amount of data that corresponding fusion center of each moment can be received, V_i,k+1Represent k+1 moment radar networks system The observation area area of i-th of radar station in system,Represent the observation area area sum of k+1 moment N number of radar station；

C is made to represent the c times iteration, c initial value is 0；Setting terminates thresholding E, E ∈ (0,0.1)；Set k+1 moment the 0th time repeatedly For the transmitted signal bandwidth β of rear radar network system_k+1,0,optFor [β_k+1,1,opt,β_k+1,2,opt,...,β_k+1,i,opt,..., β_k+1,N,opt]^T, β_k+1,i,optRepresent the transmitted signal bandwidth initial value of i-th of radar station in k+1 moment radar network systems；

(8b) is according to the transmitted signal bandwidth β of radar network system after the c times iteration of k+1 moment_k+1,c,opt, and then when obtaining k+1 Carving the object function after the c times iteration is：

$\left.\begin{array}{c}\underset{P_{i,k+1},i=1,\mathrm{...},N}{\min }\left(F\right(P_{k+1},{\mathrm{\β}}_{k+1,c,opt}\left){|}_{x_{k+1}}\right)\\ \begin{array}{cc}s.t.& P_{i,k+1}-{\stackrel{\‾}{P}}_{i\min }\≥0,i=1,\mathrm{...},N\end{array}\\ P_{i,k+1}+{\stackrel{\‾}{P}}_{i\max }\≥0\\ 1^T{P}_{k+1}=P_{total}\end{array}\right\}$

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1 And β_k+1,c,optCost function, P_i,k+1The transmission signal power of i-th of radar station in k+1 moment radar network systems is represented, S.t. constraints, P are represented_k+1Represent the set of N number of radar station transmission signal power in k+1 moment radar network systems, x_k+1 Represent the dbjective state vector at k+1 moment；

The transmission signal power initial value of N number of radar station in k+1 moment radar network systems is designated as P by (8c)_k+1,0, P_k+1,0= P_total/ N, P_totalThe transmission signal general power of N number of radar station in each moment radar network system is represented, N represents radar network The radar station total number included in system；And making l be the l times Projected Gradient iteration, l initial value is 0；Set and search respectively Suo Buchang is △ p and the termination thresholding of Projected Gradient is ε, and △ p are the positive integer of setting, and ε is the positive number less than 1；

(8d) carries out piecemeal to the object function after the c times iteration of k+1 moment, respectively obtains the l times Projected Gradient of expression The first block units matrix A after iteration_1l, the second block units matrix A after the l times Projected Gradient iteration_2l, the l times The first piecemeal column vector b after Projected Gradient iteration_1lWith the second piecemeal column vector after the l times Projected Gradient iteration b_2l；

(8e) calculates the projection matrix Pr after the l times Projected Gradient iteration_l：

(8f) calculates the transmission signal power P of N number of radar station after the l+1 times Projected Gradient iteration of k+1 moment_k+1,l+1：

$P_{k+1,l+1}=\underset{P_{k+1,l}}{\mathrm{argmin}}\{F\[{\left(P_{k+1,l}^q\right)}^{+},{\mathrm{\β}}_{k+1,c,opt}\]{|}_{x_{k+1}}\}$

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation onAnd β_k+1,c,optCost function,Represent the Q of N number of radar station after the l times Projected Gradient iteration of k+1 moment Dimensional vector transmission signal power, Represent q for 1, its Remaining position is all 0 Q dimensional vectors；Q is equal with N values；The possible value of subscript+expression, represents dot product,Table It is shown as corresponding P during minimum value_k+1,lValue, P_k+1,lRepresent N number of radar station after the l times Projected Gradient iteration of k+1 moment Transmission signal power；

(8g) ifThen by the l+1 times projection ladder of k+1 moment Spend the transmission signal power P of N number of radar station after algorithm iteration_k+1,l+1It is used as the hair of N number of radar station after the c times iteration of k+1 moment Penetrate signal power output valve P_k+1,c,opt, go to sub-step (8h)；Otherwise, make l plus 1, return to sub-step (8d)；

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1,l+1And β_k+1,c,optCost function,Represent radar network system after the c times iteration of k+1 moment Resource allocation on P_k+1,lAnd β_k+1,c,optCost function, P_k+1,l+1Represent that the l+1 times Projected Gradient of k+1 moment changes For the transmission signal power of rear N number of radar station, β_k+1,c,optRepresent the transmitting letter of radar network system after the c times iteration of k+1 moment Number bandwidth, P_k+1,lRepresent the transmission signal power of N number of radar station after the l times Projected Gradient iteration of k+1 moment；

(8h) is by the transmission signal power output value P of N number of radar station after the c times iteration of k+1 moment_k+1,c,optIt is used as k+1 moment groups N number of radar station transmission signal power in net radar system；And then calculating obtains the object function after the c times iteration of k+1 moment：

$\left.\begin{array}{c}\underset{{\mathrm{\β}}_{i,k+1},i=1,\mathrm{...},N}{\min }\left(F\right(P_{k+1,c,opt},{\mathrm{\β}}_{k+1}\left){|}_{x_{k+1}}\right)\\ \begin{array}{cc}s.t.& {\mathrm{\β}}_{i,k+1}-{\stackrel{\‾}{\mathrm{\β}}}_{i\min }\≥0,i=1,\mathrm{...},N\end{array}\\ {\mathrm{\β}}_{i,k+1}+{\stackrel{\‾}{\mathrm{\β}}}_{i\max }\≥0\\ {V_{k+1}}^T{\mathrm{\β}}_{k+1}=M_{total}\end{array}\right\}$

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1,c,optAnd β_k+1Cost function, β_k+1Represent the collection of N number of radar station transmitted signal bandwidth in k+1 moment radar network systems Close, V_k+1 ^T=[V_1,k+1,V_2,k+1,...,V_i,k+1,...,V_N,k+1]_1×N, V_i,k+1Represent in k+1 moment radar network systems i-th The observation area area of radar station, s.t. represents constraints；

The transmitted signal bandwidth initial value of N number of radar station in k+1 moment radar network systems is designated as β by (8i)_k+1,0,M_totalRepresent the corresponding fusion of each moment The maximum amount of data that center can be received, V_i,k+1Represent the observation area face of i-th of radar station in k+1 moment radar network systems Product,Represent the observation area area sum of k+1 moment N number of radar station；And make l' be changed for the l' times Projected Gradient In generation, l' initial value is 0；Setting step-size in search is △ p' respectively and the termination thresholding of Projected Gradient is ε ', and △ p' are to set Fixed positive integer, ε ' is the positive number less than 1, ()^TRepresent transposition operation；

(8j) carries out piecemeal to the object function after the c times iteration of k+1 moment, respectively obtains the l' times Projected Gradient of expression The first block units matrix A after iteration_1l', the second block units matrix A after the l' times Projected Gradient iteration_2l', The first piecemeal column vector b after l' Projected Gradient iteration_1l'With the second piecemeal after the l' times Projected Gradient iteration Column vector b_2l'；

(8k) calculates the projection matrix Pr after the l' times Projected Gradient iteration_l'： V_k+1 ^T=[V_1,k+1,V_2,k+1,...,V_i,k+1,...,V_N,k+1]_1×N, V_i,k+1Represent k+1 moment networking thunders The observation area area of i-th of radar station up in system；

(8l) according to the following formula, calculates the transmission signal power of N number of radar station after the l'+1 times Projected Gradient iteration of k+1 moment β_k+1,l'+1：

${\mathrm{\β}}_{k+1,l^{\′}+1}=\underset{{\mathrm{\β}}_{k+1,l^{\′}}}{\arg \min }\{F\[P_{k+1,c,opt},{\left({\mathrm{\β}}_{k+1,l^{\′}}^q\right)}^{+}\]{|}_{x_{k+1}}\}$

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1,c,optWithCost function, P_k+1,c,optRepresent the transmission signal work(of N number of radar station after the c times iteration of k+1 moment Rate output valve,Represent the Q dimensional vector transmission signals of N number of radar station after the l' times Projected Gradient iteration of k+1 moment Bandwidth, Represent q be 1, remaining be all 0 Q dimensions Column vector；Q is equal with N values；The possible value of subscript+expression, represents dot product,When being expressed as minimum value Corresponding β_k+1,l'Value, β_k+1,l'Represent the transmission signal band of N number of radar station after the l' times Projected Gradient iteration of k+1 moment It is wide；

(8m) ifThen by the l'+1 times projection of k+1 moment The transmitted signal bandwidth β of N number of radar station after gradient algorithm iteration_k+1,l'+1It is used as N number of radar station after the c times iteration of k+1 moment Transmitted signal bandwidth output valve β_k+1,c,opt；Otherwise, make l' plus 1, return to sub-step (8j)；

Wherein, F (P_k+1,c,opt,β_k+1,l'+1) represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1,c,optAnd β_k+1,l'+1Cost function, P_k+1,c,optRepresent the transmission signal work(of N number of radar station after the c times iteration of k+1 moment Rate output valve, β_k+1,l'+1The transmitted signal bandwidth of N number of radar station after the l'+1 times Projected Gradient iteration of k+1 moment is represented,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_{K+1, c, opt}With β_k+1,l'Cost function, β_k+1,l'Represent the transmission signal band of N number of radar station after the l' times Projected Gradient iteration of k+1 moment It is wide；

UntilIteration stopping, now respectively will be repeatedly The transmission signal power output value P of N number of radar station after the c times iteration of k+1 moment that generation obtains when stopping_k+1,c,optDuring as k+1 Carve the transmission signal power output value of N number of radar stationBy the transmitting letter of radar network system after the c times iteration of k+1 moment Number bandwidth β_k+1,c,optIt is used as the transmitted signal bandwidth output valve of k+1 moment radar network systems

Wherein,Represent the c times iteration of k+1 moment after radar network system resource allocation on P_k+1,c,optAnd β_k+1,c,optCost function, P_k+1,c,optRepresent the transmission signal work(of N number of radar station after the c times iteration of k+1 moment Rate output valve, β_k+1,c,optThe transmitted signal bandwidth of radar network system after the c times iteration of k+1 moment is represented,Represent the c-1 times iteration of k+1 moment after radar network system resource allocation on P_k+1,c-1,optAnd β_k+1,c-1,optCost function, P_k+1,c-1,optRepresent the transmitting of N number of radar station after the c-1 times iteration of k+1 moment Signal power output valve, β_k+1,c-1,optRepresent the transmitted signal bandwidth of radar network system after the c-1 times iteration of k+1 moment.

9. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 8, Characterized in that, the process of (8d) is：

Object function after the c times iteration of k+1 moment is rewritten into following formula：

$\left\{\begin{array}{c}{P}_{1,k,l}\≥{\stackrel{\‾}{P}}_{1\min }\\ \mathrm{...}\\ P_{i,k+1,l}\≥{\stackrel{\‾}{P}}_{i\min }\\ \mathrm{...}\\ P_{N,k+1,l}\≥{\stackrel{\‾}{P}}_{N\min }\\ P_{1,k+1,l}\≥-{\stackrel{\‾}{P}}_{1\max }\\ \mathrm{...}\\ P_{i,k+1,l}\≥-{\stackrel{\‾}{P}}_{i\max }\\ \mathrm{...}\\ P_{N,k+1,l}\≥-{\stackrel{\‾}{P}}_{N\max }\end{array}\right.\⇔{\left[\begin{array}{ccc}1& & \\ & \mathrm{...}& \\ & & 1\\ 1& & \\ & \mathrm{...}& \\ & & 1\end{array}\right]}_{2N\×N}\×{\left[\begin{array}{c}{P}_{1,k+1,l}\\ \mathrm{...}\\ P_{i,k+1,l}\\ \mathrm{...}\\ P_{N,k+1,l}\end{array}\right]}_{N\×1}\≥{\left[\begin{array}{c}{\stackrel{\‾}{P}}_{1\min }\\ \mathrm{...}\\ {\stackrel{\‾}{P}}_{i\min }\\ \mathrm{...}\\ {\stackrel{\‾}{P}}_{N\min }\\ -{\stackrel{\‾}{P}}_{1\max }\\ \mathrm{...}\\ -{\stackrel{\‾}{P}}_{i\max }\\ \mathrm{...}\\ -{\stackrel{\‾}{P}}_{N\max }\end{array}\right]}_{2N\×N}\⇔{\mathrm{AP}}_{k+1,l}\≥\left[\begin{array}{c}{\stackrel{\‾}{P}}_{1\min }\\ \mathrm{...}\\ {\stackrel{\‾}{P}}_{i\min }\\ \mathrm{...}\\ {\stackrel{\‾}{P}}_{N\min }\\ -{\stackrel{\‾}{P}}_{1\max }\\ \mathrm{...}\\ -{\stackrel{\‾}{P}}_{i\max }\\ \mathrm{...}\\ -{\stackrel{\‾}{P}}_{N\max }\end{array}\right]=b;$

Wherein,Expression is equivalent to, and A represents 2N × N-dimensional unit matrix,P_k+1,lRepresent k+1 moment groups Value of the transmission signal power of N number of radar station in the l times Projected Gradient iteration in net radar system,P_i,k+1,lRepresent the transmission signal power of i-th of radar station in k+1 moment radar network systems in the l times throwing Value during shadow gradient algorithm iteration；B represents N-dimensional column vector, The lower limit of i-th of radar station transmission signal power in radar network system is represented,Represent i-th in radar network system The upper limit of individual radar station transmission signal power, subscript T represents that transposition is operated；

Piecemeal is carried out respectively to 2N × N-dimensional unit matrix A and N-dimensional column vector b so thatA_1lP_k,l= b_1l, A_2lP_k,l>b_2l, A_1lRepresent the first block units matrix after the l times Projected Gradient iteration, A_2lRepresent the l times projection The second block units matrix after gradient algorithm iteration, b_1lRepresent the first piecemeal after the l times Projected Gradient iteration arrange to Amount, b_2lRepresent the second piecemeal column vector after the l times Projected Gradient iteration, P_k,lRepresent N in k moment radar network systems Value of the transmission signal power of individual radar station in the l times Projected Gradient iteration.

10. a kind of radar network system power and bandwidth combined distributing method for target following as claimed in claim 8, Characterized in that, the process of (8j) is：

Object function after the c times iteration of k+1 moment is rewritten into following formula：

$\left\{\begin{array}{c}{\mathrm{\β}}_{1,k,l_{\mathrm{\β}}}\≥{\stackrel{\‾}{\mathrm{\β}}}_{1\min }\\ \mathrm{...}\\ {\mathrm{\β}}_{i,k+1,l^{\′}}\≥{\stackrel{\‾}{\mathrm{\β}}}_{i\min }\\ \mathrm{...}\\ {\mathrm{\β}}_{N,k+1,l^{\′}}\≥{\stackrel{\‾}{\mathrm{\β}}}_{N\min }\\ {\mathrm{\β}}_{1,k+1,l^{\′}}\≥-{\stackrel{\‾}{\mathrm{\β}}}_{1\max }\\ \mathrm{...}\\ {\mathrm{\β}}_{i,k+1,l^{\′}}\≥-{\stackrel{\‾}{\mathrm{\β}}}_{i\max }\\ \mathrm{...}\\ {\mathrm{\β}}_{N,k+1,l^{\′}}\≥-{\stackrel{\‾}{\mathrm{\β}}}_{N\max }\end{array}\right.\⇔{\left[\begin{array}{ccc}1& & \\ & \mathrm{...}& \\ & & 1\\ 1& & \\ & \mathrm{...}& \\ & & 1\end{array}\right]}_{2N\×N}\×{\left[\begin{array}{c}{\mathrm{\β}}_{1,k+1,l^{\′}}\\ \mathrm{...}\\ {\mathrm{\β}}_{i,k+1,l^{\′}}\\ \mathrm{...}\\ {\mathrm{\β}}_{N,k+1,l^{\′}}\end{array}\right]}_{N\×1}\≥{\left[\begin{array}{c}{\stackrel{\‾}{\mathrm{\β}}}_{1\min }\\ \mathrm{...}\\ {\stackrel{\‾}{\mathrm{\β}}}_{i\min }\\ \mathrm{...}\\ {\stackrel{\‾}{\mathrm{\β}}}_{N\min }\\ -{\stackrel{\‾}{\mathrm{\β}}}_{1\max }\\ \mathrm{...}\\ -{\stackrel{\‾}{\mathrm{\β}}}_{i\max }\\ \mathrm{...}\\ -{\stackrel{\‾}{\mathrm{\β}}}_{N\max }\end{array}\right]}_{2N\×N}\⇔A^{\′}{\mathrm{\β}}_{k+1,l^{\′}}\≥\left[\begin{array}{c}{\stackrel{\‾}{\mathrm{\β}}}_{1\min }\\ \mathrm{...}\\ {\stackrel{\‾}{\mathrm{\β}}}_{i\min }\\ \mathrm{...}\\ {\stackrel{\‾}{\mathrm{\β}}}_{N\min }\\ -{\stackrel{\‾}{\mathrm{\β}}}_{1\max }\\ \mathrm{...}\\ -{\stackrel{\‾}{\mathrm{\β}}}_{i\max }\\ \mathrm{...}\\ -{\stackrel{\‾}{\mathrm{\β}}}_{N\max }\end{array}\right]=b^{\′};$

Wherein,Expression is equivalent to, and A' represents 2N × N-dimensional unit matrix of setting,β_k+1,l'Represent k Value of the transmitted signal bandwidth of N number of radar station in the l' times Projected Gradient iteration in+1 moment radar network system,β_i,k+1,l'Represent that the transmitted signal bandwidth of i-th of radar station in k+1 moment radar network systems exists Value during the l' times Projected Gradient iteration；B' represents the N-dimensional column vector of setting, Represent in radar network system i-th The lower limit of radar station transmitted signal bandwidth,The upper limit of i-th of radar station transmitted signal bandwidth in radar network system is represented, (·)^TRepresent transposition operation；

The N-dimensional column vector b' of 2N × N-dimensional unit matrix A' and setting to setting carry out piecemeal respectively so thatA_1l'β_k,l'=b_1l', A_2l'β_k,l'>b_2l', A_1l'Represent after the l' times Projected Gradient iteration The first block units matrix, A_2l'Represent the second block units matrix after the l' times Projected Gradient iteration, b_1l'Represent The first piecemeal column vector after the l' times Projected Gradient iteration, b_2l'Represent after the l' times Projected Gradient iteration Two piecemeal column vectors, β_k,l'Represent the transmitted signal bandwidth of N number of radar station in k moment radar network systems in the l' times projection ladder Spend value during algorithm iteration.