CN105607045A - Optimized station distribution method for netted radar unit under deceptive jamming - Google Patents

Abstract

The invention, which belongs to the field of the anti-interference technology of the radar, discloses an optimized station distribution method for a netted radar unit under deceptive jamming. The method comprises: a deceived probability of a netted radar is calculated; a target function of a minimized deceived probability is constructed; coverage ranges of all node radars in the netted radar unit are calculated and a target function of a maximized coverage range is constructed; according to the target function of the minimized deceived probability and the target function of the maximized coverage range, a combined optimized target function is established; a constraint condition of station distribution of the netted radar unit is determined; on the basis of the constraint condition of station distribution of the netted radar unit and the combined optimized target function, an optimization formula of station distribution of the netted radar unit is constructed under deceptive jamming; and station distribution positions of all node radars in the netted radar unit are obtained based on the optimization formula of the station distribution of the netted radar unit under deceptive jamming. Therefore, the radar system resources are saved and precise and effective inhibition of the deceptive jamming can be realized.

Description

A kind of formula of cheating is disturbed the optimization cloth station method of lower radar network

Technical field

The present invention relates to Anti-jamming Technology for Radar field, relate in particular to a kind of optimization cloth of cheating the lower radar network of formula interferenceThe method of standing, the method adopts radar network to be minimized with the maximized combined optimization criterion of coverage and carry out cloth by cheating probabilityStand, obtain the cloth station location of radar network, suppress thereby improve radar network the ability that deception formula is disturbed.

Background technology

Deception formula is disturbed and is referred to that interfering signal and target echo signal are difficult to differentiation in radar receiver, mixes the spurious with the genuine,Make radar target information can not correctly be detected. The operation principle that deception formula is disturbed is: to the radar emission signal receiving, warpCross and disturb modulation, change relevant parameters, then the signal of modulating is forwarded back to radar, with the echo-signal of guinea pig target.Make the true and false target of radar impalpable, thereby reach fascination and upset the object of radar to true target detection and tracking. Numeral is penetratedFrequently the maturation of memory technology makes the generation of high fidelity decoy become possibility, gives thunder on the diverse location departing from objectivesReach and produce many decoys, make this radar can not distinguish true and false target. Therefore, although real goal is included in being permitted of demonstratingWithin multiple target, if but radar is not identified the ability of true and false target, and must be using all targets all as real goal processing.If radar cannot effectively resist deception formula and disturb, must false target be remained detection, be followed the tracks of, thereby take a large amount of thundersReach system resource, have a strong impact on the data-handling capacity of radar.

Because monostatic radar visual angle is single, be difficult to it to resist. And radar network can form full side afieldPosition, three-dimensional, multi-level fight system, have the technical performances such as full frequency band, many systems, many overlap coefficients, thereby have veryStrong survival ability and antijamming capability. With regard to frequency domain antagonism, by the networking of multi-section multiband radar, impossible with an interferenceMachine disturbs so wide frequency range. With regard to space electromagnetic environment, after multi-section radar network composite, not only radiation source quantity increases, and makesThe density of signal space and distribution are more complicated, and at aspects such as frequency range, signal form, parameter type and threat levelsDifficulty is brought to reconnaissance system in capital, makes to disturb quality to be very limited.

The directly correlation test of impact to target of the relative position of each node radar in radar network, and then affect groupNet radar by cheating probability, therefore, research deception formula disturbs the optimization cloth station of lower radar network significant. By rightRadar network is carried out reasonable cloth station, can effectively reduce deception formula and disturb the threat to radar network.

Summary of the invention

For the problems referred to above, the object of the present invention is to provide a kind of formula of cheating to disturb the optimization cloth station side of lower radar networkMethod, to save radar system resource, realizes deception formula is disturbed to more accurate effectively inhibition.

For achieving the above object, embodiments of the invention adopt following technical scheme to be achieved.

The formula of cheating is disturbed an optimization cloth station method for lower radar network, and described radar network comprises multiple node radars,Described optimization cloth station method comprises the steps:

Step 1, calculate radar network by cheating probability;

Step 2, according to described radar network by cheating probability, structure radar network minimize by the target of cheating probabilityFunction;

Step 3, calculates the coverage of each node radar in described radar network covering according to described each node radarLid scope, the object function of structure radar network maximum coverage;

Step 4, minimizes by the object function of the object function of cheating probability and maximum coverage according to described, buildsVertical combined optimization object function;

Step 5, according to cloth station spacing, search coverage and the radar network between adjacent node radar in described radar networkInvestigative range, determine the constraints at radar network cloth station;

Step 6, according to the constraints at described radar network cloth station and described combined optimization object function, structure deception formulaDisturb the optimized-type at lower radar network cloth station;

Step 7, disturbs the optimized-type at lower radar network cloth station according to described deception formula, obtain each node in radar networkThe cloth station location of radar.

Tool of the present invention has the following advantages: (1) suppresses the method for distributed interference than available data processing stage, thisThe bright adverse effect that suppresses the interference of deception formula by optimizing the method at cloth station, because Optimal Station position can obtain by off-line, therefore thisThe required radar system resource taking of inventive method is less; (2) because the present invention not only considers radar coverage and networking thunderReach by cheating probability, also taken into account the factor that must consider in the engineering such as cloth station spacing and search coverage of node radar, thereforeThe present invention is more conducive to engineering practice.

Brief description of the drawings

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existingHave the accompanying drawing of required use in technical description to be briefly described, apparently, the accompanying drawing in the following describes is only thisSome embodiment of invention, for those of ordinary skill in the art, not paying under the prerequisite of creative work, all rightObtain other accompanying drawing according to these accompanying drawings.

Fig. 1 disturbs the flow process of the optimization cloth station method of lower radar network to show for a kind of formula of cheating that the embodiment of the present invention providesIntention one;

Fig. 2 disturbs the flow process of the optimization cloth station method of lower radar network to show for a kind of formula of cheating that the embodiment of the present invention providesIntention two;

Fig. 3 utilizes the radar network that the inventive method obtains to select search coverage center X under deception formula disturbed condition₀＝[0,0]^T, radius R=10km, radar network cloth station result emulation schematic diagram.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, completeDescribe, obviously, described embodiment is only the present invention's part embodiment, instead of whole embodiment wholely. Based onEmbodiment in the present invention, those of ordinary skill in the art are not making obtain under creative work prerequisite every otherEmbodiment, belongs to the scope of protection of the invention.

The embodiment of the present invention provides a kind of formula of cheating to disturb the optimization cloth station method of lower radar network, described radar network bagContaining multiple node radars, optimization cloth provided by the invention station method is carried out under an existing radar network topological structureOptimize. As shown in Figure 1, described optimization cloth station method comprises the steps:

Step 1, calculate radar network by cheating probability.

Step 1 specifically comprises following sub-step:

(1a) set up hypothesis testing model.

Sub-step (1a) specifically comprises following sub-step:

(1a1) by the mahalanobis distance d of any two node radar measurement errors_ijAs statistical check amount,Wherein △ Z=dZ_i-dZ_jPoor for any two node radar measurement errors, wherein ∑_ij＝E[(dZ_i-dZ_j)(dZ_i-dZ_j)^T] represent the covariance matrix of the difference of i node radar and j node radar measurement errors, dZ_iForMeasure error, the dZ of i node radar_jBe the measure error of j node radar, i, j=1,2 ..., Ni ≠ j, i, j represent jointThe numbering of some radar, N represents the number of node radar;

(1a2) hypothesis testing model is as follows:Wherein, note H₀Represent two measuring value Z_iAnd Z_jCorrespondingReal goal, H₁Represent two measuring value Z_iAnd Z_jCorresponding false targets,Represent that the free degree is 2,Significance is that the card side of 1-a distributes;

(1a3) at H₁Under the condition of setting up, it is E that the difference △ Z of two node radar measurement errors obeys average, covariance matrixFor ∑_ijNormal distribution, average It is i node thunderThe coordinate of the decoy reach, the radar detection of j node being arrived under same rectangular coordinate system, $\left\{\begin{array}{c}{x}_i^f=({\mathrm{\ρ}}_i+\mathrm{\Δ}d)cos\left({\mathrm{\θ}}_i\right)+x_i\\ y_i^f=({\mathrm{\ρ}}_i+\mathrm{\Δ}d)sin\left({\mathrm{\θ}}_i\right)+y_i\end{array}\right.,$ i＝1,2,…,N，ρ_iBe i node detections of radar range-to-go, θ_iBe the angle of i node detections of radar to target, △ dRepresent deception distance;

(1a4) at H₁Under the condition of setting up, the two-dimensional probability density function f of △ Z_ij(x, y) is:

$f_{ij}(x,y)=\frac{1}{2{\mathrm{\π\σ}}_x{\mathrm{\σ}}_y\sqrt{1-{\mathrm{\ρ}}^2}}\exp \{\frac{-1}{2(1-{\mathrm{\ρ}}^2)}\[\frac{{(x-u_x)}^2}{{\mathrm{\σ}}_x^2}-2\mathrm{\ρ}\frac{(x-u_x)(y-u_y)}{{\mathrm{\σ}}_x{\mathrm{\σ}}_y}+\frac{{(y-u_y)}^2}{{\mathrm{\σ}}_y^2}\]\}$

WhereinRepresent the precision of x axle measurement difference,Represent the precision of y axle measurement difference, ρ=ξ₁₂/(σ_xσ_y) represent that x axle measures the coefficient correlation of difference and y axle measurement difference, ξ₁₁，ξ₁₂，ξ₂₁，ξ₂₂For matrix ∑_ijCorresponding is eachIndividual matrix element.

(1b), according to described hypothesis testing model, calculate the probability of miscarriage of justice of any two node radars to decoy.

Exemplary, can adopt data anastomosing algorithm to calculate the probability of miscarriage of justice of any two node radars to decoy.

Sub-step (1b) specifically comprises following sub-step:

(1b1) i node radar, j node radar adopt the probability of miscarriage of justice P of data anastomosing algorithm to decoy_ijFor:

$\begin{array}{c}{P}_{ij}=P\left(H_0\right|H_1)=P(d_{ij}\≤\mathrm{\δ}|H_1)\\ =P\left(K^{\′}\right({\left(\frac{x}{{\mathrm{\σ}}_x}\right)}^2-2\mathrm{\ρ}\left(\frac{x}{{\mathrm{\σ}}_x}\right)\left(\frac{y}{{\mathrm{\σ}}_y}\right)+{\left(\frac{y}{{\mathrm{\σ}}_y}\right)}^2)\≤\mathrm{\δ}\left|H_1\right)\end{array}$

Wherein P (H₀|H₁) be illustrated in and suppose H₁Under be judged to H₀Probability, d_ijRepresent mahalanobis distance and

$d_{ij}={\mathrm{\ΔZ}}^T{\mathrm{\Σ}}^{-1}\mathrm{\Δ}Z=K^{\′}({\left(\frac{x}{{\mathrm{\σ}}_x}\right)}^2-2\mathrm{\ρ}(\frac{x}{{\mathrm{\σ}}_x}\left)\right(\frac{y}{{\mathrm{\σ}}_y})+{\left(\frac{y}{{\mathrm{\σ}}_y}\right)}^2)$

Wherein, $K=\frac{1}{{\mathrm{\σ}}_x^2{\mathrm{\σ}}_y^2(1-{\mathrm{\ρ}}^2)},K^{\′}=\frac{1}{1-{\mathrm{\ρ}}^2};$

(1b2) by probability of miscarriage of justice P_ijExpression formula be converted into integrated form, and simplify obtain:

$P_{ij}=P\left(H_0\right|H_1)={\∫}_{-\sqrt{\mathrm{\δ}}/{\mathrm{\σ}}_y}^{\sqrt{\mathrm{\δ}}/{\mathrm{\σ}}_y}{\∫}_{g_{low}\left(y\right)}^{g_{up}\left(y\right)}{f}_{ij}(x,y)dxdy$

Wherein $g_{up}\left(y\right)={\mathrm{\σ}}_x\[\sqrt{(\mathrm{\δ}-{\left(\frac{y}{{\mathrm{\σ}}_y}\right)}^2)(1-{\mathrm{\ρ}}^2)}+\mathrm{\ρ}\left(\frac{y}{{\mathrm{\σ}}_y}\right)\]$ Represent the integrating range y direction upper limit, $g_{low}\left(y\right)={\mathrm{\σ}}_x\[-\sqrt{(\mathrm{\δ}-{\left(\frac{y}{{\mathrm{\σ}}_y}\right)}^2)(1-{\mathrm{\ρ}}^2)}+\mathrm{\ρ}\left(\frac{y}{{\mathrm{\σ}}_y}\right)\]$ Represent integrating range y direction lower limit,For integrating range xThe upper limit in direction,Represent the upper limit of integrating range in x direction.

(1c) probability of miscarriage of justice to decoy according to described any two node radars, calculates the general by deception of radar networkRate.

In the situation that node radar number is greater than 2, every two node radars need to be differentiated decoy, then to instituteSome court verdicts adopts the principle of ' get with ' to carry out fusion treatment, obtains final identification result.

Sub-step (1c) specifically comprises following sub-step:

Radar network by cheating probabilityWherein P_fRepresent radar network by cheating probability, P_ijRepresent i node radar and the probability of miscarriage of justice of j node radar to decoy, ∏ represents even to take advantage of symbol.

The object of radar network being carried out to cloth station is to disturb the impact on radar network, i.e. raising group in order to suppress deception formulaThe performance of net radar under deception formula disturbed condition. For realizing this object, the optimization aim function of selection is to maximize networking thunderThe investigative range reaching with minimize radar network by the common factor of cheating probability. Concrete implementation step is as follows:

Step 2, according to described radar network by cheating probability, structure minimize by the object function of cheating probability.

Step 2 specifically comprises following sub-step:

(2a) the search coverage Ω of radar network is divided, obtain multiple sub-search coverage Ω_D, visit according to different sonsSurvey the degree of danger in region, antithetical phrase search coverage Ω_DCompose with weight coefficient w;

(2b) according to radar network by cheating probability P_f, structure minimizes by the objective function F of cheating probability₁For:

$F_1(X_1,X_2,\mathrm{...},X_N)=\underset{X_i,i=1,\mathrm{...},N}{\min }\underset{{\mathrm{\Ω}}_D}{\Σ}w\·P_f$

Wherein, optimized variable is the position coordinates Xs of all node radars under polar coordinate system_i＝(ρ_i,θ_i)，ρ_i、θ_iRespectivelyBe the position of i node radar distance and the angle in polar coordinate system, i=1,2 ..., N, N is node thunder in radar networkThe number reaching, Ω_DRepresent sub-search coverage, w represents sub-search coverage Ω_DCorresponding weight coefficient, min represents to minimize, ΣRepresent summation symbol.

Step 3, calculates the coverage of each node radar in described radar network covering according to described each node radarLid scope, the object function of structure maximum coverage.

Step 3 specifically comprises following sub-step:

(3a) calculate the coverage S of each node radar_i＝{X|||X-X_i||≤R_imax, wherein X represents target location,X_iRepresent the position of i node radar, R_imaxRepresent the maximum detectable range of i node radar, ‖ ‖ represents 2 norms;

(3b) objective function F of maximum coverage₂For:

$F_2(X_1,X_2,\mathrm{...},X_N)=\underset{X_i,i=\mathrm{1...},N}{\max }\underset{i=1}{\overset{N}{\∪}}{S}_i$

Wherein, optimized variable is the position coordinates Xs of all node radars under polar coordinate system_i＝(ρ_i,θ_i)，ρ_i、θ_iRespectivelyBe the position of i node radar distance and the angle in polar coordinate system, i=1,2 ..., N, N is node thunder in radar networkThe number reaching, S_iFor each node radar site coordinate is respectively X₁,X₂,…,X_NThe investigative range of situation, max represents to get maximumValue, ∪ represents to get ' union '.

Step 4, minimizes by the object function of the object function of cheating probability and maximum coverage according to described, buildsVertical combined optimization object function.

Step 4 specifically comprises following sub-step:

(4a) according to minimizing by the objective function F of cheating probability₁Objective function F with maximum coverage₂, set upCombined optimization objective function F is:

$F(X_1,X_2,\mathrm{...},X_N)=\left\{\begin{array}{cc}\underset{X_i,i=1,\mathrm{...},N}{\min }& \underset{{\mathrm{\Ω}}_D}{\Σ}w\·P_f\\ \underset{X_i,i=1,\mathrm{...},N}{\min }& \underset{i=1}{\∪}{S}_i\end{array}\right.$

The optimization cloth station problem of radar network is a multi-objective optimization question. To multi-objective optimization question, can be to eachMajorized function is composed with different weight coefficients, is synthesized a scalar object function, then is optimized and solves.

(4b) combined optimization objective function F is converted into:

$F(X_1,X_2,\mathrm{...},X_N)=\underset{X_i}{\min }(\mathrm{\λ}\underset{{\mathrm{\Ω}}_D}{\Σ}w\·p_f-(1-\mathrm{\λ})\underset{i=1}{\overset{N}{\∪}}{S}_i)$

Wherein,, optimized variable is the position coordinates Xs of all node radars under polar coordinate system_i＝(ρ_i,θ_i)，ρ_i、θ_iRespectivelyBe the position of i node radar distance and the angle in polar coordinate system, i=1,2 ..., N, N is node thunder in radar networkThe number reaching, S_iFor each node radar site coordinate is respectively X₁,X₂,…,X_NThe investigative range of situation, Ω_DRepresent son detectionRegion, w represents sub-search coverage Ω_DCorresponding weight coefficient, ∪ represents to get ' union ', 0≤λ≤1, the size of λ has characterized groupNet radar is to by the degree that stresses of cheating probability and coverage.

Step 5, according to the cloth station spacing between adjacent node radar, search coverage and detection model in described radar networkEnclose, determine the constraints at radar network cloth station.

Radar network is carried out to cloth station, except will considering optimization aim function, need take into account radar network system to clothThe constraints of station location, mainly comprises the following aspects: one, for ensureing advantage and the receiving target of radar network various visual anglesIncoherence between signal, the distance between two node radars can not be too near; Two, ensure the expectation of radar network to visit as far as possibleSurvey the covering of spatial domain scope.

Step 5 specifically comprises following sub-step:

(5a) requirement to the cloth station spacing between between adjacent node radar according to radar network, i.e. any two node thundersConstraints d (the X of the cloth station spacing between reaching_i,X_j)≥△R_min, the cloth station spacing d between these any two node radars(X_i,X_j) be:

$d(X_i,X_j)=\left|\right|X_i-X_j\left|\right|=\sqrt{R_i^2+R_j^2-2R_i{R}_{j}cos({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)},$

Wherein, R_i、θ_iBe respectively range information and the angle information of i node radar, R_j、θ_jBe respectively j nodeThe range information of radar and angle information, i, j are the numbering of node radar, i=1,2 ..., N, j=1,2 ..., N, i ≠ j,△R_minRepresent the minimum threshold of distance between two node radars;

(5b) the search coverage Ω of radar network to true and false target_DIn the investigative range of radar network,

$\left|\right|X_i-X\left|\right|=\sqrt{R_i^2+R-2R_{i}Rcos({\mathrm{\θ}}_i-\mathrm{\θ})}\≤R_{imax},\∀\∈{\mathrm{\Ω}}_D,X_i\∈\mathrm{\Ψ}$

Wherein, R_i、θ_iBe respectively range information and the angle information of i node radar, R, θ are respectively the distance letter of targetBreath and angle information, Ψ is the scope at radar network cloth station, Ω_DRepresent the sub-search coverage of radar network,Represent arbitrarily ∈Expression belongs to.

Step 6, according to the constraints at described radar network cloth station and described combined optimization object function, structure deception formulaDisturb the optimized-type at lower radar network cloth station.

Step 6 specifically comprises following sub-step:

According to the constraints at described radar network cloth station and described combined optimization object function, under structure deception formula is disturbedOptimized-type Q (the X at radar network cloth station₁,X₂,…,X_N)：

$Q(X_1,X_2,\mathrm{...},X_N)=\left\{\begin{array}{c}\underset{(X_1,X_2,\mathrm{...},X_N)}{\min }F(X_1,X_2,\mathrm{...},X{N}_{})\\ s.t.d(X_i,X_j)\≥{\mathrm{\ΔR}}_{\min },\∀i,j=1,2,\mathrm{...},N,j\≠j\\ s.t.\left|\right|X_i-X\left|\right|\≤R_{i\max },\∀X_i\∈{\mathrm{\Ω}}_D,X\∈\mathrm{\Ψ}\end{array}\right.$

Wherein, s.t. represents constraints,Represent arbitrarily.

Step 7, disturbs the optimized-type at lower radar network cloth station according to described deception formula, obtain each node in radar networkThe cloth station location of radar.

To the optimized-type Q (X at radar network cloth station₁,X₂,…,X_N) solve, obtain analytic solutions, rule of thumb choose and closeThe solution of reason is as the Optimal Station position of radar network

(7a) utilize the optimized-type Q (X of iterative algorithm to radar network cloth station₁,X₂,…,X_N) solve, cheatedThe optimization position coordinates of each node radar in radar network under formula disturbed conditionWherein,Be respectivelyRange information and the angle information of the i node radar that iterative algorithm obtains in polar coordinate system;

(7b) by the optimization position coordinates of each node radarBe transformed into rectangular coordinate system, obtain under rectangular coordinate systemThe rectangular co-ordinate of each node radarAs the Optimal Station position of radar network, wherein, the x of each node radarAxial coordinate and y axial coordinate are respectively: $y_i^o=R_i^{o}sin\left({\mathrm{\θ}}_i^o\right).$

A kind of formula of cheating of the embodiment of the present invention being provided in conjunction with Fig. 2 and Fig. 3 is disturbed the cloth station method of lower radar networkEffect is further verified by following emulation.

1. experiment scene:

The radar network forming taking three node radars, as example, is optimized cloth station simulation analysis, without loss of generality, establishes spySurvey region Ω_DFor border circular areas, and etc. radius ground be divided into 5 sub regions, the weight coefficient of every sub regions is from inside to outside successivelyIncrease Ω_D＝{X|||X-X₀||≤R} wherein, X₀The center of circle that represents search coverage, R is its radius. Every sub regions, and addWeight coefficient is respectively: ${\mathrm{\Ω}}_i=\left\{X\right|\frac{i-1}{5}R\≤\left|\right|X-X_0\left|\right|\≤\frac{i}{5}R\},w_i=\frac{6-i}{15},i=1,\mathrm{...},5,$ If can cloth station scope Ψ beRectangular region: x axle excursion is-80km～-40km, y axle excursion is-80km～80km, the ginseng of each node radarNumber is identical, its power range radius R_imax=100km, angle measurement accuracy 0.002rad, range accuracy 70m; Between two radarsSmall distance is restricted to △ R_min＝10km。

2. experiment content and analysis:

Experiment one: select search coverage center X₀＝[0,0]^T, radius R=10km, under different weights coefficient lambda, can obtainTo the result that three radars is optimized to cloth station, as shown in Figure 2.

As can see from Figure 2, the Optimal Station position that adopts the inventive method to obtain: the 1st joint obtaining in λ=0The cloth erect-position of some radar is set to (80 ,-40) km, and the cloth erect-position of the 2nd node radar is set to (40,80) km, the 3rd node thunderThe cloth erect-position reaching is set to (40 ,-80) km; The cloth erect-position of the 1st the node radar that λ=0.5 o'clock obtains is set to (40,80) km,The cloth erect-position of the 2nd node radar is set to (40 ,-50) km, and the cloth erect-position of the 3rd node radar is set to (40 ,-80) km; λ=The cloth erect-position of the 1st the node radar obtaining for 1 o'clock is set to (40 ,-80) km, the cloth erect-position of the 2nd node radar be set to (40 ,-50) km, the cloth erect-position of the 3rd node radar is set to (40 ,-80) km; Can find out under three kinds of situations all full from cloth station resultFoot constraints, side light the correctness of optimum results.

The above, be only the specific embodiment of the present invention, but protection scope of the present invention is not limited to this, anyBe familiar with those skilled in the art in the technical scope of the present invention's exposure, can expect easily changing or replacing, all should containCover within protection scope of the present invention. Therefore, protection scope of the present invention should be as the criterion with the protection domain of described claim.

Claims (10)

1. the formula of cheating is disturbed an optimization cloth station method for lower radar network, it is characterized in that, described radar network comprises multipleNode radar, described optimization cloth station method comprises the steps:

Step 1, calculate radar network by cheating probability;

Step 2, according to described radar network by cheating probability, structure radar network minimize by the target letter of cheating probabilityNumber;

Step 3, calculates the coverage of each node radar in described radar network, and according to the covering model of described each node radarEnclose the object function of structure radar network maximum coverage;

Step 4, minimizes by the object function of the object function of cheating probability and maximum coverage according to described, sets up connectionClose optimization aim function;

Step 5, according to the spy of cloth station spacing, search coverage and the radar network between adjacent node radar in described radar networkSurvey scope, determines the constraints at radar network cloth station;

Step 6, according to the constraints at described radar network cloth station and described combined optimization object function, structure deception formula is disturbedThe optimized-type at lower radar network cloth station;

Step 7, disturbs the optimized-type at lower radar network cloth station according to described deception formula, obtain each node radar in radar networkCloth station location.

2. a kind of formula of cheating according to claim 1 is disturbed the cloth station method of lower radar network, it is characterized in that step 1Specifically comprise following sub-step:

(1a) set up hypothesis testing model;

(1b), according to described hypothesis testing model, calculate the probability of miscarriage of justice of any two node radars to decoy;

(1c) described any two node radars are connected and taken advantage of the probability of miscarriage of justice of decoy, obtain the general by deception of radar networkRate.

3. a kind of formula of cheating according to claim 2 is disturbed the cloth station method of lower radar network, it is characterized in that sub-step(1a) specifically comprise following sub-step:

(1a1) by the mahalanobis distance d of any two node radar measurement errors_ijAs statistical check amount,Wherein △ Z=dZ_i-dZ_jPoor for any two node radar measurement errors, wherein ∑_ij＝E[(dZ_i-dZ_j)(dZ_i-dZ_j)^T]Represent the covariance matrix of the difference of i node radar and j node radar measurement errors, dZ_iIt is the measurement mistake of i node radarPoor, dZ_jBe the measure error of j node radar, i, j=1,2 ..., Ni ≠ j, i, j represent the numbering of node radar, N representsThe number of node radar;

(1a2) hypothesis testing model is as follows:Wherein, note H₀Represent two measuring value Z_iAnd Z_jCorresponding trueTarget, H₁Represent two measuring value Z_iAnd Z_jCorresponding false targets,Represent that the free degree is 2, aobviousThe card side that work property level is 1-a distributes;

(1a3) at H₁Under the condition of setting up, it is E that the difference △ Z of two node radar measurement errors obeys average, and covariance matrix is∑_ijNormal distribution, average It is i node thunderThe coordinate of the decoy reach, the radar detection of j node being arrived under same rectangular coordinate system, $\left\{\begin{array}{c}{x}_i^f=({\mathrm{\ρ}}_i+\mathrm{\Δ}d)cos\left({\mathrm{\θ}}_i\right)+x_i\\ y_i^f=({\mathrm{\ρ}}_i+\mathrm{\Δ}d)sin\left({\mathrm{\θ}}_i\right)+y_i\end{array}\right.,$ i＝1,2,···,N，ρ_iBe i node detections of radar range-to-go, θ_iBe the angle of i node detections of radar to targetDegree, △ d represents to cheat distance;

(1a4) at H₁Under the condition of setting up, the two-dimensional probability density function f of △ Z_ij(x, y) is:

$f_{ij}(x,y)=\frac{1}{2{\mathrm{\π\σ}}_x{\mathrm{\σ}}_y\sqrt{1-{\mathrm{\ρ}}^2}}\exp \{\frac{-1}{2(1-{\mathrm{\ρ}}^2)}\[\frac{{(x-u_x)}^2}{{\mathrm{\σ}}_x^2}-2\mathrm{\ρ}\frac{(x-u_x)(y-u_y)}{{\mathrm{\σ}}_x{\mathrm{\σ}}_y}+\frac{{(y-u_y)}^2}{{\mathrm{\σ}}_y^2}\]\}$

WhereinRepresent the precision of x axle measurement difference,Represent the precision of y axle measurement difference, ρ=ξ₁₂/(σ_xσ_y) represent that x axle measures the coefficient correlation of difference and y axle measurement difference, ξ₁₁，ξ₁₂，ξ₂₁，ξ₂₂For matrix ∑_ijCorresponding eachMatrix element.

4. a kind of formula of cheating according to claim 2 is disturbed the cloth station method of lower radar network, it is characterized in that sub-step(1b) specifically comprise following sub-step:

(1b1) i node radar, j node radar adopt the probability of miscarriage of justice P of data anastomosing algorithm to decoy_ijFor:

$\begin{array}{c}{P}_{ij}=P\left(H_0\right|H_1)=P(d_{ij}\≤\mathrm{\δ}|H_1)\\ =P\left(K^{\′}\right({\left(\frac{x}{{\mathrm{\σ}}_x}\right)}^2-2\mathrm{\ρ}\left(\frac{x}{{\mathrm{\σ}}_x}\right)\left(\frac{y}{{\mathrm{\σ}}_y}\right)+{\left(\frac{y}{{\mathrm{\σ}}_y}\right)}^2)\≤\mathrm{\δ}|H_1)\end{array}$

Wherein P (H₀|H₁) be illustrated in and suppose H₁Under be judged to H₀Probability, d_ijRepresent mahalanobis distance and

$d_{ij}={\mathrm{\ΔZ}}^T{\mathrm{\Σ}}^{-1}\mathrm{\Δ}Z=K^{\′}({\left(\frac{x}{{\mathrm{\σ}}_x}\right)}^2-2\mathrm{\ρ}(\frac{x}{{\mathrm{\σ}}_x}\left)\right(\frac{y}{{\mathrm{\σ}}_y})+{\left(\frac{y}{{\mathrm{\σ}}_y}\right)}^2)$

Wherein, $K=\frac{1}{{\mathrm{\σ}}_x^2{\mathrm{\σ}}_y^2(1-{\mathrm{\ρ}}^2)},H^{\′}=\frac{1}{1-{\mathrm{\ρ}}^2};$

(1b2) by probability of miscarriage of justice P_ijExpression formula be converted into integrated form, and simplify obtain:

$P_{ij}=P\left(H_0\right|H_1)={\∫}_{-\sqrt{\mathrm{\δ}}/{\mathrm{\σ}}_y}^{\sqrt{\mathrm{\δ}}/{\mathrm{\σ}}_y}{\∫}_{g_{low}\left(y\right)}^{g_{up}\left(y\right)}{f}_{ij}(x,y)dxdy$

Wherein $g_{up}\left(y\right)={\mathrm{\σ}}_x\[\sqrt{(\mathrm{\δ}-{\left(\frac{y}{{\mathrm{\σ}}_y}\right)}^2)(1-{\mathrm{\ρ}}^2)}+\mathrm{\ρ}\left(\frac{y}{{\mathrm{\σ}}_y}\right)\]$ Represent the integrating range y direction upper limit, $g_{low}\left(y\right)={\mathrm{\σ}}_x\[-\sqrt{(\mathrm{\δ}-{\left(\frac{y}{{\mathrm{\σ}}_y}\right)}^2)(1-{\mathrm{\ρ}}^2)}+\mathrm{\ρ}\left(\frac{y}{{\mathrm{\σ}}_y}\right)\]$ Represent integrating range y direction lower limit,For integrating range xThe upper limit in direction,Represent the upper limit of integrating range in x direction;

(1b3) radar network by cheating probabilityWherein P_fRepresent radar network by cheating probability, P_ijRepresent i node radar and the probability of miscarriage of justice of j node radar to decoy, ∏ represents even to take advantage of symbol.

5. a kind of formula of cheating according to claim 1 is disturbed the cloth station method of lower radar network, it is characterized in that step 2Specifically comprise following sub-step:

(2a) the search coverage Ω of radar network is divided, obtain multiple sub-search coverage Ω_D, according to the sub-detecting area of differenceThe degree of danger in territory, antithetical phrase search coverage Ω_DCompose with weight coefficient w;

(2b) according to radar network by cheating probability P_f, structure minimizes by the objective function F of cheating probability₁For:

$F_1(X_1,X_2,\mathrm{...},X_N)=\underset{X_i,i=1,\mathrm{...},N}{\min }\underset{{\mathrm{\Ω}}_D}{\Σ}w\·P_f$

Wherein, optimized variable is the position coordinates Xs of all node radars under polar coordinate system_i＝(ρ_i,θ_i)，ρ_i、θ_iBe respectively iDistance and the angle of the position of individual node radar in polar coordinate system, i=1,2,, N, N is node thunder in radar networkThe number reaching, Ω_DRepresent sub-search coverage, w represents sub-search coverage Ω_DCorresponding weight coefficient, min represents to minimize, ΣRepresent summation symbol.

6. a kind of formula of cheating according to claim 1 is disturbed the cloth station method of lower radar network, it is characterized in that step 3Specifically comprise following sub-step:

(3a) calculate the coverage S of each node radar_i＝{X|||X-X_i||≤R_imax, wherein X represents target location, X_iRepresentThe position of i node radar, R_imaxRepresent the maximum detectable range of i node radar, || || represent 2 norms;

(3b) objective function F of maximum coverage₂For:

$F_2(X_1,X_2,\mathrm{...},X_N)=\underset{X_i,i=1,...,N}{max}\underset{i=1}{\overset{N}{\∪}}{S}_i$

Wherein, optimized variable is the position coordinates Xs of all node radars under polar coordinate system_i＝(ρ_i,θ_i)，ρ_i、θ_iBe respectively iDistance and the angle of the position of individual node radar in polar coordinate system, i=1,2,, N, N is node thunder in radar networkThe number reaching, S_iFor each node radar site coordinate is respectively X₁,X₂,···,X_NThe investigative range of situation, max represents to getMaximum, ∪ represents to get ' union '.

7. a kind of formula of cheating according to claim 1 is disturbed the cloth station method of lower radar network, it is characterized in that step 4Specifically comprise following sub-step:

(4a) according to minimizing by the objective function F of cheating probability₁Objective function F with maximum coverage₂, set up associatingOptimization aim function F is:

$F(X_1,X_2,...,X_N)=\left\{\begin{array}{c}\underset{X_i,i=1,...,N}{\min }\underset{{\mathrm{\Ω}}_D}{\Σ}w\·P_f\\ \underset{X_i,i=1,...,N}{max}\underset{i=1}{\overset{N}{\∪}}{S}_i\end{array}\right.$

(4b)) combined optimization objective function F is converted into:

$F(X_1,X_2,...,X_N)=\underset{X_i}{\min }(\mathrm{\λ}\underset{{\mathrm{\Ω}}_D}{\Σ}w\·p_f-(1-\mathrm{\λ})\underset{i=1}{\overset{N}{\∪}}{S}_i)$

Wherein, optimized variable is the position coordinates Xs of all node radars under polar coordinate system_i＝(ρ_i,θ_i)，ρ_i、θ_iBe respectively iDistance and the angle of the position of individual node radar in polar coordinate system, i=1,2,, N, N is node thunder in radar networkThe number reaching, S_iFor each node radar site coordinate is respectively X₁,X₂,···,X_NThe investigative range of situation, Ω_DRepresent sonSearch coverage, w represents sub-search coverage Ω_DCorresponding weight coefficient, ∪ represents to get ' union ', 0≤λ≤1, the size of λ characterizesRadar network to by the degree that stresses of cheating probability and coverage.

8. a kind of formula of cheating according to claim 1 is disturbed the cloth station method of lower radar network, it is characterized in that step 5Specifically comprise following sub-step:

(5a) requirement to the cloth station spacing between between adjacent node radar according to radar network, any two node radars itBetween the constraints d (X of cloth station spacing_i,X_j)≥△R_min, the cloth station spacing d (X between these any two node radars_i,X_j)For:

$d(X_i,X_j)=\left|\right|X_i-X_j\left|\right|=\sqrt{R_i^2+R_j^2-2R_i{R}_{j}cos({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)},$

Wherein, R_i、θ_iBe respectively range information and the angle information of i node radar, R_j、θ_jBe respectively j node radarRange information and angle information, i, j are the numbering of node radar, i=1,2,, N, j=1,2,, N, i≠j，△R_minRepresent the minimum threshold of distance between two node radars;

(5b) the search coverage Ω of radar network to true and false target_DIn the investigative range of radar network,

$\left|\right|X_i-X\left|\right|=\sqrt{R_i^2+R-2R_{i}Rcos({\mathrm{\θ}}_i-\mathrm{\θ})}\≤R_{imax},\∀X\∈{\mathrm{\Ω}}_D,X_i\∈\mathrm{\Ψ}$

Wherein, R_i、θ_iBe respectively range information and the angle information of i node radar, R, θ be respectively target range information andAngle information, Ψ is the scope at radar network cloth station, Ω_DRepresent the sub-search coverage of radar network,Represent that ∈ represents arbitrarilyBelong to.

9. a kind of formula of cheating according to claim 1 is disturbed the cloth station method of lower radar network, it is characterized in that step 6Specifically comprise:

According to the constraints at described radar network cloth station and described combined optimization object function, structure deception formula is disturbed lower networkingOptimized-type Q (the X of Method in Positioning of Radar₁,X₂,···,X_N)：

$Q(X_1,X_2,...,X_N)=\left\{\begin{array}{c}\underset{(X_1,X_2,\mathrm{...},X_N)}{\min }F(X_1,X_2,...,X_N)\\ \begin{array}{cc}s.t.& d(X_i,X_j)\≥{\mathrm{\ΔR}}_{\min },\∀i,j=1,2,...,N,i\≠j\end{array}\\ \begin{array}{cc}s.t.& \left|\right|X_i-X\left|\right|\≤R_{imax},\∀X_i\∈{\mathrm{\Ω}}_D,X\∈\mathrm{\Ψ}\end{array}\end{array}\right..$

10. a kind of formula of cheating according to claim 1 is disturbed the cloth station method of lower radar network, it is characterized in that step 7Specifically comprise:

(7a) the optimized-type Q (X to the lower radar network cloth of deception formula interference station₁,X₂,···,X_N) solve, cheatedFormula is disturbed the optimization position coordinates of each node radar in lower radar networkWherein,Be respectively iRange information and the angle information of individual node radar in polar coordinate system;

(7b) by the optimization position coordinates of each node radarBe transformed into rectangular coordinate system, obtain each node radar under rectangular coordinate systemRectangular co-ordinateWherein, the x axial coordinate of each node radar and y axial coordinate are respectively: $x_i^o=R_i^{o}cos\left({\mathrm{\θ}}_i^o\right),y_i^o=R_i^{o}sin\left({\mathrm{\θ}}_i^o\right).$