CN105891845A - Fixed target protection-based satellite navigation signal repeater deception jamming system and method thereof - Google Patents

Abstract

The invention provides a fixed target protection-based satellite navigation signal repeater deception jamming system and a method thereof. The system comprises multiple satellites, multiple repeaters, a real target point and a set false target point, wherein the number of the repeaters is the same as that of the satellites, one repeater receives navigation satellite signals broadcasted by one satellite, the multiple repeaters receive navigation satellite signals broadcasted by multiple satellites respectively and time delay of the multiple repeaters is controlled respectively through a digital delay line technology, the multiple navigation satellite signals after certain time delay are broadcasted via the multiple repeaters respectively, and thus, an enemy weapon guided by using the navigation satellite signals in an effective jamming area is further deceived to deviate from the real target point and advance to the set false target point. The problem that the traditional repeater deception can not handle receiver inertial navigation detection can be solved, and an important role is played in protecting a fixed important target.

Description

Satellite navigation signals deceiving jamming system and method based on fixing protection of goal

Technical field

The present invention relates to technical field of satellite navigation, the satellite navigation signals relay type deception being based particularly on fixing protection of goal is dry Disturb system and method.

Background technology

Satellite navigation signals deception jamming system, by broadcasting the spurious signal of generation or real satellite signal being injected time delay, makes Obtain the signal after receiver receives forwarding, thus form location of mistake result and target is carried out cheating interference.

Forwarding cheating interference context of detection, the forwarding cheating interference detection algorithm of main flow inevitably comes with some shortcomings, because of Form for forward signal is identical with actual signal, so merely by detection mode based on signal parameter thresholding (such as letter Number encrypting and decrypting mode etc.) it is not easy to forwarding cheating interference to detect.Generally, receiver is cheated for relay type The detection of interference is all based on inertial navigation detection.Therefore, relay type deception needs to seek more effectively to resist the cheating interference inspection of inertial navigation Survey mode.

Can the meaning of research real target point false target vertex neighborhood radius ratio, essentially consist in and accomplish R_r=F_r, i.e. F_r/R_r=1 or Person F_r/R_r→ 1, wherein R_rRepresent the real target point radius of neighbourhood, F_rRepresent false target vertex neighborhood radius.Take advantage of because existing The mode deceiving Interference Detection is broadly divided into the Digital Detecting of signal parameter thresholding and physical detection based on inertial navigation.Relay type is taken advantage of Deceive detection and in signal format, do not carry out any change, so the emphasis of its anti-fraud detection should be the inspection for anti-inertial navigation Survey.If able to accomplish F_r/R_r→ 1, then just can preferably tackle receiver based on the detection of inertial navigation, thus significantly Improve the success rate of cheating interference.

Tradition deceiving jamming system there is no the specific implementation method for the detection of receiver inertial navigation unit.A new generation's accurately system Lead weapon and generally carry the receiver of inertial navigation detector unit, therefore tradition forwards fraud system and method to implement to there is the biggest difficulty.

Summary of the invention

It is an object of the invention to provide a kind of satellite navigation signals deceiving jamming system based on fixing protection of goal and side thereof Method, utilizes the enemy weapon deviation real target point that navigation signal guides, goes to the virtual vacation of setting in guiding effective interference region Impact point, successfully manages the inertial navigation unit detection that weapon receiver carries simultaneously, solves tradition and forwards deception cannot tackle receiver The problem of inertial navigation detection, important goal fixing to protection is of great importance.

Specifically, the technical scheme is that

A kind of satellite navigation signals deceiving jamming system based on fixing protection of goal, including multi-satellite, multiple forwarding The false target point of device, real target point and setting, the number of transponder is identical with number of satellite, and a transponder receives one The navigation satellite signal that satellite is broadcast, multiple transponders are received navigation satellite signal that multi-satellite broadcasts respectively and are prolonged by numerical control Line technology controls the time delay of multiple transponder respectively late, by the multiple navigation satellite signals after a fixed response time respectively by multiple forwardings Device is broadcast, and utilizes the enemy weapon deviation real target point that navigation satellite signal guides, go in then cheating effective interference region The false target point set.

Selecting number of satellite in the present invention is 4, and transponder number is 4, and four transponders are arranged on real goal null circle On the inverted cone baseplane of conical point, elevation angle and the terrain clearance of the setting of four transponders are the most identical.

Further, elevation angle δ=25 of described four transponders～40 °, terrain clearance is 20km.Preferably, described four The elevation angle of individual transponder is 38 °.

The present invention provides a kind of satellite navigation signals deceiving jamming method based on fixing protection of goal, including following step Rapid:

(1) multi-satellite is selected；Set the false target point F intending guiding enemy weapon to go to；Then will be with selection number of satellite Identical transponder is arranged on on the inverted cone baseplane of real target point conical tip, the elevation angle of the setting of multiple transponders And terrain clearance is the most identical；

(2) receive, by multiple transponders, navigation signal that multiple satellite broadcasts respectively and controlled respectively by numerical control delay line technique Make the time delay of multiple transponder, the multiple navigation satellite signals after a fixed response time are broadcast by these multiple transponders respectively；

(3) enemy weapon is by receiving the spurious signal that multiple transponders are broadcast, and makes enemy weapon receiver positioning calculation result go out Now offseting, enemy weapon receiver positioning result is no longer to resolve, based on actual signal, the positioning result obtained, but through time delay The spurious signal that control processes resolves the positioning result obtained, and utilizes the enemy that navigation signal guides in then cheating effective interference region Side's weapon deviation real target point, goes to the false target point of setting.

The invention has the beneficial effects as follows:

Because the form of forward signal is identical with actual signal, so merely by detection mode based on signal parameter thresholding (such as signal encryption manner of decryption etc.) is not easy to forwarding cheating interference to detect.Generally, receiver is for forwarding The detection of formula cheating interference is all based on inertial navigation detection.Tradition deceiving jamming system there is no to be examined for receiver inertial navigation unit The specific implementation method surveyed.A new generation's precision guided weapon generally carries the receiver of inertial navigation detector unit, therefore tradition forwards deception System and method for is implemented to there is the biggest difficulty.F under correspondence arrangement manner of the present invention_r/R_r→ 1, therefore can effectively cope with receiver Based on the detection of inertial navigation, thus be greatly improved the success rate of cheating interference.

In sum, the present invention receives, by four transponders, navigation signal that four satellites broadcast respectively and passes through numerical control delay line Technology controls the time delay of four transponders respectively, is broadcast by transponder by the satellite-signal after a fixed response time.Then deception is effectively Utilize the enemy weapon deviation real target point that navigation signal guides in interference region, go to the virtual decoy point of setting.This The bright deceiving jamming utilizing navigation signal, can successfully boot up enemy weapon and fly to specify region, simultaneously effective resist The inertial navigation unit detection that weapon receiver carries, important goal fixing to protection is of great importance.

Accompanying drawing explanation

Fig. 1 is the cloth station signal that a kind of multistation being effective against receiver inertial navigation detection that the present invention proposes forwards deception jamming system Figure；

Fig. 2 is the flat distribution map of the multistation forwarding cheating interference transponder of the present invention；

Fig. 3 is transponder elevation angle and effectively interference radius relationship figure in the present invention；

Fig. 4 is that in the present invention, transponder elevation angle compares graph of a relation with mapping radius of neighbourhood optimization；

Fig. 5 is the forwarding deception area maps design sketch of the present invention；

In figure, parameter declaration used see table:

Detailed description of the invention

Below with reference to specific embodiment and Figure of description, the present invention is described in further details.

With reference to Fig. 1, for the cloth of a kind of multistation forwarding deception jamming system being effective against receiver inertial navigation detection that the present invention proposes Stand schematic diagram, including four satellite S_i(i=1,2,3,4), four transponder J_i(i=1,2,3,4) real target point R of protection, is intended The false target point F gone to plan guiding enemy weapon.Four transponder J_i(i=1,2,3,4) it is arranged on real target point circular cone On the inverted cone baseplane on summit, transponder J is set simultaneously_i(i=1,2,3,4) elevation angle is 38 °, and terrain clearance is 20km. By four transponder J_i(i=1,2,3,4) four satellite S are received respectively_i(i=1,2,3,4) navigation signal broadcast also is prolonged by numerical control Line technology controls four transponder J respectively late_iThe time delay of (i=1,2,3,4), passes through transponder by the satellite-signal after a fixed response time J_i(i=1,2,3,4) broadcast.Then the enemy weapon deviation real target point that navigation signal guides is utilized in cheating effective interference region R, goes to the false target point F of setting.The present invention utilizes the deceiving jamming of navigation signal, can successfully boot up enemy military Device flies to specify region, the inertial navigation unit detection that simultaneously effective counterweapon receiver carries, and important goal fixing to protection has Important meaning.

A kind of satellite navigation signals deceiving jamming method based on fixing protection of goal, comprises the following steps:

(1) according to four satellite S that location visible satellite situation selection GDOP value is relatively good_i(i=1,2,3,4).GDOP Refer to satellite geometry dilution of precision.GDOP value preferably be it is generally acknowledged less than 3.For real target point R of plan protection, Ke Yitong Cross delay of control and the false target point F intending guiding enemy weapon to go to is set.By four transponder J_i(i=1,2,3,4) be arranged on On the inverted cone baseplane of real target point conical tip, transponder J is set simultaneously_i(i=1,2,3,4) elevation angle is 38 °, liftoff It is highly 20km.

(2) by four transponder J_i(i=1,2,3,4) four satellite S are received respectively_i(i=1,2,3,4) navigation signal broadcast also leads to Cross numerical control delay line technique (numerical control delay line technique is referred to document: HUANGLONG, Gong Hang, Zhu Xiangwei, Wang Feixue. award for GNSS Time receiver deceiving jamming technical research [J]. National University of Defense technology journal .Vol.35, No.4, pp.93-94,2013.) point Kong Zhi the time delay of four transpondersSatellite-signal after one fixed response time is broadcast by transponder.Because serving as reasons The spurious signal power that transponder forwards is generally higher than actual signal, so effectively interference region internal object receiver only receives forwarding After spurious signal.The transponder arranged in the present embodiment, with real target point as the center of circle, 42km is the district in radius Territory is effective interference region.

(3) enemy weapon is by receiving the spurious signal that multiple transponders are broadcast, and makes enemy weapon receiver positioning calculation result go out Now offseting, enemy weapon receiver positioning result is no longer to resolve, based on actual signal, the positioning result obtained, but through time delay The spurious signal that control processes resolves the positioning result obtained.Then the enemy that navigation signal guides is utilized in cheating effective interference region Side's weapon deviation real target point, goes to the virtual decoy point of setting.The method can not only successful implementation cheating interference, also Being effective against the detection based on inertial navigation of enemy weapon receiver, important goal fixing to protection has great significance.

The principle of satellite navigation system multistation based on timing_delay estimation relay type deception controls each satellite exactly and receives to enemy weapon The time delay of machine, makes the positioning equation of enemy weapon generation error, guides it to reach the position of mistake.

First, according to the ultimate principle of GNSS satellite location, its computation of pseudoranges formula is as follows:

ρ_i=[(X_i-X)²+(Y_i-Y)²+(Z_i-Z)²]^1/2+c*Δt_d (1)

Without loss of generality, the present embodiment being assumed, receiver receives 4 satellite S_i(i=1,2,3,4) signal.So X_i,Y_i,Z_i (i=1,2,3,4) is each satellite coordinate in ground is felt concerned about, and is known to enemy weapon receiver, Δ t_dIt it is enemy weapon Receiver clock and the time difference of satellite clock, and enemy weapon receiver coordinate (X, Y, Z) is 4 undetermined parameters.General logical Cross 4 pseudorange equation group of simultaneous and obtain enemy weapon receiver self-position.

Add transponder J_iAfter (i=1,2,3,4), pseudorange becomes R_si+R_oi+ c* Δ t, wherein c* Δ t is error correction values.Side Cheng Bianwei:

R_si+R_oi+ c* Δ t=[(X_i-X)²+(Y_i-Y)²+(Z_i-Z)²]^1/2+c*Δt_d (2)

Wherein: R_si(i=1,2,3,4) each satellite distance to respective transponders is represented；R_oi(i=1,2,3,4) represent each Individual transponder is to the distance of real target point；

Then the resolving equation at real target point R point reception curve is:

$\left\{\begin{array}{c}{R}_{s1}+R_{o1}+c*{\mathrm{\Δt}}_1={\[{(X_1-X)}^2+{(Y_1-Y)}^2+{(Z_1-Z)}^2\]}^{1/2}+c*{\mathrm{\Δt}}_d\\ R_{s2}+R_{o2}+c*{\mathrm{\Δt}}_2={\[{(X_2-X)}^2+{(Y_2-Y)}^2+{(Z_2-Z)}^2\]}^{1/2}+c*{\mathrm{\Δt}}_d\\ R_{s3}+R_{o3}+c*{\mathrm{\Δt}}_3={\[{(X_3-X)}^2+{(Y_3-Y)}^2+{(Z_3-Z)}^2\]}^{1/2}+c*{\mathrm{\Δt}}_d\\ R_{s4}+R_{o4}+c*{\mathrm{\Δt}}_4={\[{(X_4-X)}^2+{(Y_4-Y)}^2+{(Z_4-Z)}^2\]}^{1/2}+c*{\mathrm{\Δt}}_d\end{array}\right.---\left(3\right)$

The poorest, eliminate Δ t_d, the mode at corresponding the present embodiment cloth station, should there is R_o1=R_o2=R_o3=R_o4, the equation:

$\left\{\begin{array}{c}{R}_{f1}-R_{f2}=(R_{s1}+R_{o1}+c*\∂t_1)-(R_{s2}+R_{o2}+c*\∂t_2)\\ R_{f2}-R_{f3}=(R_{s2}+R_{o2}+c*\∂t_2)-(R_{s3}+R_{o3}+c*\∂t_3)\\ R_{f3}-R_{f4}=(R_{s3}+R_{o3}+c*\∂t_3)-(R_{s4}+R_{o4}+c*\∂t_4)\end{array}\right.---\left(4\right)$

Wherein,The time delay of Shi Ge road signal.

Four transponders are located on the inverted cone baseplane with R as conical tip, and no matter how transponder position height is arranged, Rs Length all can change along element of cone, be thus easy to calculate the change of its precision.Such arrangement manner ensures that 4 Individual transponder to real target point apart from identical, such R_oiIt is exactly consistent, equation can eliminate R_oiThis amount.Equation becomes For:

$\left\{\begin{array}{c}{R}_{f1}-R_{f2}=(R_{s1}-R_{s2})+c*({\∂}_{t1}-{\∂}_{t2})\\ R_{f2}-R_{f3}=(R_{s2}-R_{s3})+c*({\∂}_{t2}-{\∂}_{t3})\\ R_{f3}-R_{f4}=(R_{s3}-R_{s4})+c*({\∂}_{t3}-{\∂}_{t4})\end{array}\right.---\left(5\right)$

Assuming that during virtual point invariant position, it is assumed that ground central control station updates transponder time delay one second once, because co-ordinates of satellite is one In second, change is the least can ignore, R_fi-R_fi+1It is a constant, R might as well be set_fi-R_fi+1=C_iAndIt is controlled, If it is D_i.Equation can be deformed into (6):

$A\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}y\\ \mathrm{\Δ}z\end{array}\right]=B---\left(6\right)$

Wherein

Wherein: [Δ x, Δ y, Δ z] is transponder coordinate knots modification.Notice that real-time four transponders of this variable of transponder coordinate always become here Change amount.Due to four its being distributed symmetrically property of transponder and the concordance of height, height and position (z) change of single transponder can Being interpreted as the 1/4 of total variation with approximation, (x, y) change can approximate and be interpreted as corresponding x, y total coordinate transponder transverse and longitudinal coordinate Variable quantity open root.

Revised transponder coordinate is [x+ Δ x, y+ Δ y, z+ Δ z], and such iteration updates several times, can update accordingly Precision.

Fig. 2 illustrates the floor map of arrangement manner lower four transponders distribution that the present invention proposes, and starts with energy from geometrical relationship Enough represent each transponder J well_i(i=1,2,3,4) effectively disturbs radius, thus carries out multistation forwarding and effectively disturb radius Calculating.

Because R_eFor earth radius (6370km), h is receiver height, and δ is elevation angle, and transponder height is H, transponder Effectively interference radius be r, have:

$r=(R+h)*\sin \[\frac{\mathrm{\π}}{2}-\mathrm{\δ}-arcsin\left(\frac{(R+h)*sin(\frac{\mathrm{\π}}{2}+\mathrm{\δ})}{R+H}\right)\]---\left(7\right)$

It is each at a distance of 30km on x, y direction that the present invention sets real target point, false target point.Due to real target point Being about 42.42km with false target point air line distance, according to final state effect, its minimum effectively interference region scope need to be more than true Impact point and 2 times of false target point air line distance, i.e. 84.84km.

By experiment simulation, transponder elevation angle δ-value and multistation forward effectively interference radius r_effRelation is as it is shown on figure 3, the least Elevation angle can affect the GDOP value of satellite, the condition adding final state effect limits, and further clear and definite elevation angle scope is δ=25～40 °.

From accompanying drawing 3, transponder relative distance r_iWith the relational expression of δ as r_i=H*tan (90-δ), so in the value of δ In the range of choose different δ, so that it is determined that different r_i, i.e. transponder is relative to several values of position change, thus finally determines and may be used F can be realized_r/R_rThe optimized δ of=1.

Then arranging optimization function R_opt is:

$R\_opt=|min(\frac{a_i-c_i}{R},\frac{b_i-d_i}{R})-1|---\left(8\right)$

Wherein (a_i,b_i) it is that (x, y) coordinate, (c are felt concerned about in the ground of true vertex neighborhood marginal point_i,d_i) it is False Intersection Points neighborhood marginal point after mapping Ground feel concerned about (x, y) coordinate, R_trueFor the true vertex neighborhood radius arranged.

Algorithm key step is specific as follows:

1) in the span of δ, i.e.Choosing uniformly takes a little.Condition is set according to cloth station, determines that the precision of δ is 1 ° and loop structure is set until meet required precision stop；

2) all kinds of for equation parameters are converted into constant or the parameter directly related with the value of δ；

3) set according to optimal function, in conjunction with the parameters such as satellite and false target point distance, transponder spacing, each road time delay, table The equation group of δ is shown；

4) by Newton iteration method lienarized equation group；

5) utilize the system of linear equations after Newton iteration, in conjunction with optimal function, solve the solution of optimal function；

6) the relatively different real target point radius of neighbourhood conditions impact on the solution of optimal function, it is judged that the real target point radius of neighbourhood The optimal value arranged and the transponder elevation angle of its correspondence arrange value.

Below from simulation result deployment analysis, simulation result as shown in Figure 4:

In accompanying drawing 4, a, b respectively show R_trueWhen=10 (km) and 20 (km), δ and the relation of optimal function.

Simulation result shows:

During R=10km, when δ is 38 °, optimal function obtains minima 0.16, it is meant that based on this cloth station condition, can make F_r/R_r∈(0,0.84]∪[1.16,32.5)；

R_trueDuring=20km, optimal function acquirement minima 0.68 when δ is 34.2 °, the most now F_r/R_r∈(0,0.32]∪[1.68,16.3)。

Therefore, it is 20km that optimization arrangement manner should arrange transponder height, and elevation angle is 38 °.Under this arrangement manner, Real target point and false target point constitute the radius of neighbourhood ratio mapped and can level off to the full extent for 1 (as shown in Figure 5). The deception of enemy weapon in can realizing effective interference region while can effectively tackling inertial navigation detection.In sum, The method is of great importance to realizing fixing protection of goal.

In sum, although the present invention is disclosed above with preferred embodiment, so it is not limited to the present invention, any ability Territory those of ordinary skill, without departing from the spirit and scope of the present invention, when various change and retouching can be made, the therefore present invention Protection domain is when defining in the range of standard depending on claims.

Claims (7)

1. a satellite navigation signals deceiving jamming system based on fixing protection of goal, it is characterised in that: include many The false target point of satellite, multiple transponder, real target point and setting, the number of transponder is identical with number of satellite, one Transponder receives the navigation satellite signal that a satellite is broadcast, and multiple transponders receive the aeronautical satellite letter that multi-satellite is broadcast respectively Number and control the time delay of multiple transponder respectively by numerical control delay line technique, the multiple navigation satellite signals after a fixed response time are divided Not broadcast by multiple transponders, the enemy weapon deviation utilizing navigation satellite signal to guide in then cheating effective interference region is true Real impact point, goes to the false target point of setting.

Satellite navigation signals deceiving jamming system based on fixing protection of goal the most according to claim 1, its Being characterised by: number of satellite is 4, transponder number is 4, and four transponders are arranged on real target point conical tip Inverted cone baseplane on, elevation angle and the terrain clearance of the setting of four transponders are the most identical.

Satellite navigation signals deceiving jamming system based on fixing protection of goal the most according to claim 2, its Being characterised by: elevation angle δ=25 of described four transponders～40 °, terrain clearance is 20km.

Satellite navigation signals deceiving jamming system based on fixing protection of goal the most according to claim 3, its It is characterised by: the elevation angle of described four transponders is 38 °.

5. a satellite navigation signals deceiving jamming method based on fixing protection of goal, it is characterised in that include with Lower step:

(1) multi-satellite is selected；Set the false target point F intending guiding enemy weapon to go to；Then will be with selection number of satellite Identical transponder is arranged on on the inverted cone baseplane of real target point conical tip, the elevation angle of the setting of multiple transponders And terrain clearance is the most identical；

(2) receive, by multiple transponders, navigation signal that multiple satellite broadcasts respectively and controlled respectively by numerical control delay line technique Make the time delay of multiple transponder, the multiple navigation satellite signals after a fixed response time are broadcast by these multiple transponders respectively；

(3) enemy weapon is by receiving the spurious signal that multiple transponders are broadcast, and makes enemy weapon receiver positioning calculation result go out Now offseting, enemy weapon receiver positioning result is no longer to resolve, based on actual signal, the positioning result obtained, but through time delay The spurious signal that control processes resolves the positioning result obtained, and utilizes the enemy that navigation signal guides in then cheating effective interference region Side's weapon deviation real target point, goes to the false target point of setting.

Satellite navigation signals deceiving jamming method based on fixing protection of goal the most according to claim 5, it is special Levy and be, in step (1), select the GDOP value four satellites less than 3 according to location visible satellite situation S_i(i=1,2,3,4, transponder arranges 4 equally, respectively J_i(i=1,2,3,4).

A kind of satellite navigation signals deceiving jamming method based on fixing protection of goal the most according to claim 6, It is characterized in that, the computational methods of the position coordinates of four transponders in step (1):

First, according to the ultimate principle of GNSS satellite location, its computation of pseudoranges formula is as follows:

ρ_i=[(X_i-X)²+(Y_i-Y)²+(Z_i-Z)²]^1/2c*Δt_d (1)

Wherein: X_i,Y_i,Z_i(i=1,2,3,4) is each satellite coordinate in ground is felt concerned about, and is to enemy weapon receiver Know；Δt_dIt is enemy weapon receiver clock and the time difference of satellite clock and enemy weapon receiver coordinate (X, Y, Z) is 4 Undetermined parameter；

After adding transponder, the pseudorange of enemy weapon receiver becomes R_si+R_oi+ c* Δ t, wherein c* Δ t is error correction values. Formula (1) becomes:

R_si+R_oi+ c* Δ t=[(X_i-X)²+(Y_i-Y)²+(Z_i-Z)²]^1/2+c*Δt_d (2)

Wherein: R_si(i=1,2,3,4) each satellite distance to respective transponders is represented；R_oi(i=1,2,3,4) represent each Individual transponder is to the distance of real target point；

Then the resolving equation at real target point R point reception curve is:

$\left\{\begin{array}{c}{R}_{s1}+R_{o1}+c*{\mathrm{\Δt}}_1={\[{(X_1-X)}^2+{(Y_1-Y)}^2+{(Z_1-Z)}^2\]}^{1/2}+c*{\mathrm{\Δt}}_d\\ R_{s2}+R_{o2}+c*{\mathrm{\Δt}}_2={\[{(X_2-X)}^2+{(Y_2-Y)}^2+{(Z_2-Z)}^2\]}^{1/2}+c*{\mathrm{\Δt}}_d\\ R_{s3}+R_{o3}+c*{\mathrm{\Δt}}_3={\[{(X_3-X)}^2+{(Y_3-Y)}^2+{(Z_3-Z)}^2\]}^{1/2}+c*{\mathrm{\Δt}}_d\\ R_{s4}+R_{o4}+c*{\mathrm{\Δt}}_4={\[{(X_4-X)}^2+{(Y_4-Y)}^2+{(Z_4-Z)}^2\]}^{1/2}+c*{\mathrm{\Δt}}_d\end{array}\right.---\left(3\right)$

The poorest, eliminate Δ t_d, another because there being R_o1=R_o2=R_o3=R_o4, can obtain:

$\left\{\begin{array}{c}{R}_{f1}-R_{f2}=(R_{s1}+R_{o1}+c*\∂t_1)-(R_{s2}+R_{o2}+c*\∂t_2)\\ R_{f2}-R_{f3}=(R_{s2}+R_{o2}+c*\∂t_2)-(R_{s3}+R_{o3}+c*\∂t_3)\\ R_{f3}-R_{f4}=(R_{s3}+R_{o3}+c*\∂t_3)-(R_{s4}+R_{o4}+c*\∂t_4)\end{array}\right.---\left(4\right)$

Four transponders are located on the inverted cone baseplane with R as conical tip, and no matter how transponder position height is arranged, Rs Length all can change along element of cone, due to 4 transponders to real target point apart from identical, so R_o1=R_o2=R_o3=R_o4, equation can eliminate R in (4)_oi(i=1,2,3,4) this amount, equation becomes:

$\left\{\begin{array}{c}{R}_{f1}-R_{f2}=(R_{s1}-R_{s2})+c*({\∂}_{t1}-{\∂}_{t2})\\ R_{f2}-R_{f3}=(R_{s2}-R_{s3})+c*({\∂}_{t2}-{\∂}_{t3})\\ R_{f3}-R_{f4}=(R_{s3}-R_{s4})+c*({\∂}_{t3}-{\∂}_{t4})\end{array}\right.---\left(5\right)$

Assuming that during virtual target point F invariant position, it is assumed that central control station renewal transponder time delay in ground is once ignored satellite and is sat for one second It is marked on the change in a second, R_fi-R_fi+1It is a constant, if R_fi-R_fi+1=C_iAndIt is controlled, if it is D_i； Equation (5) can be deformed into (6):

$A\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}y\\ \mathrm{\Δ}z\end{array}\right]=B---\left(6\right)$

Wherein

[Δ x, Δ y, Δ z] is transponder coordinate knots modification；

Revised transponder coordinate is [x+ Δ x, y+ Δ y, z+ Δ z], and such iteration updates several times, can be by the seat of transponder Mark updates to corresponding precision.