CN103576138B - A kind of spaceborne passive radar localization method based on GNSS-R signal geometric relationship - Google Patents

Abstract

Based on a spaceborne passive radar localization method for GNSS-R signal geometric relationship, step:: the direct signal moment that receiver receives gps satellite is t ₁, receiving the reflected signal moment of associated GPS satellites signal to target is t ₂; Two: according to the due in of signal, calculate direct path length L and the reflection paths length D of signal; Three: the position T (x of transmitter computes and receiver _t, y _t, z _t) and R (x _r, y _r, z _r); Four: the angle α calculating direct signal and reflected signal, determine the vector of reflected signal; Five: extend to a N at the vector of reflected signal along the opposite direction propagated, make receiver R to some N distance with reflected path apart from identical, and solve the coordinate of N; Six: set the vector T N mid point of transmitter T to some N as M, ask M coordinate; Seven: on plane TRN, cross the vertical line that M point makes TN, hand over RN vector in P point, P point and target work as moment position, calculation level P coordinate.Present invention reduces clearing difficulty, improve the efficiency of location, decrease location cost.

Description

A kind of spaceborne passive radar localization method based on GNSS-R signal geometric relationship

(1) technical field:

The present invention relates to a kind of single star passive radar sea and coastal waters object localization method, in particular to relevant with the geometric relationship of receiver, transmitter and target based on GLONASS (Global Navigation Satellite System) reflected signal (GlobalNavigation Satellite System Reflect signal, GNSS-R) localization method, the method can be used for, to coastal waters low target and sea single goal location, being applicable to the system that passive radar receiver has Rotation of receiver antenna or has angle measurement function.The method can realize succinct efficient single star location, belongs to wireless communication technology field.

(2) technical background:

Radar system is the mainstay of Homeland air defense, they are since nineteen forties is formally equipped, due to its have operating distance far away, round-the-clock, in target detection, location and tracking, play the irreplaceable vital role of other sensor by advantages such as natural environment and climate variable effect are little.But to the modern times, along with electronic interferences, stealth technology, antiradiation missile are attacked and the emergence and development of the radar electronic warfare such as low latitude, ultra-low altitude penetration technology, traditional radar system has been difficult to exploit one's power as before, and the existence of himself has also become pressing problem, passive detection technology be exactly under this background emergence and development get up.

Passive location method has that operating distance is far away, antijamming capability is strong, realize lobe-on-receive to target, the ability of location and tracking plays an important role for the survivability and warfighting capabilities of raising system under Electronic Warfare Environment.Because the frequency of navigation satellite signal and power are fixed, and receiver reads the factor such as the moment of signal transmitting and the speed of satellite by the ephemeris file in its signal, GPS (Global PositioningSystem, the GPS) satellite-signal spread all over the world becomes the main signal of passive location radar for target detection, remote sensing and location.

Passive radar target location algorithm based on GNSS-R is a kind of location technology having taken into account passive radar and GPS double dominant, effectively utilize GNSS-R signal and carry out the disguise that passive location had both added system, expand again the orientation range of passive radar, and transmitter (gps satellite) and receiver (low orbit satellite can be calculated according to the almanac data in navigation signal, Low Earth Orbit, LEO) position, reduce the complicacy of location Calculation, conveniently geometric relationship modeling is carried out to reflected signal, realize optimization location, this is the characteristic that other signals do not have.

Along with based on the passive radar remote sensing of GNSS-R signal, the development of the technology such as detection and location, space-based passive radar localization method is subject to domestic and international researcher and more and more pays close attention to, as single star frequency measurement passive location technology, based on the object technology etc. of difference time of arrival.Current localization method utilizes the delay inequality of reflected signal and direct signal to list Nonlinear System of Equations mostly, the redundancy in system of equations is used to be that linear equation carries out calculating or positioning according to the Doppler parameter measured by non-linear equation, this kind of localization method principle is simple, but because parameter is too much, add the complicacy of location algorithm, introduce a large amount of measuring error simultaneously.By the cell site of gps satellite as passive radar receiver, because itself has positioning function, therefore effective reflected signal geometric relationship can be provided, and utilize reflected signal to position with the geometric relationship between transceiver.Simple and convenient due to the method, one of its study hotspot becoming location algorithm.Its principle is after determining gps satellite and the spaceborne receiver location of LEO, according to the relation received between reflected path and transceiver, calculates the algorithm of the relative position of target with solid geometry field relevant knowledge.This algorithm is transformed into the target localization of two-dimensional space objective location, has simplified location Calculation difficulty, has been conducive to real-time location.The shortcoming utilizing reflected signal geometric relationship to locate is more responsive to measurement mistake, further by target correlation parameter repetitive measurement, can be averaged on fore-and-aft survey result the impact that means such as removing error reduce error.What the passive radar localization method be somebody's turn to do based on geometric relationship was used for locates sea low target or sea-surface target, makes greatly to reduce the positioning calculation difficulty of target, decreases calculated amount, thus simplified apparatus, obtain location efficiently by less input.

(3) summary of the invention:

1, object: for realizing the location utilizing the spaceborne passive radar of GNSS-R signal geometric relationship in coastal waters low target and sea-surface target, the method combined based on GNSS-R signal geometric relationship and spaceborne passive radar is called this technical field popular research direction in recent years.But, traditional geometric relationship location algorithm, what be confined to the region that reflected signal and direct signal path surround carries out cartesian geometry computing, not only need to record direct projection and reflection paths delay, also need the relations such as the beam angle of transmitter, calculation step is many and calculated amount large, depends on and estimates and non-measured, cause error larger to the angular relationship transmitted.Remote according to the distance of transceiver and target, target is considered as particle by the present invention, the reflected signal of target is considered as ray, gps signal from be transmitted into its target echo be received machine receive only need 0.06s, during this period by target, Receiver And Transmitter is considered as geo-stationary, in order to improve the various and dependence to the angular relationship that transmits of conventional geometric relation localization method calculation procedure, objective location is converted into the geometric relationship by evaluating objects and transceiver on the two dimensional surface formed at transmitter receiver line and reflected signal, target is accurately located.

2, technical scheme: the present invention is characterized in: by the conversion of the problem of three-dimensional localization by geometric relationship, become the location of two dimensional surface, decrease operand, especially for the target of the low dry running in sea, eliminates the step estimating its height.Due in tradition utilize geometric relationship localization method to be confined to region that reflected signal and direct signal surround, so location depends on the factors such as the scanning angle that transmitter transmits, cause evaluated error can cause the inaccurate of final positioning result to the estimation of angle, this is also that geometric relationship location is used for theory orientation, and the reason that actual location effect is undesirable.Geometric relationship location proposed by the invention only need know that the time delay of target echo and direct signal and reflected signal deflection just can carry out simple and direct location to sea low target or sea-surface target.

The concrete steps of this method are as follows:

Step one: the direct signal moment that receiver receives from gps satellite is t ₁, in the ephemeris file in gps signal, comprise t launch time that transmits ₀, receiver receives the reflected signal moment of associated GPS satellites signal to target is in addition t ₂.

Step 2: according to the due in of signal, calculates direct path length L and the reflection paths length D of signal.Computation process is as follows:

1) direct path length: L=(t ₁-t ₀) × c

Wherein c is the light velocity, c=3 × 10 ⁸m/s, t ₀and t ₁for the launch time of signal and the time of reception of direct signal.

2) reflection paths length: D=L+ (t2-t1) × c

Wherein c is the light velocity, and L is direct path length, t ₂and t ₁for the time of reception of reflected signal time of reception and direct signal.

Step 3: the position T (x of transmitter computes and receiver _t, y _t, z _t) and R(x _r, y _r, z _r)

Transmitter computes position T (x _t, y _t, z _t) and the position R(x of receiver _r, y _r, z _r) and speed be common method, therefore omit.

Step 4: the angle α calculating direct signal and reflected signal, determines the vector of reflected signal

Calculate the angle α of direct path and reflected signal:

Receiver has rotating antenna, and reflected signal and direct signal are received by the antenna of two different azimuth on receiver respectively, and the angle α both this is known.

Negate and penetrate signal vector step:

1) reflected signal receiving antenna and receiver track section angle β ' known.Then can show that reflected signal ray and receiver track section inter normal angle are the direction of motion angle of reflection signal receiver antenna and receiver is γ.

2) receiver speed section inter normal vector is: $\stackrel{\→}{n}=\stackrel{\→}{\mathrm{RO}}=(-x_r,{-y}_r,-z_r)$

3) normal passes through some R and its direction vector known, and obtaining receiver section normal equation is:

$\stackrel{\→}{n}:\frac{x-x_r}{-x_r}=\frac{y-y_r}{-y_r}=\frac{z-z_r}{-z_r}$

4) solve with for axis, take β as the conical surface of bus and turning axle angle.

By 2) the direction vector of axis is if M(x, y, z) be on conical surface non-summit a bit, then the direction vector crossing the bus of some M is thus have: $\frac{\stackrel{\→}{v_1}\·\stackrel{\→}{v_2}}{\left|\stackrel{\→}{v_1}\right|\·\left|\stackrel{\→}{v_2}\right|}=-\cos \mathrm{\β}$

By vector with substitution above formula obtains conical surface equation and is:

$\frac{-(x-x_r)x_r-(y-y_r)y_r-(z-z_r)z_r}{\sqrt{x_r^2+y_r^2+z_r^2}\·\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=-\cos \mathrm{\β}$

5) equation of direct signal place straight line is calculated

Known receiver coordinate R (x _r, y _r, z _r) and transmitter coordinate T (x _t, y _t, z _t)

Ray TR(is by the ray of transmitter T beacon receiver R) direction vector be: (x _r-x _t, y _r-y _t, z _r-z _t)

Straight line TR(is by the straight line of transmitter T beacon receiver R) equation be:

$\frac{x-x_r}{x_r-x_t}=\frac{y-y_r}{y_r-y_t}=\frac{z-z_r}{z_r-z_t}$

6) calculate with TR straight line for axle, reflected ray is the conical surface of bus.

Known reflected signal ray and direct signal angle are α, method for solving and 4) in identical, trying to achieve conical surface is:

$\begin{array}{c}\frac{(x-x_r)(x_r-x_t)+(y-y_r)(y_r-y_t)+(z-z_r)(z_r-z_t)}{\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}\·\sqrt{{(x_r-x_t)}^2+{(y_r-y_t)}^2+{(z_r-z_t)}^2}}\\ =\cos \mathrm{\α}\end{array}$

7) computational reflect signal place straight-line equation

By 4) in and 6) in gained conic section simultaneous, two curve intersections.

$\left\{\begin{array}{c}\frac{-(x-x_r)x_r-(y-y_r)y_r-(z-z_r)z_r}{\sqrt{x_r^2+y_r^2+z_r^2}\·\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=-\cos \mathrm{\β}\\ \frac{(x-x_r)(x_r-x_t)+(y-y_r)(y_r-y_t)+(z-z_r)(z_r-z_t)}{\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}\·\sqrt{{(x_r-x_t)}^2+{(y_r-y_t)}^2+{(z_r-z_t)}^2}}=\cos \mathrm{\α}\end{array}\right.$

1 ', target is when specular reflection point place, then above-mentioned two conical surfaces have unique intersection, and this intersection is the equation of reflected signal place straight line.

2 ', target is not or not minute surface launching site place, and above-mentioned equation has two groups of solutions.

● remove fuzzy solution

Known receiver antenna and receiver direction of motion angle are γ, if receiver is constant in location moment direction of motion, direction of motion vector is: (v _x, v _y, v _z)

Reflected signal place straight line can be obtained by above-mentioned two conditions to be positioned at (v _x, v _y, v _z) for the straight line of direction vector be axle, on the circular conical surface being γ with bus and axis angle.

This circular conical surface can be asked, for:

$\frac{v_x(x-x_r)+v_y(y-y_r)+v_z(z-z_r)}{\sqrt{{v_x}^2+{v_y}^2+{v_z}^2}\·\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=\cos \mathrm{\γ}$

Above formula is intersected the equation that can obtain reflected signal place straight line with the conical surface obtained before

Step 5: extend to a N along the opposite direction propagated at the vector of reflected signal, makes receiver R to some N distance with reflected path apart from identical, and solves the coordinate of N.

Solve the coordinate of N:

The path of reflected signal is D, by step 2 2) draw.

If N coordinate is (x _n, y _n, z _n), then have:

$\left\{\begin{array}{c}{(x_n-x_r)}^2+{(y_n-y_r)}^2+{(z_n-z_r)}^2=D^2\\ f(x_n,y_n,z_n)=0\end{array}\right.$

Wherein f (x, y, z)=0 is the equation of reflected signal place straight line.

Step 6: set the vector T N mid point of transmitter T to some N as M, ask M coordinate.

Ask the calculation procedure of M coordinate as follows:

Ask M coordinate:

If M coordinate is (x _m, y _m, z _m), then have:

$\left\{\begin{array}{c}{x}_m=\frac{x_t+x_n}{2}\\ y_m=\frac{y_t+y_n}{2}\\ z_m=\frac{z_t+z_n}{2}\end{array}\right.$

Wherein x _t, y _tand z _tbe respectively the coordinate of three axis of transmitter T.

Step 7: at plane TRN(by transmitter T, the plane that receiver R forms with some N) went up the vertical line that M point makes TN, hand over RN vector in P point, P point and target work as moment position, calculation level P coordinate.

Ask the computation process of P coordinate as follows:

If the coordinate of P is (x _p, y _p, z _p)

$\left\{\begin{array}{c}(x_p-x_m)m+(y_p-y_m)p+(z_p-z_m)q=0\\ f(x_p,y_p,z_p)=0\end{array}\right.$

In above formula, (m, p, q) is the direction vector of reflected signal place straight-line equation.

3, advantage and effect

This sea-surface target based on GNSS-R signal geometric relationship that the present invention proposes and sea low target localization method, not only eliminate and step is obtained for sea low target high computational, simplify difficulty in computation, improve location efficiency, and take full advantage of transmitter, the angular relationship of receiver and reflected signal three, the geometric relationships such as distance relation, simple and clear solid geometry theorem is used to achieve the efficient location in space, this method is to transmitter endless number system simultaneously, single star can be used to locate, also multiple satellite location can be used, reduce positioning difficulty and cost.Therefore, the present invention is applicable to the target localization that utilizes the GNSS-R reflected signal of target to the low dry running of sea-surface target and sea.The sea-surface target and the sea low target localization method advantage that the present invention is based on GNSS-R signal can be summarized as follows:

1. take full advantage of the geometric relationships such as the position relationship between reflected signal, receiver, transmitter, angular relationship, using simple and clear analytic geometry method accurately to locate target, is a kind of new localization method.

2. this algorithm adopts analytic geometry method to calculate the exact position of target, eliminates the calculating to its height especially, therefore improve the efficiency of location for coastal waters low target.

3. location three-dimensional localization being converted to two dimensional surface is sterically defined innovation, is also sterically defined trend, this method avoids the conversion of traditional algorithm to Nonlinear System of Equations, reduces clearing difficulty.

4. this algorithm does not have mandatory requirement to transmitter number, and both having may be used for single star location (receiver transmitter) has and can be used as multiple satellite location (a multiple transmitter of receiver), decreases location cost, is conducive to the popularization of algorithm.

4, the feasibility analysis of algorithm

Known: as shown in Figure 2, the position of Receiver And Transmitter is respectively T and R, and the vector at reflected signal place is l _instead, direct path length is L, and reflection paths length is D.By l _insteadthe opposite direction propagated along reflected signal extends to N, makes RN=D, connects TN, gets TN mid point M.Cross some M and make linear vertical in TN, hand over RN in P.

Solve: then P point is target place.

Prove: establish target to be positioned at some Q, a P ≠ Q

Vectorial l is positioned at by the known target that obtains _insteadon, there is TQ+RQ=D

∵ RN=RQ+QN=D again

∴TQ＝QN

Connect QM, then have QM ⊥ TN

∵ PM ⊥ TN again, P is positioned at vectorial l _insteadand P ≠ Q

∴QM≠PM

Then this hypothesis violates axiom: excessively plane a bit have and only have straight line perpendicular to known straight line.

Therefore, suppose to be false.

Namely P=Q, P are target place.

(4) accompanying drawing illustrates:

Fig. 1 the method for the invention FB(flow block).

The geometric relationship of Fig. 2 the present invention two-dimentional GNSS-R target echo in transmitter, receiver and reflected signal composition plane.

(5) embodiment:

See Fig. 1, 2, under WGS-84 coordinate system, in units of rice, receiver R coordinate is made to be (-4069896,-3583236, 4527639), transmitter T coordinate is (-11178791,-13160191, 20341528), record reflected signal and direct signal angle is arccos (-0.4778), be arccos (-0.1394) with receiver velocity reversal angle, the normal vector angle of reflected signal and motion tangent plane is reflected signal vector is arccos (0.5881), wherein the normal vector of motion tangent plane is (-4069896,-3583236, 4527639), receiver velocity is (-4738,-1796,-5654), direct signal vector is (7108895, 9576955,-15813889)

A kind of object localization method concrete steps based on GNSS-R geometric relationship of the present invention are as follows:

Step one: the direct signal moment that receiver receives from gps satellite is t ₁, in the ephemeris file in gps signal, comprise t launch time that transmits ₀, receiver receives the reflected signal moment of associated GPS satellites signal to target is in addition t ₂.

Step 2: according to the due in of signal, calculates direct path length L and the reflection paths length D of signal.

Computation process is as follows:

1) direct path length: L=(t ₁-t ₀) × c

Wherein c is the light velocity, c=3 × 10 ⁸m/s, t ₀and t ₁for the launch time of signal and the time of reception of direct signal.If τ ₁=t ₁-t ₀=0.0660247s, then direct path length is: 19807411.2517858m

2) reflection paths length: D=L+ (t ₂-t ₁) × c

Wherein c is the light velocity, and L is direct path length, t ₂and t ₁for the time of reception of reflected signal time of reception and direct signal.

τ ₂=t ₂-t ₁=0.0063251s, then reflection paths length is 21704947.2266282m.

Step 3: the position T (x of transmitter computes and receiver _t, y _t, z _t) and R(x _r, y _r, z _r)

Transmitter computes position T (x _t, y _t, z _t) and the position R(x of receiver _r, y _r, z _r) and speed be common method, therefore omit.Receiver R position is (-4069896 ,-3583236,4527639) herein, and transmitter T position is (-11178791 ,-13160191,20341528).

Step 4: the angle α calculating direct signal and reflected signal, determines the vector of reflected signal

Calculate the angle α of direct path and reflected signal:

Receiver has rotating antenna, and reflected signal and direct signal are received by the antenna of two different azimuth on receiver respectively, and the angle α both this is known.α=arccos (-0.4778) herein

Negate and penetrate signal vector step:

1) reflected signal receiving antenna and receiver track section angle β ' known.Then can show that reflected signal ray and receiver track section inter normal angle are the direction of motion angle of reflection signal receiver antenna and receiver is γ.

β=arccos (0.5881), γ=arccos (-0.1394) in this example

2) receiver speed section inter normal vector is: $\stackrel{\→}{n}=\stackrel{\→}{\mathrm{RO}}=(-x_r,{-y}_r,-z_r)$

Normal passes through some R and its direction vector known, and obtaining receiver section normal equation is:

$\stackrel{\→}{n}:\frac{x-x_r}{-x_r}=\frac{y-y_r}{-y_r}=\frac{z-z_r}{-z_r}$

This routine normal equation is:

$\stackrel{\→}{n}:\frac{x+4069896}{4069896}=\frac{y+3583236}{3583236}=\frac{z-4527639}{-4527639}$

3) solve with for axis, take β as the conical surface of bus and turning axle angle.

By 2) the direction vector of axis is if M(x, y, z) be on conical surface non-summit a bit, then the direction vector crossing the bus of some M is thus have: $\frac{\stackrel{\→}{v_1}\·\stackrel{\→}{v_2}}{\left|\stackrel{\→}{v_1}\right|\·\left|\stackrel{\→}{v_2}\right|}=-\cos \mathrm{\β}$

By vector with substitution above formula obtains conical surface equation and is:

$\frac{-(x-x_r)x_r-(y-y_r)y_r-(z-z_r)z_r}{\sqrt{x_r^2+y_r^2+z_r^2}\·\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=-\cos \mathrm{\β}$

Bring known terms into can obtain:

$\begin{array}{c}\frac{(x+4069896)4069896+(y+3583236)3583236-(z-4527639)4527639}{\sqrt{{4069896}^2+{3583236}^2+{4527639}^2}\·\sqrt{{(x+4069896)}^2+{(y+3583236)}^2+{(z-4527639)}^2}}\\ =-0.5881\end{array}$

4) equation of direct signal place straight line is calculated

Known receiver coordinate R (x _r, y _r, z _r) and transmitter coordinate T (x _t, y _t, z _t)

By the direction vector of the ray TR of transmitter T to receiver R be: (x _r-x _t, y _r-y _t, z _r-z _t)

The equation of the straight line TR that transmitter T and receiver R determines is:

$\frac{x-x_r}{x_r-x_t}=\frac{y-y_r}{y_r-y_t}=\frac{z-z_r}{z_r-z_t}$

Have in this example:

$\frac{x+4069896}{-4069896+11178791}=\frac{y+3583236}{-3583236+13160191}=\frac{z-4527639}{4527639-20341528}$

Abbreviation obtains:

$\frac{x+4069896}{7108895}=\frac{y+3583236}{9576955}=\frac{z-4527639}{-15813889}$

5) calculate with TR ray for axle, reflected signal ray is the conical surface of bus.

Known reflected signal ray and direct signal angle are α, method for solving and 4) in identical, trying to achieve conical surface is:

$\begin{array}{c}\frac{(x-x_r)(x_r-x_t)+(y-y_r)(y_r-y_t)+(z-z_r)(z_r-z_t)}{\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}\·\sqrt{{(x_r-x_t)}^2+{(y_r-y_t)}^2+{(z_r-z_t)}^2}}\\ =\cos \mathrm{\α}\end{array}$

Have in this example:

$\begin{array}{c}\frac{(x+4069896)\×7108895+(y+3583236)\×9576955-(z-4527639)\×15813889}{\sqrt{{(x+4069896)}^2+{(y+3583236)}^2+{(z-4527639)}^2}\·\sqrt{{7108895}^2+{9576955}^2+{15813889}^2}}\\ =-0.4778\end{array}$

6) computational reflect signal place straight-line equation

By 3) in and 5) in gained conic section simultaneous, two curve intersections.

$\left\{\begin{array}{c}\frac{-(x-x_r)x_r-(y-y_r)y_r-(z-z_r)z_r}{\sqrt{x_r^2+y_r^2+z_r^2}\·\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=-\cos \mathrm{\β}\\ \frac{(x-x_r)(x_r-x_t)+(y-y_r)(y_r-y_t)+(z-z_r)(z_r-z_t)}{\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}\·\sqrt{{(x_r-x_t)}^2+{(y_r-y_t)}^2+{(z_r-z_t)}^2}}=\cos \mathrm{\α}\end{array}\right.$

That is:

$\left\{\begin{array}{c}\frac{(x+4069896)4069896+(y+3583236)3583236-(z-4527639)4527639}{\sqrt{{4069896}^2+{3583236}^2+{4527639}^2}\·\sqrt{{(x+4069896)}^2+{(y+3583236)}^2+{(z-4527639)}^2}}=-0.5881\\ \frac{(x+4069896)\×7108895+(y+3583236)\×9576955-(z-4527639)\×15813889}{\sqrt{{(x+4069896)}^2+{(y+3583236)}^2+{(z-4527639)}^2}\·\sqrt{{7108895}^2+{9576955}^2+{15813889}^2}}=-0.4778\end{array}\right.$

1 ', target is when specular reflection point place, then above-mentioned two conical surfaces have unique intersection, and this intersection is anti-

Penetrate the equation of signal place straight line.

2 ', target is not or not minute surface launching site place, and above-mentioned equation has two groups of solutions.

● remove fuzzy solution

Known receiver antenna and receiver direction of motion angle are γ, if receiver is constant in location moment direction of motion, direction of motion vector is: (v _x, v _y, v _z), reflected signal place straight line can be obtained by known (-4738 ,-1796 ,-5654) by above-mentioned two conditions and be positioned at (v _x, v _y, v _z) for the straight line of direction vector be axle, on the circular conical surface being γ with bus and axis angle.

This circular conical surface can be asked, for:

$\frac{v_x(x-x_r)+v_y(y-y_r)+v_z(z-z_r)}{\sqrt{{v_x}^2+{v_y}^2+{v_z}^2}\·\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=\cos \mathrm{\γ}$

Have in this example:

$\begin{array}{c}\frac{-4738(x+4069896)-1796(y+3583236)-5654(z-4527369)}{\sqrt{{4738}^2+1796^2+{5654}^2}\·\sqrt{{(x+4069896)}^2+{(y+3583236)}^2+{(z-4527639)}^2}}\\ =-0.1394\end{array}$

Above formula is intersected the equation that can obtain reflected signal place straight line with the conical surface obtained before

Bring receiver coordinate, receiver velocity and angular relationship into above-mentioned equation to obtain:

$\left\{\begin{array}{c}\frac{(x+4069896)4069896+(y+3583236)3583236-(z-4527639)4527639}{\sqrt{{4069896}^2+{3583236}^2+{4527639}^2}\·\sqrt{{(x+4069896)}^2+{(y+3583236)}^2+{(z-4527639)}^2}}=-0.5881\\ \frac{(x+4069896)\×7108895+(y+3583236)\×9576955-(z-4527639)\×15813889}{\sqrt{{(x+4069896)}^2+{(y+3583236)}^2+{(z-4527639)}^2}\·\sqrt{{71008895}^2+{9576955}^2+{15813889}^2}}=-0.4778\\ \frac{-4738(x+4069896)-1796(y+3583236)-5654(z-4527639)}{\sqrt{{4738}^2+{1796}^2+{5654}^2}\·\sqrt{{(x+4069896)}^2+{(y+3583236)}^2+{(z-4527639)}^2}}=-0.1394\end{array}\right.$

Step 5: extend to a N along the opposite direction propagated at the vector of reflected signal, making receiver R to putting N distance with reflected path apart from identical, solving the coordinate of N.

Solve the coordinate of N:

The path of reflected signal is D, by step 2 2) draw.

If N coordinate is (x _n, y _n, z _n), then have:

$\left\{\begin{array}{c}{(x_n-x_r)}^2+{(y_n-y_r)}^2+{(z_n-z_r)}^2=D^2\\ f(x_n,y_n,z_n)=0\end{array}\right.$

And $\sqrt{x_n^2+y_n^2+z_n^2}<\sqrt{x_r^2+y_r^2+z_r^2}$

Wherein f (x, y, z)=0 is the equation of reflected signal place straight line.

Bring known receiver coordinate and the reflected signal straight-line equation obtained into can try to achieve N point accurate coordinates.

Step 6: establish transmitter T to some N vector T N mid point M, ask the target of a M.

The calculation procedure of solution point M coordinate:

Ask M coordinate:

If M coordinate is (x _m, y _m, z _m), then have:

$\left\{\begin{array}{c}{x}_m=\frac{x_t+x_n}{2}\\ y_m=\frac{y_t+y_n}{2}\\ z_m=\frac{z_t+z_n}{2}\end{array}\right.$

Wherein x _t, y _tand z _tbe respectively the coordinate of three axis of transmitter T.

Transmitter coordinate and the N point coordinate of having tried to achieve are brought into and can obtain M point coordinate.

Step 7: cross M point and make the vertical line of transmitter T with the line segment TN of some N composition on the plane TRN that transmitter T, receiver R and some N form, friendship RN(receiver R is formed by connecting with some N) vector is in P point, and P point and target are when moment position.

The process of calculation level P coordinate:

If the coordinate of P is (x _p, y _p, z _p)

$\left\{\begin{array}{c}(x_p-x_m)m+(y_p-y_m)p+(z_p-z_m)q=0\\ f(x_p,y_p,z_p)=0\end{array}\right.$

In above formula, (m, p, q) is the direction vector of reflected signal place straight-line equation.

Try to achieve P coordinate for (-3000000 ,-4000000,4000000), be target location.

Below concrete position fixing process is just completed once.

In sum, a kind of localization method based on GNSS-R signal geometric relationship of the present invention, the angular relationship that can make full use of on the one hand between the normal of the same direct signal of reflected signal, receiver direction of motion and receiver motion section is carried out simplification and is calculated, use solid geometry correlation theorem on the other hand, eliminate the estimation to object height, avoid estimating to object height the error that causes.In addition because the present invention can realize single star location, namely gps satellite number is not limited, greatly reduce location cost, convenient popularization.When visible star is more than one, different receiver transmitter integrated positionings can be used further, realize positioning precision and optimize further, improve efficiency and the reliability of positioning system.

Claims (4)

1., based on a spaceborne passive radar localization method for GNSS-R signal geometric relationship, it is characterized in that: the method concrete steps are as follows:

Step one: the direct signal moment that receiver receives from gps satellite is t ₁, in the ephemeris file in gps signal, comprise t launch time that transmits ₀, receiver receives the reflected signal moment of associated GPS satellites signal to target is in addition t ₂;

Step 2: according to the due in of signal, calculates direct path length L and the reflection paths length D of signal; Its computation process is as follows:

1) direct path length: L=(t ₁-t ₀) × c

Wherein c is the light velocity, c=3 × 10 ⁸m/s, t ₀and t ₁for the launch time of signal and the time of reception of direct signal;

2) reflection paths length: D=L+ (t ₂-t ₁) × c

Wherein c is the light velocity, and L is direct path length, t ₂and t ₁for the time of reception of reflected signal time of reception and direct signal;

Step 3: the position T (x of transmitter computes and receiver _t, y _t, z _t) and R (x _r, y _r, z _r):

According to common method transmitter computes position T (x _t, y _t, z _t) and the position R (x of receiver _r, y _r, z _r) and speed;

Step 4: the angle α calculating direct signal and reflected signal, determines the vector of reflected signal;

Calculate the angle α of direct path and reflected signal:

Receiver has rotating antenna, and reflected signal and direct signal are received by the antenna of two different azimuth on receiver respectively, and the angle α both this is known;

The step of penetrating signal vector of negating is as follows:

1) reflected signal receiving antenna and receiver track section angle β ' known, then show that reflected signal ray and receiver track section inter normal angle are the direction of motion angle of reflection signal receiver antenna and receiver is γ;

2) receiver speed section inter normal vector is:

3) normal passes through some R and its direction vector known, and obtaining receiver section normal equation is:

$\stackrel{\&RightArrow;}{n}:\frac{x-x_r}{-x_r}=\frac{y-y_r}{-y_r}=\frac{z-z_r}{-z_r};$

4) solve with for axis, take β as the conical surface of bus and turning axle angle,

By 2) the direction vector of axis is if M (x, y, z) be on conical surface non-summit a bit, then the direction vector crossing the bus of some M is thus have: $\frac{\stackrel{\&RightArrow;}{v_1}\&CenterDot;\stackrel{\&RightArrow;}{v_2}}{|\stackrel{\&RightArrow;}{v_1|}\&CenterDot;|\stackrel{\&RightArrow;}{v_2|}}=-\cos \mathrm{\&beta;}$

By vector with substitution above formula obtains conical surface equation and is:

$\frac{-(x-x_r)x_r-(y-y_r)y_r-(z-z_r)z_r}{\sqrt{x_r^2+y_r^2+z_r^2}\&CenterDot;\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=-\cos \mathrm{\&beta;};$

5) equation of direct signal place straight line is calculated:

Known receiver coordinate R (x _r, y _r, z _r) and transmitter coordinate T (x _t, y _t, z _t)

The direction vector of ray TR is: (x _r-x _t, y _r-y _t, z _r-z _t)

The equation of straight line TR is:

$\frac{x-x_r}{x_r-x_t}=\frac{y-y_r}{y_r-y_r}=\frac{z-z_r}{z_r-z_t};$

6) calculate with TR straight line for axle, reflected ray is the conical surface of bus:

Known reflected signal ray and direct signal angle are α, method for solving and 4) in identical, trying to achieve conical surface is:

$\frac{(x-x_r)(x_r-x_t)+(y-y_r)(y_r-y_t)+(z-z_r)(z_r-z_t)\underset{}{}}{\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}\&CenterDot;\sqrt{{(x_r-x_t)}^2+{(y_r-y_t)}^2+{(z_r-z_t)}^2}}=\cos \mathrm{\&alpha;}\begin{array}{}\end{array};$

7) computational reflect signal place straight-line equation:

By 4) in and 6) in gained conic section simultaneous, two curve intersections,

$\left\{\begin{array}{c}\frac{-(x-x_r)x_r-(y-y_r)y_r-(z-z_r)z_r}{\sqrt{x_r^2+y_r^2+z_r^2}\&CenterDot;\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=-\cos \mathrm{\&beta;}\\ \frac{(x-x_r)(x_r-x_t)+(y-y_r)(y_r-y_t)+(z-z_r)(z_r-z_t)}{\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}\&CenterDot;\sqrt{{(x_r-x_t)}^2+{(y_r-y_t)}^2+{(z_r-z_t)}^2}}=\cos \mathrm{\&alpha;}\end{array}\right.$

1 ', target is when specular reflection point place, then above-mentioned two conical surfaces have unique intersection, and this intersection is the equation of reflected signal place straight line;

2 ', target is not or not minute surface launching site place, and above-mentioned equation has two groups of solutions:

● remove fuzzy solution

Known receiver antenna and receiver direction of motion angle are γ, if receiver is constant in location moment direction of motion, direction of motion vector is: (v _x, v _y, v _z)

Obtain reflected signal place straight line by above-mentioned two conditions to be positioned at (v _x, v _y, v _z) for the straight line of direction vector be axle, on the circular conical surface being γ with bus and axis angle;

This circular conical surface can be asked, for:

$\frac{v_x(x-x_r)+v_y(y-y_r)+v_z(z-z_r)}{\sqrt{{v_x}^2+{v_y}^2+{v_z}^2}\&CenterDot;\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=\cos \mathrm{\&gamma;}$

Above formula is intersected with the conical surface obtained before the equation obtaining reflected signal place straight line

L _instead:

$\left\{\begin{array}{c}\frac{-(x-x_r)x_r-(y-y_r)y_r-(z-z_r)z_r}{\sqrt{x_r^2+y_r^2+z_r^2}\&CenterDot;\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=-\cos \mathrm{\&beta;}\\ \frac{(x-x_r)(x_r-x_t)+(y-y_r)(y_r-y_t)+(z-z_r)(z_r-z_t)}{\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}\&CenterDot;\sqrt{{(x_r-x_t)}^2+{(y_r-y_t)}^2+{(z_r-z_t)}^2}}=\cos \mathrm{\&alpha;}\\ \frac{v_x(x-x_r)+v_y(y-y_r)+v_z(z-z_r)}{\sqrt{{v_x}^2+{v_y}^2+{v_z}^2}\&CenterDot;\sqrt{{(x-x_r)}^2+{(y-y_r)}^2+{(z-z_r)}^2}}=\cos \mathrm{\&gamma;}\end{array}\right.;$

Step 5: extend to a N along the opposite direction propagated at the vector of reflected signal, makes receiver R to some N distance with reflected path apart from identical, and solves the coordinate of N;

Step 6: set the vector T N mid point of transmitter T to some N as M, ask M coordinate;

Step 7: cross the vertical line that M point makes TN on plane TRN, hand over RN vector in P point, P point and target work as moment position, calculation level P coordinate.

2. a kind of spaceborne passive radar localization method based on GNSS-R signal geometric relationship according to claim 1, it is characterized in that: " and solving the coordinate of N " described in step 5, its seat calibration method solving N is as follows: the path of reflected signal is D, by in step 2 2) draw

If N coordinate is (x _n, y _n, z _n), then have:

$\left\{\begin{array}{c}{(x_n-x_r)}^2+{(y_n-y_r)}^2+{(z_n-z_r)}^2=D^2\\ f(x_n,y_n,z_n)=0\end{array}\right.$

Wherein f (x, y, the z) equation that is reflected signal place straight line.

3. a kind of spaceborne passive radar localization method based on GNSS-R signal geometric relationship according to claim 1, it is characterized in that: " asking M coordinate " described in step 6, it asks the calculation procedure of M coordinate as follows:

Ask M coordinate:

If M coordinate is (x _m, y _m, z _m), then have:

$\left\{\begin{array}{c}{x}_m=\frac{x_t+x_n}{2}\\ y_m=\frac{y_t+y_n}{2}\\ z_m=\frac{z_t+z_n}{2}\end{array}\right.$

Wherein (x _t, y _t, z _t) be respectively the coordinate of three axis of transmitter T.

4. a kind of spaceborne passive radar localization method based on GNSS-R signal geometric relationship according to claim 1, it is characterized in that: " calculation level P coordinate " described in step 7, the computation process of its P coordinate is as follows:

If the coordinate of P is (x _p, y _p, z _p)

$\left\{\begin{array}{c}(x_p-x_m)m+(y_p-y_m)p+(z_p-z_m)q=0\\ f(x_p,y_p,z_p)=0\end{array}\right.$

In above formula, (m, p, q) is the direction vector of reflected signal place straight-line equation.