CN103576138A - Satellite-borne passive radar location method based on GNSS-R (global navigation satellite system-reflection) signal geometrical relationship - Google Patents

Abstract

A satellite-borne passive radar location method based on a GNSS-R (global navigation satellite system-reflection) signal geometrical relationship comprises steps as follows: step one, the moment when a receiver receives a direct signal of a GPS satellite is marked as t1, and the moment when the receiver receives a reflected signal to a target by a related GPRS satellite signal is marked as t2; step two, a direct path length L and a reflection path length D of the signal are calculated according to the arrival moment of the signal; step three, the position coordinate T ( xt, yt, zt) and the position coordinate R (xr, yr, zr) of a transmitter and the receiver are calculated; step four, the included angle alpha between the direct signal and the reflected signal is calculated, and the vector of the reflected signal is determined; step five, the vector of the reflected signal is lengthened to the point N in the transmission direction, so that the distance between R of the receiver and the point N is equal to the distance of the reflected signal path, and a coordinate of N is calculated; step six, a midpoint of a vector TN from T of the transmitter to the point N is set to be M, and a coordinate of M is calculated; and step seven, a TN vertical line passing the point M is drawn on a plane TRN, the vertical line intersects with a vector RN at the point P which is the position of the target at the moment, and a coordinate of the point P is calculated. According to the method, the calculation difficulty is reduced, the location efficiency is improved, and the location cost is reduced.

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, be particularly related to relevant to GLONASS (Global Navigation Satellite System) reflected signal (Global Navigation Satellite System Reflect signal with the geometric relationship of receiver, transmitter and target, 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 receiving 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 since nineteen forties is formally equipped, due to its have operating distance far away, round-the-clock, be subject to the advantages such as natural environment and climate variable effect is little and aspect target detection, location and tracking, bringing into play the irreplaceable vital role of other sensor.But to the modern times, generation and development along with radar electronic warfare technology such as electronic interferences, stealth technology, antiradiation missile attack and low latitude, ultra-low altitude penetrations, traditional radar system has been difficult to exploit one's power as before, and the existence of himself also become pressing problem, passive detection technology produces and grows up under this background.

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

Passive radar target localization algorithm based on GNSS-R is a kind of location technology of 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 increased system, expanded again the orientation range of passive radar, and can calculate according to the almanac data in navigation signal transmitter (gps satellite) and receiver (low orbit satellite, Low Earth Orbit, LEO) position, reduce the complicacy of location Calculation, conveniently reflected signal is carried out to geometric relationship modeling, realize optimization location, this is the characteristic that other signals do not have.

Development along with the technology such as passive radar remote sensing, detection and location based on GNSS-R signal, 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, the object technology based on differing from time of arrival etc.Localization method utilizes the delay inequality of reflected signal and direct signal to list Nonlinear System of Equations mostly at present, using the redundancy in system of equations is that linear equation calculates or positions according to the Doppler parameter of measuring by non-linear equation, this class localization method principle is simple, but because parameter is too much, increase the complicacy of location algorithm, introduced a large amount of measuring error simultaneously.Cell site by gps satellite as passive radar receiver, because itself has positioning function, thus 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, it becomes one of study hotspot of location algorithm.Its principle is after gps satellite and the spaceborne receiver location of LEO are determined, according to the relation receiving between reflected path and transceiver, calculates the algorithm of the relative position of target by solid geometry domain-specific knowledge.This algorithm is transformed into objective location the target localization of two-dimensional space, has simplified location Calculation difficulty, is conducive to real-time location.The shortcoming of utilizing reflected signal geometric relationship location is more responsive to measuring mistake, can, further by target correlation parameter is repeatedly measured, on fore-and-aft survey result, be averaged the impact that means such as removing error reduce error.Should take geometric relationship as basic passive radar localization method for to sea low target or sea-surface target location, make the positioning calculation difficulty of target greatly reduce, reduced calculated amount, thereby simplified apparatus obtains location efficiently by input still less.

(3) summary of the invention:

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

2, technical scheme: the present invention is characterized in: the problem of three-dimensional localization, by the conversion of geometric relationship, is become to the location of two dimensional surface, reduced operand, especially for the target of the low dry running in sea, saved the step of estimating its height.Because tradition is utilized geometric relationship localization method and is confined in region that reflected signal and direct signal surround, so location depends on the factors such as scanning angle that transmitter transmits, to the estimation of angle, cause evaluated error can cause the inaccurate of final positioning result, this is also that geometric relationship location is used for theoretical location, and the undesirable reason of actual location effect.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 1: the direct signal that receiver receives from gps satellite is t constantly ₁, in the ephemeris file in gps signal, comprise t launch time that transmits ₀, to receive relevant gps satellite signal be t to the reflected signal of target to receiver constantly in addition ₂.

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

1) direct projection path: 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 projection path, t ₂and t ₁time of reception for 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: calculate the angle α of direct signal and reflected signal, determine the vector of reflected signal

Calculate the angle α of direct projection path and reflected signal:

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

Negate and penetrate signal vector step:

1) reflected signal receiving antenna and receiver track section angle β ' are known.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 known its direction vector, obtains receiver section normal equation and 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 the conical surface of β as 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, the direction vector of crossing the bus of some M is

thereby 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:

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

5) calculate the equation of direct signal place straight line

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 and take TR straight line as axle, the conical surface that reflected ray is bus.

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

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

7) calculate reflected 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, and 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, and direction of motion is constant constantly in location to establish receiver, and direction of motion vector is: (v _x, v _y, v _z)

By above-mentioned two conditions, can obtain reflected signal place straight line is positioned at (v _x, v _y, v _z) for the straight line of direction vector is axle, take on the circular conical surface that bus and axis angle be γ.

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 to the equation that can obtain reflected signal place straight line with the conical surface obtaining before

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

Solve the coordinate of N:

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

If N coordinate is (x _n, y _n, z _n), 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: establishing transmitter T is M to the vector T N mid point of putting N, asks M coordinate.

Ask the calculation procedure of M coordinate as follows:

Ask M coordinate:

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

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

X wherein _t, y _tand z _tbe respectively three axial coordinates of transmitter T.

Step 7: at plane TRN(by transmitter T, the plane that receiver R and some N form) go up the vertical line that M point is made TN, hand over RN vector in P point, P point is that target is worked 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 and the sea low target localization method based on GNSS-R signal geometric relationship that the present invention proposes, not only omitted for sea low target high computational and obtained step, simplify difficulty in computation, improve location efficiency, and take full advantage of transmitter, receiver and reflected signal three's angular relationship, the geometric relationships such as distance relation, use simple and clear solid geometry theorem to realize the efficient location in space, this method is unrestricted to transmitter quantity simultaneously, can use single star location, also can use multiple satellite location, positioning difficulty and cost have been reduced.Therefore the target localization of the GNSS-R reflected signal that, the present invention is applicable to utilize 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. taking full advantage of the geometric relationships such as position relationship between reflected signal, receiver, transmitter, angular relationship, use 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, has omitted the calculating to its height especially for coastal waters low target, has therefore improved the efficiency of location.

3. the location that three-dimensional localization is converted to two dimensional surface is sterically defined innovation, is also sterically defined trend, and this method has been avoided the conversion of traditional algorithm to Nonlinear System of Equations, has reduced clearing difficulty.

4. this algorithm does not have mandatory requirement to transmitter number, both can have and can be used as multiple satellite location (a plurality of transmitters of receiver) for single star location (transmitter of a receiver), has reduced 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, the vector at reflected signal place is l _instead, direct projection path is L, reflection paths length is D.By l _insteadthe opposite direction of propagating along reflected signal extends to N, makes RN=D, connects TN, gets TN mid point M.Cross some M and make straight line perpendicular to TN, hand over RN in P.

Solve: P point is target place.

Proof: establish target and be positioned at a Q, P ≠ Q

By the known target that obtains, be positioned at vectorial l _insteadupper, there is TQ+RQ=D

∵ RN=RQ+QN=D again

∴TQ＝QN

Connect QM, have QM ⊥ TN

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

∴QM≠PM

This hypothesis has been violated axiom: cross in plane and a bit have and only have straight line perpendicular to known straight line.

Therefore supposing is false.

Be P=Q, P is target place.

(4) accompanying drawing explanation

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

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

(5) embodiment

See Fig. 1, 2, under WGS-84 coordinate system, Yi meter Wei unit, making receiver R coordinate is (4069896,-3583236, 4527639), transmitter T coordinate is (11178791,-13160191, 20341528), recording reflected signal and direct signal angle is arccos (0.4778), with receiver velocity reversal angle be arccos (0.1394), the normal vector angle of reflected signal and motion tangent plane is that 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 1: the direct signal that receiver receives from gps satellite is t constantly ₁, in the ephemeris file in gps signal, comprise t launch time that transmits ₀, to receive relevant gps satellite signal be t to the reflected signal of target to receiver constantly in addition ₂.

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

Computation process is as follows:

1) direct projection path: 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, direct projection path is: 19807411.2517858m

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

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

τ ₂=t ₂-t ₁=0.0063251s, 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: calculate the angle α of direct signal and reflected signal, determine the vector of reflected signal

Calculate the angle α of direct projection path and reflected signal:

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

Negate and penetrate signal vector step:

1) reflected signal receiving antenna and receiver track section angle β ' are known.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 in this example (0.5881), γ=arccos (0.1394)

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 known its direction vector, obtains receiver section normal equation and 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 the conical surface of β as 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, the direction vector of crossing the bus of some M is

thereby 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:

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

Bringing 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) calculate the equation of direct signal place straight line

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

By transmitter T, to the direction vector of the ray TR of 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 determine is:

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

In this example, have:

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

Abbreviation obtains:

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

5) calculate and take TR ray as axle, the conical surface that reflected signal ray is bus.

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

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

In this example, have:

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

6) calculate reflected 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, and 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, and direction of motion is constant constantly in location to establish receiver, and direction of motion vector is: (v _x, v _y, v _z), by known (4738 ,-1796 ,-5654), by above-mentioned two conditions, can obtain reflected signal place straight line and be positioned at (v _x, v _y, v _z) for the straight line of direction vector is axle, take on the circular conical surface that bus and axis angle be γ.

This circular conical surface can be asked, for:

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

In this example, have:

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

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

Bringing receiver coordinate, receiver velocity and angular relationship into above-mentioned equation obtains:

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

Step 5: the vector at reflected signal extends to a N along the opposite direction of propagating, makes receiver R identical with reflected path distance to some N distance, solves the coordinate of N.

Solve the coordinate of N:

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

If N coordinate is (x _n, y _n, z _n), 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.

Known receiver coordinate and the reflected signal straight-line equation obtained are brought into and can be tried to achieve the accurate coordinates that N is ordered.

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), have:

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

X wherein _t, y _tand z _tbe respectively three axial coordinates of transmitter T.

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

Step 7: cross the vertical line that M point is made the line segment TN that transmitter T forms with some N on the plane TRN forming at transmitter T, receiver R and some N, hand over RN(receiver R to be formed by connecting with some N) vector is in P point, and P point is that target is worked as 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 just completed once concrete position fixing process.

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 same direct signal of reflected signal, receiver direction of motion and receiver motion section normal is simplified calculating, use on the other hand solid geometry correlation theorem, save the estimation to object height, avoided object height to estimate the error causing.In addition because the present invention can realize single star location,, to the not restriction of gps satellite number, greatly reduced location cost, convenient popularization.In the situation that visible star surpasses one, can further use different receiver transmitter integrated positionings, realize positioning precision and further optimize, improve efficiency and the reliability of positioning system.

Claims (4)

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

Step 1: the direct signal that receiver receives from gps satellite is t constantly ₁, in the ephemeris file in gps signal, comprise t launch time that transmits ₀, to receive relevant gps satellite signal be t to the reflected signal of target to receiver constantly in addition ₂;

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

1) direct projection path: 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 projection path, t ₂and t ₁time of reception for 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: calculate the angle α of direct signal and reflected signal, determine the vector of reflected signal;

Calculate the angle α of direct projection path and reflected signal:

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

Negating, it is as follows to penetrate the step of signal vector:

1) reflected signal receiving antenna and receiver track section angle β ' are known, 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: $\stackrel{\&RightArrow;}{n}=\stackrel{\&RightArrow;}{\mathrm{RO}}=(-x_r,{-y}_r,-z_r);$

3) normal passes through some R and known its direction vector, obtains receiver section normal equation and 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, the conical surface that the β of take is 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, the direction vector of crossing the bus of some M is

thereby have: $\frac{\stackrel{\&RightArrow;}{v_1}\&CenterDot;\stackrel{\&RightArrow;}{v_2}}{\left|\stackrel{\&RightArrow;}{v_1}\right|\&CenterDot;\left|\stackrel{\&RightArrow;}{v_2}\right|}=-\cos \mathrm{\&beta;}$

By vector

with

substitution above formula obtains conical surface equation:

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

5) calculate the equation of direct signal place straight line:

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:

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

6) calculate and take TR straight line as axle, the conical surface that reflected ray is bus:

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

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

;

7) calculate reflected 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, and 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, and direction of motion is constant constantly in location to establish receiver, and direction of motion vector is: (v _x, v _y, v _z)

By above-mentioned two conditions, obtaining reflected signal place straight line is positioned at (v _x, v _y, v _z) for the straight line of direction vector is axle,

Take on the circular conical surface that bus and axis angle be γ;

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 to the equation that obtains reflected signal place straight line with the conical surface obtaining before

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

Step 6: establishing transmitter T is M to the vector T N mid point of putting N, asks M coordinate;

Step 7: cross the vertical line that M point is made TN on plane TRN, hand over RN vector in P point, P point is that target is when 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 solve N coordinate " described in step 5, its seat calibration method that solves N is as follows: the path of reflected signal is D, in step 2 2) draw

If N coordinate is (x _n, y _r, 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) is the equation of 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, 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, have:

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

X wherein _t, y _tbe respectively three axial coordinates of transmitter T.

4. a kind of spaceborne passive radar localization method based on GNSS-R signal geometric relationship according to claim 1, is characterized in that: at " 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 _t

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

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

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