CN100578144C - Method for checking train integrity based on GPS and dummy satellite combined positioning - Google Patents

Abstract

The invention belongs to the vehicle positioning technical field, in particular relates to a method for positioning and examining integrity of trains on the basis of combining GPS and virtual satellite. Under the condition that satellite signal which is received by GPS receiver on the rear portion of a train is incomplete, namely when the number of the satellite is three, longitude, latitude and altitude information which are output by the GPS receiver on the upper part of engines of the head portion of the train are used to provide the virtual satellite for positioning the rear portion of the train, and a fourth constraining equation is established to realize positioning resolve of the rear portion of the train. The invention can still examine the integrity of trains under the condition that the satellite signal which is received by the GPS receiver on the rear portion of the train is incomplete, which guarantees driving safety of the train.

Description

Method based on GPS and virtual satellite integrated positioning inspection integrity of train

Technical field

The invention belongs to the vehicle positioning technology field, particularly a kind of method based on GPS and virtual satellite integrated positioning inspection integrity of train.

Background technology

Because railway car interconnects by hook and forms,, guarantee the complete of train and inspection that carry out is called the integrity of train inspection for guaranteeing that train does not derail, do not break off relations.The integrity of train inspection is a key link that is related to railway system's security, if the integrity of train inspection was lost efficacy, is retained in the barrier that vehicle on interval or the station track will become follow-up train, directly jeopardizes traffic safety.

At present, Chang Yong integrity of train inspection method is a kind of is that last vehicle of train is installed safety device (abbreviation train ' s tail device).Train ' s tail device communicates by the locomotive vehicle-mounted device of the locomotive station in the train radio dispatching system and this train.Locomotive station and train ' s tail device main frame constitute " one to one " relation by wireless encoding, in case this signal interruption can think that then integrity of train goes wrong, but this method is faced with many-sided problems such as management, scheduling, maintenance, owner.Another kind method is a train ' s tail device energy real-time inspection last vehicle of train airduct blast, and feed back to the locomotive vehicle-mounted device with what blast information was not stopped, realize undervoltage warning, the prompting driver takes emergency measures such as brake hard, can effectively prevent to be in operation train angle cock is closed, airduct fractures, airduct leaks out or accident such as train separation takes place.When the train separation, airduct disconnects and leaking out, and when leakage rate surpassed setting, train ' s tail device can in time send caution to the locomotive steward, reminds the locomotive steward to note train operation state.But in use also there are some problems in train ' s tail device, and as: the train ' s tail device strong sections of feeble field such as tunnel or tunnel group of growing up at some, the trunking traffic function that train dispatch radio communication possessed can not normally be used; Existing or newly-increased train dispatch radio communication does not have the spare interface of train ' s tail device driver control enclosure, gives to install and use brings difficulty; The frequency of utilization of train dispatch radio communication is improper, causes mutual interference mutually between train ' s tail device main frame and train dispatch radio communication in the hinge, influences setting out of train; Train ' s tail device is not enough to the enquiry frequency of blast, had plenty of one minute in addition a few minutes inquiries once, the real-time of integrity checking is too poor like this.

GPS (Global Positioning System) is GPS, and it is to utilize Aerospace Satellite to finish the system of radiolocation as guidance station.Each satellite continuously sends traceable unique coded sequence to the GPS receiver, the GPS receiver can be according to coding identification related satellite, and then calculate the definite position and the correct time of receiver, wherein the pseudorange method is the basic skills of GPS navigation location.

In recent years, satellite positioning tech is used and is obtained development at full speed, satnav is widely used in aviation, space delivery guiding, navigation and land, wherein the applied research on land is mainly in fields such as urban transportation, special vehicle such as police car, armoured van management and dispatchings, and less research in railway applications.

How satellite positioning tech is incorporated into the integrity of train inspection and does not also have theory and technology maturely, can not replace train ' s tail device at present in actual applications fully and independently carry out the integrity of train inspection, but can assist or in conjunction with present train ' s tail device, by comparing and fusion, constitute the integrity of train check system of a redundancy with train ' s tail device information.Qinghai-Tibet Railway is realized with train ' s tail device for the integrity of train inspection, and can be implemented uninterrupted the inspection in conjunction with the other device of rail or by mobile unit to the integrality of train in the overall process of train operation.Based on the integrity of train check system of satnav by train head and last vehicle of train real-time positioning measuring and calculating vehicle commander are realized, if the visible aerial scope of last vehicle of train GPS receiver be obstructed (blocking) in the process of train driving as the compartment, four of the visible satellite number deficiency that last vehicle of train receives, conventional satellite positioning method is restricted.

Summary of the invention

The GPS receiver that is installed in train head and last vehicle of train in the prior art is to train head and last vehicle of train real-time positioning, calculates in real time according to positional information then that the vehicle commander realizes, when finding that train has the spiral seed separator phenomenon, sends warning message immediately.But in practical operation situation, because blocking of last vehicle of train compartment, last vehicle of train GPS receiver only can receive three visible satellite signals, therefore conventional satellite positioning method is restricted, and the present invention has proposed a kind of method based on GPS and virtual satellite integrated positioning inspection integrity of train especially.

Technical scheme of the present invention is as follows:

Train is in the process of travelling, and the continual receiving satellite signal of GPS receiver that is installed in train head and last vehicle of train positions and resolves, in real time longitude, latitude and the elevation information of output train head and last vehicle of train.If certain moment last vehicle of train GPS receiver is owing to the signal that has received only three visible satellites that blocks in compartment, ultimate principle according to the gps satellite location, this moment, the receiver of last vehicle of train did not receive enough number of satellite, in real time the positional information of output train afterbody.Utilize this moment longitude, latitude and the elevation information of train head GPS receiver output to provide an imaginary satellite for the last vehicle of train location, i.e. virtual satellite, and set up the 4th equation of constraint, can realize the positioning calculation of last vehicle of train.At last train head and last vehicle of train coordinate projection are arrived Gaussian plane, calculate train length in real time, finish the integrity of train inspection.

Stipulate according to China railways line standard, in the difficult location of III level railway, track grade be restricted to 20/1000ths, calculate by 300 meters train lengths, the train head and the last vehicle of train discrepancy in elevation also only are 0.9 meter, and the elevation of thinking that can be similar to also is to differ 0.9 meter.Simultaneously, travel by the train North and South direction, this moment, latitude differed maximum, was α=D/r, and wherein D is a train length, and r is earth mean radius (6371.03km).Calculate by 300 meters train lengths, latitude differs 4.71 * 10 ^-5Radian.The radius of curvature in prime vertical of this moment $N_P=\frac{a}{\sqrt{1-{\left(e\sin B_P\right)}^2}}$ Only differ 4.73 * 10 ^-5Rice.Therefore by utilizing the train header information to determine virtual satellite, the train head to the geometric distance S of virtual satellite be used as last vehicle of train to virtual satellite apart from ρ ₄Be rationally available.

The specific implementation step of the real-time integrity checking of train is as follows:

Step 1 is set up the 4th equation of constraint,

Above the locomotive of train head, set up a virtual satellite along the extended line of ellipsoid normal and the intersection point place of Z axle at P ', the three-dimensional coordinate of this satellite be (0,0, z _c), virtual satellite is to the pseudorange ρ of last vehicle of train ₄Represent to the geometric distance S above the locomotive of train head with it, i.e. ρ ₄=S; Wherein: S=N _P+ H _P, N _pBe the radius of curvature in prime vertical of train head, H _pBe the elevation of train head, then the 4th equation of constraint is

${\mathrm{\ρ}}_4=\sqrt{{(x_4-x_u)}^2+{(y_4-y_u)}^2+{(z_4-z_u)}^2},$

Wherein: x ₄=0, y ₄=0, z ₄=z _cBe the three-dimensional coordinate of virtual satellite, (x _u, y _u, z _u) be the last vehicle of train coordinate that will find the solution;

Step 2 is set up observation equation, finds the solution the last vehicle of train coordinate,

Three visible satellite signals that the last vehicle of train receiver receives obtain three equation of constraint:

${\mathrm{\ρ}}_1=\sqrt{{(x_1-x_u)}^2+{(y_1-y_u)}^2+{(z_1-z_u)}^2}+\mathrm{c\δ}{t}_u$ ... ... ... ... ... ... ... ... 3 formulas

${\mathrm{\ρ}}_2=\sqrt{{(x_2-x_u)}^2+{(y_2-y_u)}^2+{(z_2-z_u)}^2}+\mathrm{c\δ}{t}_u$ ... ... ... ... ... ... ... 4 formulas

${\mathrm{\ρ}}_3=\sqrt{{(x_3-x_u)}^2+{(y_3-y_u)}^2+{(z_3-z_u)}^2}+\mathrm{c\δ}{t}_u$ ... ... ... ... ... ... ... the ..5 formula

(x wherein _i, y _i, z _j) and ρ _jBe respectively the three-dimensional coordinate of visible satellite and visible satellite pseudorange to last vehicle of train, j=1,2,3; δ t _uBe the skew between GPS receiver clock and the system clock;

Above-mentioned four equations of simultaneous obtain following Nonlinear System of Equations:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_1=\sqrt{{(x_1-x_u)}^2+{(y_1-y_u)}^2+{(z_1-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_2=\sqrt{{(x_2-x_u)}^2+{(y_2-y_u)}^2+{(z_2-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_3=\sqrt{{(x_3-x_u)}^2+{(y_3-y_u)}^2+{(z_3-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_4=\sqrt{{(x_4-x_u)}^2+{(y_4-y_u)}^2+{(z_4-z_u)}^2}\end{array}\right.$ 6 formulas

At above-mentioned the 4th equation of constraint ρ _j=ρ ₄, j=4;

Above-mentioned Nonlinear System of Equations is carried out linearization process

Suppose With

Be respectively (x _u, y _u, z _u) and δ t _uEstimated value, (Δ x _u, Δ y _u, Δ z _u) and Δ t _uBe respectively (x _u, y _u, z _u) and δ t _uThe side-play amount of estimated value, order:

${\mathrm{\ρ}}_j=\sqrt{{(x_j-x_u)}^2+{(y_j-y_u)}^2+{(z_j-z_u)}^2}+\mathrm{c\δ}{t}_u=f_j(x_u,y_u,z_u,{\mathrm{\δt}}_u)$ 7 formulas

${\widehat{\mathrm{\ρ}}}_j=\sqrt{{(x_j-{\hat{x}}_u)}^2+{(y_j-{\hat{y}}_u)}^2+{(z_j-{\hat{z}}_u)}^2}+\mathrm{c\δ}{\hat{t}}_u=f_j({\hat{x}}_u,{\hat{y}}_u,{\hat{z}}_u,\mathrm{\δ}{\hat{t}}_u)$ 8 formulas

Promptly have:

$f_j(x_u,y_u,z_u,\mathrm{\δ}{t}_u)=f_j({\hat{x}}_u+\mathrm{\Δ}{x}_u,{\hat{y}}_u+\mathrm{\Δ}{y}_u,{\hat{z}}_u+\mathrm{\Δ}{z}_u,\mathrm{\δ}{\hat{t}}_u+\mathrm{\Δ}{t}_u)$ 9 formulas

Use Taylor series at some the relational expression on 9 formula equal signs the right

Expansion is also ignored high-order term, and with 7 formulas, 8 formula substitution fundamental equations, 9 formulas, obtain linear relation through arrangement:

${\mathrm{\ρ}}_j={\widehat{\mathrm{\ρ}}}_j-\frac{x_j-{\hat{x}}_u}{{\hat{r}}_j}\mathrm{\Δ}{x}_u-\frac{y_j-{\hat{y}}_u}{{\hat{r}}_j}\mathrm{\Δ}{y}_u-\frac{z_j-{\hat{z}}_u}{{\hat{r}}_j}\mathrm{\Δ}{z}_u+\mathrm{c\Δ}{t}_u$ 10 formulas

Wherein ${\hat{r}}_j=\sqrt{{(x_j-{\hat{x}}_u)}^2+{(y_j-{\hat{y}}_u)}^2+{(z_j-{\hat{z}}_u)}^2}$

Introduce following new variables to simplify 10 formulas:

$\left.\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_j={\widehat{\mathrm{\ρ}}}_j-{\mathrm{\ρ}}_j\\ a_{\mathrm{xj}}=\frac{x_j-{\hat{x}}_u}{{\hat{r}}_j}\\ a_{\mathrm{yj}}=\frac{y_j-{\hat{y}}_u}{{\hat{r}}_j}\\ a_{\mathrm{zj}}=\frac{z_j-{\hat{z}}_u}{{\hat{r}}_j}\end{array}\right\}$ 11 formulas

Obtain following system of equations by above-mentioned linearization:

$\left\{\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_1=a_{x1}\mathrm{\Δ}{x}_u+a_{y1}\mathrm{\Δ}{y}_u+a_{z1}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_2=a_{x2}\mathrm{\Δ}{x}_u+a_{y2}\mathrm{\Δ}{y}_u+a_{z2}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_3=a_{x3}\mathrm{\Δ}{x}_u+a_{y3}\mathrm{\Δ}{y}_u+a_{z3}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_4=a_{x4}\mathrm{\Δ}{x}_u+a_{y4}\mathrm{\Δ}{y}_u+a_{z4}\mathrm{\Δ}{z}_u\end{array}\right.$ 12 formulas

Write as matrix form:

Δ ρ=H Δ x ... 13 formulas

Wherein:

$\mathrm{\Δ\ρ}=\left[\begin{array}{c}{\mathrm{\Δ\ρ}}_1\\ {\mathrm{\Δ\ρ}}_2\\ {\mathrm{\Δ\ρ}}_3\\ {\mathrm{\Δ\ρ}}_4\end{array}\right],$ $H=\left[\begin{array}{cccc}{a}_{x1}& a_{y1}& a_{z1}& 1\\ a_{x2}& a_{y2}& a_{z2}& 1\\ a_{x3}& a_{y3}& a_{z3}& 1\\ a_{x4}& a_{y4}& a_{z4}& 0\end{array}\right],$

It is separated and is Δ X=H ^-1Δ ρ

Then the last vehicle of train position coordinates is $\left\{\begin{array}{c}{x}_u={\hat{x}}_u+\mathrm{\Δ}{x}_u\\ y_u={\hat{y}}_u+\mathrm{\Δ}{y}_u\\ z_u={\hat{z}}_u+\mathrm{\Δ}{z}_u\end{array}\right.,$ And $\mathrm{\δ}{t}_u=\mathrm{\δ}{\hat{t}}_u+\mathrm{\Δ}{t}_u$

Step 3 is calculated train length, judges whether train is complete, finishes the integrity of train inspection and can calculate the three-dimensional coordinate of last vehicle of train according to above algorithm, then headstock coordinate and last vehicle of train coordinate projection is arrived Gaussian plane, calculates train length in real time $L=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}.$ Wherein: (x ₁, y ₁) be the headstock planimetric coordinates, (x ₂, y ₂) be the last vehicle of train planimetric coordinates.By comparing, then realize the real-time integrity checking of train with the train physical length.

The invention has the beneficial effects as follows: when last vehicle of train GPS receiver only can receive three visible satellite signals, the latitude, longitude and the elevation information that provide by the train head, increase the 4th equation of constraint and still can realize the location, overcome deficiency of the prior art, still can carry out the integrity of train inspection, guarantee the traffic safety of train.

Description of drawings

Fig. 1 is a train integrity checking system construction drawing under the incomplete condition of GPS.

Fig. 2 is that GPS and virtual satellite integrated positioning are checked the integrity of train program flow diagram.

Fig. 3 determines the virtual satellite position view by the train head position under the meridian ellipse rectangular coordinate system.

Embodiment

Below by the drawings and specific embodiments the present invention is described in further detail.

Referring to accompanying drawing 1, train is in the process of travelling, by the train information transmission system longitude, latitude and the elevation information of the output of train head receiver are sent to last vehicle of train equipment, under the situation of known train head and last vehicle of train three-dimensional coordinate, realize the integrity of train inspection by real-time measuring and calculating vehicle commander, when finding that train has the spiral seed separator phenomenon, send warning message immediately.But owing to blocking of compartment, last vehicle of train GPS receiver only can receive three visible satellite signals, and conventional satellite positioning method is restricted.

By following embodiment, the present invention will be further described in conjunction with Fig. 2, Fig. 3.

Embodiment:

1, gathers ephemeris, the pseudo range data of satellites in view, receive headstock information (as shown in Figure 3), gather pseudorange, the almanac data of satellites in view with the GPS receiver, receive longitude, latitude and the elevation information of train head receiver output by the train information transmission system.

2, calculate the satellites in view coordinate;

3, co-ordinates of satellite and pseudorange are carried out error correction

The present invention considers practicality, and co-ordinates of satellite and pseudorange error have been carried out earth rotation effect error correction, satellite-signal x time error correction and relativity error correction.

4, set up virtual satellite by headstock information

Shown in Figure 2, the space terrestrial coordinate depends on reference ellipsoid.For setting up the mathematical relation of terrestrial coordinate and rectangular coordinate, must at first define reference ellipsoid.Set up meridian ellipse rectangular coordinate system XOZ.Because reference ellipsoid is rotational symmetric, so only need in the XOZ plane right-angle coordinate, to consider as two-dimensional problems.

P ' is the position of train head;

The P point is P ' some intersection point that measures ellipsoid along the ellipsoid normal;

H _pMeasure the distance of ellipsoid for P ' along the ellipsoid normal, be called the ellipsoid elevation, abbreviate geodetic height as;

The W point was the center of curvature of the P prime vertical of ordering, and was positioned on the turning axle of ellipsoid, and promptly P ' along the extended line of ellipsoid normal and the intersection point of Z axle;

N _pFor crossing the radius of curvature in prime vertical that P is ordered, equal the length of normal between ellipsoid and minor axis, i.e. the P point distance of ordering to W.

Set up a virtual satellite at the W point, and convert the terrestrial coordinate of current train head longitude, latitude and elevation to the WGS-84 rectangular space coordinate:

$\left\{\begin{array}{c}x=(N_p+H_p)\cos B\·\cos L\\ y=(N_p+H_p)\cos B\·\sin L\\ z=[N_p(1-e^2)+H_p]\sin B\end{array}\right.$ 1 formula

By the radius of curvature in prime vertical formula $N_P=\frac{a}{\sqrt{1-{\left(e\sin B_P\right)}^2}}$ Can try to achieve virtual satellite to the geometric distance of train head is: S=N _P+ H _P, wherein a is the major semi-axis of earth reference ellipsoid, e is an earth reference ellipsoid excentricity.

By the range formula between 2 o'clock $S=\sqrt{{(x-x_4)}^2+{(y-y_4)}^2+{(z-z_4)}^2}$ The three-dimensional coordinate of solving virtual satellite, wherein x ₄=0, y ₄=0, z ₄=z _cThree-dimensional coordinate for virtual satellite.

5, set up the 4th equation of constraint

Obtain finding the solution the 4th equation of constraint of last vehicle of train real time position by virtual satellite:

${\mathrm{\ρ}}_4=\sqrt{{(x_4-x_u)}^2+{(y_4-y_u)}^2+{(z_4-z_u)}^2}$ 2 formulas

(x wherein _u, y _u, z _u) be the last vehicle of train coordinate that will find the solution.

6, set up observation equation, find the solution the last vehicle of train coordinate

The last vehicle of train receiver receives the information of three visible satellites, obtains three equation of constraint to be:

${\mathrm{\ρ}}_1=\sqrt{{(x_1-x_u)}^2+{(y_1-y_u)}^2+{(z_1-z_u)}^2}+\mathrm{c\δ}{t}_u$ 3 formulas

${\mathrm{\ρ}}_2=\sqrt{{(x_2-x_u)}^2+{(y_2-y_u)}^2+{(z_2-z_u)}^2}+\mathrm{c\δ}{t}_u$ 4 formulas

${\mathrm{\ρ}}_3=\sqrt{{(x_3-x_u)}^2+{(y_3-y_u)}^2+{(z_3-z_u)}^2}+\mathrm{c\δ}{t}_u$ 5 formulas

X wherein _j, y _j,, z _j, ρ _j, j=1,2,3rd, the three-dimensional coordinate of visible satellite and pseudorange, (x _u, y _u, z _u) be the last vehicle of train coordinate, δ t _uSkew between during for receiver clock and system.

Above-mentioned four equations of simultaneous obtain following Nonlinear System of Equations:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_1=\sqrt{{(x_1-x_u)}^2+{(y_1-y_u)}^2+{(z_1-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_2=\sqrt{{(x_2-x_u)}^2+{(y_2-y_u)}^2+{(z_2-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_3=\sqrt{{(x_3-x_u)}^2+{(y_3-y_u)}^2+{(z_3-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_4=\sqrt{{(x_4-x_u)}^2+{(y_4-y_u)}^2+{(z_4-z_u)}^2}\end{array}\right.$ 6 formulas

At above-mentioned the 4th equation of constraint ρ _j=ρ ₄, j=4;

Above-mentioned Nonlinear System of Equations is carried out linearization process

At first suppose

With

Be respectively (x _u, y _u, z _u) and δ t _uEstimated value, (Δ x _u, Δ y _u, Δ z _u) and Δ t _uBe respectively (x _u, y _u, z _u) and δ t _uThe side-play amount of estimated value, order:

${\mathrm{\ρ}}_j=\sqrt{{(x_j-x_u)}^2+{(y_j-y_u)}^2+{(z_j-z_u)}^2}+\mathrm{c\δ}{t}_u=f_j(x_u,y_u,z_u,{\mathrm{\δt}}_u)$ 7 formulas

${\widehat{\mathrm{\ρ}}}_j=\sqrt{{(x_j-{\hat{x}}_u)}^2+{(y_j-{\hat{y}}_u)}^2+{(z_j-{\hat{z}}_u)}^2}+\mathrm{c\δ}{\hat{t}}_u=f_j({\hat{x}}_u,{\hat{y}}_u,{\hat{z}}_u,\mathrm{\δ}{\hat{t}}_u)$ 8 formulas

Promptly have:

$f_j(x_u,y_u,z_u,\mathrm{\δ}{t}_u)=f_j({\hat{x}}_u+\mathrm{\Δ}{x}_u,{\hat{y}}_u+\mathrm{\Δ}{y}_u,{\hat{z}}_u+\mathrm{\Δ}{z}_u,\mathrm{\δ}{\hat{t}}_u+\mathrm{\Δ}{t}_u)$ 9 formulas

Use Taylor series at some the relational expression on 9 formula equal signs the right

Expansion is also ignored high-order term, and 7 formulas, 8 formula substitution fundamental equations are obtained linear relation through arrangement:

${\mathrm{\ρ}}_j={\widehat{\mathrm{\ρ}}}_j-\frac{x_j-{\hat{x}}_u}{{\hat{r}}_j}\mathrm{\Δ}{x}_u-\frac{y_j-{\hat{y}}_u}{{\hat{r}}_j}\mathrm{\Δ}{y}_u-\frac{z_j-{\hat{z}}_u}{{\hat{r}}_j}\mathrm{\Δ}{z}_u+\mathrm{c\Δ}{t}_u$ 10 formulas

Wherein ${\hat{r}}_j=\sqrt{{(x_j-{\hat{x}}_u)}^2+{(y_j-{\hat{y}}_u)}^2+{(z_j-{\hat{z}}_u)}^2}$

Introduce following new variables to simplify 10 formulas:

$\left.\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_j={\widehat{\mathrm{\ρ}}}_j-{\mathrm{\ρ}}_j\\ a_{\mathrm{xj}}=\frac{x_j-{\hat{x}}_u}{{\hat{r}}_j}\\ a_{\mathrm{yj}}=\frac{y_j-{\hat{y}}_u}{{\hat{r}}_j}\\ a_{\mathrm{zj}}=\frac{z_j-{\hat{z}}_u}{{\hat{r}}_j}\end{array}\right\}$ 11 formulas

Obtain following system of equations by above-mentioned linearization:

$\left\{\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_1=a_{x1}\mathrm{\Δ}{x}_u+a_{y1}\mathrm{\Δ}{y}_u+a_{z1}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_2=a_{x2}\mathrm{\Δ}{x}_u+a_{y2}\mathrm{\Δ}{y}_u+a_{z2}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_3=a_{x3}\mathrm{\Δ}{x}_u+a_{y3}\mathrm{\Δ}{y}_u+a_{z3}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_4=a_{x4}\mathrm{\Δ}{x}_u+a_{y4}\mathrm{\Δ}{y}_u+a_{z4}\mathrm{\Δ}{z}_u\end{array}\right.$ 12 formulas

Write as matrix form: Δ ρ=H Δ x ... 13 formulas

Wherein:

$\mathrm{\Δ\ρ}=\left[\begin{array}{c}{\mathrm{\Δ\ρ}}_1\\ {\mathrm{\Δ\ρ}}_2\\ {\mathrm{\Δ\ρ}}_3\\ {\mathrm{\Δ\ρ}}_4\end{array}\right],$ $H=\left[\begin{array}{cccc}{a}_{x1}& a_{y1}& a_{z1}& 1\\ a_{x2}& a_{y2}& a_{z2}& 1\\ a_{x3}& a_{y3}& a_{z3}& 1\\ a_{x4}& a_{y4}& a_{z4}& 0\end{array}\right],$ $\mathrm{\ΔX}=\left[\begin{array}{c}\mathrm{\Δ}{x}_u\\ \mathrm{\Δ}{y}_u\\ \mathrm{\Δ}{z}_u\\ -\mathrm{c\Δ}{t}_u\end{array}\right]$

It is separated and is Δ X=H ^-1Δ ρ

Then the last vehicle of train position coordinates is $\left\{\begin{array}{c}{x}_u={\hat{x}}_u+\mathrm{\Δ}{x}_u\\ y_u={\hat{y}}_u+\mathrm{\Δ}{y}_u\\ z_u={\hat{z}}_u+\mathrm{\Δ}{z}_u\end{array}\right.,$ And $\mathrm{\δ}{t}_u=\mathrm{\δ}{\hat{t}}_u+\mathrm{\Δ}{t}_u$

If skew has surpassed acceptable value, just iteration said process, i.e. point coordinate (x again to calculate _u, y _u, z _u) and δ t _uAs new estimated value, to replace

7, calculate train length, judge that whether train is complete, finishes the integrity of train inspection

Can calculate the three-dimensional coordinate of last vehicle of train according to above algorithm, then headstock coordinate and last vehicle of train coordinate projection to Gaussian plane, calculate train length in real time $L=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}.$ Wherein: (x ₁, y ₁) be the headstock planimetric coordinates, (x ₂, y ₂) be last vehicle of train planimetric coordinates (as shown in Figure 2).

Claims (1)

1. method of checking integrity of train based on GPS and virtual satellite integrated positioning, train places 2 GPS receivers respectively above the hitch of the locomotive top of train head and last vehicle of train, the GPS of last vehicle of train receiver it is characterized in that: when can only receive 3 visible satellite signals, utilize the longitude of the GPS receiver output of train head locomotive top, latitude and elevation information provide a virtual satellite for the last vehicle of train location, set up the 4th equation of constraint, and three equation of constraint obtaining of 3 visible satellite signals receiving of simultaneous last vehicle of train GPS receiver, thereby draw the last vehicle of train three-dimensional coordinate, realization last vehicle of train location specifically comprises the steps:

Step 1 for setting up the 4th equation of constraint, is set up a virtual satellite along the extended line of ellipsoid normal and the intersection point place of Z axle at P ' above the locomotive of train head, the three-dimensional coordinate of this virtual satellite be (0,0, z _c), virtual satellite is to the pseudorange ρ of last vehicle of train ₄Represent to the geometric distance S above the locomotive of train head with it, i.e. ρ ₄=S; Wherein: S=N _P+ H _P, N _pBe the radius of curvature in prime vertical of train head, H _pBe the elevation of train head, then the 4th equation of constraint is ${\mathrm{\ρ}}_4=\sqrt{{(x_4-x_u)}^2+{(y_4-y_u)}^2+{(z_4-z_u)}^2},$

Wherein: x ₄=0, y ₄=0, z ₄=z _cBe the three-dimensional coordinate of virtual satellite, (x _u, y _u, z _u) be the last vehicle of train coordinate that will find the solution;

Step 2,

Set up observation equation, find the solution the last vehicle of train coordinate, three visible satellite signals that last vehicle of train GPS receiver receives obtain three equation of constraint and are:

${\mathrm{\ρ}}_1=\sqrt{{(x_1-x_u)}^2+{(y_1-y_u)}^2+{(z_1-z_u)}^2}+\mathrm{c\δ}{t}_u$ ... ... ... ... ... ... the ..3 formula

${\mathrm{\ρ}}_2=\sqrt{{(x_2-x_u)}^2+{(y_2-y_u)}^2+{(z_2-z_u)}^2}+\mathrm{c\δ}{t}_u$ ... ... ... ... ... ... the ..4 formula

${\mathrm{\ρ}}_3=\sqrt{{(x_3-x_u)}^2+{(y_3-y_u)}^2+{(z_3-z_u)}^2}+\mathrm{c\δ}{t}_u$ ... ... ... ... ... ... the ..5 formula

(x wherein _j, y _j, z _j) and ρ _jBe respectively the three-dimensional coordinate of visible satellite and visible satellite pseudorange to last vehicle of train, j=1,2,3; δ t _uBe the skew between receiver clock and the system clock;

Above-mentioned four equations of simultaneous obtain following Nonlinear System of Equations:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_1=\sqrt{{(x_1-x_u)}^2+{(y_1-y_u)}^2+{(z_1-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_2=\sqrt{{(x_2-x_u)}^2+{(y_2-y_u)}^2+{(z_2-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_3=\sqrt{{(x_3-x_u)}^2+{(y_3-y_u)}^2+{(z_3-z_u)}^2}+\mathrm{c\δ}{t}_u\\ {\mathrm{\ρ}}_4=\sqrt{{(x_4-x_u)}^2+{(y_4-y_u)}^2+{(z_4-z_u)}^2}\end{array}\right.$ 6 formulas

At above-mentioned the 4th equation of constraint ρ _j=ρ ₄, j=4;

Above-mentioned Nonlinear System of Equations is carried out linearization process

Suppose

With

Be respectively (x _u, y _u, z _u) and δ t _uEstimated value, (Δ x _u, Δ y _u, Δ z _u) and Δ t _uBe respectively (x _u, y _u, z _u) and δ t _uThe side-play amount of estimated value, order:

${\mathrm{\ρ}}_j=\sqrt{{(x_j-x_u)}^2+{(y_j-y_u)}^2+{(z_j-z_u)}^2}+\mathrm{c\δ}{t}_u=f_j(x_u,y_u,z_u,\mathrm{\δ}{t}_u)$ ... ... ... ... 7 formulas

${\widehat{\mathrm{\ρ}}}_j=\sqrt{{(x_j-{\hat{x}}_u)}^2+{(y_j-{\hat{y}}_u)}^2+{(z_j-{\hat{z}}_u)}^2}+\mathrm{c\δ}{\hat{t}}_u=f_j({\hat{x}}_u,{\hat{y}}_u,{\hat{z}}_u,\mathrm{\δ}{\hat{t}}_u)$ ... ... ... ... 8 formulas

Promptly have:

$f_j(x_u,y_u,z_u,\mathrm{\δ}{t}_u)=f_j({\hat{x}}_u+\mathrm{\Δ}{x}_u,{\hat{y}}_u+\mathrm{\Δ}{y}_u,{\hat{z}}_u+\mathrm{\Δ}{z}_u,\mathrm{\δ}{\hat{t}}_u+\mathrm{\Δ}{t}_u)$ ... ... ... ... 9 formulas

Use Taylor series at some the relational expression on 9 formula equal signs the right

Expansion is also ignored high-order term, and with 7 formulas, 8 formula substitution fundamental equations, 9 formulas, obtain linear relation through arrangement:

${\mathrm{\ρ}}_j={\widehat{\mathrm{\ρ}}}_j-\frac{x_j-{\hat{x}}_u}{{\hat{r}}_j}\mathrm{\Δ}{x}_u-\frac{y_j-{\hat{y}}_u}{{\hat{r}}_j}\mathrm{\Δ}{y}_u-\frac{z_j-{\hat{z}}_u}{{\hat{r}}_j}\mathrm{\Δ}{z}_u+\mathrm{c\Δ}{t}_u$ ... ... ... ... ... the .10 formula

Wherein ${\hat{r}}_j=\sqrt{{(x_j-{\hat{x}}_u)}^2+{(y_j-{\hat{y}}_u)}^2+{(z_j-{\hat{z}}_u)}^2}$

Introduce following new variables to simplify 10 formulas:

$\left.\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_j={\widehat{\mathrm{\ρ}}}_j-{\mathrm{\ρ}}_j\\ a_{\mathrm{xj}}=\frac{x_j-{\hat{x}}_u}{{\hat{r}}_j}\\ a_{\mathrm{yj}}=\frac{y_j-{\hat{y}}_u}{{\hat{r}}_j}\\ a_{\mathrm{zj}}=\frac{z_j-{\hat{z}}_u}{{\hat{r}}_j}\end{array}\right\}$ ... ... ... ... ... ... ... ... ... the ..11 formula

In above-mentioned 7-11 formula, as Δ t _u, δ t _uBe 0 o'clock, ρ _j=ρ ₄, j=4;

Obtain following system of equations by above-mentioned linearization:

$\left\{\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_1=a_{x1}\mathrm{\Δ}{x}_u+a_{y1}\mathrm{\Δ}{y}_u+a_{z1}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_2=a_{x2}\mathrm{\Δ}{x}_u+a_{y2}\mathrm{\Δ}{y}_u+a_{z2}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_3=a_{x3}\mathrm{\Δ}{x}_u+a_{y3}\mathrm{\Δ}{y}_u+a_{z3}\mathrm{\Δ}{z}_u-\mathrm{c\Δ}{t}_u\\ \mathrm{\Δ}{\mathrm{\ρ}}_4=a_{x4}\mathrm{\Δ}{x}_u+a_{y4}\mathrm{\Δ}{y}_u+a_{z4}\mathrm{\Δ}{z}_u\end{array}\right.$ ... ... ... ... ... ... ... ... ... the ..12 formula

Write as matrix form: Δ ρ=H Δ x.........................13 formula

Wherein:

$\mathrm{\Δ\ρ}=\left[\begin{array}{c}\mathrm{\Δ}{\mathrm{\ρ}}_1\\ \mathrm{\Δ}{\mathrm{\ρ}}_2\\ \mathrm{\Δ}{\mathrm{\ρ}}_3\\ \mathrm{\Δ}{\mathrm{\ρ}}_4\end{array}\right],$ $H=\left[\begin{array}{cccc}{a}_{x1}& a_{y1}& a_{z1}& 1\\ a_{x2}& a_{y2}& a_{z2}& 1\\ a_{x3}& a_{y3}& a_{z3}& 1\\ a_{x4}& a_{y4}& a_{z4}& 0\end{array}\right],$ $\mathrm{\ΔX}=\left[\begin{array}{c}\mathrm{\Δ}{x}_u\\ \mathrm{\Δ}{y}_u\\ \mathrm{\Δ}{z}_u\\ -\mathrm{c\Δ}{t}_u\end{array}\right]$

It is separated and is Δ X=H ^-1Δ ρ

Then the last vehicle of train position coordinates is $\left\{\begin{array}{c}{x}_u={\hat{x}}_u+\mathrm{\Δ}{x}_u\\ y_u={\hat{y}}_u+\mathrm{\Δ}{y}_u\\ z_u={\hat{z}}_u+\mathrm{\Δ}{z}_u\end{array}\right.,$ And $\mathrm{\δ}{t}_u=\mathrm{\δ}{\hat{t}}_u+\mathrm{\Δ}{t}_u$

Step 3 is calculated train length, judges whether train is complete,

Can calculate the three-dimensional coordinate of last vehicle of train according to above algorithm, then train head coordinate and last vehicle of train coordinate projection to Gaussian plane, calculate train length in real time $L=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2},$ Wherein: (x ₁, y ₁) be train header planes coordinate, (x ₂, y ₂) be the last vehicle of train planimetric coordinates; By comparing, then realize the real-time integrity checking of train with the train physical length.

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