CN103728642B - Localization method and system - Google Patents

Abstract

The invention discloses a kind of localization method and system, comprising: the wireless signal being received the signal emitting-source synchronized transmissions of more than five by receiver; Obtain the time of reception that described receiver receives at least two group wireless signals; According to the time of reception often organizing four wireless signals in wireless signal of the light velocity and acquisition, calculate the distance of receiver to an every signal emitting-source corresponding to group wireless signal, respectively with receiver to the range difference often organizing other three signal emitting-sources corresponding to wireless signal; The range difference often organizing wireless signal obtained is substituted into corresponding positioning precision GDOP formula, obtains and often organize dilution of precision corresponding to wireless signal; By respectively organizing dilution of precision corresponding to wireless signal, obtaining one group of wireless signal that the minimum dilution of precision of numerical value is corresponding, and being located the positional information of described receiver by this group wireless signal.Implement method and system of the present invention, the impact of clock drift on the positioning precision factor can be eliminated, improve positional accuracy.

Description

Localization method and system

Technical field

The present invention relates to wireless measurement technical field, particularly relate to a kind of localization method and system.

Background technology

At present in GPS, positioning precision depends on the geometric parameter of radio signal source or the array of sensor element, by the GDOP(GeometricDilutionofPrecision of four satellites, geometric dilution of precision) characterize, the less positioning precision of geometric dilution of precision is higher.

Geometric dilution of precision is defined and is normally calculated by satellite grain number and receiver estimated position.GDOP numerical value is usually calculated by navigational solution processing procedure, and the numerical value of parameter GDOP is larger, and the volume of representative unit vector body is less.GDOP comprises geometry of position dilution of precision PDOP, horizontal geometric dilution of precision HDOP, vertical dilution of precision VDOP and time geometry dilution of precision TDOP tetra-parameters, and these four parameters represent positioning timing total error σ respectively _g, site error σ _p, lateral error σ _h, upright position error σ _vwith clocking error σ _cto range error σ _oenlargement factor, that is:

$\mathrm{GDOP}=\sqrt{g_{11}+g_{22}+g_{33}+g_{44}}={\mathrm{\σ}}_g/{\mathrm{\σ}}_o;$

$\mathrm{PDOP}=\sqrt{g_{11}+g_{22}+g_{33}}={\mathrm{\σ}}_p/{\mathrm{\σ}}_o;$

$\mathrm{GDOP}=\sqrt{g_{11}+g_{22}}={\mathrm{\σ}}_h/{\mathrm{\σ}}_o;$

$\mathrm{VDOP}=\sqrt{g_{33}}={\mathrm{\σ}}_v/{\mathrm{\σ}}_o;$

$\mathrm{TDOP}=\sqrt{g_{44}}={\mathrm{\σ}}_c/{\mathrm{\σ}}_o;$

Wherein, gii (i=1 ..., 4) and be G-(H ^th) ^-1diagonal entry, H is observing matrix.

But clock drift can affect the numerical value of above-mentioned time dilution of precision, and then reduce the positioning precision of positioning system.

Summary of the invention

Based on this, be necessary in above-mentioned GPS, the numerical value of the influence time dilution of precision of clock drift meeting, and then the problem of the positioning precision of reduction positioning system, a kind of localization method and system are provided.

A kind of localization method, comprises the following steps:

The wireless signal of the signal emitting-source synchronized transmissions of more than five is received by receiver;

Obtain the time of reception that described receiver receives at least two group wireless signals, wherein, often organize the wireless signal that wireless signal comprises four described signal emitting-source synchronized transmissions, in four described signal emitting-sources, at least one is different from the signal emitting-source of other any one group of wireless signals;

According to the time of reception often organizing four wireless signals in wireless signal of the light velocity and acquisition, calculate described receiver to the range difference of the distance often organizing a signal emitting-source corresponding to wireless signal respectively and between the distance arriving other three signal emitting-sources; The range difference often organizing wireless signal obtained is substituted into corresponding positioning precision GDOP formula as pseudo range measurement error, obtain and often organize dilution of precision corresponding to wireless signal, wherein, build the covariance matrix of the pseudo range measurement error of described positioning precision GDOP formula, be made up of the partial derivative of the location resolution solution formula of described receiver;

By respectively organizing dilution of precision corresponding to wireless signal, obtaining one group of wireless signal that the minimum dilution of precision of numerical value is corresponding, and being located the positional information of described receiver by this group wireless signal.

A kind of positioning system, comprising:

Receiver module, for receiving the wireless signal of signal emitting-source synchronized transmissions of more than five by receiver;

Acquisition module, the time of reception of at least two group wireless signals is received for obtaining described receiver, wherein, often organize the wireless signal that wireless signal comprises four described signal emitting-source synchronized transmissions, in four described signal emitting-sources, at least one is different from the signal emitting-source of other any one group of wireless signals;

Pseudorange module, for the time of reception often organizing four wireless signals in wireless signal according to the light velocity and acquisition, calculate described receiver to the range difference of the distance often organizing a signal emitting-source corresponding to wireless signal respectively and between the distance arriving other three signal emitting-sources;

Precision module, the range difference often organizing wireless signal for obtaining substitutes into corresponding positioning precision GDOP formula as pseudo range measurement error, obtain and often organize dilution of precision corresponding to wireless signal, wherein, build the covariance matrix of the pseudo range measurement error of described positioning precision GDOP formula, be made up of the partial derivative of the location resolution solution formula of described receiver;

Locating module, for by respectively organizing dilution of precision corresponding to wireless signal, being obtained one group of wireless signal that the minimum dilution of precision of numerical value is corresponding, and being located the positional information of described receiver by this group wireless signal.

Localization method of the present invention and system, by the positioning precision GDOP formula that the location resolution solution formula that range difference corresponding for each group of wireless signal substitutes into receiver is derived, obtain the positioning precision factor of four signal emitting-sources corresponding to each group of wireless signal, four signal emitting-sources choosing dilution of precision minimum position described receiver, four signal emitting-sources only selecting positioning precision the highest according to the geometric position feature of each signal emitting-source and receiver position, eliminate clock drift (time dilution of precision) to the impact of the positioning precision factor, greatly improve the accuracy of location.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of localization method first embodiment of the present invention;

Fig. 2 is the schematic flow sheet of localization method first embodiment of the present invention;

Fig. 3 is the coordinate schematic diagram of receiver and signal emitting-source in method shown in Fig. 2 of the present invention;

Fig. 4 is the schematic flow sheet of positioning system first embodiment of the present invention.

Embodiment

Refer to Fig. 1, Fig. 1 is the schematic flow sheet of localization method first embodiment of the present invention.

The localization method of present embodiment comprises the following steps:

Step 101, receives the wireless signal of the signal emitting-source synchronized transmissions of more than five by receiver.

Step 102, obtain the time of reception that described receiver receives at least two group wireless signals, wherein, often organize the wireless signal that wireless signal comprises four described signal emitting-source synchronized transmissions, in four described signal emitting-sources, at least one is different from the signal emitting-source of other any one group of wireless signals.

Step 103, according to the time of reception often organizing four wireless signals in wireless signal of the light velocity and acquisition, calculates described receiver to the range difference of the distance often organizing a signal emitting-source corresponding to wireless signal respectively and between the distance arriving other three signal emitting-sources.

Step 104, the range difference often organizing wireless signal obtained is substituted into corresponding positioning precision GDOP formula as pseudo range measurement error, obtain and often organize dilution of precision corresponding to wireless signal, wherein, build the covariance matrix of the pseudo range measurement error of described positioning precision GDOP formula, be made up of the partial derivative of the location resolution solution formula of described receiver.

Step 105, by respectively organizing dilution of precision corresponding to wireless signal, being obtained one group of wireless signal that the minimum dilution of precision of numerical value is corresponding, and being located the positional information of described receiver by this group wireless signal.

The localization method of present embodiment, by the positioning precision GDOP formula that the location resolution solution formula that range difference corresponding for each group of wireless signal substitutes into receiver is derived, obtain the positioning precision factor of four signal emitting-sources corresponding to each group of wireless signal, four signal emitting-sources choosing dilution of precision minimum position described receiver, four signal emitting-sources only selecting positioning precision the highest according to the geometric position feature of each signal emitting-source and sensor position, eliminate clock drift (time dilution of precision) to the impact of the positioning precision factor, greatly improve the accuracy of location.

Wherein, for step 101, described receiver preferably, is other receivers that wireless RF receivers, acoustic receiver or those skilled in the art are usual.Described signal emitting-source preferably, is other emissive sources that satellite, wireless radio transmission source, acoustic emission source or those skilled in the art are usual.

In one embodiment, described to be received the step of the wireless signal of the signal emitting-source synchronized transmissions of more than five by receiver before, further comprising the steps of:

With reference to same clock source, by the wireless signal transmission source wireless signal emission at one time of more than five.

For step 102, the group number of wireless signal can set according to location requirement, the number of group number minimum value to be CN4, N be described signal emitting-source.

Preferably, when receiver receives the wireless signal of signal emitting-source synchronized transmission of described more than five, the time of reception of each wireless signal can be recorded, then according to wireless signal group, transfers the time of reception of the wireless signal of each group.

In one embodiment, before the described receiver of described acquisition receives the step of the time of reception of at least two group wireless signals, further comprising the steps of:

From the wireless signal of more than five received, choose four wireless signals combine, obtain k group wireless signal group, wherein, k is more than or equal to 2.

In other embodiments, before execution step 101, four signal emitting-sources can also be chosen in advance from the wireless signal transmission source of described more than five and combine, obtain k group wireless signal group.

For step 103, preferably, can according to difference TDOA algorithm time of arrival, calculate the distance of described receiver to a signal emitting-source corresponding to often group wireless signal, respectively with described receiver to the range difference often organizing other three signal emitting-sources corresponding to wireless signal.Often group can calculate three range differences.

In other embodiments, the transmitting time that also can send from signal emitting-source according to each wireless signal and the launch time of acquisition, calculate described receiver to the distance often organizing a signal emitting-source corresponding to wireless signal, respectively with described receiver to the range difference often organizing other three signal emitting-sources corresponding to wireless signal.Often group can calculate three range differences.

For step 104, described positioning precision GDOP formula is only relevant to the geometric position feature of each signal emitting-source and receiver.

Preferably, when not importing the position data of four signal emitting-sources corresponding with often organizing wireless signal in described positioning precision GDOP formula, the position data of four corresponding signal emitting-sources need be obtained, and position data is substituted corresponding parameter.

For step 105, preferably, can based on difference TDOA algorithm time of arrival, the position of described receiver is oriented by one group of wireless signal that dilution of precision that numerical value is minimum is corresponding.

In one embodiment, described step of locating the positional information of described receiver by this group wireless signal comprises the following steps:

By the range difference of corresponding for dilution of precision minimum for numerical value one group of wireless signal, the location resolution solution formula substituting into this group wireless signal corresponding solves, and obtains the position coordinates of described receiver.

In other embodiments, can also by the usual other technologies means of those skilled in the art, by one group of wireless signal that dilution of precision that numerical value is minimum is corresponding, locate the position of described receiver.

Refer to Fig. 2, Fig. 2 is the schematic flow sheet of localization method second embodiment of the present invention.

The localization method of present embodiment and the difference of the first embodiment are: described the range difference often organizing wireless signal obtained substituted into the step of positioning precision GDOP formula before, further comprising the steps of:

Step 201, obtains and sends four signal emitting-sources often organizing wireless signal and launch positional information when often organizing wireless signal.

Step 202, according to distance between two points formula in three-dimensional coordinate coefficient, builds the location resolution solution formula of the described receiver corresponding with each group of wireless signal by the positional information obtained.

Step 203, by asking partial derivative to the location resolution solution formula often organizing wireless signal corresponding respectively, obtaining and often organizing covariance matrix corresponding to wireless signal, and obtaining the positioning precision GDOP formula corresponding with often organizing wireless signal respectively according to described covariance matrix.

The localization method of present embodiment, according to corresponding with often organizing wireless signal four signal emitting-source positional informations its, build new positioning precision GDOP formula, be the closed analytic solution computing method of one, the elegant impact on the positioning precision factor of clock can be eliminated.

Wherein, for step 201, the definition of the positioning precision GDOP adopted in present embodiment is different from traditional definition.The definition of the GDOP of present embodiment derives from the analytic solution of the novelty of three-dimensional TDOA source electricity.GDOP model is:

GDOP=△OutputLocation/（C*△TDOA）

Wherein, C is the light velocity.

Preferably, a kind of method of analytic solution of closing form can be adopted directly to find out TDOA three-dimensional source coordinate (X, Y, Z).

In one embodiment, Fig. 3 shows satellite S1, S2, S3 and S4 of optional position in four satellites (signal emitting-source) or three dimensional euclidean space.Because Euclidean plane can not had three of conllinear summits define, therefore, with No. 1 satellite for starting point, S1, S2 and S3 definable Euclid plane (XOY), S2 is positioned at x-axis, and coordinate is (a, 0,0), S3 is positioned at plane X OY, and coordinate is (b, c, 0).S4 can be positioned on any position of this three dimensional euclidean space, and coordinate is (d, e, f).Parameter a, b, c, d, e, f can be any real numbers.Receiver coordinate U(X, Y, Z) be positioned in the same rectangular coordinate system shown in Fig. 3.

Before the derivation of positioning precision GDOP formula, pre-defined following parameter:

D _ifor satellite i is to the distance of receiver U, d _i'=d _ithe pseudorange of+β * c satellite i to receiver U, β is the clock drift between GPS user's (or receiver) and satellite.Mi=d ₁'-d _i+1'=d1-d _i+1, be No. 1 satellite and the microspur measuring error of i satellite respectively and between receiver, L _ijfor the distance between Si and Sj, V ₁₂₃₄for the tetrahedral volume defined by S1, S2, S3 and S4, S ₁₂₃for the leg-of-mutton size defined by S1, S2 and S3.

Preferably, in coordinate system shown in Fig. 3, according to distance between two points formula, following No. 1 satellite and i(2,3,4 can be drawn) the range difference formula of number satellite respectively and between receiver:

M1＝(x ²+y ²+z ²) ^1/2-[(x-a) ²+y ²+z ²] ^1/2

M2＝(x ²+y ²+z ²) ^1/1-[(x-b) ²+(y-c) ²+z ²] ^1/2(1)

M3＝(x ²+y ²+z ²) ^1/2-[(x-d) ²+(y-e) ²+(z-f) ²] ^1/2

Wherein x, y and z are the three-dimensional coordinates of GPS user, and as shown in Figure 3, S5 is the intersection point of plane X OY and line segment (S4, S5), line segment (S4, S5) perpendicular to plane X OY wherein, a=L ₁₂, b=L ₁₃* cos ∠ 312, c=(L ₁₃ ²– b ²) ^1/2, c>0, d=L ₁₅* cos ∠ 512, e=(b ²+ c ²– 2*b*d-L ₃₄ ²+ L ₁₄ ²)/(2*c), f=3*V ₁₂₃₄/ S ₁₂₃.

Preferably, e is uniquely determined by following equalities:

(d ²+e ²+f ²)–[(d-b) ²+(e-c) ²+f ²]=L ₁₄ ²–L ₃₄ ²；

cos∠312=(L ₁₂ ²+L ₁₃ ²-L ₂₃ ²)/(2*L ₁₂*L ₁₃)；

V ₁₂₃₄=1/12*[4*(L ₁₂*L ₁₃*L ₁₄) ²-L ₁₂ ²*T ₃₄ ²-L ₁₃ ²*T ₂₄ ²-L ₁₄ ²*T ₂₃ ²+T ₂₃*T ₂₄*T ₃₄] ^1/2

T ₃₄=(L ₁₃ ²+L ₁₄ ²-L ₃₄ ²)

T ₂₄=(L ₁₂ ²+L ₁₄ ²-L ₂₄ ²)

T ₂₃=(L ₁₂ ²+L ₁₃ ²-L ₂₃ ²)

S ₁₂₃=[P*(P-L ₁₂)*(P-L ₁₃)*(P-L ₂₃)] ^1/w

P=(L ₁₂+L ₁₃+L ₂₃)/2

cos∠512=(L ₁₂ ²+L ₁₅ ²-L ₂₅ ²)/(2*L ₁₂*L ₁₅)

L ₁₅=(L ₁₄ ²–f ²) ^1/2

L ₂₅=(L ₂₄ ²–f ²) ^1/2

For in step 202, the positional information often organizing four signal emitting-sources corresponding to wireless signal can be converted to three-dimensional coordinate, substitute into above-mentioned formula (1), preferably can use MATLAB solution formula (1), obtain the analytic solution formula of the following double-enclosure form of x, y and z:

x=X(Mi)=[-Bx+(Bx ²-4*Ax*Cx) ^1/2]/(2*Ax)

Or x=X (Mi)=[-Bx-(Bx ²-4*Ax*Cx) ^1/2]/(2*Ax)

y=Y(Mi)=[-By+(By ²-4*Ay*Cy) ^1/2]/(2*Ay)

Or y=Y (Mi)=[-By-(By ²-4*Ay*Cy) 1/2]/(2*Ay)

z=Z(Mi)=[-Bz+(Bz ²-4*Az*Cz) ^1/2]/(2*Az)

Or z=Z (Mi)=[-Bz-(Bz ²-4*Az*Cz) ^1/2]/(2*Az)

Wherein:

Ay=c*M1*Ax；

By=(M2*a-b*M1)*Bx;

Az=f*c*M1*Ax;

symsxyzabcdefM1M2M3;

S=solve('(x^2+y^2+z^2)^(1/2)-((x-a)^2+y^2+z^2)^(1/2)=M1',...

'(x^2+y^2+z^2)^(1/2)-((x-b)^2+(y-c)^2+z^2)^(1/2)=M2',...

'(x^2+y^2+z^2)^(1/2)-((x-d)^2+(y-e)^2+(z-f)^2)^(1/2)=M3')；

Ax=

(-2*M2*a*b*M1*f^2-a^2*c^2*f^2+d^2*M1^2*c^2+e^2*M2^2*a^2+b^2*M1^2*e^2+M3^2*a^2*c^2-2*e^2*M2*a*b*M1-2*e*M2*a^2*M3*c+2*e*M2*a*d*M1*c+2*e*b*M1*M3*a*c-2*e*b*M1^2*d*c-2*M3*a*d*M1*c^2+f^2*M1^2*c^2+M2^2*a^2*f^2+b^2*M1^2*f^2)；

Bx=

-(c*M1*e*M2*a*f^2-2*e*M2*a^3*M3*c+2*e*M2*a*M3*M1^2*c-e*M2*a*M3^2*M1*c+e*M2*a*d^2*M1*c+e^3*M2*a*M1*c+e*b*M1*M3*a^2*c-e*b*M1^3*M3*c+e*b*M1^2*M3^2*c-e*b*M1^2*d^2*c-e^3*b*M1^2*c+M3*a*c^3*e*M1+M3*a*c*e*b^2*M1-M3*a*c*e*M2^2*M1+d*M1*c*e*M2*a^2-d*M1^3*c*e*M2-d*M1^2*c^3*e-d*M1^2*c*e*b^2+d*M1^2*c*e*M2^2+M1^3*M2*b*f^2-M2*a^2*b*M1*f^2-M2*a*c^2*M1*f^2-M2*a*b^2*M1*f^2+M2^3*a*M1*f^2-M2^2*a*M1^2*f^2+a*M1^2*c^2*f^2+d*M1^2*c^2*f^2-b*M1^2*M2^2*f^2+b*M1^2*c^2*f^2-a^3*c^2*f^2-a*M1*M3*c^2*f^2-c*M1^2*e*b*f^2-M3*a*e^2*M1*c^2-M3*a*d^2*M1*c^2-a*M1*M2*e^2*c^2-e^2*M2*a^2*b*M1-e^2*M2*a*b^2*M1-M3*a^2*d*M1*c^2+M2^2*a^3*f^2+M3^2*a^3*c^2+e^2*b^3*M1^2+e^2*M2^2*a^3+d^3*M1^2*c^2-M3^2*a*M1^2*c^2+b^3*M1^2*f^2+b*M1^2*e^2*c^2+e^2*M2^3*a*M1-e^2*M2^2*a*M1^2-d*M1^2*M3^2*c^2+d*M1^2*e^2*c^2+M3*M1^3*d*c^2+M3^3*a*M1*c^2-e^2*M2^2*M1^2*b+e^2*M1^3*M2*b)；

Cx=

1/4*M2^4*M1^2*f^2+1/2*b^2*M1^2*c^2*f^2+1/2*e^2*a^2*M1*M2^3-1/2*M2^2*b^2*M1^2*f^2+1/4*c^2*M1^2*e^4-1/2*c^2*M1^2*M2^2*f^2+1/4*M3^4*M1^2*c^2-1/4*M1^4*c^2*f^2-1/2*M1^3*M3^3*c^2+1/4*d^4*M1^2*c^2+1/4*M3^2*M1^4*c^2+1/4*c^4*M1^2*f^2+1/4*b^4*M1^2*f^2+1/4*c^2*M1^2*f^4+1/2*d^2*M1^3*c^2*M3-1/2*d^2*M1^2*c^2*M3^2+1/2*c^2*M1^3*f^2*M3+1/2*c^2*M1^2*f^2*d^2-1/2*c^2*M1^2*f^2*M3^2+1/2*M2*M1^3*f^2*c^2+1/2*M2*b^2*M1^3*f^2+1/4*M2^2*M1^4*f^2+1/4*a^4*f^2*M2^2-1/4*a^4*c^2*f^2+1/4*a^4*M3^2*c^2+1/4*e^2*M2^4*M1^2-1/2*e^2*M1^3*M2^3+1/4*e^2*M2^2*M1^4+1/4*e^2*M1^2*c^4+1/4*e^2*b^4*M1^2-1/2*e^3*M1^2*c^3-1/2*M1^3*f^2*M2^3+1/2*a^2*M1*f^2*M2^3-1/2*a^2*M1^2*f^2*M2^2+1/2*a^2*M3^3*c^2*M1-1/2*a^2*M3^2*M1^2*c^2+1/2*a^2*f^2*M1^2*c^2-1/2*a^2*M3*c^2*d^2*M1-1/2*a^2*c^2*M1*f^2*M3-1/2*a^2*M2*c^2*f^2*M1-1/2*a^2*M2*b^2*M1*f^2+1/4*e^2*M2^2*a^4-1/2*e^2*a^2*M1^2*M2^2-1/2*e^2*M2^2*b^2*M1^2-1/2*e^2*c^2*M1^2*M2^2-1/2*e^2*a^2*M2*b^2*M1-1/2*e^2*a^2*M2*M1*c^2-1/2*e^2*a^2*M3*c^2*M1+1/2*e^2*M2*M1^3*c^2+1/2*e^2*f^2*M1^2*c^2+1/2*e^2*d^2*M1^2*c^2-1/2*e^2*M3^2*M1^2*c^2+1/2*e^2*c^2*M1^2*b^2+1/2*e^2*M1^3*M3*c^2-1/2*e*M1^2*c^3*f^2+1/2*e*M3^2*M1^2*c^3-1/2*e*M1^3*M3*c^3-1/2*e*d^2*M1^2*c^3+1/2*e^3*M1^2*c*M2^2-1/2*e^3*M1^3*c*M2-1/2*e^3*M1^2*c*b^2+1/2*e^2*M2*M1^3*b^2-1/2*e*M2*c*M1^3*f^2-1/2*e*c*M1^2*f^2*b^2-1/2*e*M1^3*M3*c*b^2+1/2*e*M3^2*M1^2*c*b^2-1/2*e*d^2*M1^2*c*b^2+1/2*e^3*M1*c*M2*a^2-1/2*e*M3*c*M2*a^4-1/2*e*a^2*M3*c*M1*M2^2+1/2*e*a^2*M2*c*M1*f^2+e*a^2*M2*M3*c*M1^2+1/2*e*a^2*M2*d^2*M1*c-1/2*e*a^2*M2*M3^2*M1*c+1/2*e*a^2*M3*c^3*M1+1/2*e*a^2*M3*c*b^2*M1+1/2*e*M2^2*c*M1^2*f^2+1/2*e*M2^2*d^2*M1^2*c+1/2*e*M2^2*M1^3*M3*c-1/2*e*M2^2*M3^2*M1^2*c+1/2*e*M2*M3^2*M1^3*c-1/2*e*M2*d^2*M1^3*c-1/2*e*M2*M1^4*M3*c；

Cy=

1/4*M1*c*(-2*e^2*a^2*M2*M3*b^2-2*e^2*a^2*M2*M3*c^2-2*e^2*a^2*M1*b^2*M3-2*e^2*a*M1*d*M2^3+M2^4*d^2*M1^2-a^2*c^4*f^2+a^2*M2^2*d^4-2*a^2*M2^3*M3^3-a^2*M2^4*f^2+a^2*M3^2*c^4-a^2*f^2*b^4+a^2*M3^2*b^4+a^2*M2^4*M3^2-2*a^3*M2^2*d^3+2*a^3*f^2*b^3-2*a^3*M3^2*b^3+a^4*M2^2*d^2+a^4*M2^2*f^2-a^4*b^2*f^2+a^4*b^2*M3^2-2*a*b*M1^2*c^2*f^2+a^2*M2^2*f^4+2*a*M2^2*b*M1*M3^3-2*a*M2^2*M3^2*M1^2*b-2*a*M2^2*d*M1^2*M3^2+2*a*M2*d^3*M1*b^2+2*a*M2*d^3*M1*c^2-2*a*M2*b*M1*M3^4-2*a*M2*b*M1*d^4+2*a*M2*M3^3*M1^2*b-2*a*M2*M1*b*f^4-2*a*M2^2*b*M1*d^2*M3+4*a*M2^2*M3*c^2*M1*d-2*a*M2^2*M3*M1*b*f^2+4*a*M2*b*M1*M3^2*f^2+2*a*M2*d*M1*b^2*f^2+2*a*M2^3*M3*M1^2*d-2*a*M2^3*d*M1*f^2+2*a^3*M2*M3*c^2*d+2*a^3*M2*M3*b^2*d+2*a^3*M2*b*M3*d^2+2*a^3*M2*b*M3*f^2-2*a^4*b*M3*d*M2-4*e^2*M2*a*b*M1*f^2-2*a^2*M2*M3*b^2*d^2-2*a^2*M2^2*b*M1*M3*d+2*a^2*M2*d*M1*b*f^2-2*a^2*M2*b*M1*M3^2*d-2*a^2*M2*M3*b^2*f^2-2*a^2*M2*d^2*M1*b^2+2*a^2*M2*b*M1*d^3-2*a^2*M2*c^2*f^2*M3-2*a^2*M2*M1*c^2*f^2-2*a^2*M2*M1*f^2*b^2-2*a^2*M2*M3*c^2*d^2+4*a^2*M2*b*M1^2*M3*d-2*a^2*b^2*M1*d^2*M3-2*a^2*M2*d^2*M1*c^2-2*a^2*b^2*M1*M3*f^2-2*a^2*b^2*M2^2*M3^2+2*e^2*a^2*M2*M1*b*d-2*e^2*a*M2^2*M1*b*M3+2*e^2*a*M2^2*M1^2*d+2*e^2*a*M1*b^3*M3-2*e^2*a*M2*M1^2*b*M3-4*e^2*a*M2*b*M1*d^2+2*e^2*a*M2*M1*d*b^2+2*e^2*a*M2*M1*c^2*d+4*e^2*a*M2*b*M1*M3^2+2*e^2*a*M1*c^2*b*M3-2*e^4*M2*a*b*M1+4*a*M2^2*d*M1*b^2*M3-2*a*M2^3*d^3*M1+2*a*M2^2*d^3*M1^2+2*a^2*M2^2*b^2*f^2-2*a^2*c^2*f^2*b^2+2*a^2*M2^3*M3*f^2+2*a*M2^2*d*M1^2*f^2+2*a*b*M1^2*M2^2*f^2-2*a*M3*M1*d*M2^4-2*M2^2*M1^2*b^2*d^2-2*M2^2*M1^2*b^2*f^2-2*e^2*M1^2*c^2*b*d-2*M2^2*f^2*M1^2*c^2-2*a*M2*M1^2*f^2*b*M3+4*a*M2*b*M1*d^2*M3^2-2*a*M2*d*M1*b^2*M3^2-2*a*M2*b^2*M1^2*d*M3-2*a*M2*M1*M3^2*c^2*d-4*a*M2*b*M1*d^2*f^2-2*a*M2*M3*c^2*M1^2*d+2*a*M2*d*M1*c^2*f^2-2*a*M2*d^2*M1^2*b*M3-4*a*M3*c^2*M1*d*b^2+2*a*M3*c^2*M1*b*f^2+2*a*M3*c^2*M1*b*d^2+2*a^2*M2^3*M1*f^2+2*a^2*b^2*M1^2*f^2+2*a^2*M2^3*d^2*M1+2*a^2*b^3*M1*M3*d-2*c^2*M3^2*a^2*M2^2+2*a^2*d*M1*c^2*b*M3+2*c^2*M1^2*f^2*b^2-2*b^2*M1^2*M3^2*f^2-2*b*M1^2*d^3*c^2-2*d*M1^2*b^3*f^2+2*M1^3*b^2*f^2*M3+2*b^2*M1^3*d^2*M3+2*b^2*M1^2*d^2*f^2+d^2*M1^2*c^4+2*e^2*M1^2*b*d*M2^2+2*e^2*a^3*b*M3*M2+2*M2^2*d*M1^2*b*f^2-2*M2^2*d^2*M1^2*c^2+2*M2*d^2*M1^3*c^2-2*M2*b*M1^3*d^3+2*M2*d^2*M1^3*b^2+2*M2*b^2*M1^3*f^2+2*M2*M1^3*f^2*c^2-2*e^2*M1^3*b*d*M2+2*e^2*M2^2*a^2*f^2+2*e^2*b^2*M1^2*f^2+2*e^2*M1^3*b^2*M3+2*e^2*M1^2*b^2*d^2-2*e^2*M1^2*b^3*d-2*e^2*M1^2*b^2*M3^2+2*e^2*a^2*M2^2*d^2+2*e^2*a^2*M3*M2^3-2*e^2*a^3*d*M2^2-2*e^2*a^2*M2^2*M3^2+2*M1^2*M3^2*c^2*b*d-2*b^3*M1^3*M3*d+2*M2^2*b*M1^2*d^3+b^2*M1^2*M3^4-2*b^2*M1^3*M3^3+d^2*M1^2*b^4+b^2*M1^2*d^4-b^2*M1^4*f^2+M1^2*b^2*f^4+M2^4*M1^2*f^2-2*a*b^3*M1^2*f^2-2*a*M3^3*b^3*M1+2*a*M3^2*b^3*M1^2-2*c^2*M1^2*f^2*b*d+2*d^2*M1^2*c^2*b^2+2*b^3*M1^2*M3^2*d-2*b^2*M1^2*d^2*M3^2+a^2*M2^2*M3^4+b^4*M1^2*f^2+2*a^2*M2^3*M3*d^2+2*a^2*M2^2*f^2*d^2-2*a^2*M2^2*M1^2*f^2-2*a^2*M2^2*d^2*M3^2-2*a^2*M2^2*d^2*M1^2+2*a^2*M2^2*c^2*f^2-2*a^2*M2^2*f^2*M3^2+2*a^2*M2*M3^3*c^2+2*a^2*M2*M3^3*b^2-2*a^3*d*M3*M2^3-2*a^3*M2^2*b*f^2+2*a^3*M2^2*b*M3^2-2*a^3*M2^2*d*f^2+2*a^3*M2^2*d*M3^2-2*a^3*M2*b*M3^3-2*a^3*M3^2*c^2*b+2*a^3*c^2*f^2*b+e^4*M2^2*a^2+2*a*M2^3*d*M1*M3^2+2*a*M3*b^3*M1*d^2+2*a*M3*b^3*M1*f^2+2*a*M3^2*c^2*M1^2*b-2*a*M3*c^4*M1*d-2*a*M3*b^4*M1*d-2*a*M3^3*c^2*M1*b+e^4*b^2*M1^2+2*c^2*M3^2*a^2*b^2+2*M3^3*M1*a^2*b^2-2*M3^2*M1^2*a^2*b^2-2*M2^2*b*M1^2*M3^2*d+2*M2*b*M1^3*M3^2*d-2*M2*d*M1^4*b*M3-2*M2*d*M1^3*b*f^2+2*M2^2*M3*M1^3*b*d-2*d*M1^3*c^2*b*M3+b^2*M1^4*M3^2-2*b^3*M1^2*d^3+c^4*M1^2*f^2+M2^2*d^2*M1^4+M2^2*f^2*M1^4-2*M2^3*d^2*M1^3-2*M2^3*f^2*M1^3)；

Bz=

(M3*a^2*c-M1^2*M3*c-e*M2*a^2+e*M2*M1^2+M3^2*M1*c-d^2*M1*c-e^2*M1*c-f^2*M1*c+e*b^2*M1+e*c^2*M1-e*M2^2*M1)*(-2*M2*a*b*M1*f^2-a^2*c^2*f^2+d^2*M1^2*c^2+e^2*M2^2*a^2+b^2*M1^2*e^2+M3^2*a^2*c^2-2*e^2*M2*a*b*M1-2*e*M2*a^2*M3*c+2*e*M2*a*d*M1*c+2*e*b*M1*M3*a*c-2*e*b*M1^2*d*c-2*M3*a*d*M1*c^2+f^2*M1^2*c^2+M2^2*a^2*f^2+b^2*M1^2*f^2)+(d*M1*c-M3*a*c+e*M2*a-e*b*M1)*(c*M1*e*M2*a*f^2-2*e*M2*a^3*M3*c+2*e*M2*a*M3*M1^2*c-e*M2*a*M3^2*M1*c+e*M2*a*d^2*M1*c+e^3*M2*a*M1*c+e*b*M1*M3*a^2*c-e*b*M1^3*M3*c+e*b*M1^2*M3^2*c-e*b*M1^2*d^2*c-e^3*b*M1^2*c+M3*a*c^3*e*M1+M3*a*c*e*b^2*M1-M3*a*c*e*M2^2*M1+d*M1*c*e*M2*a^2-d*M1^3*c*e*M2-d*M1^2*c^3*e-d*M1^2*c*e*b^2+d*M1^2*c*e*M2^2+M1^3*M2*b*f^2-M2*a^2*b*M1*f^2-M2*a*c^2*M1*f^2-M2*a*b^2*M1*f^2+M2^3*a*M1*f^2-M2^2*a*M1^2*f^2+a*M1^2*c^2*f^2+d*M1^2*c^2*f^2-b*M1^2*M2^2*f^2+b*M1^2*c^2*f^2-a^3*c^2*f^2-a*M1*M3*c^2*f^2-c*M1^2*e*b*f^2-M3*a*e^2*M1*c^2-M3*a*d^2*M1*c^2-a*M1*M2*e^2*c^2-e^2*M2*a^2*b*M1-e^2*M2*a*b^2*M1-M3*a^2*d*M1*c^2+M2^2*a^3*f^2+M3^2*a^3*c^2+e^2*b^3*M1^2+e^2*M2^2*a^3+d^3*M1^2*c^2-M3^2*a*M1^2*c^2+b^3*M1^2*f^2+b*M1^2*e^2*c^2+e^2*M2^3*a*M1-e^2*M2^2*a*M1^2-d*M1^2*M3^2*c^2+d*M1^2*e^2*c^2+M3*M1^3*d*c^2+M3^3*a*M1*c^2-e^2*M2^2*M1^2*b+e^2*M1^3*M2*b)；

Cz=

-1/4*f*M1*c*(2*a^2*M3*d^2*M1*c^2-2*a^2*b^3*M1*M3*d+2*a^2*M2^2*b*M1*M3*d+2*a^2*M2*b*M1*d*M3^2+2*a^2*M2*M3*b^2*f^2-2*a^2*M2*b*M1*d^3+a^2*M3^4*c^2-a^2*M2^2*f^4-e^2*M1^2*c^4-2*e^3*b*M1^2*c*a+2*e^3*M1^2*c^3-e^4*M2^2*a^2+e^4*a^2*c^2-e^4*b^2*M1^2-e^4*c^2*M1^2-2*e^2*M2^2*b*M1^2*d+2*e^2*M2*b*M1^3*d+2*e^2*b*M1^2*d*c^2-2*e^2*a*M2*M1*d*b^2+4*e^2*a*M2*M1*b*d^2-2*e^2*a*M2*d*M1*c^2-4*e^2*a*M2*M1*b*M3^2-2*e^3*a^2*M1*c*M2-2*e^3*a^2*c*b^2-2*e^3*M1^2*c*M2^2+2*e^3*M1^3*c*M2+2*e^3*b^2*M1^2*c-2*e*a^2*c^3*d^2-2*e*a^2*c^3*f^2+2*e*M1^2*c^3*f^2-2*e*M3^2*c^3*M1^2+2*e*M3*c^3*M1^3-2*a^2*M3*d*M1*c^2*b+2*a^2*M3*c^2*f^2*M1+2*a^2*M2*d^2*M1*c^2+2*a^2*M2*b^2*M3*d^2+2*a^2*M2*M3*c^2*f^2+2*a^2*b^2*M1*M3*d^2+2*a^2*M3*b^2*M1*f^2-a^2*M2^4*M3^2-a^4*M2^2*d^2+a^4*c^2*d^2-a^4*b^2*M3^2-a^4*M3^2*c^2-e^2*b^4*M1^2+e^2*a^2*b^4-e^2*M2^2*M1^4+2*e^2*M1^3*M2^3+2*a^3*M3^2*b^3+2*a^2*b^2*M2^2*M3^2+2*e*a^4*M3*c*M2-2*e*a^4*b*d*c-2*e*a^3*d*c*M2^2-2*e*a^3*M3^2*c*b+2*e*a^3*b*c*f^2+2*e*a^3*b*d^2*c+2*e*a^3*d*c*b^2+2*e*a^2*M2^2*d^2*c-2*e*a^2*M2^2*M3^2*c+2*e*a^2*M2^2*c*f^2-2*a*M1^2*b*M3^2*c^2-2*a*M3*b^3*M1*f^2+4*a*M3*d*M1*c^2*b^2+2*a*d*M1^2*c^2*f^2-2*a*b*M1*M3*c^2*d^2-2*a*d*M1^2*M3^2*c^2-4*a*M2^2*M3*d*M1*c^2+2*e*a^2*M3^2*c*b^2+2*e*a^2*M2^2*M3*c*M1+2*e*a^2*M2*M3^2*M1*c-4*e*a^2*M2*M1^2*M3*c-2*e*a^2*M2*f^2*M1*c-2*e*a^2*M2*d^2*M1*c+4*e*a^2*b*M1^2*d*c-2*e*a^2*M3*c^3*M1-2*e*a^2*c*d^2*b^2-2*e*a*d*M1^2*c^3-2*e*a^2*c*f^2*b^2-2*e*a^2*M3*c*M1*b^2-2*e*b^2*M1^2*M3^2*c+2*e*M3*c*M1^3*b^2+2*e*M1^2*d^2*b^2*c+2*e*c*M1^2*f^2*b^2+2*e*c^3*d^2*M1^2-d^2*M1^2*b^4+2*a*M2^2*M3*b*M1*f^2+2*a*M3*d*M1*M2^4-2*a*M2^3*M1*d*M3^2+2*a*M2^3*d*M1*f^2-2*a*M2^3*M1^2*M3*d-2*a*M2^2*b*M1*M3^3+2*a*M2^2*b*M1^2*M3^2+2*a*M2^2*M1^2*d*M3^2-2*a^3*c^2*d^3+e^2*b^2*M1^4+2*d*M1^2*c^2*b*f^2-M3^2*c^2*M1^4+2*a*M2^2*b*M1*M3*d^2-2*a*M2^2*d*M1^2*f^2+2*a*M2*b*M1*d^4+2*a*M2*M1*b*f^4-2*a*M2*M1^2*b*M3^3+2*a*M2*b*M1*M3^4-2*a*M2*b^2*M1*d^3-2*a*M2*d^3*M1*c^2-2*a*b^3*M1*M3*d^2+2*a*M3^3*c^2*M1*b+2*a*M3*d*M1*c^4+2*a*M3*d*M1*b^4-2*a*M3*c^2*b*M1*f^2+2*a*M2^3*M1*d^3-2*a*M2^2*M1^2*d^3+2*a^3*M3*d*M2^3+2*a^3*M2^2*d^3-2*a^3*M2*M3*b*f^2-2*a^3*M2*b*M3*d^2+2*a^3*M2*b*M3^3+2*a^3*M3^2*c^2*b+2*a^3*M3^2*c^2*d-2*a^3*d*c^2*f^2-2*a^3*M2*b^2*M3*d-4*a*M2^2*b^2*M1*M3*d-2*a*M2*d*M1*b^2*f^2+2*a*M2*b^2*M1^2*M3*d+2*a*M2*M1^2*M3*b*f^2-2*a*M2*d*M1*c^2*f^2+2*a*M2*b^2*M1*d*M3^2+4*a*M2*d^2*M1*f^2*b+2*a*M2*M3*d*M1^2*c^2+2*a*M2*M1^2*b*M3*d^2-4*a*M2*M3^2*M1*f^2*b-4*a*M2*b*M1*d^2*M3^2+2*a*M2*M3^2*d*M1*c^2-2*a^3*M2^2*b*M3^2-2*a^3*M2^2*d*M3^2+2*a^3*M2^2*d*f^2-d^4*M1^2*c^2-c^2*M1^2*f^4-d^2*M1^2*c^4-b^2*M1^2*d^4-b^2*M1^4*M3^2+2*d^2*M1^3*M2^3-a^2*M3^2*b^4+a^2*c^2*d^4+a^2*c^2*f^4-a^2*M3^2*c^4-2*M3^2*d*M1^2*c^2*b+2*d*M1^2*b^3*f^2-2*M1^3*M3*c^2*f^2+2*M3^2*M1^2*b^2*f^2+2*c^2*M1^2*f^2*M3^2-2*M3*d^2*M1^3*c^2+2*b*M1^2*d^3*c^2-2*M2*d^2*M1^3*b^2-2*e*b*M1^4*d*c+2*e*M2^2*M1^2*c*M3^2-2*e*M2^2*M3*c*M1^3-2*e*M2^2*M1^2*f^2*c-2*e*M2^2*d^2*M1^2*c+2*e*M2*M3*c*M1^4+2*e*M2*d^2*M1^3*c-2*e*M2*M1^3*c*M3^2+2*e*M2*M1^3*f^2*c+2*e^4*M2*a*b*M1+2*e*a*d*M1^2*c*M2^2-2*e*a*b*M1^2*c*f^2-2*e*a*d*M1^2*c*b^2+2*e*a*M3^2*c*M1^2*b-2*e*a*b*M1^2*d^2*c+2*e*a^3*d*c^3+2*e*a^2*c^3*M3^2-2*a^3*M2*M3*c^2*d+2*a^4*b*M3*d*M2-2*e^2*a^2*M2*b*M1*d+2*e^2*a^2*M2*M1*c^2+2*e^2*a^2*b^2*M1*M3+2*e^2*a^2*M3*c^2*M1-2*e^2*a^2*M2^3*M1-2*e^2*f^2*M1^2*c^2-2*e^2*M3^2*a^2*c^2+2*c^2*M3^2*a^2*M2^2+2*M2*M1^4*b*M3*d-2*M2*M1^3*b*d*M3^2+2*M2*M1^3*b*d^3-M2^2*d^2*M1^4-2*e^2*M2^2*a^2*f^2-2*e^2*a^3*c^2*d-2*e^2*a^3*c^2*b-2*e^2*a^2*M2^2*d^2-2*e^2*a^2*M2^3*M3-2*e^2*a^2*M2^2*b^2+2*e^2*a^2*M2^2*M1^2+2*e^2*a^2*M2^2*M3^2+2*e^2*a^2*c^2*d^2-2*e^2*a^2*b^2*M1^2-2*e^2*d^2*M1^2*c^2+2*e^2*a^3*M2^2*b+2*e^2*a*b^3*M1^2+2*e^2*a^3*M2^2*d+2*e^2*M2^2*b^2*M1^2+2*e^2*a^2*c^2*f^2-2*e^2*c^2*M1^2*b^2+2*e^2*c^2*a^2*b^2-2*e^2*a^2*c^2*M2^2+2*e^3*b*c*a^3+2*e^3*a^2*c*M2^2-2*e^2*b^2*M1^2*f^2+2*M2*d*M1^3*f^2*b-2*M2*M1^3*d^2*c^2-2*M2^2*b*M1^2*d^3+2*M2^2*b^2*M1^2*d^2+4*e^2*M2*a*b*M1*f^2+2*e^2*c^2*M1^2*M2^2-2*e^2*M2*M1^3*c^2+2*e^2*M1^2*c^2*M3^2-2*M2^2*d*M1^2*f^2*b-2*M2^2*b*M1^3*M3*d+2*M2^2*b*M1^2*d*M3^2-a^2*M2^2*M3^4-b^2*M1^2*M3^4-M1^2*c^2*M3^4+2*a^2*M1^2*c^2*M3^2-2*a^2*M2^2*d^2*f^2+2*a^2*M2^2*d^2*M3^2+2*a^2*M2^2*M3^2*f^2-2*a^2*M2*M3^3*c^2-2*a^2*M2*b^2*M3^3+2*a^2*M2^2*d^2*M1^2-2*a^2*d^2*M1^2*c^2-a^2*M2^2*d^4+2*M3^3*c^2*M1^3+2*b^2*M1^3*M3^3-M1^2*b^2*f^4+d^2*M1^4*c^2+2*d^3*M1^2*b^3-M2^4*d^2*M1^2+2*e^2*a*M1*d*M2^3-2*e^2*a*M2^2*M1^2*b-2*e^2*a*M2^2*M1^2*d+2*e^2*a*M2*M1^2*b*M3-2*e^2*a*b*M1*c^2*M3-2*e^2*a*b^3*M1*M3+2*e^2*a*d*M1^2*c^2-2*e^2*a^3*b*M3*M2+2*e^2*a^2*M2*M3*b^2+2*e^2*a^2*M2*M1*b^2+2*e^2*a^2*M2*c^2*M3+2*e^2*a*M2^2*b*M1*M3+2*e^2*a*M1^2*c^2*b+e^2*a^2*c^4+e^2*a^2*M2^4-e^2*a^4*M2^2+e^2*a^4*b^2-2*e^2*a^3*b^3-e^2*M2^4*M1^2-2*e^3*a^2*c^3+2*a^2*M2*d^2*M1*b^2+2*a^2*M2*M3*c^2*d^2-4*a^2*M2*M1^2*b*M3*d-2*a^2*M2*d*M1*f^2*b+2*a^2*d^2*c^2*f^2-2*a^2*M3^2*c^2*f^2-2*a^2*M3^3*c^2*M1-2*a^2*M3^2*c^2*d^2-2*a^2*M2^3*M3*d^2-2*a^2*M2^3*d^2*M1-2*a^2*M2^3*M3*f^2+2*a*d^3*M1^2*c^2-2*a*b^3*M1^2*M3^2+2*a*b^3*M1*M3^3+2*a^2*M2^3*M3^3-2*b^2*M1^2*c^2*d^2+2*M3*d*M1^3*c^2*b-2*c^2*M1^2*f^2*d^2-2*M1^3*M3*b^2*f^2-2*b^2*M1^3*M3*d^2+2*d^2*M1^2*c^2*M3^2+2*b^2*M1^2*d^2*M3^2+2*b^3*M1^3*M3*d-2*b^3*M1^2*d*M3^2-2*d^2*M1^2*b^2*f^2-2*c^2*M3^2*a^2*b^2-2*M3^3*M1*a^2*b^2+2*M3^2*M1^2*a^2*b^2+2*d^2*M1^2*c^2*M2^2+2*e^2*b^2*M1^2*M3^2-2*e^2*b^2*M1^2*d^2-2*e^2*b^2*M1^3*M3+2*e^2*b^3*M1^2*d-2*e^2*M3*c^2*M1^3-2*e^2*M2*b^2*M1^3)。

For step 103, the analytic solution of x, y and z can represent with following formula:

x＝X(M1,M2,M3)；

y＝Y(M1,M2,M3)；

z＝Z(M1,M2,M3)；

Wherein, Mi, i=1,2,3 is the pseudo range measurement error defined in above-mentioned formula (1).

Preferably.Simulation result shows, the analytic solution (such as in GPS location) of the double-enclosure form of x, y and z can be separated by enough far away, therefore as the position (x of provided approximate receiver separately _r, y _r, z _r) the closed analytic solution of x, y and z uniquely can be determined close to the position of actual receiver.For an approximate receiver position (x _r, y _r, z _r), a linear hypothesis is rational for the enough little caused change in interval.Therefore, the total differential of x, y and z can be written as:

$\mathrm{dx}=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{X}^{\′}\left(M_i\right){\mathrm{dM}}_i$

$\mathrm{dy}=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}Y\left(M_i\right){\mathrm{dM}}_i$

$\mathrm{dz}=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}Z\left(M_i\right){\mathrm{dM}}_i$

Reorganizing its matrix formulation form being compact is:

$\mathrm{dx}=\left(\begin{array}{c}\mathrm{dx}\\ \mathrm{dy}\\ \mathrm{dz}\end{array}\right)=\left(\begin{array}{ccc}{X}^{\′}\left(M_1\right)& X^{\′}\left(M_2\right)& X^{\′}\left(M_3\right)\\ Y^{\′}\left(M_1\right)& Y^{\′}\left(M_2\right)& Y^{\′}\left(M_3\right)\\ Z^{\′}\left(M_1\right)& Z^{\′}\left(M_2\right)& Z^{\′}\left(M_3\right)\end{array}\right)\left(\begin{array}{c}{\mathrm{dM}}_1\\ {\mathrm{dM}}_2\\ {\mathrm{dM}}_3\end{array}\right)=K\·\mathrm{dm}---\left(2\right)$

Covariance dx can be write as

cov(dx)＝E(dxdx ^T)＝KK ^Tcov(dm)＝Qcov(dm)(3)

Wherein matrix Q is provided by following formula:

$Q=K^{T}K=\left(\begin{array}{ccc}{q}_{11}& q_{12}& q_{13}\\ q_{21}& q_{22}& q_{23}\\ q_{31}& q_{32}& q_{33}\end{array}\right)---\left(4\right)$

If we suppose that the error of TDOA is independent identically distributed, the covariance of dm can be expressed as further:

cov(dm)＝σ ₀ ²I(5)

When I is unit matrix, the covariance matrix association dm of pseudo range measurement error is

$\mathrm{cov}\left(\mathrm{dx}\right)=\left(\begin{array}{ccc}{{\mathrm{\σ}}_x}^2& \·& \·\\ \·& {{\mathrm{\σ}}_y}^2& \·\\ \·& \·& {{\mathrm{\σ}}_2}^2\end{array}\right)---\left(6\right)$

(5) are substituted in (3), has

cov(dx)＝σ ₀ ²Q(7)

Positioning precision GDOP formula is as follows, and the standard deviation that may be defined as pseudo range measurement error amplifies the outgoing position realized:

$\mathrm{GDOP}=\sqrt{{{\mathrm{\σ}}_x}^2+{{\mathrm{\σ}}_y}^2+{{\mathrm{\σ}}_z}^2}/{\mathrm{\σ}}_0=\sqrt{(q_{11}+q_{22}+q_{33}){{\mathrm{\σ}}_0}^2}/{\mathrm{\σ}}_0=\sqrt{\mathrm{tr}\left(Q\right)}---\left(8\right)$

In other embodiments, those skilled in the art also can before positioning (before performing step 101), according to four emissive sources and any one receptacle of setting arbitrarily, the positional information of setting four emissive sources, according to above-mentioned building process, construct the above-mentioned formula of positioning precision GDOP, in concrete position fixing process, the positional information of the emissive source of reality and the actual range difference obtained are substituted into the positioning precision GDOP formula constructed in advance, asks for the concrete numerical value of the positioning precision factor.

Refer to Fig. 4, Fig. 4 is the structural representation of positioning system first embodiment of the present invention.

The positioning system method of present embodiment comprises receiver module 100, acquisition module 200, pseudorange module 300, precision module 400 and locating module 500, wherein:

Receiver module 100, for receiving the wireless signal of signal emitting-source synchronized transmissions of more than five by receiver.

Acquisition module 200, the time of reception of at least two group wireless signals is received for obtaining described receiver, wherein, often organize the wireless signal that wireless signal comprises four described signal emitting-source synchronized transmissions, in four described signal emitting-sources, at least one is different from the signal emitting-source of other any one group of wireless signals.

Pseudorange module 300, for the time of reception often organizing four wireless signals in wireless signal according to the light velocity and acquisition, calculate described receiver to the range difference of the distance often organizing a signal emitting-source corresponding to wireless signal respectively and between the distance arriving other three signal emitting-sources.

Precision module 400, the range difference often organizing wireless signal for obtaining substitutes into corresponding positioning precision GDOP formula as pseudo range measurement error, obtain and often organize dilution of precision corresponding to wireless signal, wherein, build the covariance matrix of the pseudo range measurement error of described positioning precision GDOP formula, be made up of the partial derivative of the location resolution solution formula of described receiver.

Locating module 500, for by respectively organizing dilution of precision corresponding to wireless signal, being obtained one group of wireless signal that the minimum dilution of precision of numerical value is corresponding, and being located the positional information of described receiver by this group wireless signal.

The positioning system of present embodiment, by the positioning precision GDOP formula that the location resolution solution formula that range difference corresponding for each group of wireless signal substitutes into receiver is derived, obtain the positioning precision factor of four signal emitting-sources corresponding to each group of wireless signal, four signal emitting-sources choosing dilution of precision minimum position described receiver, four signal emitting-sources only selecting positioning precision the highest according to the geometric position feature of each signal emitting-source and sensor position, eliminate clock drift (time dilution of precision) to the impact of the positioning precision factor, greatly improve the accuracy of location.

Wherein, for receiver module 100, described receiver preferably, is other receivers that wireless RF receivers, acoustic receiver or those skilled in the art are usual.Described signal emitting-source preferably, is other emissive sources that satellite, wireless radio transmission source, acoustic emission source or those skilled in the art are usual.

In one embodiment, also comprise sending module, for reference to same clock source, by the wireless signal transmission source wireless signal emission at one time of more than five.

For acquisition module 200, the group number of wireless signal can set according to location requirement, and group number minimum value is n is the number of described signal emitting-source.

Preferably, when receiver receives the wireless signal of signal emitting-source synchronized transmission of described more than five, the time of reception of each wireless signal can be recorded, then according to wireless signal group, transfers the time of reception of the wireless signal of each group.

In one embodiment, acquisition module 200 also can be used for choosing four wireless signals from the wireless signal of more than five received and combines, and obtain k group wireless signal group, wherein, k is more than or equal to 2.

In other embodiments, acquisition module 200 also can be chosen four signal emitting-sources in advance and combine from the wireless signal transmission source of described more than five, obtains k group wireless signal group.

For pseudorange module 300, preferably, can according to difference TDOA algorithm time of arrival, calculate the distance of described receiver to a signal emitting-source corresponding to often group wireless signal, respectively with described receiver to the range difference often organizing other three signal emitting-sources corresponding to wireless signal.Often group can calculate three range differences.

In other embodiments, the transmitting time that also can send from signal emitting-source according to each wireless signal and the launch time of acquisition, calculate described receiver to the distance often organizing a signal emitting-source corresponding to wireless signal, respectively with described receiver to the range difference often organizing other three signal emitting-sources corresponding to wireless signal.Often group can calculate three range differences.

For precision module 400, described positioning precision GDOP formula is only relevant to the geometric position feature of each signal emitting-source and receiver.

Preferably, when not importing the position data of four signal emitting-sources corresponding with often organizing wireless signal in described positioning precision GDOP formula, the position data of four corresponding signal emitting-sources need be obtained, and position data is substituted corresponding parameter.

For locating module 500, preferably, can based on difference TDOA algorithm time of arrival, the position of described receiver is oriented by one group of wireless signal that dilution of precision that numerical value is minimum is corresponding.

In one embodiment, locating module 500 can be used for the range difference of corresponding for dilution of precision minimum for numerical value one group of wireless signal, and the location resolution solution formula substituting into this group wireless signal corresponding solves, and obtains the position coordinates of described receiver.

In other embodiments, locating module 500 can also by the usual other technologies means of those skilled in the art, by one group of wireless signal that dilution of precision that numerical value is minimum is corresponding, locate the position of described receiver.

The following stated positioning system second of the present invention embodiment.

The positioning system of present embodiment and the difference of the first embodiment are: precision module 400 also can be used for:

Obtain and send four signal emitting-sources often organizing wireless signal and launch positional information when often organizing wireless signal.

According to distance between two points formula in three-dimensional coordinate coefficient, built the location resolution solution formula of the described receiver corresponding with each group of wireless signal by the positional information obtained.

By asking partial derivative to the location resolution solution formula often organizing wireless signal corresponding respectively, obtaining and often organizing covariance matrix corresponding to wireless signal, and obtaining the positioning precision GDOP formula corresponding with often organizing wireless signal respectively according to described covariance matrix.

The positioning system of present embodiment, according to corresponding with often organizing wireless signal four signal emitting-source positional informations its, build new positioning precision GDOP formula, be the closed analytic solution computing method of one, the elegant impact on the positioning precision factor of clock can be eliminated.

In other embodiments, those skilled in the art also can before positioning, according to four emissive sources and any one receptacle of setting arbitrarily, the positional information of setting four emissive sources, according to above-mentioned building process, construct the above-mentioned formula of positioning precision GDOP, in concrete position fixing process, the positional information of the emissive source of reality and the actual range difference obtained are substituted into the positioning precision GDOP formula constructed in advance, asks for the concrete numerical value of the positioning precision factor.

The above embodiment only have expressed several embodiment of the present invention, and it describes comparatively concrete and detailed, but therefore can not be interpreted as the restriction to the scope of the claims of the present invention.It should be pointed out that for the person of ordinary skill of the art, without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.Therefore, the protection domain of patent of the present invention should be as the criterion with claims.

Claims (10)

1. a localization method, is characterized in that, comprises the following steps:

The wireless signal of the signal emitting-source synchronized transmissions of more than five is received by receiver;

Obtain the time of reception that described receiver receives at least two group wireless signals, wherein, often organize the wireless signal that wireless signal comprises four described signal emitting-source synchronized transmissions, in four described signal emitting-sources, at least one is different from the signal emitting-source of other any one group of wireless signals;

According to the time of reception often organizing four wireless signals in wireless signal of the light velocity and acquisition, calculate described receiver to the range difference of the distance often organizing a signal emitting-source corresponding to wireless signal respectively and between the distance arriving other three signal emitting-sources;

The range difference often organizing wireless signal obtained is substituted into corresponding positioning precision GDOP formula as pseudo range measurement error, obtain and often organize dilution of precision corresponding to wireless signal, wherein, the covariance matrix building the pseudo range measurement error of described positioning precision GDOP formula is made up of the partial derivative of the location resolution solution formula of described receiver;

By respectively organizing dilution of precision corresponding to wireless signal, obtaining one group of wireless signal that the minimum dilution of precision of numerical value is corresponding, and being located the positional information of described receiver by this group wireless signal.

2. localization method according to claim 1, is characterized in that, described to be received the step of the wireless signal of the signal emitting-source synchronized transmissions of more than five by receiver before, further comprising the steps of:

With reference to same clock source, by the wireless signal transmission source wireless signal emission at one time of more than five.

3. localization method according to claim 1, is characterized in that, before the described receiver of described acquisition receives the step of the time of reception of at least two group wireless signals, further comprising the steps of:

From the wireless signal of more than five received, choose four wireless signals combine, obtain k group wireless signal group, wherein, k is more than or equal to 2.

4. localization method according to claim 1, is characterized in that, before the described range difference often organizing wireless signal by acquisition substitutes into the step of positioning precision GDOP formula, further comprising the steps of:

Obtain and send four signal emitting-sources often organizing wireless signal and launch positional information when often organizing wireless signal;

According to distance between two points formula in three-dimensional coordinate coefficient, built the location resolution solution formula of the described receiver corresponding with each group of wireless signal by the positional information obtained;

By asking partial derivative to the location resolution solution formula often organizing wireless signal corresponding respectively, obtaining and often organizing covariance matrix corresponding to wireless signal, and obtaining the positioning precision GDOP formula corresponding with often organizing wireless signal respectively according to described covariance matrix.

5. localization method as claimed in any of claims 1 to 4, is characterized in that, described step of locating the positional information of described receiver by this group wireless signal comprises the following steps:

By the range difference of corresponding for dilution of precision minimum for numerical value one group of wireless signal, the location resolution solution formula substituting into this group wireless signal corresponding solves, and obtains the position coordinates of described receiver.

6. a positioning system, is characterized in that, comprising:

Receiver module, for receiving the wireless signal of signal emitting-source synchronized transmissions of more than five by receiver;

Acquisition module, the time of reception of at least two group wireless signals is received for obtaining described receiver, wherein, often organize the wireless signal that wireless signal comprises four described signal emitting-source synchronized transmissions, in four described signal emitting-sources, at least one is different from the signal emitting-source of other any one group of wireless signals;

Pseudorange module, for the time of reception often organizing four wireless signals in wireless signal according to the light velocity and acquisition, calculate described receiver to the range difference of the distance often organizing a signal emitting-source corresponding to wireless signal respectively and between the distance arriving other three signal emitting-sources;

Precision module, the range difference often organizing wireless signal for obtaining substitutes into corresponding positioning precision GDOP formula as pseudo range measurement error, obtain and often organize dilution of precision corresponding to wireless signal, wherein, build the covariance matrix of the pseudo range measurement error of described positioning precision GDOP formula, be made up of the partial derivative of the location resolution solution formula of described receiver;

Locating module, for by respectively organizing dilution of precision corresponding to wireless signal, being obtained one group of wireless signal that the minimum dilution of precision of numerical value is corresponding, and being located the positional information of described receiver by this group wireless signal.

7. positioning system according to claim 6, is characterized in that, also comprises sending module, for reference to same clock source, by the wireless signal transmission source wireless signal emission at one time of more than five.

8. positioning system according to claim 6, is characterized in that, described acquisition module also combines for choosing four wireless signals from the wireless signal of more than five received, and obtain k group wireless signal group, wherein, k is more than or equal to 2.

9. positioning system according to claim 6, is characterized in that, described precision module also for:

Obtain and send four signal emitting-sources often organizing wireless signal and launch positional information when often organizing wireless signal;

According to distance between two points formula in three-dimensional coordinate coefficient, built the location resolution solution formula of the described receiver corresponding with each group of wireless signal by the positional information obtained;

By asking partial derivative to the location resolution solution formula often organizing wireless signal corresponding respectively, obtaining and often organizing covariance matrix corresponding to wireless signal, and obtaining the positioning precision GDOP formula corresponding with often organizing wireless signal respectively according to described covariance matrix.

10. according to the positioning system in claim 6 to 9 described in any one, it is characterized in that, described locating module is also for the range difference by corresponding for dilution of precision minimum for numerical value one group of wireless signal, the location resolution solution formula substituting into this group wireless signal corresponding solves, and obtains the position coordinates of described receiver.