CN102680991A - Technology optimizing pseudolite laying through optimal observation matrix - Google Patents

Abstract

The invention relates to technology of laying pseudolites. As for traditional technology, the optimal matrix is obtained first. The technology provided by the invention has the characteristic of purposefulness. Due to the adoption of the technology, the pseudolites can be laid onto ideal positions, the laying process is simple, and the stimulation analysis load is small. Moreover, the technology utilizes the relation of the observation matrix and the GDOP (Geometric Dilution of Precision), can effectively improve the positioning precision and is an effective method for optimizing pseudolite laying.

Description

A kind of technology of utilizing best observing matrix to optimize the pseudo satellite, pseudolite laying

Technical field

The present invention relates to a kind of technology of laying pseudo satellite, pseudolite, specifically, be meant to utilize and seek GDOP (Geometrical Dilution of Precision) minimum value, the best observing matrix of deriving, and utilize best observing matrix to lay the technology of pseudo satellite, pseudolite.

Background technology

Laying technology for general pseudo satellite, pseudolite, generally is that pseudo satellite, pseudolite is laid on the corner, and the solid figure volume that pseudo satellite, pseudolite is constituted is maximum; Position operation and precision simulation analysis then; Pass judgment on out at last optimized constellation structures, thereby layout has no purpose, the simulation work amount is big.

Utilizing best observing matrix to lay pseudo satellite, pseudolite is under the technology of traditional laying pseudo satellite, pseudolite, at first will need positioned area to carry out piecemeal based on landform and handle the operation of obtaining best matrix to each piece.Observing matrix is a very important parameter in the positioning action, and the GDOP factor is to be derived by observing matrix.The size of GDOP directly influences bearing accuracy.The technology that pseudo satellite, pseudolite is laid in this optimization has purpose, can more accurately pseudo satellite, pseudolite be deployed on the ideal position, makes the laying process simple, and the simulation analysis workload is little.

The relation of the best observing matrix of this utilization has been optimized techniques make use that pseudo satellite, pseudolite lays observing matrix and GDOP can effectively improve bearing accuracy, is the effective ways of optimizing the pseudo satellite, pseudolite laying.

Summary of the invention

The objective of the invention is to: proposed a kind of method that pseudo satellite, pseudolite is laid of optimizing, the simulation analysis workload is reduced significantly, accurately pseudo satellite, pseudolite has been distributed to ideal position, improved bearing accuracy.

Technical scheme of the present invention is: before laying pseudo satellite, pseudolite; At first the needs positioned area is carried out piecemeal and handle, obtain best observing matrix, utilize the relation of GDOP and observing matrix to each piece according to landform; When GDOP hour, observing matrix is best observing matrix.Utilize observing matrix then, in conjunction with actual geographical environment distribution pseudo satellite, pseudolite.The signal of ground receiver reception this moment pseudo satellite, pseudolite positions, and can obtain desirable bearing accuracy.

Advantage of the present invention is: provide a kind of utilization to obtain best observing matrix and optimized the technology that pseudo satellite, pseudolite is laid; The advantage of this method is at first to obtain best observing matrix; Lay pseudo satellite, pseudolite through observing matrix; Reduce the blindness when laying pseudo satellite, pseudolite, reduced the workload of simulation analysis, effectively improved bearing accuracy.

Description of drawings

Fig. 1 utilizes to obtain the overall framework figure that best observing matrix is optimized pseudo satellite, pseudolite laying technology.

Fig. 2 is the frame diagram that obtains best observing matrix.

Embodiment

To combine accompanying drawing that the present invention is done further detailed description below.

Like Fig. 1, the present invention lays at traditional pseudo satellite, pseudolite technically have been increased best observing matrix and has obtained operation, lays pseudo satellite, pseudolite based on the best observing matrix that gets access to then.

Like Fig. 2, of the present inventionly obtain the operation of best observing matrix.This operation combines actual geographical environment, at first the environment piecemeal is handled, and each piece is chosen its geometric center point, utilizes operation as follows, obtains best observing matrix:

The pseudo satellite, pseudolite numbering is respectively s1, s2, and s3 ..., sn.Element a in the observing matrix _i=(a _Xi, a _Yi, a _Zi) be the unit vector of pointing to i pseudo satellite, pseudolite position with linearization point.Get wherein that s1 is positioned on the x axle, s2 is positioned on the xy plane, and the user is positioned at initial point.Then observing matrix H is: $H=\left[\begin{array}{cccc}1& 0& 0& 1\\ a_{x2}& a_{y2}& 0& 1\\ a_{x3}& a_{y3}& a_{z3}& 1\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ a_{\mathrm{Xn}}& a_{\mathrm{Yn}}& a_{\mathrm{Zn}}& 1\end{array}\right],$ Order $H^{T}H=\left[\begin{array}{ccccc}1& a_{x2}& a_{x3}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{\mathrm{Xn}}\\ 0& a_{y2}& a_{y3}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{\mathrm{Yn}}\\ 0& 0& a_{z3}& \&CenterDot;\&CenterDot;\&CenterDot;& a_{\mathrm{Zn}}\\ 1& 1& 1& \&CenterDot;\&CenterDot;\&CenterDot;& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 1\\ a_{x2}& a_{y2}& 0& 1\\ a_{x3}& a_{y3}& a_{z3}& 1\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ a_{\mathrm{Xn}}& a_{\mathrm{Yn}}& a_{\mathrm{<figure-callout\; id="1"\; label="Zn"\; filenames="HDA00001720689600011.png"\; state="\{\{state\}\}">Zn</figure-callout>}}& 1\end{array}\right]=M=\left[\begin{array}{cccc}{m}_{11}& m_{12}& m_{13}& m_{14}\\ m_{21}& m_{22}& m_{23}& m_{24}\\ m_{31}& m_{32}& m_{33}& m_{34}\\ m_{41}& m_{42}& m_{43}& m_{44}\end{array}\right],$ Utilize H ^TH=M is a symmetrical matrix, simultaneously

Have after handling calculating:

$\left\{\begin{array}{c}{m}_{11}=1+a_{x2}^2+a_{x3}^2+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xi}}^2+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xn}}^2\\ m_{12}=a_{x2}{a}_{y2}+a_{x3}{a}_{y3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xi}}{a}_{\mathrm{yi}}+\&CenterDot;\&CenterDot;\&CenterDot;a_{\mathrm{xn}}{a}_{\mathrm{yn}}\\ m_{13}=a_{x3}{a}_{z3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xi}}{a}_{\mathrm{zi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xn}}{a}_{\mathrm{zn}}\\ m_{14}=1+a_{x2}+a_{x3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xn}}\end{array}\right.$

$\left\{\begin{array}{c}{m}_{21}=a_{y2}{a}_{x2}+a_{y3}{a}_{x3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yi}}{a}_{\mathrm{xi}}+\&CenterDot;\&CenterDot;\&CenterDot;a_{\mathrm{yn}}{a}_{\mathrm{<figure-callout\; id="22"\; label="xn\; m"\; filenames="HDA00001720689600011.png"\; state="\{\{state\}\}">xn</figure-callout>}}& \\ m_{}{}_{22}=a_{y2}^2+a_{y3}^2+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yi}}^2+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yn}}^2\\ m_{23}=a_{y3}{a}_{z3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yi}}{a}_{\mathrm{zi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yn}}{a}_{\mathrm{zn}}\\ m_{24}=a_{y2}+a_{y3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yn}}\end{array}\right.$

$\left\{\begin{array}{c}{m}_{31}=a_{z3}{a}_{x3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zi}}{a}_{\mathrm{yi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zn}}{a}_{\mathrm{xn}}\\ m_{32}=a_{z3}{a}_{y3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zi}}{a}_{\mathrm{yi}}+a_{\mathrm{zn}}{a}_{\mathrm{yn}}\\ m_{33}=a_{z3}^2+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zi}}^2+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zn}}^2\\ m_{34}=a_{z3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zn}}\end{array}\right.$

$\left\{\begin{array}{c}{m}_{41}=1+a_{x2}+a_{x3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{xn}}\\ m_{42}=a_{y2}+a_{y3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{yn}}\\ m_{43}=a_{z3}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zi}}+\&CenterDot;\&CenterDot;\&CenterDot;+a_{\mathrm{zn}}\\ m_{44}=n\end{array}\right.$

m ₁₂=m ₂₁, m ₁₃=m ₃₁, m ₁₄=m ₄₁, m ₂₃=m ₃₂, m ₂₄=m ₄₂, m ₃₄=m ₄₃, M is a symmetrical matrix.The eigenwert of matrix M is λ, and E is a unit matrix, utilizes the knowledge of linear algebra to know, | M-λ E|=0 perseverance in plural scope is separated, and the proper vector of real symmetric matrix is real number, so | M-λ E|=0 must separate and separate and be real number.The proper vector of matrix M:

$|M-\mathrm{\&lambda;E}|=|H^{T}H-\mathrm{\&lambda;E}|=\left|\begin{array}{cccc}{m}_{11}-\mathrm{\&lambda;}& m_{12}& m_{13}& m_{14}\\ m_{12}& m_{22}-\mathrm{\&lambda;}& m_{23}& m_{24}\\ m_{13}& m_{23}& m_{33}-\mathrm{\&lambda;}& m_{34}\\ m_{14}& m_{24}& m_{34}& m_{44}-\mathrm{\&lambda;}\end{array}\right|$

$={\mathrm{\&lambda;}}^4-{\mathrm{\&lambda;}}^3(m_{11}+{\mathrm{<figure-callout\; id="22"\; label="m"\; filenames="HDA00001720689600011.png"\; state="\{\{state\}\}">m</figure-callout>}}_{22}+m_{33}+m_{44})+{\mathrm{\&lambda;}}^2{m}_{11}{\mathrm{<figure-callout\; id="22"\; label="m"\; filenames="HDA00001720689600011.png"\; state="\{\{state\}\}">m</figure-callout>}}_{22}+{\mathrm{\&lambda;}}^2{m}_{11}{m}_{33}+{\mathrm{\&lambda;}}^2{m}_{11}{m}_{44}-{\mathrm{\&lambda;}}^2{m_{12}}^2-{\mathrm{\&lambda;}}^2{m_{13}}^2$

$-{\mathrm{\&lambda;}}^2{m_{14}}^2+{\mathrm{\&lambda;}}^2{m}_{22}{m}_{33}+{\mathrm{\&lambda;}}^2{A}_{22}{m}_{44}-{\mathrm{\&lambda;}}^2{m_{23}}^2-{\mathrm{\&lambda;}}^2{m_{24}}^2+{\mathrm{\&lambda;}}^2{m}_{33}{m}_{44}-{\mathrm{\&lambda;}}^2{m_{34}}^2$

$-\mathrm{\&lambda;}{m}_{11}{m}_{22}{m}_{33}-\mathrm{\&lambda;}{m}_{11}{m}_{22}{m}_{44}+\mathrm{\&lambda;}{m}_{11}{m_{23}}^2+\mathrm{\&lambda;}{m}_{11}{m_{24}}^2-\mathrm{\&lambda;}{m}_{11}{m}_{33}{m}_{44}+\mathrm{\&lambda;}{m}_{11}{m_{34}}^2$

$+\mathrm{\&lambda;}{m_{12}}^2{m}_{33}+\mathrm{\&lambda;}{m_{12}}^2{m}_{44}-2\mathrm{\&lambda;}{m}_{12}{m}_{13}{m}_{23}-2\mathrm{\&lambda;}{m}_{12}{m}_{14}{m}_{24}+\mathrm{\&lambda;}{m_{13}}^2{\mathrm{<figure-callout\; id="22"\; label="m"\; filenames="HDA00001720689600011.png"\; state="\{\{state\}\}">m</figure-callout>}}_{22}+\mathrm{\&lambda;}{m_{13}}^2{m}_{44}$

$-2\mathrm{\&lambda;}{m}_{13}{m}_{14}{m}_{34}+\mathrm{\&lambda;}{m_{14}}^2{\mathrm{<figure-callout\; id="22"\; label="m"\; filenames="HDA00001720689600011.png"\; state="\{\{state\}\}">m</figure-callout>}}_{22}+\mathrm{\&lambda;}{m_{14}}^2{m}_{33}$

$-\mathrm{\&lambda;}{m}_{22}{m}_{33}{m}_{44}+\mathrm{\&lambda;}{m}_{22}{m_{34}}^2+\mathrm{\&lambda;}{m_{23}}^2{m}_{44}-2\mathrm{\&lambda;}{m}_{23}{m}_{24}{m}_{34}+\mathrm{\&lambda;}{m}_{33}{m_{24}}^2$

$+m_{11}{m}_{22}{m}_{33}{m}_{44}-m_{11}{m}_{22}{m_{34}}^2-m_{11}{m_{23}}^2{m}_{44}+2m_{11}{m}_{23}{m}_{24}{m}_{34}-m_{11}{m}_{33}{m_{24}}^2-{m_{12}}^2{m}_{33}{m}_{44}$

$+{m_{12}}^2{m_{34}}^2+2m_{12}{m}_{13}{m}_{23}{m}_{44}-2m_{12}{m}_{13}{m}_{24}{m}_{34}-2m_{12}{m}_{14}{m}_{23}{m}_{34}$

$+2m_{12}{m}_{14}{m}_{24}{m}_{33}-{m_{13}}^2{m}_{22}{m}_{44}+{m_{13}}^2{m_{24}}^2+2m_{13}{m}_{14}{m}_{22}{m}_{34}-2m_{13}{m}_{14}{m}_{23}{m}_{24}$

$-{m_{14}}^2{m}_{22}{m}_{33}+{m_{14}}^2{m_{23}}^2$

| M-λ E| is the quadravalence polynomial expression of λ, and the eigenwert of establishing M is x, y, and z, v,

|M-λE|＝(λ-x)(λ-y)(λ-z)(λ-v)

＝λ ⁴－(x+y+z+v)λ ³+(xy+xz+xv+yz+yv+zv)λ ²

－(xyz+xyv+xzv+yzv)λ+xyzv

Utilize | M-λ E| expression formula respective items equates, x, y, z, v can use m _IjShow.The eigenwert of the inverse matrix of known matrix is the inverse of its eigenwert,

Be M ^-1Proper vector, $\mathrm{GDOP}=\sqrt{\mathrm{trace}\left({\left(\begin{array}{cc}{H}^T& H\end{array}\right)}^{-1}\right)}=\sqrt{\mathrm{trace}\left(M^{-1}\right)}=\sqrt{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}+\frac{1}{v}}=\sqrt{\frac{\mathrm{yzv}+\mathrm{xzv}+\mathrm{xyv}+\mathrm{xyz}}{\mathrm{xyzv}}}$ Make the GDOP minimum can be in the hope of x, y, z, the value of v, thus can obtain m _IjValue, can draw a then _i=(a _Xi, a _Yi, a _Zi) value, promptly best observing matrix.

Through best observing matrix, can the pseudo satellite, pseudolite layout of this fritter be confirmed.Piecemeal to all is as above handled, and the pseudo satellite, pseudolite that can obtain Zone Full is laid scheme.

Claims (4)

1. one kind is utilized the calculating optimum observing matrix to optimize the technology that pseudo satellite, pseudolite is laid, and traditional technical, has increased optimum observing matrix derivation part.

2. the technology of pseudo satellite, pseudolite is laid in optimization according to claim 1, it is characterized in that geometric dilution of precision GDOP (Geometrical Dilution of Precision) is sought the method used in the minimum value process.

3. the technology of pseudo satellite, pseudolite is laid in optimization according to claim 1, it is characterized in that searching optimum observing matrix based on the GDOP minimum value.

4. the technology of pseudo satellite, pseudolite is laid in optimization according to claim 1, it is characterized in that utilizing best observing matrix to lay pseudo satellite, pseudolite, obtains the optimum position that pseudo satellite, pseudolite is laid, and makes geometric dilution of precision minimum, and bearing accuracy is best.

Images