CN104864876A - Lunar rover joint positioning method and system - Google Patents

Abstract

The invention provides a lunar rover joint positioning method and system. The method comprises the following steps: inputting an approximate coordinate of a lunar rover, observed value time difference of VLBI and an observed value of celestial navigation, calculating a partial derivative of the celestial navigation part, and composing a coefficient matrix of the celestial navigation part; calculating a partial derivative of the VLBI part, and composing a coefficient matrix of the VLBI part; calculating a partial derivative of a VLBI limiting condition, and composing a coefficient matrix of the VLBI limiting condition; calculating a partial derivative of the constraint condition of a joint system, and composing a coefficient matrix of the constraint condition of the joint system; calculating an approximate value of the celestial navigation, and composing a corresponding matrix; calculating the difference of the approximate value and the observed value of VLBI, and composing a corresponding matrix; composing a coefficient matrix of the joint system for balancing, and judging whether the calculated result conforms to a convergence condition or not; if yes, outputting the result; if not, iterating again until the calculated result conforms to the convergence condition. By adopting the technical scheme, the positioning precision and stability can be improved.

Description

Lunar vehicle combined positioning method and system

Technical Field

The invention belongs to the technical field of deep space exploration, and particularly relates to a lunar rover positioning method and system combining astronomical navigation and VLBI.

Background

When positioning the lunar rover, high precision, all-weather observation and stability are basic requirements of a positioning system. Currently, positioning is mainly performed by using an astronomical navigation positioning technology or a VLBI (very long baseline interferometry) technology. The astronomical navigation positioning technology is an absolute positioning method. The position coordinates of the object carrier observed by the device do not include errors which become larger as time and sum distances increase. Astronomical navigation mainly obtains position information of a target by means of observation information of the earth, the sun and other celestial bodies. The VLBI technology measures the time difference of the same signal sent by the lunar rover from the two measuring stations on the ground through different distances between the lunar rover and the two measuring stations on the ground, thereby establishing a geometric measurement relation between the detector and the two measuring stations, and calculating the position of the detector through a large number of observed values and the known positions of the measuring stations.

However, both techniques have their own drawbacks:

(1) VLBI positioning techniques can provide highly accurate position information, but will not work if its signal cannot be received for some external reason.

(2) The positioning precision of the lunar vehicle adopting the astronomical navigation positioning technology is lower than that of the VLBI technology at present.

Disclosure of Invention

Aiming at the problems, the invention further innovates and improves on the basis of the research of the prior scholars, and provides a lunar rover combined positioning method and system with high precision and high stability.

The technical scheme of the invention provides a lunar vehicle combined positioning method, which executes the following steps,

step 1, setting the position of the lunar vehicle as the parameter vectorLabeling of respective approximationsWherein (x)_s,y_s,z_s) Showing the rectangular coordinates of the lunar vehicle,is the geodetic coordinates of the lunar vehicle,the right ascension and the declination of the lunar vehicle in a lunar fixation coordinate system respectively;

inputting lunar rover approximate coordinatesAnd time difference of observation τ of VLBI₀And observation values sin h and tan A of astronomical navigation, wherein h represents the altitude angle of the observation celestial body, and A is the azimuth angle of the observation celestial body; wherein, approximate coordinates of the lunar vehicleAs an initial approximation(x_s0,y_s0,z_s0) Represents an initial value of the rectangular coordinates of the lunar vehicle,an initial value representing its geodetic coordinates;

step 2, calculating a partial derivative of the astronomical navigation part, and forming a coefficient matrix of the astronomical navigation part; calculating partial derivatives of the VLBI part and forming a coefficient matrix of the VLBI part; calculating partial derivatives of the VLBI constraint condition, and forming a coefficient matrix of the VLBI constraint condition; calculating partial derivatives of the constraint conditions of the joint system, and forming a coefficient matrix of the constraint conditions of the joint system; calculating approximate values of astronomical navigation and forming a corresponding matrix; calculating the difference between the approximate value of the VLBI and the observed value, and forming a corresponding matrix; the realization is as follows,

according to formula and according to the current approximationMiddle parameterCalculating partial derivative of the astronomical navigation part, and forming a coefficient matrix B of the astronomical navigation part according to the formula_CNS；

Is like

Wherein, alpha is the observed right ascension and declination of the celestial body, and GHA is the Greenwich mean time angle of spring points;

formula II

Wherein,for the parameters soughtThe number of corrections of (a);

according to equation three and according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivatives of the VLBI portions and forming a coefficient matrix B of the VLBI portions according to the formula_VLBI；

$\left\{\begin{array}{c}{a}_{11}=\frac{x_1-x_s}{r_1}-\frac{x_2-x_s}{r_2}\\ a_{12}=\frac{y_1-y_s}{r_1}-\frac{y_2-y_s}{r_2}\\ a_{13}=\frac{z_1-z_s}{r_1}-\frac{z_2-z_s}{r_2}\end{array}\right.$ Formula III

In the formula, a₁₁、a₁₂、a₁₃In order to observe the values of the coefficients of the equation,partial derivatives respectively equal to VLBI portions (x₁,y₁,z₁) Coordinates of station 1 are shown, (x)₂,y₂,z₂) Coordinates of the station 2, r₁、r₂Represents the distance value between the lunar probe and the station 1 and the station 2;

<math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>dx</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dy</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math> formula IV

Wherein,for the parameter (x) sought_s,y_s,z_s) The number of corrections of (a); c represents the speed of light; tau is₀Is the time delay observation for the VLBI; tau is_cIs a theoretical geometric time delay value; dx (x)_s,dy_s,dz_sThe correction number of the coordinate of the lunar vehicle is obtained;

according to equation five and according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivative of VLBI restriction condition, and forming coefficient matrix B of VLBI restriction condition according to formula six_{VLBI_Lmt}；

$\begin{array}{c}0=\frac{x_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dx}}_S+\frac{y_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dy}}_S+\frac{z_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dz}}_S\\ ={\mathrm{ladx}}_S+{\mathrm{lbdy}}_S+{\mathrm{lcdz}}_S\end{array}$ Formula five

$\left\{\begin{array}{c}{l}_{\mathrm{VLBI}\_\mathrm{Lmt}}=0\\ B_{\mathrm{VLBI}\_\mathrm{Lmt}}=\left[\begin{array}{ccc}\mathrm{la}& \mathrm{lb}& \mathrm{lc}\end{array}\right]\end{array}\right.$ Formula six

Wherein l_{VLBI_Lmt}Represents the difference between the observed value of the VLBI constraint and its approximate value;

according to the formula seven and according to the current approximationCalculating partial derivative of constraint condition of combined system, and forming combined system according to formula eightCoefficient matrix B of constraint conditions_{dbl_Lmt}；

Formula seven

Wherein k is₁₁,k₁₂,…,k₃₅Coefficients representing the observation equation for the constraint of the joint system are respectively equal to the corresponding partial derivatives of the constraint of the joint system; n is a radical of₀Representing an initial value of the radius of the Mao-unitary ring, wherein H is the elevation of the lunar surface; a represents the ellipsoid major semi-axis, e represents the ellipsoid first eccentricity;

$\left\{\begin{array}{c}{l}_{\mathrm{dbl}\_\mathrm{Lmt}}=0\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}=\left[\begin{array}{ccccc}{k}_{11}& k_{12}& k_{13}& 0& 0\\ k_{21}& k_{22}& 0& k_{24}& 0\\ k_{31}& 0& 0& 0& k_{35}\end{array}\right]\end{array}\right.$ type eight

Wherein l_{dbl_Lmt}A difference between the observed value representing the constraint of the joint system and an approximation thereof;

according to formula nine and according to the current approximationMiddle parameterCalculating an approximation of astronomical navigation (sin h)₀And (tan A)₀And forming a matrix l according to the difference between the approximate value and the observed value of the astronomical navigation_CNS；

Nine-degree of expression

Matrix l_CNSThe composition mode is that, $l_{\mathrm{CNS}}=\left[\begin{array}{c}\sinh -{\left(\sinh \right)}_0\\ \tan A-{\left(\tan A\right)}_0\end{array}\right];$

according to the formula ten and according to (x)_s0,y_s0,z_s0) Calculating the difference between the approximated value and the observed value of VLBI and forming a matrix l_VLBI；

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>c&tau;</mi> <mrow> <mn>120</mn> <mo>-</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mi>c</mi> <mo>[</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </math> Formula ten

In the formula, c τ_12o-cRepresenting a difference between the observed value of the VLBI and the approximate value;

matrix l_VLBIIs composed in the following manner_VLBI＝[c(τ₀-τ_c)]；

Step 3, obtaining the coefficient matrix B by the above steps_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}And a matrix l of differences between the approximation values and the observed values_CNS、l_VLBI、l_{VLBI_Lmt}、l_{dbl_Lmt}Coefficient matrix B of combined system formed according to formula eleven_dblAnd l_dblSetting parametersRepresenting a difference between the true value and the approximate value; adjustment is carried out according to the formula twelve to obtainJudging whether the result meets the convergence condition, if so, entering the step 4, otherwise, entering the stepAs a new approximationReturning to the step 2 to carry out reiterative solution until the convergence condition is met;

$\left\{\begin{array}{cc}{V}_{\mathrm{dbl}}={\left[\begin{array}{cccc}{V}_{\mathrm{CNS}}& V_{\mathrm{VLBI}}& V_{\mathrm{VLBI}\_\mathrm{Lmt}}& V_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& {\hat{x}}_{\mathrm{dbl}}=\left[\begin{array}{cc}{\hat{x}}_{\mathrm{CNS}}& {\hat{x}}_{\mathrm{VLBI}}\end{array}\right]\\ B_{\mathrm{tmp}}=\left[\begin{array}{cc}{B}_{\mathrm{CNS}}& 0\\ 0& B_{\mathrm{VLBI}}\\ 0& B_{\mathrm{VLBI}\_\mathrm{Lmt}}\end{array}\right]& B_{\mathrm{dbl}}=\left[\begin{array}{c}{B}_{\mathrm{tmp}}\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]\\ l_{\mathrm{dbl}}={\left[\begin{array}{cccc}{l}_{\mathrm{CNS}}& l_{\mathrm{VLBI}}& l_{\mathrm{VLBI}\_\mathrm{Lmt}}& l_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& \\ P_{\mathrm{dbl}}=\left[\begin{array}{cccc}{P}_{\mathrm{CNS}}& & & \\ & P_{\mathrm{VLBI}}& & \\ & & P_{\mathrm{VLBI}\_\mathrm{lmt}}& \\ & & & P_{\mathrm{dbl}\_\mathrm{lmt}}\end{array}\right]& \end{array}\right.$ formula eleven

${\hat{x}}_{\mathrm{dbl}}={\left(B_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{B}_{\mathrm{dbl}}\right)}^{-1}{B}_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{l}_{\mathrm{dbl}}$ Twelve formulas

Wherein, V_dblIndicating the correction of the observed value of the joint system, P_dblWeight matrix of constraints when solving for a combined system, where P_CNS、P_VLBI、P_{VLBI_Lmt}、P_{dbl_Lmt}Are coefficient matrices B respectively_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}A corresponding weight matrix;

step 4, solving the result according to the final parametersAnd outputting the position coordinate information of the lunar vehicle.

Furthermore, the weight matrix P of the constraint conditions when the combined system is solved in the step 3_dblDetermined according to the Hummer's Square difference component estimation method.

In step 3, the convergence condition is a parameterIn x_s、y_sAnd z_sThe corresponding difference is less than 10m,the corresponding difference is less than 10^-8The corresponding difference of lambda is less than 10^-8。

The invention also correspondingly provides a lunar rover joint positioning system which comprises the following modules,

an initialization module for setting the determined lunar vehicle position as represented by a parameter vectorLabeling of respective approximationsWherein (x)_s,y_s,z_s) Showing the rectangular coordinates of the lunar vehicle,is the geodetic coordinate of lunar vehicle, lambda,The right ascension and the declination of the lunar vehicle in a lunar fixation coordinate system respectively;

inputting lunar rover approximate coordinatesAnd time difference of observation τ of VLBI₀And observed values sin h and tan of astronomical navigationA, h represents the altitude angle of the observation celestial body, and A is the azimuth angle of the observation celestial body; wherein, approximate coordinates of the lunar vehicleAs an initial approximation(x_s0,y_s0,z_s0) Represents an initial value of the rectangular coordinates of the lunar vehicle,an initial value representing its geodetic coordinates;

the matrix establishing module is used for calculating the partial derivative of the astronomical navigation part and forming a coefficient matrix of the astronomical navigation part; calculating partial derivatives of the VLBI part and forming a coefficient matrix of the VLBI part; calculating partial derivatives of the VLBI constraint condition, and forming a coefficient matrix of the VLBI constraint condition; calculating partial derivatives of the constraint conditions of the joint system, and forming a coefficient matrix of the constraint conditions of the joint system; calculating approximate values of astronomical navigation and forming a corresponding matrix; calculating the difference between the approximate value of the VLBI and the observed value, and forming a corresponding matrix; the realization is as follows,

according to formula and according to the current approximationMiddle parameterCalculating partial derivative of the astronomical navigation part, and forming a coefficient matrix B of the astronomical navigation part according to the formula_CNS；

Is like

Wherein, alpha is the observed right ascension and declination of the celestial body, and GHA is the Greenwich mean time angle of spring points;

formula II

Wherein,for the parameters soughtThe number of corrections of (a);

according to equation three and according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivatives of the VLBI portions and forming a coefficient matrix B of the VLBI portions according to the formula_VLBI；

$\left\{\begin{array}{c}{a}_{11}=\frac{x_1-x_s}{r_1}-\frac{x_2-x_s}{r_2}\\ a_{12}=\frac{y_1-y_s}{r_1}-\frac{y_2-y_s}{r_2}\\ a_{13}=\frac{z_1-z_s}{r_1}-\frac{z_2-z_s}{r_2}\end{array}\right.$ Formula III

In the formula, a₁₁、a₁₂、a₁₃For values of the observation equation coefficients, respectively equal to the partial derivatives of the VLBI sections (x₁,y₁,z₁) Coordinates of station 1 are shown, (x)₂,y₂,z₂) Coordinates of the station 2, r₁、r₂Represents the distance value between the lunar probe and the station 1 and the station 2;

<math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>dx</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dy</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math> formula IV

Wherein,for the parameter (x) sought_s,y_s,z_s) The number of corrections of (a); c represents the speed of light; tau is₀Is the time delay observation for the VLBI; tau is_cIs a theoretical geometric time delay value; dx (x)_s,dy_s,dz_sThe correction number of the coordinate of the lunar vehicle is obtained;

according to equation five and according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivative of VLBI restriction condition, and forming coefficient matrix B of VLBI restriction condition according to formula six_{VLBI_Lmt}；

$\begin{array}{c}0=\frac{x_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dx}}_S+\frac{y_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dy}}_S+\frac{z_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dz}}_S\\ ={\mathrm{ladx}}_S+{\mathrm{lbdy}}_S+{\mathrm{lcdz}}_S\end{array}$ Formula five

$\left\{\begin{array}{c}{l}_{\mathrm{VLBI}\_\mathrm{Lmt}}=0\\ B_{\mathrm{VLBI}\_\mathrm{Lmt}}=\left[\begin{array}{ccc}\mathrm{la}& \mathrm{lb}& \mathrm{lc}\end{array}\right]\end{array}\right.$ Formula six

Wherein l_{VLBI_Lmt}Represents the difference between the observed value of the VLBI constraint and its approximate value;

according to the formula seven and according to the current approximationCalculating partial derivative of constraint condition of combined system, and forming coefficient matrix B of constraint condition of combined system according to formula eight_{dbl_Lmt}；

Formula seven

Wherein k is₁₁,k₁₂,…,k₃₅Coefficients representing the observation equation for the constraint of the joint system are respectively equal to the corresponding partial derivatives of the constraint of the joint system; n is a radical of₀Representing an initial value of the radius of the Mao-unitary ring, wherein H is the elevation of the lunar surface; a represents the ellipsoid major semi-axis, e represents the ellipsoid first eccentricity;

$\left\{\begin{array}{c}{l}_{\mathrm{dbl}\_\mathrm{Lmt}}=0\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}=\left[\begin{array}{ccccc}{k}_{11}& k_{12}& k_{13}& 0& 0\\ k_{21}& k_{22}& 0& k_{24}& 0\\ k_{31}& 0& 0& 0& k_{35}\end{array}\right]\end{array}\right.$ type eight

Wherein l_{dbl_Lmt}A difference between the observed value representing the constraint of the joint system and an approximation thereof;

according to formula nine and according to the current approximationMiddle parameterFor calculating astronomical navigationApproximation (sin h)₀And (tan A)₀And forming a matrix l according to the difference between the approximate value and the observed value of the astronomical navigation_CNS；

Nine-degree of expression

Matrix l_CNSThe composition mode is that, $l_{\mathrm{CNS}}=\left[\begin{array}{c}\sinh -{\left(\sinh \right)}_0\\ \tan A-{\left(\tan A\right)}_0\end{array}\right];$

according to the formula ten and according to (x)_s0,y_s0,z_s0) Calculating the difference between the approximated value and the observed value of VLBI and forming a matrix l_VLBI；

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>c&tau;</mi> <mrow> <mn>120</mn> <mo>-</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mi>c</mi> <mo>[</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </math> Formula ten

In the formula, c τ_12o-cRepresenting a difference between the observed value of the VLBI and the approximate value;

matrix l_VLBIIs composed in the following manner_VLBI＝[c(τ₀-τ_c)]；

A positioning calculation module, a coefficient matrix B obtained by the matrix establishment module_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}And a matrix l of differences between the approximation values and the observed values_CNS、l_VLBI、l_{VLBI_Lmt}、l_{dbl_Lmt}Coefficient matrix B of combined system formed according to formula eleven_dblAnd l_dblSetting parametersRepresenting a difference between the true value and the approximate value; adjustment is carried out according to the formula twelve to obtainJudging whether the result meets the convergence condition, if so, commanding the result output module to work, and if not, commanding the result output module to workAs a new approximationThe command matrix building module iterates again until a convergence condition is met;

$\left\{\begin{array}{cc}{V}_{\mathrm{dbl}}={\left[\begin{array}{cccc}{V}_{\mathrm{CNS}}& V_{\mathrm{VLBI}}& V_{\mathrm{VLBI}\_\mathrm{Lmt}}& V_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& {\hat{x}}_{\mathrm{dbl}}=\left[\begin{array}{cc}{\hat{x}}_{\mathrm{CNS}}& {\hat{x}}_{\mathrm{VLBI}}\end{array}\right]\\ B_{\mathrm{tmp}}=\left[\begin{array}{cc}{B}_{\mathrm{CNS}}& 0\\ 0& B_{\mathrm{VLBI}}\\ 0& B_{\mathrm{VLBI}\_\mathrm{Lmt}}\end{array}\right]& B_{\mathrm{dbl}}=\left[\begin{array}{c}{B}_{\mathrm{tmp}}\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]\\ l_{\mathrm{dbl}}={\left[\begin{array}{cccc}{l}_{\mathrm{CNS}}& l_{\mathrm{VLBI}}& l_{\mathrm{VLBI}\_\mathrm{Lmt}}& l_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& \\ P_{\mathrm{dbl}}=\left[\begin{array}{cccc}{P}_{\mathrm{CNS}}& & & \\ & P_{\mathrm{VLBI}}& & \\ & & P_{\mathrm{VLBI}\_\mathrm{lmt}}& \\ & & & P_{\mathrm{dbl}\_\mathrm{lmt}}\end{array}\right]& \end{array}\right.$ formula eleven

${\hat{x}}_{\mathrm{dbl}}={\left(B_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{B}_{\mathrm{dbl}}\right)}^{-1}{B}_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{l}_{\mathrm{dbl}}$ Twelve formulas

Wherein, V_dblIndicating the correction of the observed value of the joint system, P_dblWeight matrix of constraints when solving for a combined system, where P_CNS、P_VLBI、P_{VLBI_Lmt}、P_{dbl_Lmt}Are coefficient matrices B respectively_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}A corresponding weight matrix;

a result output module for solving the result according to the final parametersAnd outputting the position coordinate information of the lunar vehicle.

Furthermore, the weight matrix P of the constraint conditions when the combined system is used for solving in the positioning and resolving module_dblDetermined according to the Hummer's Square difference component estimation method.

Furthermore, the convergence condition in the positioning calculation module is a parameterIn x_s、y_sAnd z_sThe corresponding difference is less than 10m,the corresponding difference is less than 10^-8The corresponding difference of lambda is less than 10^-8。

The invention considers that the astronomical navigation technology observes natural celestial bodies, so that continuous observation can be realized, and when the VLBI signal cannot be received, the astronomical navigation technology can be used for providing position information for the lunar rover; at the same time, the VLBI technique can provide high accuracy location information. Therefore, the technical scheme of the invention provides that the positioning precision and stability can be improved by adopting the combined system for positioning. And aiming at the problem of determining the weights of different observation systems, a weighting strategy after the Hummer equation component test is adopted is provided, so that the lunar rover positioning error caused by unreasonable weights is avoided. The invention has important practical popularization value and application prospect, and has considerable effect on the development of national economy and the improvement of the living standard of people.

Drawings

FIG. 1 is a flow chart of an embodiment of the present invention.

Fig. 2 is an astronomical navigation schematic diagram of an embodiment of the present invention.

Fig. 3 is a schematic view of VLBI single point location in accordance with an embodiment of the present invention.

Detailed Description

The technical scheme of the invention is explained in detail in the following by combining the drawings and the embodiment.

For the sake of reference, the astronomical navigation principle and VLBI single point location principle involved in the present invention will be described first:

(1) astronomical navigation principle derivation

A celestial sphere is made through the observation celestial body S with the observation platform P as the center, as shown in fig. 2. The equatorial plane of the celestial sphere intersects with the orbital plane of the revolution of the earth at the spring equinox point and the autumn equinox point. Since the rotation and revolution law of the earth is fixed relative to the inertial reference system, it can be seen that the coordinates of the spring and fall points in the inertial reference system are also fixed. Meanwhile, the spring equinox is at an infinite distance from the earth, so the spring equinox is overlapped with a connecting line at any place on the earth. Denote the spring point as; PZ_GRepresenting the greenwich meridian direction; GHA is Greenwich mean time angle of spring division; p for north direction of the zenith axis_NRepresents; the south direction of the zenith axis is denoted by P ". And the sight line direction of the observation celestial body is expressed by PS; an extension of the projection of PS in the equatorial plane of the celestial sphere is also denoted as PS ". Through the above setting, the right ascension α of the observed celestial body in the celestial sphere reference system can be expressed as: α ═ PS "; the celestial declination of the observed celestial body can be expressed as ═ SPS "; the included angle between the sight line direction PS of the observation celestial body and the zenith direction PZ is 90-h, and h represents the height angle of the observation celestial body; a is the azimuth angle of the observation celestial body; the angle formed between the north direction PPN of the zenith axis and the zenith direction PZ isNorth direction PPN of zenith axis and observation celestial body sight direction PSThe included angle between them is 90 deg. -. In an astronomical triangle P_NIn ZS, order

In summary, in fig. 2, h and a are the altitude angle and the azimuth angle of the observation celestial body in the local horizontal coordinate system; lambda andthe right ascension and declination of the lunar vehicle in a lunar fixation coordinate system; alpha and is the observed right ascension and declination of the celestial body.

The following cosine theorem and cotangent theorem exist in the spherical triangle:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>cos</mi> <mi>&eta;</mi> <mo>=</mo> <mi>cos</mi> <mi></mi> <mi>&beta;</mi> <mi>cos</mi> <mi>&gamma;</mi> <mo>+</mo> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>sin</mi> <mi></mi> <mi>&gamma;</mi> <mi>cos</mi> <mi>LHA</mi> </mtd> </mtr> <mtr> <mtd> <mi>cot</mi> <mi>A</mi> <mi>sin</mi> <mi>LHA</mi> <mo>=</mo> <mi>cot</mi> <mi></mi> <mi>&gamma;</mi> <mi>sin</mi> <mi>&beta;</mi> <mo>-</mo> <mi>cos</mi> <mi></mi> <mi>&tau;</mi> <mi>cos</mi> <mi>&beta;</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

by substituting formula (1) for formula (2), it is possible to obtain:

equation (3) is the observation equation of the astronomical navigation positioning technology.

(2) VLBI Point location principle derivation

As in fig. 3, O1, O2 represent stations 1,2, which constitute baseline 12; s represents a lunar vehicle; t is t₁、t₂Indicating the time of arrival of the signal at the stations 1, 2. The lunar probe and the distance value between them can be respectively expressed as r₁、r₂：

$r_2=\sqrt{{(x_2-x_s)}^2+{(y_2-y_s)}^2+{(z_2-z_s)}^2},r_1=\sqrt{{(x_1-x_s)}^2+{(y_1-y_s)}^2+{(z_1-z_s)}^2}---\left(4\right)$

Thus, it is possible to obtain:

<math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>=</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

equation (5) is the observation equation for the VLBI positioning technique, where τ₁₂Represents the time difference between the arrival of the signal at station 2 and station 1; c represents the speed of light; (x)₁,y₁,z₁) Coordinates of station 1 are shown, (x)₂,y₂,z₂) Coordinates representing the station 2; (x)_s,y_s,z_s) Representing the coordinates of the lunar vehicle.

The invention combines an astronomical navigation observation model and an observation model of VLBI to establish a mathematical model of a combined system. Aiming at the combined system, firstly, the influence of the precision of the celestial body sensor on the positioning precision of the lunar rover is analyzed by using simulation data.

And determining weights among different observation systems by adopting a Helmer specific weight strategy. Aiming at the problem of weight determination of different astronomical navigation positioning systems and VLBI positioning systems, a Helmer specific weight method is adopted, and a combined positioning method and a single positioning method are aimed at. And analyzing the precision of the results obtained by the combination method and the independent adoption of the astronomical navigation positioning method, and analyzing the precision of the lunar rover positioning results obtained by the combination method and the independent adoption of the VLBI positioning method.

The embodiment is realized as follows:

a) and establishing a least square model for positioning the lunar vehicle by an astronomical navigation positioning technology.

For the astronomical navigation observation equation (3), for the convenience of derivation, sin h and tan a are taken as virtual observation values and are linearized to obtain:

wherein, (sin h)₀And (tan A)₀The approximate value of the virtual observation value in the actual adjustment is shown, and equation (6) includes:

writing equation (6) in the form of an error equation:

$V_{\mathrm{CNS}}=B_{\mathrm{CNS}}{\hat{x}}_{\mathrm{CNS}}-l_{\mathrm{CNS}}---\left(8\right)$

in the above formula, V_CNSAn error value representing astronomical navigation;the number of the corrections of the parameters; l_CNSRepresenting a difference between the observed value and an approximate value thereof; b is_CNSIs a matrix of coefficients. Specifically, it can be expressed as:

when the number of the observed celestial bodies is not less than 2, an adjustment model can be formed:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mi>CNS</mi> </msub> <mo>=</mo> <msub> <mi>B</mi> <mi>CNS</mi> </msub> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>CNS</mi> </msub> <mo>-</mo> <msub> <mi>l</mi> <mi>CNS</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mi>CNS</mi> </msub> <mo>=</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mn>0</mn> <mi>CNS</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>P</mi> <mi>CNS</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein D is_CNSThe variance matrix is an observed value and is determined by the size of an observation error;representing the error in the unit weight before the test when solving the astronomical navigation; p_CNSIs a weighted array of observations. In practice, the sun and the earth are generally used for observing the celestial body.

b) And establishing a least square model for positioning the lunar rover by the VLBI positioning technology.

The observation equation (5) for VLBI is linearized and expanded in a taylor series, retaining only the first order term, and can be obtained:

<math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>v</mi> <mn>12</mn> </msub> <mo>=</mo> <msub> <mi>c&tau;</mi> <mrow> <mn>12</mn> <mi>o</mi> <mo>-</mo> <mi>c</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> </mrow> </mfrac> <msub> <mi>dx</mi> <mi>s</mi> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> </mrow> </mfrac> <msub> <mi>dy</mi> <mi>s</mi> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> </mrow> </mfrac> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <msub> <mi>c&tau;</mi> <mrow> <mn>12</mn> <mi>o</mi> <mo>-</mo> <mi>c</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>11</mn> </msub> <msub> <mi>dx</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>12</mn> </msub> <msub> <mi>dy</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>13</mn> </msub> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

in the formula:

$a_{11}=\frac{x_1-x_s}{r_1}-\frac{x_2-x_s}{r_2}$

$a_{12}=\frac{y_1-y_s}{r_1}-\frac{y_2-y_s}{r_2}$

(12)

$a_{13}=\frac{z_1-z_s}{r_1}-\frac{z_2-z_s}{r_2}$

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>c&tau;</mi> <mrow> <mn>120</mn> <mo>-</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mi>c</mi> <mo>[</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </math>

in the formula, c τ_12o-cRepresenting a difference between the observed value of the VLBI and the approximate value; a is₁₁、a₁₂、a₁₃For values of the observation equation coefficients, respectively equal to the partial derivatives of the VLBI sectionsv₁₂Representing an error value; tau is₀Is the time delay observation for the VLBI; tau is_cIs a theoretical geometric time delay value; (x)_s0,y_s0,z_s0) Is the initial value of the lunar rover coordinate; dx (x)_s,dy_s,dz_sThe correction number of the coordinates of the lunar vehicle is shown. Writing equation (11) in matrix form:

$V_{\mathrm{VLBI}}=B_{\mathrm{VLBI}}{\hat{x}}_{\mathrm{VLBI}}-l_{\mathrm{VLBI}}---\left(13\right)$

in the above formula, V_VLBIAn error value representing the VLBI;as a correction of the parameter sought, l_VLBIRepresenting a difference between the observed value and an approximate value thereof; b is_VLBIIs a coefficient matrix, and can be specifically expressed as:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>dx</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dy</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>l</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo>[</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> </mrow> </mfrac> <mi></mi> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> </mrow> </mfrac> <mi></mi> </mtd> <mtd> <mi></mi> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

the base line 12 formed by any observation stations 1 and 2 is the ith base line, and because 4 VLBI stations exist in China at present, six base lines can be formed, and a block model can be formed.

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mi>VLBI</mi> </msub> <mo>=</mo> <msub> <mi>B</mi> <mi>VLBI</mi> </msub> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>-</mo> <msub> <mi>l</mi> <mi>VLBI</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mi>VLBI</mi> </msub> <mo>=</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mn>0</mn> <mi>VLBI</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>P</mi> <mi>VLBI</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein D is_VLBIThe variance matrix is an observed value and is determined by the size of an observation error;representing the error in unit weight when solving for VLBI; p_VLBIIs a weighted array of observations.

In particular, each baseline may form a corresponding matrix V_{VLBI_i}、B_{VLBI_i}And l_{VLBI_i}(i＝1,2,…,6)，V_{VLBI_i}An error value representing the VLBI corresponding to the ith baseline;as a correction of the parameter sought, l_{VLBI_i}Representing the difference between the observed value corresponding to the ith base line and the approximate value thereof;

B_{VLBI_i}a corresponding coefficient matrix for the ith baseline, <math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>dx</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dy</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>l</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>[</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> </mrow> </mfrac> <mi></mi> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> </mrow> </mfrac> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> <mo></mo> </mtd> <mtd> <mi></mi> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>

the corresponding adjustment model may be expressed in particular as, <math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>all</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>all</mi> </mrow> </msub> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>-</mo> <msub> <mi>l</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>all</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mi>VLBI</mi> </msub> <mo>=</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mn>0</mn> <mi>VLBI</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>P</mi> <mi>VLBI</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>all</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>V</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>V</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mn>6</mn> </mrow> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>all</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>B</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>B</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mn>6</mn> </mrow> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> <mtr> <mtd> <msub> <mi>l</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>all</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>l</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>l</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mn>6</mn> </mrow> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> </mtable> </mfenced> </math>

wherein, V_{VLBI_all}A matrix of error values for all baseline corresponding VLBI, B_{VLBI_all}For all base line corresponding coefficient matrices, l_{VLBI_all}The difference between the corresponding observed value and its approximate value for all baselines.

Similarly, the adjustment based on a plurality of observation celestial bodies can be implemented by those skilled in the art according to the specific observation celestial body.

Since the distance constraint is not used when the measurement is performed by using the VLBI, and only the delay information obtained by the VLBI is used to convert the delay information into the angular position information, a large error is caused. Therefore, during actual calculation, distance constraint of the lunar rover needs to be added, so that the position information of the lunar rover with higher precision can be obtained from the VLBI observation information. A lunar vehicle distance conditional restriction equation may be established.

$\sqrt{x_{s0}^2+y_{s0}^2+z_{s0}^2}-\sqrt{x_s^2+y_s^2+z_s^2}=0---\left(16\right)$

Linearizing equation (16):

$\begin{array}{c}0=\frac{x_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dx}}_S+\frac{y_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dy}}_S+\frac{z_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dz}}_S\\ ={\mathrm{ladx}}_S+{\mathrm{lbdy}}_S+{\mathrm{lcdz}}_S\end{array}---\left(17\right)$

an adjustment model can be composed:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> </msub> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>-</mo> <msub> <mi>l</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mn>0</mn> <mi>VLBI</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>P</mi> <mrow> <mi>VLBI</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein:

$\left\{\begin{array}{c}{l}_{\mathrm{VLBI}\_\mathrm{Lmt}}=0\\ B_{\mathrm{VLBI}\_\mathrm{Lmt}}=\left[\begin{array}{ccc}\mathrm{la}& \mathrm{lb}& \mathrm{lc}\end{array}\right]\end{array}\right.---\left(19\right)$

in the formula (18), la, lb, and lc represent coefficients of the constraint; v_{VLBI_Lmt}An error value representing the VLBI constraint;the number of the corrections of the parameters; l_{VLBI_Lmt}Represents the difference between the observed value of the VLBI constraint and its approximate value; b is_{VLBI_Lmt}A coefficient matrix that is a VLBI constraint; d_{VLBI_Lmt}A variance matrix of the lunar rover prior position and the lunar center distance is obtained;representing the error in unit weight when solving for VLBI; p_{VLBI_Lmt}Weight matrices when solving for VLBI.

c) And establishing a least square model of lunar vehicle positioning combining an astronomical navigation positioning technology and a VLBI positioning technology.

From the above steps a) and b), the solution parameters of the combined system can be set asNamely, it isSince the moon center rectangular coordinates and the moon center geodetic coordinates can be converted by:

in the above formula, N represents a radius of a unitary-and-mortise ring, and may be represented as:

wherein a represents the major semi-axis of the ellipsoid, and e represents the first eccentricity of the ellipsoid. And the 'ChangE III' land successfully at the junction of the front rainbow bay of the moon and the rain sea area, and the elevation change is very small according to a moon digital elevation model. Therefore, in the positioning process, the lunar surface elevation H is assumed to be constant, and the value is-2.64 km. Linearizing equation (20):

wherein k is₁₁,k₁₂,…,k₃₅Coefficients representing observation equations for constraint conditions of the joint system; (x)_s0,y_s0,z_s0) Represents an initial value of the rectangular coordinates of the lunar vehicle,initial value, N, representing its geodetic coordinates₀Representing the initial radius value of the prime cycle and can be based on the approximate coordinates of the lunar roverAnd equation (23).

An adjustment model can be composed:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mrow> <mi>dbl</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow> <mi>dbl</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> </msub> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>dbl</mi> </msub> <mo>-</mo> <msub> <mi>l</mi> <mrow> <mi>dbl</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mrow> <mi>dbl</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mn>0</mn> <mi>dbl</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>P</mi> <mrow> <mi>dbl</mi> <mo>_</mo> <mi>Lmt</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein:

$\left\{\begin{array}{c}{l}_{\mathrm{dbl}\_\mathrm{Lmt}}=0\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}=\left[\begin{array}{ccccc}{k}_{11}& k_{12}& k_{13}& 0& 0\\ k_{21}& k_{22}& 0& k_{24}& 0\\ k_{31}& 0& 0& 0& k_{35}\end{array}\right]\end{array}\right.---\left(24\right)$

in the formula (23), V_{dbl_Lmt}An error value representing a constraint of the joint system;the number of corrections to the parameters sought for the combined system; l_{dbl_Lmt}A difference between the observed value representing the constraint of the joint system and an approximation thereof; b is_{dbl_Lmt}A coefficient matrix that is a constraint; d_{dbl_Lmt}A variance matrix which is a constraint of the joint system;representing the error in the unit weight before the test when the combined system is solved; p_{dbl_Lmt}And (4) solving a weight matrix for the combined system.

From the above derivation, the least square adjustment model of the joint system can be set as:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mi>dbl</mi> </msub> <mo>=</mo> <msub> <mi>B</mi> <mi>dbl</mi> </msub> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>dbl</mi> </msub> <mo>-</mo> <msub> <mi>l</mi> <mi>dbl</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>D</mi> <mi>dbl</mi> </msub> <mo>=</mo> <msubsup> <mi>&sigma;</mi> <mrow> <mn>0</mn> <mi>dbl</mi> </mrow> <mn>2</mn> </msubsup> <msub> <mi>P</mi> <mi>dbl</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow> </math>

in formula (25):

$\left\{\begin{array}{cc}{V}_{\mathrm{dbl}}={\left[\begin{array}{cccc}{V}_{\mathrm{CNS}}& V_{\mathrm{VLBI}}& V_{\mathrm{VLBI}\_\mathrm{Lmt}}& V_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& {\hat{x}}_{\mathrm{dbl}}=\left[\begin{array}{cc}{\hat{x}}_{\mathrm{CNS}}& {\hat{x}}_{\mathrm{VLBI}}\end{array}\right]\\ B_{\mathrm{tmp}}=\left[\begin{array}{cc}{B}_{\mathrm{CNS}}& 0\\ 0& B_{\mathrm{VLBI}}\\ 0& B_{\mathrm{VLBI}\_\mathrm{Lmt}}\end{array}\right]& B_{\mathrm{dbl}}=\left[\begin{array}{c}{B}_{\mathrm{tmp}}\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]\\ l_{\mathrm{dbl}}={\left[\begin{array}{cccc}{l}_{\mathrm{CNS}}& l_{\mathrm{VLBI}}& l_{\mathrm{VLBI}\_\mathrm{Lmt}}& l_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& \\ P_{\mathrm{dbl}}=\left[\begin{array}{cccc}{P}_{\mathrm{CNS}}& & & \\ & P_{\mathrm{VLBI}}& & \\ & & P_{\mathrm{VLBI}\_\mathrm{lmt}}& \\ & & & P_{\mathrm{dbl}\_\mathrm{lmt}}\end{array}\right]& \end{array}\right.---\left(26\right)$

in the formula (25), V_dblIndicating the correction of the observed value of the joint system, D_dblIs a variance matrix of the joint system;representing the error in the unit weight before the test when the combined system is solved; p_dblWeight matrix of constraints when solving for a combined system, where P_CNS、P_VLBI、P_{VLBI_Lmt}、P_{dbl_Lmt}Are coefficient matrices B respectively_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}And corresponding weight matrix.

In specific implementation, because there are 6 baselines, correspondingly,

$\left\{\begin{array}{cc}{V}_{\mathrm{dbl}}={\left[\begin{array}{cccc}{V}_{\mathrm{CNS}}& V_{\mathrm{VLBI}}& V_{\mathrm{VLBI}\_\mathrm{Lmt}}& V_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& {\hat{x}}_{\mathrm{dbl}}=\left[\begin{array}{cc}{\hat{x}}_{\mathrm{CNS}}& {\hat{x}}_{\mathrm{VLBI}}\end{array}\right]\\ B_{\mathrm{tmp}}=\left[\begin{array}{cc}{B}_{\mathrm{CNS}}& 0\\ 0& B_{\mathrm{VLBI}}\\ 0& B_{\mathrm{VLBI}\_\mathrm{Lmt}}\end{array}\right]& B_{\mathrm{dbl}}=\left[\begin{array}{c}{B}_{\mathrm{tmp}}\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]\\ l_{\mathrm{dbl}}={\left[\begin{array}{cccc}{l}_{\mathrm{CNS}}& l_{\mathrm{VLBI}\_\mathrm{all}}& l_{\mathrm{VLBI}\_\mathrm{Lmt}}& l_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& \\ P_{\mathrm{dbl}}=\left[\begin{array}{cccc}{P}_{\mathrm{CNS}}& & & \\ & P_{\mathrm{VLBI}}& & \\ & & P_{\mathrm{VLBI}\_\mathrm{lmt}}& \\ & & & P_{\mathrm{dbl}\_\mathrm{lmt}}\end{array}\right]& \end{array}\right.$

after the formula (26) is formed, the parameter value can be obtained by solving the formula (27)

${\hat{x}}_{\mathrm{dbl}}={\left(B_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{B}_{\mathrm{dbl}}\right)}^{-1}{B}_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{l}_{\mathrm{dbl}}---\left(27\right)$

In equation (25), 4 types of observations including VLBI observations, distance constraints, astronomical navigation observations, and space rectangular coordinates and geodetic coordinates constraints are referred to.

In specific implementation, those skilled in the art can preset the weight matrix P of the 4 kinds of observed quantities_CNS、P_VLBI、P_{VLBI_Lmt}、P_{dbl_Lmt}. The invention further considers that if a reasonable empirical value is not adopted, the weight determination can be realized by adopting a Hummer square difference component estimation method. The basic method of estimation of the difference components of the Hummer squares is to use the sum of the squares of the different kinds of corrections after each calculationTo determineI is 1,2,3,4, i is used to represent the 4 types of observations, V_iAn error value representing the observed value is determined,error in unit weight, P, representing observed value_iA weight matrix representing the observed values, and the sum of the squares of the residuals is determinedThe relation between them. The following approximate formula can be obtained by the adjustment method:

<math> <mrow> <msubsup> <mover> <mi>&sigma;</mi> <mo>^</mo> </mover> <mrow> <mn>0</mn> <mi>i</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>V</mi> <mi>i</mi> <mi>T</mi> </msubsup> <msub> <mi>P</mi> <mi>i</mi> </msub> <msub> <mi>V</mi> <mi>i</mi> </msub> <mo>/</mo> <msub> <mi>n</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow> </math>

in the formula, n_iRepresenting the number of types of measurements.

For reference purposes, the particular iterative calculation steps provided for the application of the Hummer square difference estimation method to the combined system are as follows:

1) determining the initial weight matrix before calculation, including determining the weight matrix P before calculation of four types of observed values_i(ii) a Initializing the current iteration number I to 1,

2) for obtaining various observed values by performing adjustment for the first time

3) Estimating variance after I-th calculation to obtain I-th estimation value of unit weight variance of various observed valuesAnd determining the weight according to the formula (29):

<math> <mrow> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mi>c</mi> <mrow> <msubsup> <mover> <mi>&sigma;</mi> <mo>^</mo> </mover> <mrow> <mn>0</mn> <mi>i</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>P</mi> <mi>i</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein c is an arbitrary constant, and is usually selected(ii) an amount of (a) in (b),a weight matrix representing the observed values after the solution;

4) according to the result obtained in the execution of 3) this timeAs a new weight matrix P_iLet I ═ I-1, return to 2) for the next iteration, which repeats 2), 3) until the ratio of the unit weight variances of the four classes of observations is considered by inspectionEqual to 1:1:1: 1.

After the weighting determination is carried out by adopting the Hummer method, the result obtained by 3) being executed for the last time can be obtainedAs a final weight matrix, the joint error equation (25) can then be solved according to the least squares criterion. And respectively and jointly adopting the VLBI actual measurement data of ChangE III and the simulation observation data of astronomical navigation to compare and analyze the results.

In specific implementation, the process of the present invention can be implemented in a software manner, and referring to fig. 1, the process of the embodiment is as follows:

let the determined lunar vehicle position be represented by a parameter vector asLabeling of respective approximationsWherein (x)_s,y_s,z_s) Showing the rectangular coordinates of the lunar vehicle,is the geodetic coordinates of the lunar vehicle,the right ascension and the declination of the lunar vehicle in a lunar fixation coordinate system respectively;

inputting approximate coordinates of lunar vehicleAnd time difference of observation τ of VLBI₀And observation values sin h and tan A of astronomical navigation, wherein h represents the altitude angle of the observation celestial body, and A is the azimuth angle of the observation celestial body; wherein, approximate coordinates of the lunar vehicleAs an initial approximation(x_s0,y_s0,z_s0) Represents an initial value of the rectangular coordinates of the lunar vehicle,representing the initial value of its geodetic coordinates.

In specific implementation, the lunar vehicle approximate coordinatesCan be preset by the technicians in the field, and the error can be corrected in the subsequent operation of the invention.

② according to formula (7) and according to coordinate parameter of lunar vehicleCalculating partial derivative of the astronomical navigation part, and forming a coefficient matrix B of the astronomical navigation part according to formula (9)_CNS(ii) a According to equation (12) and according to the lunar vehicle coordinate parameter (x)_s0,y_s0,z_s0) Calculating partial derivatives of the VLBI portion and forming a coefficient matrix B of the VLBI portion according to equation (14)_VLBI(ii) a According to equation (17) and according to the lunar vehicle coordinate parameter (x)_s0,y_s0,z_s0) Calculating partial derivatives of the VLBI constraints and forming a coefficient matrix B of the VLBI constraints according to equation (19)_{VLBI_Lmt}(ii) a According to equation (22) and based on lunar vehicle coordinate parametersCalculating partial derivatives of the constraint conditions of the joint system, and forming a coefficient matrix B of the constraint conditions of the joint system according to an equation (24)_{dbl_Lmt}. According to formula (3) and according toCalculating an approximation of astronomical navigation (sin h)₀And (tan A)₀And forming a matrix l according to the formula (9)_CNS(ii) a According to formula (12) and according to (x)_s0,y_s0,z_s0) Calculating the difference between the approximated value of VLBI and the observed value, and forming a matrix l according to equation (14)_VLBI。

Thirdly, the coefficient matrix B of the combination system is formed by the coefficient matrix obtained by the steps and the matrix formed by the difference between the approximate value and the observed value according to the formula (26)_dblAnd l_dblThe parameter vector is expressed asLet it approximateRepresenting the difference between the true value and the approximated value. Adjustment according to formula (27) to obtainJudging whether the result meets the convergence condition, if so, outputting the calculation result, and if not, outputting the calculation resultAs newAnd returning to the previous step to re-iterate the solution until the condition is met. In the specific implementation, a person skilled in the art can preset the convergence condition by himself, in the embodiment, the convergence condition is a parameterIn x_s、y_sAnd z_sThe corresponding difference is less than 10m,the corresponding difference is less than 10^-8The corresponding difference of lambda is less than 10^-8。

Fourthly, solving the result according to the final parametersAnd outputting the position coordinate information of the lunar vehicle.

In specific implementation, a lunar vehicle joint positioning system can also be provided in a modular manner, and the system provided by the embodiment comprises the following modules:

an initialization module for setting the determined lunar vehicle position as represented by a parameter vectorLabeling of respective approximationsWherein (x)_s,y_s,z_s) Showing the rectangular coordinates of the lunar vehicle,is the geodetic coordinates of the lunar vehicle, the right ascension and the declination of the lunar vehicle in a lunar fixation coordinate system respectively;

inputting lunar rover approximate coordinatesAnd time difference of observation τ of VLBI₀And observation values sin h and tan A of astronomical navigation, wherein h represents the altitude angle of the observation celestial body, and A is the azimuth angle of the observation celestial body; wherein, approximate coordinates of the lunar vehicleAs an initial approximation(x_s0,y_s0,z_s0) Represents an initial value of the rectangular coordinates of the lunar vehicle,an initial value representing its geodetic coordinates;

the matrix establishing module is used for calculating the partial derivative of the astronomical navigation part and forming a coefficient matrix of the astronomical navigation part; calculating partial derivatives of the VLBI part and forming a coefficient matrix of the VLBI part; calculating partial derivatives of the VLBI constraint condition, and forming a coefficient matrix of the VLBI constraint condition; calculating partial derivatives of the constraint conditions of the joint system, and forming a coefficient matrix of the constraint conditions of the joint system; calculating approximate values of astronomical navigation and forming a corresponding matrix; calculating the difference between the approximate value of the VLBI and the observed value, and forming a corresponding matrix; the realization is as follows,

according to the current approximationMiddle parameterCalculating partial derivative of the astronomical navigation part and forming a coefficient matrix B of the astronomical navigation part_CNS；

Wherein, alpha is the observed right ascension and declination of the celestial body, and GHA is the Greenwich mean time angle of spring points;

wherein,for the parameters soughtThe number of corrections of (a);

according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivatives of the VLBI portion and forming a coefficient matrix B of the VLBI portion_VLBI；

$\left\{\begin{array}{c}{a}_{11}=\frac{x_1-x_s}{r_1}-\frac{x_2-x_s}{r_2}\\ a_{12}=\frac{y_1-y_s}{r_1}-\frac{y_2-y_s}{r_2}\\ a_{13}=\frac{z_1-z_s}{r_1}-\frac{z_2-z_s}{r_2}\end{array}\right.$

In the formula, a₁₁、a₁₂、a₁₃For values of the observation equation coefficients, respectively equal to the partial derivatives of the VLBI sections (x₁,y₁,z₁) Coordinates of station 1 are shown, (x)₂,y₂,z₂) Coordinates of the station 2, r₁、r₂Represents the distance value between the lunar probe and the station 1 and the station 2;

<math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>dx</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dy</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <msub> <mi>c&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math>

wherein,for the parameter (x) sought_s,y_s,z_s) The number of corrections of (a); c represents the speed of light; tau is₀Is the time delay observation for the VLBI; tau is_cIs a theoretical geometric time delay value; dx (x)_s,dy_s,dz_sThe correction number of the coordinate of the lunar vehicle is obtained;

according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivatives of the VLBI constraints and forming a coefficient matrix B of the VLBI constraints_{VLBI_Lmt}；

$\begin{array}{c}0=\frac{x_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dx}}_S+\frac{y_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dy}}_S+\frac{z_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dz}}_S\\ ={\mathrm{ladx}}_S+{\mathrm{lbdy}}_S+{\mathrm{lcdz}}_S\end{array}$

$\left\{\begin{array}{c}{l}_{\mathrm{VLBI}\_\mathrm{Lmt}}=0\\ B_{\mathrm{VLBI}\_\mathrm{Lmt}}=\left[\begin{array}{ccc}\mathrm{la}& \mathrm{lb}& \mathrm{lc}\end{array}\right]\end{array}\right.$

Wherein l_{VLBI_Lmt}Represents the difference between the observed value of the VLBI constraint and its approximate value;

according to the current approximationCalculating partial derivative of constraint condition of combined system and forming coefficient matrix B of constraint condition of combined system_{dbl_Lmt}；

Wherein k is₁₁,k₁₂,…,k₃₅Coefficients representing the observation equation for the constraint of the joint system are respectively equal to the corresponding partial derivatives of the constraint of the joint system; n is a radical of₀Representing an initial value of the radius of the Mao-unitary ring, wherein H is the elevation of the lunar surface; a represents the ellipsoid major semi-axis, e represents the ellipsoid first eccentricity;

$\left\{\begin{array}{c}{l}_{\mathrm{dbl}\_\mathrm{Lmt}}=0\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}=\left[\begin{array}{ccccc}{k}_{11}& k_{12}& k_{13}& 0& 0\\ k_{21}& k_{22}& 0& k_{24}& 0\\ k_{31}& 0& 0& 0& k_{35}\end{array}\right]\end{array}\right.$

wherein l_{dbl_Lmt}A difference between the observed value representing the constraint of the joint system and an approximation thereof;

according to the current approximationMiddle parameterCalculating an approximation of astronomical navigation (sin h)₀And (tan A)₀And forming a matrix l according to the difference between the approximate value and the observed value of the astronomical navigation_CNS；

Matrix l_CNSThe composition mode is that, $l_{\mathrm{CNS}}=\left[\begin{array}{c}\sinh -{\left(\sinh \right)}_0\\ \tan A-{\left(\tan A\right)}_0\end{array}\right];$

according to (x)_s0,y_s0,z_s0) Calculating the difference between the approximated value and the observed value of VLBI and forming a matrix l_VLBI；

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>c&tau;</mi> <mrow> <mn>120</mn> <mo>-</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mi>c</mi> <mo>[</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </math>

In the formula, c τ_12o-cRepresenting a difference between the observed value of the VLBI and the approximate value;

matrix l_VLBIIs composed in the following manner_VLBI＝[c(τ₀-τ_c)]；

A positioning calculation module, a coefficient matrix B obtained by the matrix establishment module_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}And a matrix l of differences between the approximation values and the observed values_CNS、l_VLBI、l_{VLBI_Lmt}、l_{dbl_Lmt}Coefficient matrix B of combined system_dblAnd l_dblSetting parametersRepresenting a difference between the true value and the approximate value; is subjected to adjustment to obtainJudging whether the result meets the convergence condition, if so, commanding the result output module to work, and if not, commanding the result output module to workAs a new approximationThe command matrix building module iterates again until a convergence condition is met;

$\left\{\begin{array}{cc}{V}_{\mathrm{dbl}}={\left[\begin{array}{cccc}{V}_{\mathrm{CNS}}& V_{\mathrm{VLBI}}& V_{\mathrm{VLBI}\_\mathrm{Lmt}}& V_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& {\hat{x}}_{\mathrm{dbl}}=\left[\begin{array}{cc}{\hat{x}}_{\mathrm{CNS}}& {\hat{x}}_{\mathrm{VLBI}}\end{array}\right]\\ B_{\mathrm{tmp}}=\left[\begin{array}{cc}{B}_{\mathrm{CNS}}& 0\\ 0& B_{\mathrm{VLBI}}\\ 0& B_{\mathrm{VLBI}\_\mathrm{Lmt}}\end{array}\right]& B_{\mathrm{dbl}}=\left[\begin{array}{c}{B}_{\mathrm{tmp}}\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]\\ l_{\mathrm{dbl}}={\left[\begin{array}{cccc}{l}_{\mathrm{CNS}}& l_{\mathrm{VLBI}}& l_{\mathrm{VLBI}\_\mathrm{Lmt}}& l_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& \\ P_{\mathrm{dbl}}=\left[\begin{array}{cccc}{P}_{\mathrm{CNS}}& & & \\ & P_{\mathrm{VLBI}}& & \\ & & P_{\mathrm{VLBI}\_\mathrm{lmt}}& \\ & & & P_{\mathrm{dbl}\_\mathrm{lmt}}\end{array}\right]& \end{array}\right.$

${\hat{x}}_{\mathrm{dbl}}={\left(B_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{B}_{\mathrm{dbl}}\right)}^{-1}{B}_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{l}_{\mathrm{dbl}}$

wherein, V_dblIndicating the correction of the observed value of the joint system, P_dblWeight matrix of constraints when solving for a combined system, where P_CNS、P_VLBI、P_{VLBI_Lmt}、P_{dbl_Lmt}Are coefficient matrices B respectively_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}A corresponding weight matrix;

a result output module for solving the result according to the final parametersAnd outputting the position coordinate information of the lunar vehicle.

The above embodiments are provided only for illustrating the present invention and not for limiting the present invention, and those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and therefore all equivalent technical solutions should also fall within the scope of the present invention, and should be defined by the claims.

Claims (6)

1. A lunar rover joint positioning method is characterized by comprising the following steps: the following steps are carried out in the following manner,

step 1, setting the position of the lunar vehicle as the parameter vectorLabeling of respective approximationsWherein (x)_s,y_s,z_s) Showing the rectangular coordinates of the lunar vehicle,is the geodetic coordinate of lunar vehicle, lambda,The right ascension and the declination of the lunar vehicle in a lunar fixation coordinate system respectively;

inputting lunar rover approximate coordinatesAnd time difference of observation τ of VLBI₀And observation values sin h and tan A of astronomical navigation, wherein h represents the altitude angle of the observation celestial body, and A is the azimuth angle of the observation celestial body; wherein, approximate coordinates of the lunar vehicleAs an initial approximation(x_s0,y_s0,z_s0) Represents an initial value of the rectangular coordinates of the lunar vehicle,an initial value representing its geodetic coordinates;

step 2, calculating a partial derivative of the astronomical navigation part, and forming a coefficient matrix of the astronomical navigation part; calculating partial derivatives of the VLBI part and forming a coefficient matrix of the VLBI part; calculating partial derivatives of the VLBI constraint condition, and forming a coefficient matrix of the VLBI constraint condition; calculating partial derivatives of the constraint conditions of the joint system, and forming a coefficient matrix of the constraint conditions of the joint system; calculating approximate values of astronomical navigation and forming a corresponding matrix; calculating the difference between the approximate value of the VLBI and the observed value, and forming a corresponding matrix; the realization is as follows,

according to formula and according to the current approximationMiddle parameterCalculating partial derivative of the astronomical navigation part, and forming a coefficient matrix B of the astronomical navigation part according to the formula_CNS；

Wherein, alpha is the observed right ascension and declination of the celestial body, and GHA is the Greenwich mean time angle of spring points;

wherein,for the parameters soughtThe number of corrections of (a);

according to equation three and according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivatives of the VLBI portions and forming a coefficient matrix B of the VLBI portions according to the formula_VLBI；

$\left\{\begin{array}{c}{a}_{11}=\frac{x_1-x_s}{r_1}-\frac{x_2-x_s}{r_2}\\ a_{12}=\frac{y_1-y_s}{r_1}-\frac{y_2-y_s}{r_2}\\ a_{13}=\frac{z_1-z_s}{r_1}-\frac{z_2-z_s}{r_2}\end{array}\right.$ Formula III

In the formula, a₁₁、a₁₂、a₁₃For values of the observation equation coefficients, respectively equal to the partial derivatives of the VLBI sections (x₁,y₁,z₁) Coordinates of station 1 are shown, (x)₂,y₂,z₂) Coordinates of the station 2, r₁、r₂Represents the distance value between the lunar probe and the station 1 and the station 2;

<math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>dx</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dy</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math> formula IV

Wherein,for the parameter (x) sought_s,y_s,z_s) C represents the speed of light; tau is₀Is the time delay observation for the VLBI; tau is_cIs a theoretical geometric time delay value; dx (x)_s,dy_s,dz_sThe correction number of the coordinate of the lunar vehicle is obtained;

according to equation five and according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivative of VLBI restriction condition, and forming coefficient matrix B of VLBI restriction condition according to formula six_{VLBI_Lmt}；

$\begin{array}{c}0=\frac{x_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dx}}_S+\frac{y_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dy}}_S+\frac{z_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dz}}_S\\ ={\mathrm{ladx}}_S+{\mathrm{lbdy}}_S+{\mathrm{lcdz}}_S\end{array}$ Formula five

$\left\{\begin{array}{c}{l}_{\mathrm{VLBI}\_\mathrm{Lmt}}=0\\ B_{\mathrm{VLBI}\_\mathrm{Lmt}}=\left[\begin{array}{ccc}\mathrm{la}& \mathrm{lb}& \mathrm{lc}\end{array}\right]\end{array}\right.$ Formula six

Wherein l_{VLBI_Lmt}Represents the difference between the observed value of the VLBI constraint and its approximate value;

according to the formula seven and according to the current approximationCalculating partial derivative of constraint condition of combined system, and forming coefficient matrix B of constraint condition of combined system according to formula eight_{dbl_Lmt}；

Wherein k is₁₁,k₁₂,…,k₃₅Coefficients representing the observation equation for the constraint of the joint system are respectively equal to the corresponding partial derivatives of the constraint of the joint system; n is a radical of₀Representing an initial value of the radius of the Mao-unitary ring, wherein H is the elevation of the lunar surface; a represents the ellipsoid major semi-axis, e represents the ellipsoid first eccentricity;

$\left\{\begin{array}{c}{l}_{\mathrm{dbl}\_\mathrm{Lmt}}=0\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}=\left[\begin{array}{ccccc}{k}_{11}& k_{12}& k_{13}& 0& 0\\ k_{21}& k_{22}& 0& k_{24}& 0\\ k_{31}& 0& 0& 0& k_{35}\end{array}\right]\end{array}\right.$ type eight

Wherein l_{dbl_Lmt}A difference between the observed value representing the constraint of the joint system and an approximation thereof;

according to formula nine and according to the current approximationMiddle parameterCalculating an approximation of astronomical navigation (sin h)₀And (tan A)₀And forming a matrix l according to the difference between the approximate value and the observed value of the astronomical navigation_CNS；

Matrix l_CNSThe composition mode is that, $l_{\mathrm{CNS}}=\left[\begin{array}{c}\sinh -{\left(\sinh \right)}_0\\ \tan A-{\left(\tan A\right)}_0\end{array}\right];$

according to the formula ten and according to (x)_s0,y_s0,z_s0) Calculating the difference between the approximated value and the observed value of VLBI and forming a matrix l_VLBI；

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>c</mi> <msub> <mi>&tau;</mi> <mrow> <mn>120</mn> <mo>-</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mi>c</mi> <mo>[</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </math> Formula ten

In the formula, c τ_12o-cRepresenting a difference between the observed value of the VLBI and the approximate value;

matrix l_VLBIIs composed in the following manner_VLBI＝[c(τ₀-τ_c)]；

Step 3, obtaining the coefficient matrix B by the above steps_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}And a matrix l of differences between the approximation values and the observed values_CNS、l_VLBI、l_{VLBI_Lmt}、l_{dbl_Lmt}Coefficient matrix B of combined system formed according to formula eleven_dblAnd l_dblSetting parametersRepresenting a difference between the true value and the approximate value; adjustment is carried out according to the formula twelve to obtainJudging whether the result meets the convergence condition, if so, entering the step 4, otherwise, entering the stepAs a new approximationReturning to the step 2 to carry out reiterative solution until the convergence condition is met;

$\left\{\begin{array}{c}\begin{array}{cc}{V}_{\mathrm{dbl}}={\left[\begin{array}{cccc}{V}_{\mathrm{CNS}}& V_{\mathrm{VLBI}}& V_{\mathrm{VLBI}\_\mathrm{Lmt}}& V_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& {\hat{x}}_{\mathrm{dbl}}=\left[\begin{array}{cc}{\hat{x}}_{\mathrm{CNS}}& {\hat{x}}_{\mathrm{VLBI}}\end{array}\right]\end{array}\\ \begin{array}{cc}{B}_{\mathrm{tmp}}=\left[\begin{array}{cc}{B}_{\mathrm{CNS}}& 0\\ 0& B_{\mathrm{VLBI}}\\ 0& B_{\mathrm{VLBI}\_\mathrm{Lmt}}\end{array}\right]& B_{\mathrm{dbl}}=\left[\begin{array}{c}{B}_{\mathrm{tmp}}\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]\end{array}\\ l_{\mathrm{dbl}}={\left[\begin{array}{cccc}{l}_{\mathrm{CNS}}& l_{\mathrm{VLBI}}& l_{\mathrm{VLBI}\_\mathrm{Lmt}}& l_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T\\ P_{\mathrm{dbl}}=\left[\begin{array}{cccc}{P}_{\mathrm{CNS}}& & & \\ & P_{\mathrm{VLBI}}& & \\ & & P_{\mathrm{VLBI}\_\mathrm{lmt}}& \\ & & & P_{\mathrm{dbl}\_\mathrm{lmt}}\end{array}\right]\end{array}\right.$ formula eleven

${\hat{x}}_{\mathrm{dbl}}={\left(B_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{B}_{\mathrm{dbl}}\right)}^{-1}{B}_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{l}_{\mathrm{dbl}}$ Twelve formulas

Wherein, V_dblIndicating the correction of the observed value of the joint system, P_dblWeight matrix of constraints when solving for a combined system, where P_CNS、P_VLBI、P_{VLBI_Lmt}、P_{dbl_Lmt}Are coefficient matrices B respectively_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}A corresponding weight matrix;

step 4, solving the result according to the final parametersAnd outputting the position coordinate information of the lunar vehicle.

2. Lunar vehicle combination according to claim 1A bit method, characterized by: step 3, weight array P of limiting conditions during solving of the combined system_dblDetermined according to the Hummer's Square difference component estimation method.

3. The lunar vehicle joint positioning method according to claim 1 or 2, characterized in that: step 3 the convergence condition is as followsIn x_s、y_sAnd z_sThe corresponding difference is less than 10m,the corresponding difference is less than 10^-8The corresponding difference of lambda is less than 10^-8。

4. The utility model provides a lunar rover joint localization system which characterized in that: comprises the following modules which are used for realizing the functions of the system,

an initialization module for setting the determined lunar vehicle position as represented by a parameter vectorLabeling of respective approximationsWherein (x)_s,y_s,z_s) Showing the rectangular coordinates of the lunar vehicle,is the geodetic coordinate of lunar vehicle, lambda,The right ascension and the declination of the lunar vehicle in a lunar fixation coordinate system respectively;

inputting lunar rover approximate coordinatesAnd time difference of observation τ of VLBI₀And observation values sin h and tan A of astronomical navigation, wherein h represents the altitude angle of the observation celestial body, and A is the azimuth angle of the observation celestial body; wherein, approximate coordinates of the lunar vehicleAs an initial approximation(x_s0,y_s0,z_s0) Represents an initial value of the rectangular coordinates of the lunar vehicle,an initial value representing its geodetic coordinates;

the matrix establishing module is used for calculating the partial derivative of the astronomical navigation part and forming a coefficient matrix of the astronomical navigation part; calculating partial derivatives of the VLBI part and forming a coefficient matrix of the VLBI part; calculating partial derivatives of the VLBI constraint condition, and forming a coefficient matrix of the VLBI constraint condition; calculating partial derivatives of the constraint conditions of the joint system, and forming a coefficient matrix of the constraint conditions of the joint system; calculating approximate values of astronomical navigation and forming a corresponding matrix; calculating the difference between the approximate value of the VLBI and the observed value, and forming a corresponding matrix; the realization is as follows,

according to formula and according to the current approximationMiddle parameterCalculating partial derivative of the astronomical navigation part, and forming a coefficient matrix B of the astronomical navigation part according to the formula_CNS；

Wherein, alpha is the observed right ascension and declination of the celestial body, and GHA is the Greenwich mean time angle of spring points;

wherein,for the parameters soughtThe number of corrections of (a);

according to equation three and according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivatives of the VLBI portions and forming a coefficient matrix B of the VLBI portions according to the formula_VLBI；

$\left\{\begin{array}{c}{a}_{11}=\frac{x_1-x_s}{r_1}-\frac{x_2-x_s}{r_2}\\ a_{12}=\frac{y_1-y_s}{r_1}-\frac{y_2-y_s}{r_2}\\ a_{13}=\frac{z_1-z_s}{r_1}-\frac{z_2-z_s}{r_2}\end{array}\right.$ Formula III

In the formula, a₁₁、a₁₂、a₁₃For values of the observation equation coefficients, respectively equal to the partial derivatives of the VLBI sections (x₁,y₁,z₁) Coordinates of station 1 are shown, (x)₂,y₂,z₂) Coordinates of the station 2, r₁、r₂Represents the distance value between the lunar probe and the station 1 and the station 2;

<math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>dx</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dy</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>dz</mi> <mi>s</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mi>VLBI</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&PartialD;</mo> <mrow> <mo>(</mo> <mi>c</mi> <msub> <mi>&tau;</mi> <mn>12</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> </math> formula IV

Wherein,for the parameter (x) sought_s,y_s,z_s) The number of corrections of (a); c represents the speed of light; tau is₀Is the time delay observation for the VLBI; tau is_cIs a theoretical geometric time delay value; dx (x)_s,dy_s,dz_sThe correction number of the coordinate of the lunar vehicle is obtained;

according to equation five and according to the current approximationMiddle parameter (x)_s0,y_s0,z_s0) Calculating partial derivative of VLBI restriction condition, and forming coefficient matrix B of VLBI restriction condition according to formula six_{VLBI_Lmt}；

$\begin{array}{c}0=\frac{x_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dx}}_S+\frac{y_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dy}}_S+\frac{z_{S0}}{\sqrt{x_{S0}^2+y_{S0}^2+z_{S0}^2}}{\mathrm{dz}}_S\\ ={\mathrm{ladx}}_S+{\mathrm{lbdy}}_S+{\mathrm{lcdz}}_S\end{array}$ Formula five

$\left\{\begin{array}{c}{l}_{\mathrm{VLBI}\_\mathrm{Lmt}}=0\\ B_{\mathrm{VLBI}\_\mathrm{Lmt}}=\left[\begin{array}{ccc}\mathrm{la}& \mathrm{lb}& \mathrm{lc}\end{array}\right]\end{array}\right.$ Formula six

Wherein l_{VLBI_Lmt}Represents the difference between the observed value of the VLBI constraint and its approximate value;

according to the formula seven and according to the current approximationCalculating partial derivative of constraint condition of combined system, and combining according to formula eightCoefficient matrix B of system constraints_{dbl_Lmt}；

Wherein k is₁₁,k₁₂,…,k₃₅Coefficients representing the observation equation for the constraint of the joint system are respectively equal to the corresponding partial derivatives of the constraint of the joint system; n is a radical of₀Representing an initial value of the radius of the Mao-unitary ring, wherein H is the elevation of the lunar surface; a represents the ellipsoid major semi-axis, e represents the ellipsoid first eccentricity;

$\left\{\begin{array}{c}{l}_{\mathrm{dbl}\_\mathrm{Lmt}}=0\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}=\left[\begin{array}{ccccc}{k}_{11}& k_{12}& k_{13}& 0& 0\\ k_{21}& k_{22}& 0& k_{24}& 0\\ k_{31}& 0& 0& 0& k_{35}\end{array}\right]\end{array}\right.$ type eight

Wherein l_{dbl_Lmt}A difference between the observed value representing the constraint of the joint system and an approximation thereof;

according to formula nine and according to the current approximationMiddle parameterCalculating an approximation of astronomical navigation (sin h)₀And (tan A)₀And forming a matrix l according to the difference between the approximate value and the observed value of the astronomical navigation_CNS；

Matrix l_CNSThe composition mode is that, $l_{\mathrm{CNS}}=\left[\begin{array}{c}\sinh -{\left(\sinh \right)}_0\\ \tan A-{\left(\tan A\right)}_0\end{array}\right];$

according to the formula ten and according to (x)_s0,y_s0,z_s0) Calculating the difference between the approximated value and the observed value of VLBI and forming a matrix l_VLBI；

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>c</mi> <msub> <mi>&tau;</mi> <mrow> <mn>120</mn> <mo>-</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mi>c</mi> <mo>[</mo> <msub> <mi>&tau;</mi> <mn>0</mn> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </math> Formula ten

In the formula, c τ_12o-cRepresenting a difference between the observed value of the VLBI and the approximate value;

matrix l_VLBIIs composed in the following manner_VLBI＝[c(τ₀-τ_c)]；

A positioning calculation module, a coefficient matrix B obtained by the matrix establishment module_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}And a matrix l of differences between the approximation values and the observed values_CNS、l_VLBI、l_{VLBI_Lmt}、l_{dbl_Lmt}Coefficient matrix B of combined system formed according to formula eleven_dblAnd l_dblSetting parametersRepresenting a difference between the true value and the approximate value; adjustment is carried out according to the formula twelve to obtainJudging whether the result meets the convergence condition, if so, commanding the result output module to work, and if not, commanding the result output module to workAs a new approximationThe command matrix building module iterates again until a convergence condition is met;

$\left\{\begin{array}{c}\begin{array}{cc}{V}_{\mathrm{dbl}}={\left[\begin{array}{cccc}{V}_{\mathrm{CNS}}& V_{\mathrm{VLBI}}& V_{\mathrm{VLBI}\_\mathrm{Lmt}}& V_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T& {\hat{x}}_{\mathrm{dbl}}=\left[\begin{array}{cc}{\hat{x}}_{\mathrm{CNS}}& {\hat{x}}_{\mathrm{VLBI}}\end{array}\right]\end{array}\\ \begin{array}{cc}{B}_{\mathrm{tmp}}=\left[\begin{array}{cc}{B}_{\mathrm{CNS}}& 0\\ 0& B_{\mathrm{VLBI}}\\ 0& B_{\mathrm{VLBI}\_\mathrm{Lmt}}\end{array}\right]& B_{\mathrm{dbl}}=\left[\begin{array}{c}{B}_{\mathrm{tmp}}\\ B_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]\end{array}\\ l_{\mathrm{dbl}}={\left[\begin{array}{cccc}{l}_{\mathrm{CNS}}& l_{\mathrm{VLBI}}& l_{\mathrm{VLBI}\_\mathrm{Lmt}}& l_{\mathrm{dbl}\_\mathrm{Lmt}}\end{array}\right]}^T\\ P_{\mathrm{dbl}}=\left[\begin{array}{cccc}{P}_{\mathrm{CNS}}& & & \\ & P_{\mathrm{VLBI}}& & \\ & & P_{\mathrm{VLBI}\_\mathrm{lmt}}& \\ & & & P_{\mathrm{dbl}\_\mathrm{lmt}}\end{array}\right]\end{array}\right.$ formula eleven

${\hat{x}}_{\mathrm{dbl}}={\left(B_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{B}_{\mathrm{dbl}}\right)}^{-1}{B}_{\mathrm{dbl}}^T{P}_{\mathrm{dbl}}{l}_{\mathrm{dbl}}$ Twelve formulas

Wherein, V_dblIndicating the correction of the observed value of the joint system, P_dblWeight matrix of constraints when solving for a combined system, where P_CNS、P_VLBI、P_{VLBI_Lmt}、P_{dbl_Lmt}Are coefficient matrices B respectively_CNS、B_VLBI、B_{VLBI_Lmt}、B_{dbl_Lmt}A corresponding weight matrix;

a result output module for solving the result according to the final parametersAnd outputting the position coordinate information of the lunar vehicle.

5. The lunar vehicle joint positioning system according to claim 4, wherein: weight array P of limiting conditions during solving of combined system in positioning and resolving module_dblDetermined according to the Hummer's Square difference component estimation method.

6. The lunar vehicle joint positioning system according to claim 4 or 5, wherein: the convergence condition in the positioning calculation module is a parameterIn x_s、y_sAnd z_sThe corresponding difference is less than 10m,the corresponding difference is less than 10^-8The corresponding difference of lambda is less than 10^-8。