CN104864876B - A kind of lunar rover combined positioning-method and system - Google Patents

A kind of lunar rover combined positioning-method and system Download PDF

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CN104864876B
CN104864876B CN201510298598.1A CN201510298598A CN104864876B CN 104864876 B CN104864876 B CN 104864876B CN 201510298598 A CN201510298598 A CN 201510298598A CN 104864876 B CN104864876 B CN 104864876B
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vlbi
formula
matrix
dbl
represent
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CN104864876A (en
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魏二虎
殷志祥
刘经南
汤深权
刘建栋
刘凡
李雪川
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武汉大学
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/24Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for cosmonautical navigation

Abstract

The invention provides a kind of lunar rover combined positioning-method and system, input lunar rover approximate coordinates and the observed reading mistiming of VLBI and the observed reading of celestial navigation, calculate the partial derivative of celestial navigation part, and form the matrix of coefficients of celestial navigation part; Calculate the partial derivative of VLBI part, and form the matrix of coefficients of VLBI part; Calculate the partial derivative of VLBI restrictive condition, and form the matrix of coefficients of VLBI restrictive condition; Calculate the partial derivative of association system constraint condition, and form the matrix of coefficients of association system constraint condition; Calculate the approximate value of celestial navigation, and form corresponding matrix; Calculate the approximate value of VLBI and the difference of observed reading, and form corresponding matrix; The matrix of coefficients of composition combined system carries out adjustment, and judges whether to reach the condition of convergence to result of calculation, if then Output rusults, if not then again iteration until reach the condition of convergence.Technical solution of the present invention can improve positioning precision and stability.

Description

A kind of lunar rover combined positioning-method and system
Technical field
The invention belongs to field of deep space exploration, particularly relate to lunar rover localization method and the system of a kind of associating celestial navigation and VLBI.
Background technology
When carrying out lunar rover location, high precision, round-the-clock observation and stability are the basic demands of positioning system.Main celestial navigation location technology or the VLBI technology (verylongbaselineinterferometry, very long baseline interferometry(VLBI technology) etc. of adopting positions it at present.Celestial navigation location technology is a kind of absolute fix method.It is adopted to carry out observing the error included by the position coordinates of the destination carrier obtained can not become large in time with apart from increasing.Celestial navigation mainly obtains the positional information of target by the observation information of the earth, the sun and other celestial bodies.VLBI technology is different apart from the distance of ground two survey station by lunar rover, therefore the mistiming that the same signal that lunar rover sends arrives two survey stations is recorded, thus set up the dimensional measurement relation of detector and two survey stations, the position of detector just can be calculated by a large amount of observed readings and known survey station position.
But these two kinds of technology have respective defect:
(1) VLBI location technology can provide high-precision positional information, but due to some external causes cause its signal to receive time, it cannot work.
(2) comparatively VLBI technology is low to adopt at present the lunar rover positioning precision of celestial navigation location technology.
Summary of the invention
For the problems referred to above, improvement is innovated further in the basis of the former scholar's research of the present invention, propose a kind of a kind of lunar rover combined positioning-method and system of high-precision and high-stability.
Technical solution of the present invention provides a kind of lunar rover combined positioning-method, performs following steps,
Step 1, if required lunar rover position is expressed as with parameter vector corresponding approximate value is labeled as wherein (x s, y s, z s) represent lunar rover rectangular coordinate, for the terrestrial coordinate of lunar rover, be respectively right ascension, the declination of lunar rover in the moon admittedly coordinate system;
Input lunar rover approximate coordinates and the observed reading mistiming τ of VLBI 0represent the elevation angle of observation celestial body with observed reading sinh and the tanA of celestial navigation, h, A is the position angle of observation celestial body; Wherein, by lunar rover approximate coordinates as initial approximate value (x s0, y s0, z s0) represent the initial value of lunar rover rectangular coordinate, represent the initial value of its terrestrial coordinate;
Step 2, calculates the partial derivative of celestial navigation part, and forms the matrix of coefficients of celestial navigation part; Calculate the partial derivative of VLBI part, and form the matrix of coefficients of VLBI part; Calculate the partial derivative of VLBI restrictive condition, and form the matrix of coefficients of VLBI restrictive condition; Calculate the partial derivative of association system constraint condition, and form the matrix of coefficients of association system constraint condition; Calculate the approximate value of celestial navigation, and form corresponding matrix; Calculate the approximate value of VLBI and the difference of observed reading, and form corresponding matrix; Realize as follows,
According to formula in the lump according to current approximate value middle parameter calculate the partial derivative of celestial navigation part, and form the matrix of coefficients B of celestial navigation part according to formula two cNS;
Formula one
Wherein, α, δ are right ascension, the declination of the celestial body of observation, and GHA is the Greenwich hour angle in the first point of Aries;
formula two
Wherein, for required parameter correction;
According to formula three and according to current approximate value middle parameter (x s0, y s0, z s0) calculate VLBI partial derivative partly, and the matrix of coefficients B of VLBI part is formed according to formula four vLBI;
a 11 = x 1 - x s r 1 - x 2 - x s r 2 a 12 = y 1 - y s r 1 - y 2 - y s r 2 a 13 = z 1 - z s r 1 - z 2 - z s r 2 Formula three
In formula, a 11, a 12, a 13for observation equation coefficient value, equal the partial derivative of VLBI part respectively (x 1, y 1, z 1) represent the coordinate of the station 1, (x 2, y 2, z 2) represent the coordinate of the station 2, r 1, r 2represent the distance value between lunar orbiter and the station 1, the station 2;
x ^ VLBI = dx s dy s dz s B VLBI = ∂ ( cτ 12 ) ∂ x s ∂ ( c τ 12 ) ∂ y s ∂ ( cτ 12 ) ∂ z s Formula four
Wherein, for required parameter (x s, y s, z s) correction; C represents the light velocity; τ 0for the time delay observed reading of VLBI; τ cfor the geometric delays value of theory; Dx s, dy s, dz sfor the correction of lunar rover coordinate;
According to formula five and according to current approximate value middle parameter (x s0, y s0, z s0) calculate the partial derivative of VLBI restrictive condition, and the matrix of coefficients B of VLBI restrictive condition is formed according to formula six vLBI_Lmt;
0 = x S 0 x S 0 2 + y S 0 2 + z S 0 2 dx S + y S 0 x S 0 2 + y S 0 2 + z S 0 2 dy S + z S 0 x S 0 2 + y S 0 2 + z S 0 2 dz S = ladx S + lbdy S + lcdz S Formula five
l VLBI _ Lmt = 0 B VLBI _ Lmt = la lb lc Formula six
Wherein, l vLBI_Lmtrepresent the observed reading of VLBI restrictive condition and the difference of its approximate value;
According to formula seven and according to current approximate value calculate the partial derivative of association system constraint condition, and form the matrix of coefficients B of association system constraint condition according to formula eight dbl_Lmt;
formula seven
Wherein, k 11, k 12..., k 35represent the coefficient of association system restrictive condition observation equation, equal the corresponding partial derivative of association system constraint condition respectively; N 0represent prime vertical radius initial value, H is lunar surface elevation; A represents semimajor axis of ellipsoid, and e represents ellipsoid first eccentricity;
l dbl _ Lmt = 0 B dbl _ Lmt = k 11 k 12 k 13 0 0 k 21 k 22 0 k 24 0 k 31 0 0 0 k 35 Formula eight
Wherein, l dbl_Lmtrepresent the observed reading of association system restrictive condition and the difference of its approximate value;
According to formula nine and according to current approximate value middle parameter calculate the approximate value (sinh) of celestial navigation 0with (tanA) 0, and form matrix l according to the approximate value of celestial navigation and the difference of observed reading cNS;
formula nine
Matrix l cNSbuilding form is, l CNS = sinh - ( sinh ) 0 tan A - ( tan A ) 0 ;
According to formula ten and according to (x s0, y s0, z s0) calculate the approximate value of VLBI and the difference of observed reading, and form matrix l vLBI;
cτ 120 - c = c ( τ 0 - τ c ) = c [ τ 0 - ( ( x 2 - x s 0 ) 2 + ( y 2 - y s 0 ) 2 + ( z 2 - z s 0 ) 2 - ( x 1 - x s 0 ) 2 + ( y 1 - y s 0 ) 2 + ( z 1 - z s 0 ) 2 ) ] Formula ten
In formula, c τ 12o-crepresent the observed reading of VLBI and the difference of approximate value;
Matrix l vLBIbuilding form is, l vLBI=[c (τ 0c)];
Step 3, the matrix of coefficients B obtained by above-mentioned steps cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtand the matrix l that the difference of approximate value and observed reading forms cNS, l vLBI, l vLBI_Lmt, l dbl_Lmtthe matrix of coefficients B of combined system is formed according to formula 11 dblwith l dbl, setting parameter represent the difference between true value and approximate value; Carry out adjustment according to formula 12, obtain and whether judged result meets the condition of convergence, if meet, enter step 4, then will not meet as new approximate value return step 2 again iterative until meet the condition of convergence;
V dbl = V CNS V VLBI V VLBI _ Lmt V dbl _ Lmt T x ^ dbl = x ^ CNS x ^ VLBI B tmp = B CNS 0 0 B VLBI 0 B VLBI _ Lmt B dbl = B tmp B dbl _ Lmt l dbl = l CNS l VLBI l VLBI _ Lmt l dbl _ Lmt T P dbl = P CNS P VLBI P VLBI _ lmt P dbl _ lmt Formula 11
x ^ dbl = ( B dbl T P dbl B dbl ) - 1 B dbl T P dbl l dbl Formula 12
Wherein, V dblrepresent the correction of association system observed reading, P dblfor association system solves the power battle array of limit condition, wherein, P cNS, P vLBI, P vLBI_Lmt, P dbl_Lmtbe respectively matrix of coefficients B cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtcorresponding power battle array;
Step 4, according to final parametric solution result export the location coordinate information of lunar rover.
And association system described in step 3 solves the power battle array P of limit condition dbldetermine according to the Helmert variance component estimation method.
And the condition of convergence described in step 3 is, parameter middle x s, y swith z scorresponding difference is less than 10m, corresponding difference is less than 10 -8, the corresponding difference of λ is less than 10 -8.
The present invention is also corresponding provides a kind of lunar rover co-located system, comprises with lower module,
Initialization module, is expressed as with parameter vector for establishing required lunar rover position corresponding approximate value is labeled as wherein (x s, y s, z s) represent lunar rover rectangular coordinate, for the terrestrial coordinate of lunar rover, λ, be respectively right ascension, the declination of lunar rover in the moon admittedly coordinate system;
Input lunar rover approximate coordinates and the observed reading mistiming τ of VLBI 0represent the elevation angle of observation celestial body with observed reading sinh and the tanA of celestial navigation, h, A is the position angle of observation celestial body; Wherein, by lunar rover approximate coordinates as initial approximate value (x s0, y s0, z s0) represent the initial value of lunar rover rectangular coordinate, represent the initial value of its terrestrial coordinate;
Matrix sets up module, for calculating the partial derivative of celestial navigation part, and forms the matrix of coefficients of celestial navigation part; Calculate the partial derivative of VLBI part, and form the matrix of coefficients of VLBI part; Calculate the partial derivative of VLBI restrictive condition, and form the matrix of coefficients of VLBI restrictive condition; Calculate the partial derivative of association system constraint condition, and form the matrix of coefficients of association system constraint condition; Calculate the approximate value of celestial navigation, and form corresponding matrix; Calculate the approximate value of VLBI and the difference of observed reading, and form corresponding matrix; Realize as follows,
According to formula in the lump according to current approximate value middle parameter calculate the partial derivative of celestial navigation part, and form the matrix of coefficients B of celestial navigation part according to formula two cNS;
Formula one
Wherein, α, δ are right ascension, the declination of the celestial body of observation, and GHA is the Greenwich hour angle in the first point of Aries;
formula two
Wherein, for required parameter correction;
According to formula three and according to current approximate value middle parameter (x s0, y s0, z s0) calculate VLBI partial derivative partly, and the matrix of coefficients B of VLBI part is formed according to formula four vLBI;
a 11 = x 1 - x s r 1 - x 2 - x s r 2 a 12 = y 1 - y s r 1 - y 2 - y s r 2 a 13 = z 1 - z s r 1 - z 2 - z s r 2 Formula three
In formula, a 11, a 12, a 13for observation equation coefficient value, equal the partial derivative of VLBI part respectively (x 1, y 1, z 1) represent the coordinate of the station 1, (x 2, y 2, z 2) represent the coordinate of the station 2, r 1, r 2represent the distance value between lunar orbiter and the station 1, the station 2;
x ^ VLBI = dx s dy s dz s B VLBI = ∂ ( cτ 12 ) ∂ x s ∂ ( c τ 12 ) ∂ y s ∂ ( cτ 12 ) ∂ z s Formula four
Wherein, for required parameter (x s, y s, z s) correction; C represents the light velocity; τ 0for the time delay observed reading of VLBI; τ cfor the geometric delays value of theory; Dx s, dy s, dz sfor the correction of lunar rover coordinate;
According to formula five and according to current approximate value middle parameter (x s0, y s0, z s0) calculate the partial derivative of VLBI restrictive condition, and the matrix of coefficients B of VLBI restrictive condition is formed according to formula six vLBI_Lmt;
0 = x S 0 x S 0 2 + y S 0 2 + z S 0 2 dx S + y S 0 x S 0 2 + y S 0 2 + z S 0 2 dy S + z S 0 x S 0 2 + y S 0 2 + z S 0 2 dz S = ladx S + lbdy S + lcdz S Formula five
l VLBI _ Lmt = 0 B VLBI _ Lmt = la lb lc Formula six
Wherein, l vLBI_Lmtrepresent the observed reading of VLBI restrictive condition and the difference of its approximate value;
According to formula seven and according to current approximate value calculate the partial derivative of association system constraint condition, and form the matrix of coefficients B of association system constraint condition according to formula eight dbl_Lmt;
formula seven
Wherein, k 11, k 12..., k 35represent the coefficient of association system restrictive condition observation equation, equal the corresponding partial derivative of association system constraint condition respectively; N 0represent prime vertical radius initial value, H is lunar surface elevation; A represents semimajor axis of ellipsoid, and e represents ellipsoid first eccentricity;
l dbl _ Lmt = 0 B dbl _ Lmt = k 11 k 12 k 13 0 0 k 21 k 22 0 k 24 0 k 31 0 0 0 k 35 Formula eight
Wherein, l dbl_Lmtrepresent the observed reading of association system restrictive condition and the difference of its approximate value;
According to formula nine and according to current approximate value middle parameter calculate the approximate value (sinh) of celestial navigation 0with (tanA) 0, and form matrix l according to the approximate value of celestial navigation and the difference of observed reading cNS;
formula nine
Matrix l cNSbuilding form is, l CNS = sinh - ( sinh ) 0 tan A - ( tan A ) 0 ;
According to formula ten and according to (x s0, y s0, z s0) calculate the approximate value of VLBI and the difference of observed reading, and form matrix l vLBI;
cτ 120 - c = c ( τ 0 - τ c ) = c [ τ 0 - ( ( x 2 - x s 0 ) 2 + ( y 2 - y s 0 ) 2 + ( z 2 - z s 0 ) 2 - ( x 1 - x s 0 ) 2 + ( y 1 - y s 0 ) 2 + ( z 1 - z s 0 ) 2 ) ] Formula ten
In formula, c τ 12o-crepresent the observed reading of VLBI and the difference of approximate value;
Matrix l vLBIbuilding form is, l vLBI=[c (τ 0c)];
Positioning calculation module, sets up by matrix the matrix of coefficients B that module obtains cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtand the matrix l that the difference of approximate value and observed reading forms cNS, l vLBI, l vLBI_Lmt, l dbl_Lmtthe matrix of coefficients B of combined system is formed according to formula 11 dblwith l dbl, setting parameter represent the difference between true value and approximate value; Carry out adjustment according to formula 12, obtain and whether judged result meets the condition of convergence, if meet, command result output module works, and then will not meet as new approximate value order matrix set up module again iteration work until meet the condition of convergence;
V dbl = V CNS V VLBI V VLBI _ Lmt V dbl _ Lmt T x ^ dbl = x ^ CNS x ^ VLBI B tmp = B CNS 0 0 B VLBI 0 B VLBI _ Lmt B dbl = B tmp B dbl _ Lmt l dbl = l CNS l VLBI l VLBI _ Lmt l dbl _ Lmt T P dbl = P CNS P VLBI P VLBI _ lmt P dbl _ lmt Formula 11
x ^ dbl = ( B dbl T P dbl B dbl ) - 1 B dbl T P dbl l dbl Formula 12
Wherein, V dblrepresent the correction of association system observed reading, P dblfor association system solves the power battle array of limit condition, wherein, P cNS, P vLBI, P vLBI_Lmt, P dbl_Lmtbe respectively matrix of coefficients B cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtcorresponding power battle array;
Result output module, for according to final parametric solution result export the location coordinate information of lunar rover.
And association system described in positioning calculation module solves the power battle array P of limit condition dbldetermine according to the Helmert variance component estimation method.
And described in positioning calculation module, the condition of convergence is, parameter middle x s, y swith z scorresponding difference is less than 10m, corresponding difference is less than 10 -8, the corresponding difference of λ is less than 10 -8.
The present invention considers to be nature celestial body due to the observation of celestial navigation technology, therefore can Continuous Observation, can by celestial navigation technology for lunar rover provides positional information when receiving VLBI signal; Meanwhile, VLBI technology can provide high-precision positional information.Therefore, technical scheme proposition employing association system of the present invention positions and can improve positioning precision and stability.And for the problem that different recording geometry weights are determined, propose to adopt Hull special formula journey component of writing from memory to test and surely weigh strategy afterwards, thus avoid the unreasonable lunar rover positioning error caused of weights.The present invention has important actual promotional value and application prospect, has very important effect to the development of national economy and the raising of living standards of the people.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of the embodiment of the present invention.
Fig. 2 is the celestial navigation schematic diagram of the embodiment of the present invention.
Fig. 3 is the VLBI One-Point Location schematic diagram of the embodiment of the present invention.
Embodiment
Below in conjunction with drawings and Examples, technical solution of the present invention is described in detail.
For the sake of ease of implementation, the celestial navigation principle that the present invention relates to and VLBI One-Point Location principle is introduced first respectively:
(1) celestial navigation principle is derived
A celestial sphere by observation celestial body S is done, as shown in Figure 2 centered by observation platform P.Because the equatorial plane of celestial sphere self and the orbital plane of revolution of earth can intersect at the first point of Aries and first point of Libra.Again because be fixing relative to the rotation of the earth inertial reference system with revolution rule, therefore the known first point of Aries and the first point of Libra coordinate in inertial reference system is also fixing.Meanwhile, the first point of Aries is at distance earth infinite point, so any one line overlaps on the first point of Aries and the earth.Γ will be expressed as the first point of Aries; PZ grepresent Greenwich meridian direction; GHA is the Greenwich hour angle in the first point of Aries; The celestial axis north is to P nrepresent; Celestial axis south " represents to P.And the direction of visual lines of observation celestial body is represented with PS; PS is expressed as PS at the extended line of the equatorial plane inner projection of celestial sphere " simultaneously.By above setting, then the right ascension α of celestial body in Celestial Reference System is observed to be expressed as: α=∠ Γ PS "; The celestial sphere declination δ of observation celestial body can be expressed as δ=∠ SPS "; Angle between the direction of visual lines PS of observation celestial body and zenith direction PZ is that 90 ° of-h, h represent the elevation angle observing celestial body; A is the position angle of observation celestial body; The north of celestial axis to angulation between PPN and zenith direction PZ is the north of celestial axis is 90 ° of-δ to the angle between PPN and observation celestial body direction of visual lines PS.At parallactic triangle P nin ZS, order
To sum up, in Fig. 2, h and A is the elevation angle and position angle of observing celestial body in local horizontal coordinates; λ with for the right ascension declination of lunar rover in the moon admittedly coordinate system; α and δ is right ascension and the declination of the celestial body of observation.
Owing to there is the following cosine law, cotangent theorem in spherical triangle:
cos η = cos β cos γ + sin β sin γ cos LHA cot A sin LHA = cot γ sin β - cos τ cos β - - - ( 2 )
Formula (1) is substituted into formula (2), can obtain:
Formula (3) is the observation equation of celestial navigation location technology.
(2) VLBI One-Point Location principle is derived
As Fig. 3, O1, O2 represent the observation station 1,2, they form baseline 12; S represents lunar rover; t 1, t 2represent that signal arrives the time of the station 1,2.Lunar orbiter and the distance value between them can be expressed as r 1, r 2:
r 2 = ( x 2 - x s ) 2 + ( y 2 - y s ) 2 + ( z 2 - z s ) 2 , r 1 = ( x 1 - x s ) 2 + ( y 1 - y s ) 2 + ( z 1 - z s ) 2 - - - ( 4 )
Therefore can obtain:
cτ 12 = c ( t 2 - t 1 ) = r 2 - r 1 = ( x 2 - x s ) 2 + ( y 2 - y s ) 2 + ( z 2 - z s ) 2 - ( x 1 - x s ) 2 + ( y 1 - y s ) 2 + ( z 1 - z s ) 2 - - - ( 5 )
Formula (5) is the observation equation of VLBI location technology, wherein, and τ 12represent that signal arrives the station 2 and the mistiming arriving the station 1; C represents the light velocity; (x 1, y 1, z 1) represent the coordinate of the station 1, (x 2, y 2, z 2) represent the coordinate of the station 2; (x s, y s, z s) represent the coordinate of lunar rover.
The observation model of celestial navigation observation model and VLBI is combined by the present invention, sets up the mathematical model of association system.For combined system, simulated data is first utilized to analyze heavenly body sensor precision to the impact of lunar rover positioning precision.
Further, adopt Hull to write from memory weights that specific weights strategy determines between different recording geometry.For different celestial navigation positioning system and the problem identificatioin of VLBI positioning system weights, Hull is adopted to write from memory specific weights method, for combined positioning-method and single localization method.The precision of analysis joint method and the independent result adopting celestial navigation localization method to obtain, and the precision of analysis joint method and the independent lunar rover positioning result adopting VLBI localization method to obtain.
Embodiment is implemented as follows:
A) the least square model that celestial navigation location technology carries out lunar rover location is set up.
For celestial navigation observation equation (3), in order to derive conveniently, being used as by sinh and tanA is dummy observation, and by its linearization, can obtain:
Wherein, (sinh) 0with (tanA) 0represent be actual adjustment time dummy observation approximate value, in addition, to formula (6), have:
Write formula (6) as error equation form:
V CNS = B CNS x ^ CNS - l CNS - - - ( 8 )
In above formula, V cNSrepresent the error amount of celestial navigation; for the correction of required parameter; l cNSrepresent the difference of observed reading and its approximate value; B cNSfor matrix of coefficients.Specifically can be expressed as:
When observing the number of celestial body be no less than 2, can adjustment Models be formed:
V CNS = B CNS x ^ CNS - l CNS D CNS = σ 0 CNS 2 P CNS - 1 - - - ( 10 )
Wherein, D cNSfor the variance matrix of observed reading, determined by the size of observational error; represent that celestial navigation tests front weight unit medial error when solving; P cNSfor the power battle array of observed reading.During concrete enforcement, observation celestial body can adopt the sun and the earth usually.
B) the least square model that VLBI location technology carries out lunar rover location is set up.
By observation equation (5) linearization of VLBI, and according to Taylor series expansion, only retain single order item, can obtain:
v 12 = cτ 12 o - c + ∂ ( cτ 12 ) ∂ x s dx s + ∂ ( cτ 12 ) ∂ y s dy s + ∂ ( cτ 12 ) ∂ z s dz s = cτ 12 o - c + a 11 dx s + a 12 dy s + a 13 dz s - - - ( 11 )
In formula:
a 11 = x 1 - x s r 1 - x 2 - x s r 2
In formula, c τ 12o-crepresent the observed reading of VLBI and the difference of approximate value; a 11, a 12, a 13for observation equation coefficient value, equal the partial derivative of VLBI part respectively v 12represent error amount; τ 0for the time delay observed reading of VLBI; τ cfor the geometric delays value of theory; (x s0, y s0, z s0) be lunar rover coordinate initial value; Dx s, dy s, dz sfor the correction of lunar rover coordinate.Write formula (11) as matrix form:
V VLBI = B VLBI x ^ VLBI - l VLBI - - - ( 13 )
In above formula, V vLBIrepresent the error amount of VLBI; for the correction of required parameter, l vLBIrepresent the difference of observed reading and its approximate value; B vLBIfor matrix of coefficients, specifically can be expressed as:
x ^ VLBI = dx s dy s dz s l VLBI _ 1 = [ c ( τ 0 - τ c ) ] B VLBI _ 1 = ∂ ( cτ 12 ) ∂ x s ∂ ( c τ 12 ) ∂ y s ∂ ( cτ 12 ) ∂ z s - - - ( 14 )
If the baseline 12 that arbitrarily the observation station 1,2 forms is i-th baseline, due to state-owned 4 VLBI stations at present, six baselines can be formed, can adjustment Models be formed.
V VLBI = B VLBI x ^ VLBI - l VLBI D VLBI = σ 0 VLBI 2 P VLBI - 1 - - - ( 15 )
Wherein, D vLBIfor the variance matrix of observed reading, determined by the size of observational error; represent weight unit medial error when VLBI solves; P vLBIfor the power battle array of observed reading.
During concrete enforcement, every bar baseline can form corresponding matrix V vLBI_i, B vLBI_iand l vLBI_i(i=1,2 ..., 6), v vLBI_irepresent the error amount of i-th corresponding VLBI of baseline; for the correction of required parameter, l vLBI_irepresent the difference of i-th corresponding observed reading of baseline and its approximate value;
B vLBI_ibe i-th baseline corresponding coefficient matrix, x ^ VLBI = dx s dy s dz s l VLBI _ i = [ c ( τ 0 - τ c ) ] B VLBI _ i = ∂ ( cτ 12 ) ∂ x s ∂ ( c τ 12 ) ∂ y s ∂ ( cτ 12 ) ∂ z s
Corresponding adjustment Models specifically can be expressed as, V VLBI _ all = B VLBI _ all x ^ VLBI - l VLBI _ all D VLBI = σ 0 VLBI 2 P VLBI - 1 V VLBI _ all = [ V VLBI _ 1 , . . . , V VLBI _ 6 ] T B VLBI _ all = [ B VLBI _ 1 , . . . , B VLBI _ 6 ] T l VLBI _ all = [ l VLBI _ 1 , . . . , l VLBI _ 6 ] T
Wherein, V vLBI_allfor the matrix that the error amount of the corresponding VLBI of all baselines is formed, B vLBI_allfor all baseline corresponding coefficient matrixes, l vLBI_allfor the difference of the corresponding observed reading of all baselines and its approximate value.
The situation of carrying out adjustment based on multiple observation celestial body is similar, and those skilled in the art can implement according to concrete observation celestial body situation.
Due to adopt VLBI measure time, do not use distance restraint, be only utilize VLBI to obtain Delay to convert angle position information to, therefore have larger error.So when actual resolving, also need the distance restraint adding lunar rover, the positional information of the higher lunar rover of precision could be obtained like this from VLBI observation information.Lunar rover distance condition constrain equation can be set up.
x s 0 2 + y s 0 2 + z s 0 2 - x s 2 + y s 2 + z s 2 = 0 - - - ( 16 )
By formula (16) linearization:
0 = x S 0 x S 0 2 + y S 0 2 + z S 0 2 dx S + y S 0 x S 0 2 + y S 0 2 + z S 0 2 dy S + z S 0 x S 0 2 + y S 0 2 + z S 0 2 dz S = ladx S + lbdy S + lcdz S - - - ( 17 )
Can adjustment Models be formed:
V VLBI _ Lmt = B VLBI _ Lmt x ^ VLBI - l VLBI _ Lmt D VLBI _ Lmt = σ 0 VLBI 2 P VLBI _ Lmt - 1 - - - ( 18 )
Wherein:
l VLBI _ Lmt = 0 B VLBI _ Lmt = la lb lc - - - ( 19 )
In formula (18), la, lb, lc represent the coefficient of restrictive condition; V vLBI_Lmtrepresent the error amount of VLBI restrictive condition; for the correction of required parameter; l vLBI_Lmtrepresent the observed reading of VLBI restrictive condition and the difference of its approximate value; B vLBI_Lmtfor the matrix of coefficients of VLBI restrictive condition; D vLBI_Lmtfor lunar rover priori position and the moon heart distance variance matrix; represent weight unit medial error when VLBI solves; P vLBI_Lmtfor power battle array when VLBI solves.
C) the least square model that the lunar rover setting up associating celestial navigation location technology and VLBI location technology is located.
By step above a), b), can set association system solve parameter as namely due to the moon heart rectangular coordinate and the moon heart terrestrial coordinate can be changed by following formula:
In above formula, N represents prime vertical radius, can be expressed as:
Wherein, a represents semimajor axis of ellipsoid, and e represents ellipsoid first eccentricity." goddess in the moon No. three " successfully lands near side of the moon Sinus Iridum and Mare Imbrium area intersection again, and according to moon digital elevation model, elevation change is herein very little.So in position fixing process, suppose that lunar surface elevation H immobilizes, its value is-2.64km.By formula (20) linearization:
Wherein, k 11, k 12..., k 35represent the coefficient of association system restrictive condition observation equation; (x s0, y s0, z s0) represent the initial value of lunar rover rectangular coordinate, represent the initial value of its terrestrial coordinate, N 0represent prime vertical radius initial value, can according to lunar rover approximate coordinates calculate with formula (23).
Can adjustment Models be formed:
V dbl _ Lmt = B dbl _ Lmt x ^ dbl - l dbl _ Lmt D dbl _ Lmt = σ 0 dbl 2 P dbl _ Lmt - 1 - - - ( 23 )
Wherein:
l dbl _ Lmt = 0 B dbl _ Lmt = k 11 k 12 k 13 0 0 k 21 k 22 0 k 24 0 k 31 0 0 0 k 35 - - - ( 24 )
In formula (23), V dbl_Lmtrepresent the error amount of association system restrictive condition; the correction of parameter required by association system; l dbl_Lmtrepresent the observed reading of association system restrictive condition and the difference of its approximate value; B dbl_Lmtfor the matrix of coefficients of restrictive condition; D dbl_Lmtfor the variance matrix of association system restrictive condition; represent that association system tests front weight unit medial error when solving; P dbl_Lmtfor power battle array when association system solves.
By above-mentioned derivation, can set the least square adjustment model of association system as:
V dbl = B dbl x ^ dbl - l dbl D dbl = σ 0 dbl 2 P dbl - - - ( 25 )
In formula (25):
V dbl = V CNS V VLBI V VLBI _ Lmt V dbl _ Lmt T x ^ dbl = x ^ CNS x ^ VLBI B tmp = B CNS 0 0 B VLBI 0 B VLBI _ Lmt B dbl = B tmp B dbl _ Lmt l dbl = l CNS l VLBI l VLBI _ Lmt l dbl _ Lmt T P dbl = P CNS P VLBI P VLBI _ lmt P dbl _ lmt - - - ( 26 )
In formula (25), V dblrepresent the correction of association system observed reading, D dblfor the variance matrix of association system; represent that association system tests front weight unit medial error when solving; P dblfor association system solves the power battle array of limit condition, wherein, P cNS, P vLBI, P vLBI_Lmt, P dbl_Lmtbe respectively matrix of coefficients B cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtcorresponding power battle array.
During concrete enforcement, owing to there being 6 baselines, have accordingly,
V dbl = V CNS V VLBI V VLBI _ Lmt V dbl _ Lmt T x ^ dbl = x ^ CNS x ^ VLBI B tmp = B CNS 0 0 B VLBI 0 B VLBI _ Lmt B dbl = B tmp B dbl _ Lmt l dbl = l CNS l VLBI _ all l VLBI _ Lmt l dbl _ Lmt T P dbl = P CNS P VLBI P VLBI _ lmt P dbl _ lmt
After composition formula (26), parameter value can be solved according to formula (27)
x ^ dbl = ( B dbl T P dbl B dbl ) - 1 B dbl T P dbl l dbl - - - ( 27 )
VLBI observed quantity is related to, distance constraints, celestial navigation observed quantity and rectangular space coordinate and this 4 class observed quantity of terrestrial coordinate constraint condition in formula (25).
During concrete enforcement, those skilled in the art can preset the power battle array P of these 4 kinds of observed quantities voluntarily cNS, P vLBI, P vLBI_Lmt, P dbl_Lmt.The present invention further contemplates, and if not the rational empirical value of employing, the Helmert variance component estimation method can be adopted to realize weights and determine.The basic skills of the Helmert variance component estimation utilizes the quadratic sum calculating rear variety classes correction each time determine value, i=1,2,3,4, i are for representing above-mentioned 4 class observed quantities, V irepresent the error amount of observed reading, represent the weight unit medial error of observed reading, P irepresent the power battle array of observed reading, therefore must determine residual sum of squares (RSS) with between relational expression.Following approximate formula can be obtained by error compensation method:
σ ^ 0 i 2 = V i T P i V i / n i - - - ( 28 )
In formula, n irepresent the number of all kinds of measured value.
For the sake of ease of implementation, to be applied to the concrete iterative computation step of combined system as follows for the special formula difference estimation technique to provide Hull to write from memory:
1) determination of the initial power battle array before calculating, comprises the power battle array P before determining four class observed readings calculating i; Initialization current iteration number of times I=1,
2) carry out the I time adjustment, try to achieve all kinds of observed reading
3) carry out resolving for the I time after variance evaluation, try to achieve the I time valuation of all kinds of observed reading variance of unit weight and carry out weights according to formula (29) and determine:
P ^ i = c σ ^ 0 i 2 P i - 1 - - - ( 29 )
In formula, c is any constant, usually selectes in an amount, represent the power battle array solving rear observed reading;
4) 3 are performed according to this) acquired results as new power battle array P i, make I=I-1, return 2) carry out next iteration, so repeatedly carry out 2), 3) until thought the ratio of four class observed reading variance of unit weights by inspection till equaling 1:1:1:1.
Hull special formula method of writing from memory is adopted to carry out after weights determine, just can to perform 3 for the last time) acquired results as final power battle array, then joint error equation (25) can solve according to criterion of least squares.With the analogue observation data of the VLBI measured data and celestial navigation of combining employing " goddess in the moon No. three ", result is analyzed respectively.
During concrete enforcement, software mode can be adopted to realize flow process of the present invention, see Fig. 1, the flow process of embodiment is as follows:
If required lunar rover position is expressed as with parameter vector corresponding approximate value is labeled as wherein (x s, y s, z s) represent lunar rover rectangular coordinate, for the terrestrial coordinate of lunar rover, be respectively right ascension, the declination of lunar rover in the moon admittedly coordinate system;
1. lunar rover approximate coordinates is inputted and the observed reading mistiming τ of VLBI 0represent the elevation angle of observation celestial body with observed reading sinh and the tanA of celestial navigation, h, A is the position angle of observation celestial body; Wherein, by lunar rover approximate coordinates as initial approximate value (x s0, y s0, z s0) represent the initial value of lunar rover rectangular coordinate, represent the initial value of its terrestrial coordinate.
During concrete enforcement, lunar rover approximate coordinates can be preset voluntarily by those skilled in the art, subsequent operation of the present invention can rectification error.
2. according to formula (7) and according to lunar rover coordinate parameters calculate the partial derivative of celestial navigation part, and form the matrix of coefficients B of celestial navigation part according to formula (9) cNS; According to formula (12) and according to lunar rover coordinate parameters (x s0, y s0, z s0) calculate VLBI partial derivative partly, and according to formula (14) composition VLBI matrix of coefficients B partly vLBI; According to formula (17) and according to lunar rover coordinate parameters (x s0, y s0, z s0) calculate the partial derivative of VLBI restrictive condition, and according to the matrix of coefficients B of formula (19) composition VLBI restrictive condition vLBI_Lmt; According to formula (22) and according to lunar rover coordinate parameters calculate the partial derivative of association system constraint condition, and form the matrix of coefficients B of association system constraint condition according to formula (24) dbl_Lmt.According to formula (3) and basis calculate the approximate value (sinh) of celestial navigation 0with (tanA) 0, and according to formula (9) composition matrix l cNS; According to formula (12) and according to (x s0, y s0, z s0) calculate the approximate value of VLBI and the difference of observed reading, and according to formula (14) composition matrix l vLBI.
The matrix that the difference of the matrix of coefficients 3. obtained by above-mentioned steps and approximate value and observed reading forms forms the matrix of coefficients B of combined system according to formula (26) dblwith l dbl, required parameter vector is expressed as if its approximate value is represent the difference between true value and approximate value.Carry out adjustment according to formula (27), obtain and whether judged result meets the condition of convergence, if meet, export result of calculation, then will not meet as new return previous step again iterative until satisfy condition.During concrete enforcement, those skilled in the art can preset the condition of convergence voluntarily, and in embodiment, the condition of convergence is, parameter middle x s, y swith z scorresponding difference is less than 10m, corresponding difference is less than 10 -8, the corresponding difference of λ is less than 10 -8.
4. according to final parametric solution result export the location coordinate information of lunar rover.
During concrete enforcement, modular mode also can be adopted to provide a kind of lunar rover co-located system, and system that embodiment provides comprises with lower module:
Initialization module, is expressed as with parameter vector for establishing required lunar rover position corresponding approximate value is labeled as wherein (x s, y s, z s) represent lunar rover rectangular coordinate, for the terrestrial coordinate of lunar rover, be respectively right ascension, the declination of lunar rover in the moon admittedly coordinate system;
Input lunar rover approximate coordinates and the observed reading mistiming τ of VLBI 0represent the elevation angle of observation celestial body with observed reading sinh and the tanA of celestial navigation, h, A is the position angle of observation celestial body; Wherein, by lunar rover approximate coordinates as initial approximate value (x s0, y s0, z s0) represent the initial value of lunar rover rectangular coordinate, represent the initial value of its terrestrial coordinate;
Matrix sets up module, for calculating the partial derivative of celestial navigation part, and forms the matrix of coefficients of celestial navigation part; Calculate the partial derivative of VLBI part, and form the matrix of coefficients of VLBI part; Calculate the partial derivative of VLBI restrictive condition, and form the matrix of coefficients of VLBI restrictive condition; Calculate the partial derivative of association system constraint condition, and form the matrix of coefficients of association system constraint condition; Calculate the approximate value of celestial navigation, and form corresponding matrix; Calculate the approximate value of VLBI and the difference of observed reading, and form corresponding matrix; Realize as follows,
According to current approximate value middle parameter calculate the partial derivative of celestial navigation part, and form the matrix of coefficients B of celestial navigation part cNS;
Wherein, α, δ are right ascension, the declination of the celestial body of observation, and GHA is the Greenwich hour angle in the first point of Aries;
Wherein, for required parameter correction;
According to current approximate value middle parameter (x s0, y s0, z s0) calculate VLBI partial derivative partly, and form the matrix of coefficients B of VLBI part vLBI;
a 11 = x 1 - x s r 1 - x 2 - x s r 2 a 12 = y 1 - y s r 1 - y 2 - y s r 2 a 13 = z 1 - z s r 1 - z 2 - z s r 2
In formula, a 11, a 12, a 13for observation equation coefficient value, equal the partial derivative of VLBI part respectively (x 1, y 1, z 1) represent the coordinate of the station 1, (x 2, y 2, z 2) represent the coordinate of the station 2, r 1, r 2represent the distance value between lunar orbiter and the station 1, the station 2;
x ^ VLBI = dx s dy s dz s B VLBI = ∂ ( cτ 12 ) ∂ x s ∂ ( c τ 12 ) ∂ y s ∂ ( cτ 12 ) ∂ z s
Wherein, for required parameter (x s, y s, z s) correction; C represents the light velocity; τ 0for the time delay observed reading of VLBI; τ cfor the geometric delays value of theory; Dx s, dy s, dz sfor the correction of lunar rover coordinate;
According to current approximate value middle parameter (x s0, y s0, z s0) calculate the partial derivative of VLBI restrictive condition, and form the matrix of coefficients B of VLBI restrictive condition vLBI_Lmt;
0 = x S 0 x S 0 2 + y S 0 2 + z S 0 2 dx S + y S 0 x S 0 2 + y S 0 2 + z S 0 2 dy S + z S 0 x S 0 2 + y S 0 2 + z S 0 2 dz S = ladx S + lbdy S + lcdz S
l VLBI _ Lmt = 0 B VLBI _ Lmt = la lb lc
Wherein, l vLBI_Lmtrepresent the observed reading of VLBI restrictive condition and the difference of its approximate value;
According to current approximate value calculate the partial derivative of association system constraint condition, and form the matrix of coefficients B of association system constraint condition dbl_Lmt;
Wherein, k 11, k 12..., k 35represent the coefficient of association system restrictive condition observation equation, equal the corresponding partial derivative of association system constraint condition respectively; N 0represent prime vertical radius initial value, H is lunar surface elevation; A represents semimajor axis of ellipsoid, and e represents ellipsoid first eccentricity;
l dbl _ Lmt = 0 B dbl _ Lmt = k 11 k 12 k 13 0 0 k 21 k 22 0 k 24 0 k 31 0 0 0 k 35
Wherein, l dbl_Lmtrepresent the observed reading of association system restrictive condition and the difference of its approximate value;
According to current approximate value middle parameter calculate the approximate value (sinh) of celestial navigation 0with (tanA) 0, and form matrix l according to the approximate value of celestial navigation and the difference of observed reading cNS;
Matrix l cNSbuilding form is, l CNS = sinh - ( sinh ) 0 tan A - ( tan A ) 0 ;
According to (x s0, y s0, z s0) calculate the approximate value of VLBI and the difference of observed reading, and form matrix l vLBI;
cτ 120 - c = c ( τ 0 - τ c ) = c [ τ 0 - ( ( x 2 - x s 0 ) 2 + ( y 2 - y s 0 ) 2 + ( z 2 - z s 0 ) 2 - ( x 1 - x s 0 ) 2 + ( y 1 - y s 0 ) 2 + ( z 1 - z s 0 ) 2 ) ]
In formula, c τ 12o-crepresent the observed reading of VLBI and the difference of approximate value;
Matrix l vLBIbuilding form is, l vLBI=[c (τ 0c)];
Positioning calculation module, sets up by matrix the matrix of coefficients B that module obtains cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtand the matrix l that the difference of approximate value and observed reading forms cNS, l vLBI, l vLBI_Lmt, l dbl_Lmtthe matrix of coefficients B of composition combined system dblwith l dbl, setting parameter represent the difference between true value and approximate value; Carry out adjustment, obtain and whether judged result meets the condition of convergence, if meet, command result output module works, and then will not meet as new approximate value order matrix set up module again iteration work until meet the condition of convergence;
V dbl = V CNS V VLBI V VLBI _ Lmt V dbl _ Lmt T x ^ dbl = x ^ CNS x ^ VLBI B tmp = B CNS 0 0 B VLBI 0 B VLBI _ Lmt B dbl = B tmp B dbl _ Lmt l dbl = l CNS l VLBI l VLBI _ Lmt l dbl _ Lmt T P dbl = P CNS P VLBI P VLBI _ lmt P dbl _ lmt
x ^ dbl = ( B dbl T P dbl B dbl ) - 1 B dbl T P dbl l dbl
Wherein, V dblrepresent the correction of association system observed reading, P dblfor association system solves the power battle array of limit condition, wherein, P cNS, P vLBI, P vLBI_Lmt, P dbl_Lmtbe respectively matrix of coefficients B cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtcorresponding power battle array;
Result output module, for according to final parametric solution result export the location coordinate information of lunar rover.
Above embodiment is used for illustrative purposes only, but not limitation of the present invention, person skilled in the relevant technique, without departing from the spirit and scope of the present invention, various conversion or modification can also be made, therefore all equivalent technical schemes also should belong within category of the present invention, should be limited by each claim.

Claims (6)

1. a lunar rover combined positioning-method, is characterized in that: perform following steps,
Step 1, if required lunar rover position is expressed as with parameter vector corresponding approximate value is labeled as wherein (x s, y s, z s) represent lunar rover rectangular coordinate, for the terrestrial coordinate of lunar rover, λ, be respectively right ascension, the declination of lunar rover in the moon admittedly coordinate system;
Input lunar rover approximate coordinates and the observed reading mistiming τ of VLBI 0represent the elevation angle of observation celestial body with observed reading sinh and the tanA of celestial navigation, h, A is the position angle of observation celestial body; Wherein, by lunar rover approximate coordinates as initial approximate value (x s0, y s0, z s0) represent the initial value of lunar rover rectangular coordinate, represent the initial value of its terrestrial coordinate;
Step 2, calculates the partial derivative of celestial navigation part, and forms the matrix of coefficients of celestial navigation part; Calculate the partial derivative of VLBI part, and form the matrix of coefficients of VLBI part; Calculate the partial derivative of VLBI restrictive condition, and form the matrix of coefficients of VLBI restrictive condition; Calculate the partial derivative of association system constraint condition, and form the matrix of coefficients of association system constraint condition; Calculate the approximate value of celestial navigation, and form corresponding matrix; Calculate the approximate value of VLBI and the difference of observed reading, and form corresponding matrix; Realize as follows,
According to formula in the lump according to current approximate value middle parameter calculate the partial derivative of celestial navigation part, and form the matrix of coefficients B of celestial navigation part according to formula two cNS;
Wherein, α, δ are right ascension, the declination of the celestial body of observation, and GHA is the Greenwich hour angle in the first point of Aries;
Wherein, for required parameter correction;
According to formula three and according to current approximate value middle parameter (x s0, y s0, z s0) calculate VLBI partial derivative partly, and the matrix of coefficients B of VLBI part is formed according to formula four vLBI;
a 11 = x 1 - x s r 1 - x 2 - x s r 2 a 12 = y 1 - y s r 1 - y 2 - y s r 2 a 13 = z 1 - z s r 1 - z 2 - z s r 2 Formula three
In formula, a 11, a 12, a 13for observation equation coefficient value, equal the partial derivative of VLBI part respectively τ 12represent that signal arrives the station 2 and the mistiming arriving the station 1; (x 1, y 1, z 1) represent the coordinate of the station 1, (x 2, y 2, z 2) represent the coordinate of the station 2, r 1, r 2represent the distance value between lunar orbiter and the station 1, the station 2;
x ^ V L B I = dx s dy s dz s B V L B I = ∂ ( cτ 12 ) ∂ x s ∂ ( cτ 12 ) ∂ y s ∂ ( cτ 12 ) ∂ z s Formula four
Wherein, for required parameter (x s, y s, z s) correction, c represents the light velocity; τ 0for the time delay observed reading of VLBI; τ cfor the geometric delays value of theory; Dx s, dy s, dz sfor the correction of lunar rover coordinate;
According to formula five and according to current approximate value middle parameter (x s0, y s0, z s0) calculate the partial derivative of VLBI restrictive condition, and the matrix of coefficients B of VLBI restrictive condition is formed according to formula six vLBI_Lmt;
0 = x S 0 x S 0 2 + y S 0 2 + z S 0 2 dx S + y S 0 x S 0 2 + y S 0 2 + z S 0 2 dy S + z S 0 x S 0 2 + y S 0 2 + z S 0 2 dz S = ladx S + lady S + ladz S Formula five
l V L B I _ L m t = 0 B V L B I _ L m t = l a l b l c Formula six
Wherein, l vLBI_Lmtrepresent the observed reading of VLBI restrictive condition and the difference of its approximate value;
According to formula seven and according to current approximate value calculate the partial derivative of association system constraint condition, and form the matrix of coefficients B of association system constraint condition according to formula eight dbl_Lmt;
Wherein, k 11, k 12..., k 35represent the coefficient of association system restrictive condition observation equation, equal the corresponding partial derivative of association system constraint condition respectively; N 0represent prime vertical radius initial value, H is lunar surface elevation; A represents semimajor axis of ellipsoid, and e represents ellipsoid first eccentricity;
l d b l _ L m t = 0 B d b l _ L m t = k 11 k 12 k 13 0 0 k 21 k 22 0 k 24 0 k 31 0 0 0 k 35 Formula eight
Wherein, l dbl_Lmtrepresent the observed reading of association system restrictive condition and the difference of its approximate value;
According to formula nine and according to current approximate value middle parameter calculate the approximate value (sinh) of celestial navigation 0with (tanA) 0, and form matrix l according to the approximate value of celestial navigation and the difference of observed reading cNS;
Matrix l cNSbuilding form is, l C N S = sin h - ( sin h ) 0 tan A - ( tan A ) 0 ;
According to formula ten and according to (x s0, y s0, z s0) calculate the approximate value of VLBI and the difference of observed reading, and form matrix l vLBI;
cτ 120 - c = c ( τ 0 - τ c ) = c [ - τ 0 ( ( x 2 - x s 0 ) 2 + ( y 2 - y s 0 ) 2 + ( z 2 - z s 0 ) 2 - ( x 1 - x s 0 ) 2 + ( y 1 - y s 0 ) 2 + ( z 1 - z s 0 ) 2 ) ] Formula ten
In formula, c τ 12o-crepresent the observed reading of VLBI and the difference of approximate value;
Matrix l vLBIbuilding form is, l vLBI=[c (τ 0c)];
Step 3, the matrix of coefficients B obtained by above-mentioned steps cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtand the matrix l that the difference of approximate value and observed reading forms cNS, l vLBI, l vLBI_Lmt, l dbl_Lmtthe matrix of coefficients B of combined system is formed according to formula 11 dblwith l dbl, setting parameter represent the difference between true value and approximate value; Carry out adjustment according to formula 12, obtain and whether judged result meets the condition of convergence, if meet, enter step 4, then will not meet as new approximate value return step 2 again iterative until meet the condition of convergence;
V d b l = V C N S V V L B I V V L B I _ L m t V d b l _ L m t T x ^ d b l = x ^ C N S x ^ V L B I B t m p = B C N S 0 0 B V L B I 0 B V L B I _ L m t B d b l = B t m p B d b l _ L m t l d b l = l C N S l V L B I l V L B I _ L m t l d b l _ L m t T P d b l = P C N S P V L B I P V L B I _ l m t P d b l _ l m t Formula 11
x ^ d b l = ( B d b l T P d b l B d b l ) - 1 B d b l T P d b l l d b l Formula 12
Wherein, V dblrepresent the correction of association system observed reading, P dblfor association system solves the power battle array of limit condition, wherein, P cNS, P vLBI, P vLBI_Lmt, P dbl_Lmtbe respectively matrix of coefficients B cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtcorresponding power battle array;
Step 4, according to final parametric solution result export the location coordinate information of lunar rover.
2. lunar rover combined positioning-method according to claim 1, is characterized in that: association system described in step 3 solves the power battle array P of limit condition dbldetermine according to the Helmert variance component estimation method.
3. lunar rover combined positioning-method according to claim 1 or 2, is characterized in that: the condition of convergence described in step 3 is, parameter middle x s, y swith z scorresponding difference is less than 10m, corresponding difference is less than 10 -8, the corresponding difference of λ is less than 10 -8.
4. a lunar rover co-located system, is characterized in that: comprise with lower module,
Initialization module, is expressed as with parameter vector for establishing required lunar rover position corresponding approximate value is labeled as wherein (x s, y s, z s) represent lunar rover rectangular coordinate, for the terrestrial coordinate of lunar rover, λ, be respectively right ascension, the declination of lunar rover in the moon admittedly coordinate system;
Input lunar rover approximate coordinates and the observed reading mistiming τ of VLBI 0represent the elevation angle of observation celestial body with observed reading sinh and the tanA of celestial navigation, h, A is the position angle of observation celestial body; Wherein, by lunar rover approximate coordinates as initial approximate value (x s0, y s0, z s0) represent the initial value of lunar rover rectangular coordinate, represent the initial value of its terrestrial coordinate;
Matrix sets up module, for calculating the partial derivative of celestial navigation part, and forms the matrix of coefficients of celestial navigation part; Calculate the partial derivative of VLBI part, and form the matrix of coefficients of VLBI part; Calculate the partial derivative of VLBI restrictive condition, and form the matrix of coefficients of VLBI restrictive condition; Calculate the partial derivative of association system constraint condition, and form the matrix of coefficients of association system constraint condition; Calculate the approximate value of celestial navigation, and form corresponding matrix; Calculate the approximate value of VLBI and the difference of observed reading, and form corresponding matrix; Realize as follows,
According to formula in the lump according to current approximate value middle parameter calculate the partial derivative of celestial navigation part, and form the matrix of coefficients B of celestial navigation part according to formula two cNS;
Wherein, α, δ are right ascension, the declination of the celestial body of observation, and GHA is the Greenwich hour angle in the first point of Aries;
Wherein, for required parameter correction;
According to formula three and according to current approximate value middle parameter (x s0, y s0, z s0) calculate VLBI partial derivative partly, and the matrix of coefficients B of VLBI part is formed according to formula four vLBI;
a 11 = x 1 - x s r 1 - x 2 - x s r 2 a 12 = y 1 - y s r 1 - y 2 - y s r 2 a 13 = z 1 - z s r 1 - z 2 - z s r 2 Formula three
In formula, a 11, a 12, a 13for observation equation coefficient value, equal the partial derivative of VLBI part respectively τ 12represent that signal arrives the station 2 and the mistiming arriving the station 1; (x 1, y 1, z 1) represent the coordinate of the station 1, (x 2, y 2, z 2) represent the coordinate of the station 2, r 1, r 2represent the distance value between lunar orbiter and the station 1, the station 2;
x ^ V L B I = dx s dy s dz s B V L B I = ∂ ( cτ 12 ) ∂ x s ∂ ( cτ 12 ) ∂ y s ∂ ( cτ 12 ) ∂ z s Formula four
Wherein, for required parameter (x s, y s, z s) correction; C represents the light velocity; τ 0for the time delay observed reading of VLBI; τ cfor the geometric delays value of theory; Dx s, dy s, dz sfor the correction of lunar rover coordinate;
According to formula five and according to current approximate value middle parameter (x s0, y s0, z s0) calculate the partial derivative of VLBI restrictive condition, and the matrix of coefficients B of VLBI restrictive condition is formed according to formula six vLBI_Lmt;
0 = x S 0 x S 0 2 + y S 0 2 + z S 0 2 dx S + y S 0 x S 0 2 + y S 0 2 + z S 0 2 dy S + z S 0 x S 0 2 + y S 0 2 + z S 0 2 dz S = ladx S + lady S + ladz S Formula five
l V L B I _ L m t = 0 B V L B I _ L m t = l a l b l c Formula six
Wherein, l vLBI_Lmtrepresent the observed reading of VLBI restrictive condition and the difference of its approximate value;
According to formula seven and according to current approximate value calculate the partial derivative of association system constraint condition, and form the matrix of coefficients B of association system constraint condition according to formula eight dbl_Lmt;
Wherein, k 11, k 12..., k 35represent the coefficient of association system restrictive condition observation equation, equal the corresponding partial derivative of association system constraint condition respectively; N 0represent prime vertical radius initial value, H is lunar surface elevation; A represents semimajor axis of ellipsoid, and e represents ellipsoid first eccentricity;
l d b l _ L m t = 0 B d b l _ L m t = k 11 k 12 k 13 0 0 k 21 k 22 0 k 24 0 k 31 0 0 0 k 35 Formula eight
Wherein, l dbl_Lmtrepresent the observed reading of association system restrictive condition and the difference of its approximate value;
According to formula nine and according to current approximate value middle parameter calculate the approximate value (sinh) of celestial navigation 0with (tanA) 0, and form matrix l according to the approximate value of celestial navigation and the difference of observed reading cNS;
Matrix l cNSbuilding form is, l C N S = sin h - ( sin h ) 0 tan A - ( tan A ) 0 ;
According to formula ten and according to (x s0, y s0, z s0) calculate the approximate value of VLBI and the difference of observed reading, and form matrix l vLBI;
cτ 120 - c = c ( τ 0 - τ c ) = c [ - τ 0 ( ( x 2 - x s 0 ) 2 + ( y 2 - y s 0 ) 2 + ( z 2 - z s 0 ) 2 - ( x 1 - x s 0 ) 2 + ( y 1 - y s 0 ) 2 + ( z 1 - z s 0 ) 2 ) ] Formula ten
In formula, c τ 12o-crepresent the observed reading of VLBI and the difference of approximate value;
Matrix l vLBIbuilding form is, l vLBI=[c (τ 0c)];
Positioning calculation module, sets up by matrix the matrix of coefficients B that module obtains cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtand the matrix l that the difference of approximate value and observed reading forms cNS, l vLBI, l vLBI_Lmt, l dbl_Lmtthe matrix of coefficients B of combined system is formed according to formula 11 dblwith l dbl, setting parameter represent the difference between true value and approximate value; Carry out adjustment according to formula 12, obtain and whether judged result meets the condition of convergence, if meet, command result output module works, and then will not meet as new approximate value order matrix set up module again iteration work until meet the condition of convergence;
V d b l = V C N S V V L B I V V L B I _ L m t V d b l _ L m t T x ^ d b l = x ^ C N S x ^ V L B I B t m p = B C N S 0 0 B V L B I 0 B V L B I _ L m t B d b l = B t m p B d b l _ L m t l d b l = l C N S l V L B I l V L B I _ L m t l d b l _ L m t T P d b l = P C N S P V L B I P V L B I _ l m t P d b l _ l m t Formula 11
x ^ d b l = ( B d b l T P d b l B d b l ) - 1 B d b l T P d b l l d b l Formula 12
Wherein, V dblrepresent the correction of association system observed reading, P dblfor association system solves the power battle array of limit condition, wherein, P cNS, P vLBI, P vLBI_Lmt, P dbl_Lmtbe respectively matrix of coefficients B cNS, B vLBI, B vLBI_Lmt, B dbl_Lmtcorresponding power battle array;
Result output module, for according to final parametric solution result export the location coordinate information of lunar rover.
5. lunar rover co-located system according to claim 4, is characterized in that: association system described in positioning calculation module solves the power battle array P of limit condition dbldetermine according to the Helmert variance component estimation method.
6. lunar rover co-located system according to claim 4 or 5, is characterized in that: described in positioning calculation module, the condition of convergence is, parameter middle x s, y swith z scorresponding difference is less than 10m, corresponding difference is less than 10 -8, the corresponding difference of λ is less than 10 -8.
CN201510298598.1A 2015-06-03 2015-06-03 A kind of lunar rover combined positioning-method and system CN104864876B (en)

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