CN105866808A - Method for confirming influence of orbit determination errors of navigation receiver to satellite attitude precision - Google Patents

Abstract

The invention discloses a method for confirming influence of orbit determination errors of a navigation receiver to satellite attitude precision. According to the method, the relationship between a position speed output from the navigation receiver and the number of orbits is sufficiently utilized, and expression equations of position and speed errors and the influence of the attitude confirmation precision are extracted; and according to the conversion relationship, transitive relation of errors of positions and speeds to attitude angles in three directions can be successfully analyzed and solved, the influence of navigation errors in any position to the attitude can be provided, and a visible method is provided for navigation error allocation and attitude confirmation error analysis in engineering design.

Description

The navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision

Technical field

The present invention relates to a kind of navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision.

Background technology

Track determines that the precision that attitude is determined by error has a great impact, and in general, Orbit Error is directly reflected into Attitude determines in error.In order to measure the accurate pointing of the metric data of unit on utility star, it is necessary to be accurately determined and defend Star position in orbit, makes orbit determination accuracy error adapt with the certainty of measurement error of star sensor.Error due to orbit determination Influence whether the precision of attitude angle, error transfer function can not be gone out by directly calculation merely with position, speed, need one intuitively Method processes and affects relation between the attitude of satellite and Orbit Error.

Summary of the invention

The present invention provides a kind of navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision, fully profit By the relation between position and speed and the orbital tracking of navigation neceiver output, it is extracted position and speed error and attitude is determined essence Expression formula between degree impact, by the transformational relation between them, successful analysis calculates the error of position and speed to appearance The transitive relation that state angle is brought respectively in three directions, can provide the impact on attitude of the optional position navigation error, to engineering In design, with attitude, navigation error distribution determines that error analysis provides direct-vision method.

In order to achieve the above object, the present invention provides the impact on attitude of satellite precision of a kind of navigation neceiver Orbit Error Determination method, comprise the steps of

Step S1, the relation determined between position and speed and three-axis attitude；

The conversion relative to geocentric inertial coordinate system of the satellite orbit coordinate system is tried to achieve in position according to certain moment with velocity Matrix A_oi, carry out Taylor expansion and retain more than second order in a small amount, obtaining position and speed to error matrix Δ A_oiImpact close System, according to the attitude of satellite and matrix A_oiRelation, determine the relation of position and speed and three-axis attitude；

Step S2, determine position and the speed each component transmission function to three-axis attitude respectively；

Utilize the relation between the feature of near-circular orbit and orbital tracking and position and speed, to position velocity error and three axles Transfer function by abbreviation between attitude, obtain expression formula intuitively.

In described step S1, determine that the step of the relation between position and speed and attitude specifically comprises the steps of

If the transition matrix of theoretical orbital coordinate system OXYZ that the position according to theory and velocity determine is A_oi, and root Border obtains factually the position with error and the orbital coordinate system that determines of velocityTransition matrix beDue to Position and speed error is in a small amount relative to position and speed, can represent its error delta A with following formula:

On the other hand, can be by the concept of " attitude angle " A_oiWithConnect, the error converting of orbital coordinate system To corresponding rolling, pitching, three attitude errors of driftageθ, ψ, when little deviation, note attitude error matrix is C:

Have

Then C=(A_oi+ΔA)A_oi ^-1=E+ Δ AA_oi ^T (4)

Consider to be accurate to single order in a small amount:

$\mathrm{\Δ}A=\frac{\∂A_{oi}}{\∂x}\mathrm{\Δ}x+\frac{\∂A_{oi}}{\∂y}\mathrm{\Δ}y+\frac{\∂A_{oi}}{\∂z}\mathrm{\Δ}z+\frac{\∂A_{oi}}{\∂\stackrel{\·}{x}}\mathrm{\Δ}\stackrel{\·}{x}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{y}}\mathrm{\Δ}\stackrel{\·}{y}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{z}}\mathrm{\Δ}\stackrel{\·}{z}---\left(5\right)$

Wushu (5) substitutes into formula (4) and obtains:

$C=E+\frac{\∂A_{oi}}{\∂x}{A_{oi}}^T\mathrm{\Δ}x+\frac{\∂A_{oi}}{\∂y}{A_{oi}}^T\mathrm{\Δ}y+\frac{\∂A_{oi}}{\∂z}{A_{oi}}^T\mathrm{\Δ}z+\frac{\∂A_{oi}}{\∂\stackrel{\·}{x}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{x}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{y}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{y}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{z}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{z}---\left(6\right)$

Brought into formula (6) left end by the C battle array approximated again, by formula (6) right-hand member by matrix operations rule launch, allow left and right two end moments In Zhen, the set of data is equal, can obtainθ, ψ and site error [Δ x, Δ y, Δ z] and velocity errorPass System, matrix is unfolded as follows:

Make corresponding element equal, solve rolling, pitching, three attitude errors of driftageθ, ψ:

$\mathrm{\θ}=A_{32}(\mathrm{\Δ}x,\mathrm{\Δ}y,\mathrm{\Δ}z,\mathrm{\Δ}\stackrel{\·}{x},\mathrm{\Δ}\stackrel{\·}{y},\mathrm{\Δ}\stackrel{\·}{z})---\left(9\right)$

In described step S2, determine that three-axis attitude is transmitted the step of function by position and each component of speed respectively concrete Comprise:

Step S2.1, calculate site error [Δ x, Δ y, Δ z] and velocity error respectivelyThree axles caused Attitude error；

Step S2.2, by three-axis attitude angle error total for each amount joint accountθ、ψ。

Described step S2.1 specifically comprises the steps of

All directions site error [Δ x, Δ y, Δ z] and velocity errorThe attitude error calculating side caused Method is similar to, and remembers that the rolling caused, pitching, three attitude errors of driftage are respectivelyθ_j、ψ_j, wherein Here the attitude error that X causes is stressed to site error Δ xθ_y、ψ_z；

For understanding the Changing Pattern of error in whole flight course, A_oiWith the conversion determined according to orbital elements accordingly Matrix represents, is otherwise determined that position vectorAnd velocity With orbital elements latitude Degree relation between argument u, right ascension of ascending node Ω, inclination angle i, for near-circular orbit, has:

From the definition of satellite orbit coordinate system, satellite orbit coordinate is tried to achieve in position and velocity according to certain moment It is the transition matrix A of relative geocentric inertial coordinate system_oiFor:

$A_{oi}(3,i)=-\frac{\stackrel{\→}{r}}{\left|\stackrel{\→}{r}\right|}---\left(13\right)$

$A_{oi}(2,i)=-\frac{\stackrel{\→}{r}\×\stackrel{\→}{v}}{|\stackrel{\→}{r}\×\stackrel{\→}{v}|}---\left(14\right)$

A_oi(1, i)=A_oi(2,j)×A_oi(3,k) (15)

Wherein i=1,2,3, corresponding to transition matrix A_oiIn three components of each row vector, A_oi(2,j)、A_oi(3,k) For transition matrix A_oiIn the second row and the row vector of the third line；

Calculate the attitude angle deviation matrix Δ A caused due to site error Δ x below_x:

$\begin{array}{c}{\mathrm{\ΔA}}_x=\frac{\∂A_{oi}}{\∂x}{A}_{oi}^T=\left[\begin{array}{ccc}\frac{y\stackrel{\·}{y}+z\stackrel{\·}{z}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}& \frac{-2x\stackrel{\·}{y}+y\stackrel{\·}{x}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}& \frac{-2x\stackrel{\·}{z}+z\stackrel{\·}{x}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}\\ 0& \stackrel{\·}{z}/|\stackrel{\→}{r}\×\stackrel{\→}{v}|& -\stackrel{\·}{y}/|\stackrel{\→}{r}\×\stackrel{\→}{v}|\\ -1/\left|\stackrel{\→}{r}\right|& 0& 0\end{array}\right]\×\\ \left[\begin{array}{ccc}-\sin u\cos \mathrm{\Ω}-\cos u\cos i\sin \mathrm{\Ω}& -\sin i\sin \mathrm{\Ω}& -\cos u\cos \mathrm{\Ω}+\sin u\cos i\sin \mathrm{\Ω}\\ -\sin u\sin \mathrm{\Ω}+\cos u\cos i\cos \mathrm{\Ω}& \sin i\cos \mathrm{\Ω}& -\cos u\sin \mathrm{\Ω}-\sin u\cos i\cos \mathrm{\Ω}\\ \cos u\sin i& -\cos i& -\sin u\sin i\end{array}\right]\end{array}---\left(16\right)$

Thus it is as follows to obtain the attitude error that site error Δ x causes:

?WithBring formula (17) into, obtain:

Owing to track is near-circular orbit, between speed and position vector, angle is close to 90 °, so that

Therefore obtain:

In like manner have:

$\begin{array}{c}{\mathrm{\θ}}_x={\mathrm{\ΔA}}_x(3,1)\mathrm{\Δ}x\\ =-\[-\sin ucos\mathrm{\Ω}-\cos u\cos isin\mathrm{\Ω}\]\mathrm{\Δ}x/\left|\stackrel{\→}{r}\right|\end{array}---\left(20\right)$

$\begin{array}{c}{\mathrm{\ψ}}_x=-{\mathrm{\ΔA}}_x(2,1)\mathrm{\Δ}x\\ =-\[\stackrel{\·}{z}(-\sin u\sin \mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})-y\left(\cos u\sin i\right)\]\mathrm{\Δ}x/|\stackrel{\→}{r}\×\stackrel{\→}{v}|\\ =-\frac{\left[\begin{array}{c}\cos u\sin i(-\sin usin\mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})-\\ (-\sin u\sin \mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})\left(\cos u\sin i\right)\end{array}\right]\mathrm{\Δ}x}{|\stackrel{\→}{r}\×\stackrel{\→}{v}|}\left|\stackrel{\→}{v}\right|\\ \≈0\end{array}---\left(21\right)$

In like manner obtain the impact on three-axis attitude of other amounts.

Described step S2.2 specifically comprises the steps of

Each amount is merged and obtains total attitude errorθ, ψ:

$\begin{array}{c}\mathrm{\θ}={\mathrm{\θ}}_x+{\mathrm{\θ}}_y+{\mathrm{\θ}}_z+{\mathrm{\θ}}_{\stackrel{\·}{x}}+{\mathrm{\θ}}_{\stackrel{\·}{y}}+{\mathrm{\θ}}_{\stackrel{\·}{z}}\\ =-\[-\sin u\cos \mathrm{\Ω}-\cos u\cos i\sin \mathrm{\Ω}\]\mathrm{\Δ}x/\left|\stackrel{\→}{r}\right|+-\[-\sin u\sin \mathrm{\Ω}+\cos u\cos i\cos \mathrm{\Ω}\]\mathrm{\Δ}y/\left|\stackrel{\→}{r}\right|\\ +-\[\cos u\sin i\]\mathrm{\Δ}z/\left|\stackrel{\→}{r}\right|+0+0+0\end{array}---\left(23\right)$

The present invention makes full use of the relation between position and speed and the orbital tracking of navigation neceiver output, is extracted position Velocity error is on the expression formula between attitude determination accuracy impact, and by the transformational relation between them, successful analysis calculates The transitive relation that attitude angle is brought respectively by the error of position and speed in three directions, can provide optional position navigation error With attitude, impact on attitude, determines that error analysis provides direct-vision method to navigation error distribution in engineering design.

Detailed description of the invention

Detailed description below presently preferred embodiments of the present invention.

The present invention provides a kind of navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision, comprise with Lower step:

Step S1, the relation determined between position and speed and three-axis attitude；

The conversion relative to geocentric inertial coordinate system of the satellite orbit coordinate system is tried to achieve in position according to certain moment with velocity Matrix A_oi, carry out Taylor expansion and retain more than second order in a small amount, obtaining position and speed to error matrix Δ A_oiImpact close System, according to the attitude of satellite and matrix A_oiRelation, determine the relation of position and speed and three-axis attitude；

Step S2, determine position and the speed each component transmission function to three-axis attitude respectively；

Utilize the relation between the feature of near-circular orbit and orbital tracking and position and speed, to position velocity error and three axles Transfer function by abbreviation between attitude, obtain expression formula intuitively.

In described step S1, determine that the step of the relation between position and speed and attitude specifically comprises the steps of

If the transition matrix of theoretical orbital coordinate system OXYZ that the position according to theory and velocity determine is A_oi, and root Border obtains factually the position with error and the orbital coordinate system that determines of velocityTransition matrix beDue to Position and speed error is in a small amount relative to position and speed, can represent its error delta A with following formula:

${\tilde{A}}_{oi}=A_{oi}+\mathrm{\Δ}A---\left(1\right)$

On the other hand, can be by the concept of " attitude angle " A_oiWithConnect, the error converting of orbital coordinate system To corresponding rolling, pitching, three attitude errors of driftageθ, ψ, when little deviation, note attitude error matrix is C:

Have

Then C=(A_oi+ΔA)A_oi ^-1=E+ Δ AA_oi ^T (4)

Consider to be accurate to single order in a small amount:

$\mathrm{\Δ}A=\frac{\∂A_{oi}}{\∂x}\mathrm{\Δ}x+\frac{\∂A_{oi}}{\∂y}\mathrm{\Δ}y+\frac{\∂A_{oi}}{\∂z}\mathrm{\Δ}z+\frac{\∂A_{oi}}{\∂\stackrel{\·}{x}}\mathrm{\Δ}\stackrel{\·}{x}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{y}}\mathrm{\Δ}\stackrel{\·}{y}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{z}}\mathrm{\Δ}\stackrel{\·}{z}---\left(5\right)$

Wushu (5) substitutes into formula (4) and obtains:

$C=E+\frac{\∂A_{oi}}{\∂x}{A_{oi}}^T\mathrm{\Δ}x+\frac{\∂A_{oi}}{\∂y}{A_{oi}}^T\mathrm{\Δ}y+\frac{\∂A_{oi}}{\∂z}{A_{oi}}^T\mathrm{\Δ}z+\frac{\∂A_{oi}}{\∂\stackrel{\·}{x}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{x}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{y}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{y}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{z}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{z}---\left(6\right)$

Brought into formula (6) left end by the C battle array approximated again, by formula (6) right-hand member by matrix operations rule launch, allow left and right two end moments In Zhen, the set of data is equal, can obtainθ, ψ and site error [Δ x, Δ y, Δ z] and velocity errorPass System, matrix is unfolded as follows:

Make corresponding element equal, solve rolling, pitching, three attitude errors of driftageθ, ψ:

$\mathrm{\θ}=A_{32}(\mathrm{\Δ}x,\mathrm{\Δ}y,\mathrm{\Δ}z,\mathrm{\Δ}\stackrel{\·}{x},\mathrm{\Δ}\stackrel{\·}{y},\mathrm{\Δ}\stackrel{\·}{z})---\left(9\right)$

In described step S2, determine that three-axis attitude is transmitted the step of function by position and each component of speed respectively concrete Comprise:

Step S2.1, calculate site error [Δ x, Δ y, Δ z] and velocity error respectivelyThree axles caused Attitude error；

Step S2.2, by three-axis attitude angle error total for each amount joint accountθ、ψ。

Described step S2.1 specifically comprises the steps of

All directions site error [Δ x, Δ y, Δ z] and velocity errorThe attitude error calculating side caused Method is similar to, and remembers that the rolling caused, pitching, three attitude errors of driftage are respectivelyθ_j、ψ_j, wherein Here the attitude error that X causes is stressed to site error Δ xθ_y、ψ_z；

For understanding the Changing Pattern of error in whole flight course, A_oiWith the conversion determined according to orbital elements accordingly Matrix represents, is otherwise determined that position vectorAnd velocity With orbital elements latitude Relation between argument u, right ascension of ascending node Ω, inclination angle i, for near-circular orbit, has:

From the definition of satellite orbit coordinate system, satellite orbit coordinate is tried to achieve in position and velocity according to certain moment It is the transition matrix A of relative geocentric inertial coordinate system_oiFor:

$A_{oi}(3,i)=-\frac{\stackrel{\→}{r}}{\left|\stackrel{\→}{r}\right|}---\left(13\right)$

$A_{oi}(2,i)=-\frac{\stackrel{\→}{r}\×\stackrel{\→}{v}}{|\stackrel{\→}{r}\×\stackrel{\→}{v}|}---\left(14\right)$

A_oi(1, i)=A_oi(2,j)×A_oi(3,k) (15)

Wherein i=1,2,3, corresponding to transition matrix A_oiIn three components of each row vector, A_oi(2,j)、A_oi(3,k) For transition matrix A_oiIn the second row and the row vector of the third line；

Calculate the attitude angle deviation matrix Δ A caused due to site error Δ x below_x:

$\begin{array}{c}{\mathrm{\ΔA}}_x=\frac{\∂A_{oi}}{\∂x}{A}_{oi}^T=\left[\begin{array}{ccc}\frac{y\stackrel{\·}{y}+z\stackrel{\·}{z}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}& \frac{-2x\stackrel{\·}{y}+y\stackrel{\·}{x}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}& \frac{-2x\stackrel{\·}{z}+z\stackrel{\·}{x}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}\\ 0& \stackrel{\·}{z}/|\stackrel{\→}{r}\×\stackrel{\→}{v}|& -\stackrel{\·}{y}/|\stackrel{\→}{r}\×\stackrel{\→}{v}|\\ -1/\left|\stackrel{\→}{r}\right|& 0& 0\end{array}\right]\×\\ \left[\begin{array}{ccc}-\sin u\cos \mathrm{\Ω}-\cos u\cos i\sin \mathrm{\Ω}& -\sin i\sin \mathrm{\Ω}& -\cos u\cos \mathrm{\Ω}+\sin u\cos i\sin \mathrm{\Ω}\\ -\sin u\sin \mathrm{\Ω}+\cos u\cos i\cos \mathrm{\Ω}& \sin i\cos \mathrm{\Ω}& -\cos u\sin \mathrm{\Ω}-\sin u\cos i\cos \mathrm{\Ω}\\ \cos u\sin i& -\cos i& -\sin u\sin i\end{array}\right]\end{array}---\left(16\right)$

Thus it is as follows to obtain the attitude error that site error Δ x causes:

?WithBring formula (17) into, obtain:

Owing to track is near-circular orbit, between speed and position vector, angle is close to 90 °, so that

Therefore obtain:

In like manner have:

$\begin{array}{c}{\mathrm{\θ}}_x={\mathrm{\ΔA}}_x(3,1)\mathrm{\Δ}x\\ =-\[-\sin ucos\mathrm{\Ω}-\cos u\cos isin\mathrm{\Ω}\]\mathrm{\Δ}x/\left|\stackrel{\→}{r}\right|\end{array}---\left(20\right)$

$\begin{array}{c}{\mathrm{\ψ}}_x=-{\mathrm{\ΔA}}_x(2,1)\mathrm{\Δ}x\\ =-\[\stackrel{\·}{z}(-\sin u\sin \mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})-y\left(\cos u\sin i\right)\]\mathrm{\Δ}x/|\stackrel{\→}{r}\×\stackrel{\→}{v}|\\ =-\frac{\left[\begin{array}{c}\cos u\sin i(-\sin usin\mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})-\\ (-\sin u\sin \mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})\left(\cos u\sin i\right)\end{array}\right]\mathrm{\Δ}x}{|\stackrel{\→}{r}\×\stackrel{\→}{v}|}\left|\stackrel{\→}{v}\right|\\ \≈0\end{array}---\left(21\right)$

In like manner obtain the impact on three-axis attitude of other amounts.

Described step S2.2 specifically comprises the steps of

Each amount is merged and obtains total attitude errorθ, ψ:

$\begin{array}{c}\mathrm{\θ}={\mathrm{\θ}}_x+{\mathrm{\θ}}_y+{\mathrm{\θ}}_z+{\mathrm{\θ}}_{\stackrel{\·}{x}}+{\mathrm{\θ}}_{\stackrel{\·}{y}}+{\mathrm{\θ}}_{\stackrel{\·}{z}}\\ =-\[-\sin u\cos \mathrm{\Ω}-\cos u\cos i\sin \mathrm{\Ω}\]\mathrm{\Δ}x/\left|\stackrel{\→}{r}\right|+-\[-\sin u\sin \mathrm{\Ω}+\cos u\cos i\cos \mathrm{\Ω}\]\mathrm{\Δ}y/\left|\stackrel{\→}{r}\right|\\ +-\[\cos u\sin i\]\mathrm{\Δ}z/\left|\stackrel{\→}{r}\right|+0+0+0\end{array}---\left(23\right)$

The present invention makes full use of the relation between position and speed and the orbital tracking of navigation neceiver output, is extracted position Velocity error is on the expression formula between attitude determination accuracy impact, and by the transformational relation between them, successful analysis calculates The transitive relation that attitude angle is brought respectively by the error of position and speed in three directions, can provide optional position navigation error With attitude, impact on attitude, determines that error analysis provides direct-vision method to navigation error distribution in engineering design.

Although present disclosure has been made to be discussed in detail by above preferred embodiment, but it should be appreciated that above-mentioned Description is not considered as limitation of the present invention.After those skilled in the art have read foregoing, for the present invention's Multiple amendment and replacement all will be apparent from.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (5)

1. the navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision, it is characterised in that comprise with Lower step:

Step S1, the relation determined between position and speed and three-axis attitude；

The satellite orbit coordinate system transition matrix relative to geocentric inertial coordinate system is tried to achieve in position according to certain moment with velocity A_oi, carry out Taylor expansion and retain more than second order in a small amount, obtaining position and speed to error matrix Δ A_oiThe relation that affects, root According to the attitude of satellite and matrix A_oiRelation, determine the relation of position and speed and three-axis attitude；

Step S2, determine position and the speed each component transmission function to three-axis attitude respectively；

Utilize the relation between the feature of near-circular orbit and orbital tracking and position and speed, to position velocity error and three-axis attitude Between transfer function by abbreviation, obtain expression formula intuitively.

2. the navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision as claimed in claim 1, it is special Levy and be, in described step S1, determine that the step of the relation between position and speed and attitude specifically comprises the steps of

If the transition matrix of theoretical orbital coordinate system OXYZ that the position according to theory and velocity determine is A_oi, and according to reality The orbital coordinate system that the position with error of border acquisition and velocity determineTransition matrix beDue to position Velocity error is in a small amount relative to position and speed, can represent its error delta A with following formula:

${\tilde{A}}_{oi}=A_{oi}+\mathrm{\Δ}A---\left(1\right)$

On the other hand, can be by the concept of " attitude angle " A_oiWithConnect, the error converting of orbital coordinate system to phase The rolling answered, pitching, three attitude errors of driftageθ, ψ, when little deviation, note attitude error matrix is C:

Have

Then

Consider to be accurate to single order in a small amount:

$\mathrm{\Δ}A=\frac{\∂A_{oi}}{\∂x}\mathrm{\Δ}x+\frac{\∂A_{oi}}{\∂y}\mathrm{\Δ}y+\frac{\∂A_{oi}}{\∂z}\mathrm{\Δ}z+\frac{\∂A_{oi}}{\∂\stackrel{\·}{x}}\mathrm{\Δ}\stackrel{\·}{x}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{y}}\mathrm{\Δ}\stackrel{\·}{y}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{z}}\mathrm{\Δ}\stackrel{\·}{z}---\left(5\right)$

Wushu (5) substitutes into formula (4) and obtains:

$C=E+\frac{\∂A_{oi}}{\∂x}{A_{oi}}^T\mathrm{\Δ}x+\frac{\∂A_{oi}}{\∂y}{A_{oi}}^T\mathrm{\Δ}y+\frac{\∂A_{oi}}{\∂z}{A_{oi}}^T\mathrm{\Δ}z+\frac{\∂A_{oi}}{\∂\stackrel{\·}{x}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{x}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{y}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{y}+\frac{\∂A_{oi}}{\∂\stackrel{\·}{z}}{A_{oi}}^T\mathrm{\Δ}\stackrel{\·}{z}---\left(6\right)$

Brought into formula (6) left end by the C battle array approximated again, formula (6) right-hand member is launched by matrix operations rule, allow in the matrix of two ends, left and right The set of data is equal, can obtainθ, ψ and site error [Δ x, Δ y, Δ z] and velocity errorRelation, matrix It is unfolded as follows:

Make corresponding element equal, solve rolling, pitching, three attitude errors of driftageθ, ψ:

$\mathrm{\θ}=A_{32}(\mathrm{\Δ}x,\mathrm{\Δ}y,\mathrm{\Δ}z,\mathrm{\Δ}\stackrel{\·}{x},\mathrm{\Δ}\stackrel{\·}{y},\mathrm{\Δ}\stackrel{\·}{z})---\left(9\right)$

3. the navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision as claimed in claim 1, it is special Levy and be, in described step S2, determine that three-axis attitude is transmitted the step of function by position and each component of speed respectively concrete Comprise:

Step S2.1, calculate site error [Δ x, Δ y, Δ z] and velocity error respectivelyThe three-axis attitude caused Angle error；

Step S2.2, by three-axis attitude angle error total for each amount joint accountθ、ψ。

4. the navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision as claimed in claim 3, it is special Levying and be, described step S2.1 specifically comprises the steps of

All directions site error [Δ x, Δ y, Δ z] and velocity errorThe attitude error computational methods class caused Seemingly, note cause rolling, pitching, three attitude errors of driftage be respectivelyθ_j、ψ_j, whereinHere Stress the attitude error that X causes to site error Δ xθ_y、ψ_z；

For understanding the Changing Pattern of error in whole flight course, A_oiWith the transition matrix determined according to orbital elements accordingly Represent, be otherwise determined that position vectorAnd velocity With orbital elements latitude width Relation between angle u, right ascension of ascending node Ω, inclination angle i, for near-circular orbit, has:

From the definition of satellite orbit coordinate system, satellite orbit coordinate system phase is tried to achieve in position and velocity according to certain moment Transition matrix A to geocentric inertial coordinate system_oiFor:

$A_{oi}(3,i)=-\frac{\stackrel{\→}{r}}{\left|\stackrel{\→}{r}\right|}---\left(13\right)$

$A_{oi}(2,i)=-\frac{\stackrel{\→}{r}\×\stackrel{\→}{v}}{|\stackrel{\→}{r}\×\stackrel{\→}{v}|}---\left(14\right)$

A_oi(1, i)=A_oi(2,j)×A_oi(3,k) (15)

Wherein i=1,2,3, corresponding to transition matrix A_oiIn three components of each row vector, A_oi(2,j)、A_oi(3, k) for turning Change matrix A_oiIn the second row and the row vector of the third line；

Calculate the attitude angle deviation matrix Δ A caused due to site error Δ x below_x:

${\mathrm{\ΔA}}_x=\frac{\∂A_{oi}}{\∂x}{A}_{oi}^T=\left[\begin{array}{ccc}\frac{y\stackrel{\·}{y}+z\stackrel{\·}{z}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}& \frac{-2x\stackrel{\·}{y}+y\stackrel{\·}{x}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}& \frac{-2x\stackrel{\·}{z}+z\stackrel{\·}{x}}{\left|\stackrel{\→}{r}\right||\stackrel{\→}{r}\×\stackrel{\→}{v}|}\\ 0& \stackrel{\·}{z}/|\stackrel{\→}{r}\×\stackrel{\→}{v}|& -\stackrel{\·}{y}/|\stackrel{\→}{r}\×\stackrel{\→}{v}|\\ -1/\left|\stackrel{\→}{r}\right|& 0& 0\end{array}\right]\×---\left(16\right)$

$\left[\begin{array}{ccc}-\sin ucos\mathrm{\Ω}-\cos u\cos isin\mathrm{\Ω}& -\sin isin\mathrm{\Ω}& -\cos ucos\mathrm{\Ω}+\sin u\cos isin\mathrm{\Ω}\\ -\sin usin\mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω}& \sin i\cos \mathrm{\Ω}& -\cos usin\mathrm{\Ω}-\sin u\cos icos\mathrm{\Ω}\\ \cos u\sin i& -\cos i& -\sin u\sin i\end{array}\right]$

Thus it is as follows to obtain the attitude error that site error Δ x causes:

?WithBring formula (17) into, obtain:

Owing to track is near-circular orbit, between speed and position vector, angle is close to 90 °, so that

$|\stackrel{\→}{r}\×\stackrel{\→}{v}|\≈\left|\stackrel{\→}{r}\right|\left|\stackrel{\→}{v}\right|;$

Therefore obtain:

In like manner have:

$\begin{array}{c}{\mathrm{\θ}}_x={\mathrm{\ΔA}}_x(3,1)\mathrm{\Δ}x\\ =-\[-\sin ucos\mathrm{\Ω}-\cos u\cos isin\mathrm{\Ω}\]\mathrm{\Δ}x/\left|\stackrel{\→}{r}\right|\end{array}---\left(20\right)$

$\begin{array}{c}{\mathrm{\ψ}}_x=-{\mathrm{\ΔA}}_x(2,1)\mathrm{\Δ}x\\ =-\[\stackrel{\·}{z}(-\sin u\sin \mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})-\stackrel{\·}{y}\left(\cos u\sin i\right)\]\mathrm{\Δ}x/|\stackrel{\→}{r}\×\stackrel{\→}{v}|\\ =-\frac{\left[\begin{array}{c}\cos u\sin i(-\sin usin\mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})-\\ (-\sin u\sin \mathrm{\Ω}+\cos u\cos icos\mathrm{\Ω})\left(\cos u\sin i\right)\end{array}\right]\mathrm{\Δ}x}{|\stackrel{\→}{r}\×\stackrel{\→}{v}|}\left|\stackrel{\→}{v}\right|\\ \≈0\end{array}---\left(21\right)$

In like manner obtain the impact on three-axis attitude of other amounts.

5. the navigation neceiver Orbit Error determination method on the impact of attitude of satellite precision as claimed in claim 3, it is special Levying and be, described step S2.2 specifically comprises the steps of

Each amount is merged and obtains total attitude errorθ, ψ:

$\begin{array}{c}\mathrm{\θ}={\mathrm{\θ}}_x+{\mathrm{\θ}}_y+{\mathrm{\θ}}_z+{\mathrm{\θ}}_{\stackrel{\·}{x}}+{\mathrm{\θ}}_{\stackrel{\·}{y}}+{\mathrm{\θ}}_{\stackrel{\·}{z}}\\ =-\[-\sin u\cos \mathrm{\Ω}-\cos u\cos i\sin \mathrm{\Ω}\]\mathrm{\Δ}x/\left|\stackrel{\→}{r}\right|+-\[-\sin u\sin \mathrm{\Ω}+\cos u\cos i\cos \mathrm{\Ω}\]\mathrm{\Δ}y/\left|\stackrel{\→}{r}\right|\\ +-\[\cos u\sin i\]\mathrm{\Δ}z/\left|\stackrel{\→}{r}\right|+0+0+0\end{array}---\left(23\right)$