CN105424047A - Spacecraft attitude pointing error identification method based on road sign information - Google Patents

Abstract

The invention provides a spacecraft attitude pointing error identification method based on road sign information. The method comprises the steps that 1, a mathematical statistic model for sensor vector measurement and installation error angles is built; 2, an installation error angle observation equation between a full attitude sensor and a single vector sensor is constructed; 3, an optimal estimation method is designed to estimate an installation error angle between the full attitude sensor and the single vector sensor within some interval; 4, data fitting is performed on error angle data within different intervals to obtain a basic time varying installation error angle equation. The pointing error identification method is simple and accurate, the attitude angle and the angular speed of a spacecraft do not need to be calculated, attitude data of the spacecraft do not need to be acquired in real time, insensitivity on long-term data loss is achieved, and the practicability is high.

Description

Based on the spacecraft attitude error in pointing discrimination method of mark information

Technical field

The present invention relates to spacecraft attitude error determination technology in-orbit, particularly, relate to a kind of spacecraft based on mark information attitude error method of estimation in-orbit.

Background technology

Remote sensing satellite points to in-orbit determines precision index, is directly connected to target geographic position determination precision level.The size of spacecraft error in pointing can comprehensively weigh out spacecraft in-orbit attitude determine and gesture stability situation, along with the continuous lifting of space mission demand, need badly and accurately provide spacecraft error in pointing and effectively revise.

Current domestic correlative study work mainly concentrates on spacecraft body attitude determines, points to the research determined less for spacecraft.Experience intense impact effect in Spacecraft Launch process, in orbit, be subject to the impact of the external environments such as different illumination conditions, cause the attitude of spacecraft itself and load to be pointed to and there is larger difference.Therefore, for the correlated results that spacecraft body attitude is determined, spacecraft can not be solved and point to the problem determined.In addition, on a small quantity for the result of study that spacecraft error in pointing is determined, need the attitude information utilizing spacecraft itself, need to carry out identification by the data of several orbital period, the requirement for data acquisition is higher.

The invention provides a kind of spacecraft attitude error in pointing discrimination method based on mark information, according to road sign point benchmark and observation information, spacecraft attitude information and auxiliary data thereof, obtain spacecraft real directional information in-orbit.Compared with the prior art, this discrimination method simple structure, identification result are accurate; The method, without the need to calculating attitude angle and the angular velocity of spacecraft, without the need to Real-time Obtaining spacecraft attitude data, is lost insensitive, practical to long term data.

Summary of the invention

For defect of the prior art, the object of this invention is to provide a kind of spacecraft attitude error in pointing discrimination method based on mark information.

According to the spacecraft attitude error in pointing discrimination method based on mark information provided by the invention, comprise the steps:

Step 1: the mathematical statistical model setting up sensor measurement and fix error angle;

Set up the mathematical statistical model of sensor vector measurement, alignment error, provide the estimated value of the initial value of single vector sensor observation vector under body coordinate system, full attitude sensor observation vector;

Step 2: build error in pointing angle observation equation according to the initial value of the observation vector of single vector sensor under body coordinate system, the estimated value of the full observation vector of attitude sensor under body coordinate system;

Step 3: according to the statistical property at error in pointing angle observation equation and error in pointing angle, statistical estimate is carried out to attitude error angle, obtains attitude error angular estimation value;

Step I: repeat step 1 to step 3, obtain different time sections attitude error angular estimation value in same track, carries out curve fitting to described different time sections attitude error angular estimation value and obtains long period attitude error fundamental equation.

Preferably, described step 1 comprises:

Step 1.1: the mathematical statistical model setting up sensor vector measurement, alignment error, specifically comprises following sub-step:

Step 1.1.1, sets up sensor reference measurement vector as follows:

${\hat{U}}_{j,k}={\hat{U}}_{j,k}^{true}+\mathrm{\Δ}{\hat{U}}_{j,k}---\left(1\right)$

In formula, the direction vector measured value of sensor j, direction of measurement true value, be the measurement noises of sensor j, subscript k is the numbering of time, k=1,2 ..., N;

Step 1.1.2, determines that vector and installation relation is measured by satellite body system as follows:

${\hat{W}}_{j,k}=S_j{\hat{U}}_{j,k}^{true}+S_j\mathrm{\Δ}{\hat{U}}_{j,k}={\hat{W}}_{j,k}^{true}+\mathrm{\Δ}{\hat{W}}_{j,k}---\left(2\right)$

In formula, S _jfor sensor j installs matrix, for the direction vector under spacecraft body series, for the direction vector true value under spacecraft body series, for the direction vector noise under spacecraft body series;

Step S1.1.3, alignment error define method is as follows:

$S_j=M_j{S}_j^0---\left(3\right)$

Wherein, S _jthe installation matrix of sensor j, demarcate for ground and obtain matrix initial value being installed, M _jfor alignment error matrix, M _jdefinition as shown in formula (4):

I is unit matrix, and O () represents higher-order shear deformation, θ _jfor alignment error matrix corner vector, for vectorial θ _jnegative symmetric matrix, as shown in formula (5).

Step 1.2: utilize the installation matrix initial value of the observed reading of a certain single vector sensor, this single vector sensor to obtain at body coordinate system observation vector initial value, computing formula is as follows:

In formula: represent that single vector sensor j is at t _kthe initial value of the observation vector during moment under body coordinate system, represent the initial installation matrix of single vector sensor j, represent that single vector sensor j is at t _kthe measured value in moment, represent the benchmark terrestrial reference vector of a certain single vector sensor j, A _krepresent attitude matrix, θ _jrepresent the fix error angle of a certain single vector sensor j, represent that a certain single vector sensor j is at t _kobservation vector error during the moment under body coordinate system.

Step 1.3: according to a certain full attitude sensor at moment t _kthe base vector of the attitude of satellite obtained, a certain single vector sensor obtains the estimated value of this full attitude sensor at body coordinate system observation vector, and computing formula is as follows:

In formula: represent that a certain full attitude sensor i is at moment t _kthe estimated value of the observation vector under body coordinate system that corresponding a certain single vector sensor j obtains, ξ _i,krepresent that a certain full attitude sensor i is at t _kmoment measuring error, θ _irepresent the fix error angle of a certain full attitude sensor i, represent that a certain full attitude sensor i is at t _kthe body attitude matrix estimated value that moment obtains, comprises full attitude sensor i measuring error ξ _i,kwith fix error angle θ _ithe evaluated error introduced.

Preferably, described step 2 comprises:

Build error in pointing angle observation equation according to the estimated value of the initial value of the observation vector of a certain single vector sensor under body coordinate system, the observation vector of a certain full attitude sensor under body coordinate system, the equation of structure is as follows:

$P\left({\hat{W}}_{j,k}^o\right){\hat{W}}_{ij,k}^{o*}\×{\hat{W}}_{j,k}^o=P\left({\hat{W}}_{j,k}^o\right)({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)+{\mathrm{\Δz}}_{ij,k};---\left(8\right)$

In formula: (θ _j-θ _i) be the error angle between a certain full attitude sensor i and a certain single vector sensor j, namely need the error in pointing solved, represent and vector vertical matrix, △ z _{ij, k}between a certain full attitude sensor i and a certain single vector sensor j in error angle observation equation at moment t _kobservation noise.

Preferably, described step 3 comprises:

According to error in pointing angle observation equation and statistical property, application least square method or Maximum Likelihood Estimation carry out statistical estimate to attitude error angle;

-application least square method obtains following accounting equation:

$\hat{X}={\left(H^{T}H\right)}^{-1}{H}^{T}Z;---\left(9\right)$

In formula represent state variable to be estimated, H represents observing matrix, and Z represents observed quantity, () ^t() ^-1representing matrix transposition, matrix inversion operation respectively;

-application maximum-likelihood method obtains following accounting equation:

$\hat{X}={\left(H^T{R}^{-1}H\right)}^{-1}{H}^T{R}^{-1}Z;---\left(10\right)$

In formula, R represents random vector △ z _{ij, k}covariance matrix.

Preferably, described step I comprises:

According to benchmark mark information in different time sections in same track namely on ground certain road sign point to the direction vector R of spacecraft centroid _ts, full attitude sensor i is at t _kthe body attitude matrix that moment obtains single vector sensor j is at t _kthe measured value in moment and the initial installation matrix of sensor j repeat step 2 to step 3, obtain different time sections attitude error angle (θ in same track _j-θ _i) estimated value; The form of Fourier series is adopted to represent fundamental equation F (u) at attitude error angle in the whole orbital period, as shown in formula (11),

F(u)＝x ₀+x ₁sin(u)+x ₂cos(u)+x ₃sin(u)+x ₄cos(u)+...(11)

U is satellite ascending node argument.Utilize nonlinear least square fitting method, find the coefficient x meeting following equation,

$\underset{x}{min}\left|\right|F(x,xdata)-ydata|{|}_2^2=\underset{x}{min}\underset{i}{\Σ}{\left(F\right(x_i,{\mathrm{xdata}}_i)-{\mathrm{ydata}}_i)}^2---\left(12\right)$

Wherein ∑ is for adding and sign of operation, and min, for getting minimum operation symbol, obtains the Fourier coefficient (x in fundamental equation F (u) ₀, x ₁, x ₂, x ₃, x ₄...) estimated value, x represents Fourier coefficient, and xdata represents the input data of fundamental equation F (u), xdata _irepresent i-th group of data of xdata.Ydata represents the observation data of fundamental equation F (u), ydata _irepresent i-th group of data of ydata.

Compared with prior art, the present invention has following beneficial effect:

1, the spacecraft attitude error in pointing discrimination method based on mark information provided by the invention, according to road sign point benchmark and observation information, spacecraft attitude information and auxiliary data thereof, obtain spacecraft real directional information in-orbit, compared with the prior art, this discrimination method simple structure, identification result are accurate.

2, the spacecraft attitude error in pointing discrimination method based on mark information provided by the invention, the method, without the need to calculating attitude angle and the angular velocity of spacecraft, without the need to Real-time Obtaining spacecraft attitude data, is lost insensitive, practical to long term data.

Accompanying drawing explanation

By reading the detailed description done non-limiting example with reference to the following drawings, other features, objects and advantages of the present invention will become more obvious:

Fig. 1 is the process flow diagram of the spacecraft attitude error in pointing discrimination method based on mark information provided by the invention.

Fig. 2 is road sign base vector graph of a relation provided by the invention.

Embodiment

Below in conjunction with concrete enforcement, the present invention is described in detail.Below implement to contribute to those skilled in the art and understand the present invention further, but do not limit the present invention in any form.It should be pointed out that to those skilled in the art, without departing from the inventive concept of the premise, some distortion and improvement can also be made.These all belong to protection scope of the present invention.

According to the spacecraft attitude error in pointing discrimination method based on mark information provided by the invention, provide concrete implementation step in practical application.

1, identification desired data and acquisition methods thereof

Star responsive relatively and between load the estimation of fix error angle need J2000.0 geocentric equatorial polar coordinate lower platform attitude data with road sign base vector road sign measurement vector under camera coordinates system and matrix initial value installed by load camera further, the observation vector estimated value under body series is converted it into and observation vector initial value under body series

1.1 platform stance data

The attitude matrix A of platform relative orbit system can be obtained by image auxiliary data _boand track system relative inertness Conversion Matrix of Coordinate A _oi, through type (1) can obtain

$A_{i,k}^{o*}=A_{bo}^{*}{A}_{oi}^{*}---\left(1\right)$

1.2 road sign base vectors

Road sign base vector for road sign point is to the direction vector R of spacecraft centroid _ts, R _etfor I system initial point O _ethe direction vector of direction disk point T, R _esfor I system initial point O _epoint to spacecraft centroid O _sdirection vector.Base vector with vectorial R _et, R _esrelation such as formula (2) ~ (3), || || represent the computing of delivery value.

R _ts＝R _es-R _et(2)

${\hat{V}}_{j,k}=\frac{R_{ts}}{\left|\right|R_{ts}\left|\right|}---\left(3\right)$

(1) GoogleEarth first, is utilized to find the longitude α of certain road sign point under the earth's core sphere is connected coordinate system (WGS84) _ewith latitude δ _e, utilize formula (4) that the direction vector R ' of road sign point under WGS84 coordinate system can be obtained _et.According to the temporal information in image auxiliary data, obtain WGS84 coordinate and be tied to J2000 Conversion Matrix of Coordinate A _wGS84ToJ2000, vector R can be obtained according to formula (5) _et, r in formula _efor the radius of the earth;

$R_{et}^{\′}=\left[\begin{array}{c}cos{\mathrm{\δ}}_{e}cos{\mathrm{\α}}_e\\ {\mathrm{cos\δ}}_e{\mathrm{sin\α}}_e\\ {\mathrm{sin\δ}}_e\end{array}\right]---\left(4\right)$

R _et＝r _eA _WGS84ToJ2000R′ _et(5)

(2) secondly, according to the position x of spacecraft in inertial space, y, z can obtain vector R _es, as formula (6);

R _es＝[xyz] ^T(6)

(3) by vector R _etand R _esroad sign base vector can be tried to achieve in substitution formula (2) ~ (3)

1.3 road sign measurement vectors

This coordinate (x under camera coordinates is obtained according to certain road sign point position in load diagram picture _c, y _c), combining camera focal distance f can obtain measurement vector shown in (7),

${\hat{U}}_{j,k}=\frac{1}{\sqrt{x_C^2+y_C^2+f^2}}{\[x_C,y_C,-f\]}^T---\left(7\right)$

1.4 full attitude sensor i are at t _kthe vector that moment attitude obtains observation vector estimated value under body series

${\hat{W}}_{ij,k}^{o*}\≡k_{i,k}^{o*}{\hat{V}}_{j,k};---\left(8\right)$

1.5 single vector sensor j are at t _kmoment observed reading and initially matrix is installed observation vector initial value under the body series obtained

${\hat{W}}_{j,k}^o\≡S_j^o{\hat{U}}_{j,k};---\left(9\right)$

2, constant error angular estimation in certain time interval

Image and auxiliary data thereof are converted to the data of above-mentioned needs, and long data are carried out segmentation.Recycle formula (10), (11) or (12) to obtain in different time interval corresponding constant error angle.

$P\left({\hat{W}}_{j,k}^o\right){\hat{W}}_{ij,k}^{o*}\×{\hat{W}}_{j,k}^o=P\left({\hat{W}}_{j,k}^o\right)({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)+{\mathrm{\Δz}}_{ij,k}---\left(10\right)$

$\hat{X}={\left(H^{T}H\right)}^{-1}{H}^{T}Z;---\left(11\right)$

$\hat{X}={\left(H^T{R}^{-1}H\right)}^{-1}{H}^T{R}^{-1}Z;---\left(12\right)$

represent and vector vertical matrix, △ z _{ij, k}between a certain full attitude sensor i and a certain single vector sensor j in error angle observation equation at moment t _kobservation noise. represent state variable to be estimated, H represents observing matrix, and Z represents observed quantity, () ^t() ^-1representing matrix transposition and matrix inversion operation respectively, in formula, R represents random vector △ z _{ij, k}covariance matrix.

3, constant error angular estimation in certain time interval

Application of formula (13) ~ (14), become the coefficient (x of Fourier series in alignment error fundamental equation (13) when obtaining ₀, x ₁, x ₂, x ₃, x ₄...).And then become fix error angle contour curve when can obtain.

F(u)＝x ₀+x ₁sin(u)+x ₂cos(u)+x ₃sin(u)+x ₄cos(u)+...(13)

$\underset{x}{min}\left|\right|F(x,xdata)-ydata|{|}_2^2=\underset{x}{min}\underset{i}{\Σ}{\left(F\right(x_i,{\mathrm{xdata}}_i)-{\mathrm{ydata}}_i)}^2---\left(14\right)$

Wherein, u is satellite ascending node argument, and ∑ is for adding and sign of operation, and min is for getting minimum operation symbol.

Above specific embodiments of the invention are described.It is to be appreciated that the present invention is not limited to above-mentioned particular implementation, those skilled in the art can make various distortion or amendment within the scope of the claims, and this does not affect flesh and blood of the present invention.

Claims (5)

1., based on a spacecraft attitude error in pointing discrimination method for mark information, it is characterized in that, comprise the steps:

Step 1: the mathematical statistical model setting up sensor measurement and fix error angle;

Set up the mathematical statistical model of sensor vector measurement, alignment error, provide the estimated value of the initial value of single vector sensor observation vector under body coordinate system, full attitude sensor observation vector;

Step 2: build error in pointing angle observation equation according to the initial value of the observation vector of single vector sensor under body coordinate system, the estimated value of the full observation vector of attitude sensor under body coordinate system;

Step 3: according to the statistical property at error in pointing angle observation equation and error in pointing angle, statistical estimate is carried out to attitude error angle, obtains attitude error angular estimation value;

Step I: repeat step 1 to step 3, obtain different time sections attitude error angular estimation value in same track, carries out curve fitting to described different time sections attitude error angular estimation value and obtains long period attitude error fundamental equation.

2. the spacecraft attitude error in pointing discrimination method based on mark information according to claim 1, it is characterized in that, described step 1 comprises:

Step 1.1: the mathematical statistical model setting up sensor vector measurement, alignment error, specifically comprises following sub-step:

Step 1.1.1, sets up sensor reference measurement vector as follows:

${\hat{U}}_{j,k}={\hat{U}}_{j,k}^{true}+\mathrm{\Δ}{\hat{U}}_{j,k}---\left(1\right)$

In formula, the direction vector measured value of sensor j, direction of measurement true value, be the measurement noises of sensor j, subscript k is the numbering of time, k=1,2 ..., N;

Step 1.1.2, determines that vector and installation relation is measured by satellite body system as follows:

${\hat{W}}_{j,k}=S_j{\hat{U}}_{j,k}^{true}+S_j\mathrm{\Δ}{\hat{U}}_{j,k}={\hat{W}}_{j,k}^{true}+\mathrm{\Δ}{\hat{W}}_{j,k}---\left(2\right)$

In formula, S _jfor sensor j installs matrix, for the direction vector under spacecraft body series, for the direction vector true value under spacecraft body series, for the direction vector noise under spacecraft body series;

Step S1.1.3, alignment error define method is as follows:

$S_j=M_j{S}_j^0---\left(3\right)$

Wherein, S _jthe installation matrix of sensor j, demarcate for ground and obtain matrix initial value being installed, M _jfor alignment error matrix, M _jdefinition as shown in formula (4):

I is unit matrix, and O () represents higher-order shear deformation, θ _jfor alignment error matrix corner vector, for vectorial θ _jnegative symmetric matrix, as shown in formula (5);

Step 1.2: utilize the installation matrix initial value of the observed reading of a certain single vector sensor, this single vector sensor to obtain at body coordinate system observation vector initial value, computing formula is as follows:

In formula: represent that single vector sensor j is at t _kthe initial value of the observation vector during moment under body coordinate system, represent the initial installation matrix of single vector sensor j, represent that single vector sensor j is at t _kthe measured value in moment, represent the benchmark terrestrial reference vector of a certain single vector sensor j, A _krepresent attitude matrix, θ _jrepresent the fix error angle of a certain single vector sensor j, represent that a certain single vector sensor j is at t _kobservation vector error during the moment under body coordinate system;

Step 1.3: according to a certain full attitude sensor at moment t _kthe base vector of the attitude of satellite obtained, a certain single vector sensor obtains the estimated value of this full attitude sensor at body coordinate system observation vector, and computing formula is as follows:

In formula: represent that a certain full attitude sensor i is at moment t _kthe estimated value of the observation vector under body coordinate system that corresponding a certain single vector sensor j obtains, ξ _i,krepresent that a certain full attitude sensor i is at t _kmoment measuring error, θ _irepresent the fix error angle of a certain full attitude sensor i, represent that a certain full attitude sensor i is at t _kthe body attitude matrix estimated value that moment obtains, comprises full attitude sensor i measuring error ξ _i,kwith fix error angle θ _ithe evaluated error introduced.

3. the spacecraft attitude error in pointing discrimination method based on mark information according to claim 1, it is characterized in that, described step 2 comprises:

Build error in pointing angle observation equation according to the estimated value of the initial value of the observation vector of a certain single vector sensor under body coordinate system, the observation vector of a certain full attitude sensor under body coordinate system, the equation of structure is as follows:

$P\left({\hat{W}}_{j,k}^o\right){\hat{W}}_{ij,k}^{o*}\×{\hat{W}}_{j,k}^o=P\left({\hat{W}}_{j,k}^o\right)({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)+{\mathrm{\Δz}}_{ij,k};---\left(8\right)$

In formula: (θ _j-θ _i) be the error angle between a certain full attitude sensor i and a certain single vector sensor j, namely need the error in pointing solved, represent and vector vertical matrix, Δ z _{ij, k}between a certain full attitude sensor i and a certain single vector sensor j in error angle observation equation at moment t _kobservation noise.

4. the spacecraft attitude error in pointing discrimination method based on mark information according to claim 1, it is characterized in that, described step 3 comprises:

According to error in pointing angle observation equation and statistical property, application least square method or Maximum Likelihood Estimation carry out statistical estimate to attitude error angle;

-application least square method obtains following accounting equation:

$\hat{X}={\left(H^{T}H\right)}^{-1}{H}^{T}Z;---\left(9\right)$

In formula represent state variable to be estimated, H represents observing matrix, and Z represents observed quantity, () ^t, () ^-1representing matrix transposition, matrix inversion operation respectively;

-application maximum-likelihood method obtains following accounting equation:

$\hat{X}={\left(H^T{R}^{-1}H\right)}^{-1}{H}^T{R}^{-1}Z;---\left(10\right)$

In formula, R represents random vector Δ z _{ij, k}covariance matrix.

5. the spacecraft attitude error in pointing discrimination method based on mark information according to claim 1, it is characterized in that, described step I comprises:

According to benchmark mark information in different time sections in same track namely on ground certain road sign point to the direction vector R of spacecraft centroid _ts, full attitude sensor i is at t _kthe body attitude matrix that moment obtains single vector sensor j is at t _kthe measured value in moment and the initial installation matrix of sensor j repeat step 2 to step 3, obtain different time sections attitude error angle (θ in same track _j-θ _i) estimated value; The form of Fourier series is adopted to represent fundamental equation F (u) at attitude error angle in the whole orbital period, as shown in formula (11),

F(u)＝x ₀+x ₁sin(u)+x ₂cos(u)+x ₃sin(u)+x ₄cos(u)+...(11)

U is satellite ascending node argument; Utilize nonlinear least square fitting method, find the coefficient x meeting following equation,

$\underset{x}{min}\left|\right|F(x,xdata)-ydata|{|}_2^2=\underset{x}{min}\underset{i}{\Σ}{\left(F\right(x_i,{\mathrm{xdata}}_i)-{\mathrm{ydata}}_i)}^2---\left(12\right)$

Wherein Σ is for adding and sign of operation, and min, for getting minimum operation symbol, obtains the Fourier coefficient (x in fundamental equation F (u) ₀, x ₁, x ₂, x ₃, x ₄...) estimated value, x represents Fourier coefficient, and xdata represents the input data of fundamental equation F (u), xdata _irepresent i-th group of data of xdata.Ydata represents the observation data of fundamental equation F (u), ydata _irepresent i-th group of data of ydata.