CN101013033A - Zero deflection band based star sensor ground surface calibration method - Google Patents

Abstract

The invention is a space measurement technology, involving the improvement to the star sensor calibration method. The invention uses the calibration system which comprising the air cushion platform, single star starlight simulator, star sensor, two-dimensional axial turntable and data processing computer, and its steps are: 1. establish the star sensor imaging model; 2. parameters calibrating. The invention uses no deviation strip to calibration focus and radial distortion coefficient, eliminating the internal parameter estimation effect by the external installation error; the method has simple model and small computing volume, particularly applied to the star sensor calibration based on radial distortion.

Description

A kind of star sensor ground surface calibration method based on Zero deflection band

Technical field

Aerospace measurement technology of the present invention relates to the improvement to star sensor calibrating method.

Background technology

Star sensor is a kind of star observation that utilizes, and the aerospace measurement instrument of high-precision attitude information is provided for spacecraft.Its principle of work is: star sensor front end camera unit by using CCD (or CMOS) imageing sensor is taken and is obtained star map image, obtain the center-of-mass coordinate of fixed star picture point and the information of brightness through image processing program, the importance in star map recognition program utilizes these information to find corresponding fixed star in navigation star database then, calculates the three-axis attitude of star sensor at last.Before star sensor came into operation, inner parameters such as its principal point, focal length and distortion factor must be measured accurately, were called the star sensor calibration.Common star sensor ground surface calibration method mainly contains two kinds: a kind of is to utilize starlight analog device to cooperate 2 turntables of high precision to carry out data acquisition and calibration in the starlight laboratory; Another kind is in the good place of atmospheric environment the sunny night sky to be taken to obtain data and to calibrate.Be illustrated in figure 1 as laboratory inner star sensor calibration system synoptic diagram, this calibration system mainly contains hover platform, single star optical simulator, and star sensor, 2 axial turntables of dimension and data handling machine are formed.Present calibration steps is: (1) adopts the method for whole modeling, sets up coordinate system with the initial position of turntable, sets starlight direction and the installation deviation of star sensor on turntable, sets up the model of inner focal length of star sensor and distortion.(2) then according to shown in Figure 2, rotating table is gathered the asterism data continuously, and record turntable rotational coordinates at that time, finally makes the asterism data spread all over whole star sensor imageing sensor target surface.(3) according to the method for parameter estimation of non-linear least square, the parameter error of block mold is estimated.Loop iteration obtains the internal and external parameter of star sensor calibration system.The problem that above method exists is: (1) calculated amount is big.(2) there is coupling phenomenon in internal and external parameter.

Summary of the invention

The objective of the invention is:, propose a kind of star sensor calibrating method based on the Zero deflection band sampling at the problem that above-mentioned calibration steps exists.Sampled point in this Zero deflection band is insensitive to pitching and driftage installation deviation, the radial distortion that the data of gathering in this zone can be used for calibrating star sensor.This method has been simplified the star sensor model, can reduce the calibration calculations amount, the more important thing is that it has separated coupling phenomenon between the internal and external parameter, can improve the satellite sensor calibration precision based on radial distortion.

Technical scheme of the present invention is: a kind of star sensor ground surface calibration method based on Zero deflection band, to use by hover platform, and the calibration system that single star optical simulator, star sensor, the 2 axial turntables of dimension and data handling machine are formed is characterized in that,

1, sets up the star sensor imaging model; Its step is as follows:

1.1, to be located at the turntable initial coordinate be among the N, the starlight vector that starlight analog device takes place is:

v _n＝[n ₁ n ₂ n ₃] ^T (1)

In the formula, n ₁, n ₂, n ₃Be vector v _n3 coordinate components in coordinate system N;

This starlight vector can also be expressed with formula (2):

In the formula, α is the angle of rotation around housing axle Ny, and β is the angle of rotation around inner axis Nx;

1.3, the installation deviation of star sensor on turntable represent that by 3 angles of rotation they are respectively that turntable housing rotation direction deviation angle is pitch deviation angle θ, deviation angle φ and around the lift-over deviation angle ψ of the star sensor optical axis promptly goes off course at inside casing rotational variations angle;

1.4, the transformational relation from turntable coordinate system N to star sensor coordinate system F is:

v _f＝R _fnv _n (3)

In the formula, v _fStarlight vector under the expression star sensor coordinate system, R _FnExpression turntable coordinate is tied to the transition matrix of star sensor coordinate system;

When adjusting starlight analog device and star sensor and be in the autocollimation state, promptly the starlight direction is consistent with the star sensor boresight direction, then α=-θ, β=-φ;

1.5, set up target surface coordinate system ∑, target surface coordinate system Σ is O '-X-Y, O ' is the intersection point of the star sensor optical axis and target surface, parallel respectively X and the Y direction with target surface of X and Y-axis;

1.6, set up star sensor coordinate system F, star sensor coordinate system F is O-Xf-Yf-Zf, the O point is a camera lens centre of perspectivity point, Xf and Yf are parallel to target surface coordinate system X and Y-axis, the Zf axle is the star sensor optical axis;

1.7, set up the perspective imaging model of star sensor;

If the starlight vector in star sensor coordinate system F is:

v _f＝[f ₁ f ₂ f ₃] ^T (5)

Here, f1, f2, f3 are 3 coordinate components of starlight vector under the star sensor coordinate system;

So the perspective imaging model of star sensor is:

$\mathrm{\λ}\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_c& 0& x_c\\ 0& f_c& x_c\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]\left[\begin{array}{c}{n}_1\\ n_2\\ n_3\end{array}\right]---\left(6\right)$

In the formula, λ is an arbitrary parameter, f _cBe focal length, x, y be for being the asterism image coordinate of unit with the millimeter, x _c, y _cBe principal point image coordinate, r ₁₁～r ₃₃Be corresponding R _Fn9 parameters;

1.8, set up the radial distortion model, establish actual spot of measurement for (x _d, y _d), the linear model estimation point be (x, y), then the radial distortion model is:

dx＝x _d-x＝kx(x ²+y ²)

；(7)

dy＝x _d-y＝ky(x ²+y ²)

2, parametric calibration, its step is as follows:

2.1, data acquisition;

2.1.1, rotating table, with 0.5 the degree be a collection position, in each station acquisition n secondary data, finally make the asterism imaging spread all over target surface, formula is:

$\tilde{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i---\left(8\right)$

$\tilde{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i---\left(8\right)$

N can get 10～100 times.The data of gathering are designated as data acquisition Ω 1;

2.1.2, carry out high-density acquisition at Zero deflection band; Along the y=0 axis, revolution moved 0.1 degree as a collection position, each station acquisition n time, and n can get 10～100 times.The data of gathering are designated as data acquisition Ω 2;

2.2, the self-collimation measurement of principal point position;

Adjust turntable, make starlight and star sensor target surface that starlight analog device sends be in the autocollimation state, and note image coordinate point and the revolving table position of this moment, be principal point coordinate (x _c, y _c), record revolving table position, housing α angle and inside casing β angle; Simultaneously, with measurement point (x _d, y _d) be transformed into principal point (x _c, y _c) be in the new target surface coordinate system at center, have:

${\stackrel{\‾}{x}}_d=x_d-x_c$

${\stackrel{\‾}{y}}_d=y_d-y_c---\left(9\right)$

In the formula,

Be the asterism measurement coordinate system after the conversion;

2.3, estimate focal length deviation, coefficient of radial distortion and installation lift-over deviation angle;

According to the data acquisition Ω 2 in the Zero deflection band, utilize least square method to estimate the focal length deviation, coefficient of radial distortion and installation lift-over deviation angle; After the principal point position was determined, the relational expression of installation lift-over deviation angle in the target surface coordinate system of star sensor was:

$\left[\begin{array}{c}{\tilde{x}}_d\\ {\tilde{y}}_d\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\ψ}& \sin \mathrm{\ψ}\\ -\sin \mathrm{\ψ}& \cos \mathrm{\ψ}\end{array}\right]\left[\begin{array}{c}{x}_r\\ y_r\end{array}\right]---\left(10\right)$

In the formula, (x _r, y _r) be that the preceding target surface asterism coordinate of lift-over takes place,

For the target surface asterism coordinate after the generation lift-over, be right

Estimation;

Because the lift-over deviation angle is less usually, so formula (10) is reduced to:

$\left[\begin{array}{c}{\tilde{x}}_d\\ {\tilde{y}}_d\end{array}\right]=\left[\begin{array}{cc}1& \mathrm{\ψ}\\ -\mathrm{\ψ}& 1\end{array}\right]\left[\begin{array}{c}{x}_r\\ y_r\end{array}\right]---\left(11\right)$

According to formula (5) and (6), obtain imaging formula and be:

${\tilde{x}}_d=f_c(\frac{n_1}{n_3}+\mathrm{\ψ}\frac{n_2}{n_3})(1+{\mathrm{kr}}^2)$

${\tilde{y}}_d=f_c(-\mathrm{\ψ}\frac{n_1}{n_3}+\frac{n_2}{n_3})(1+{\mathrm{kr}}^2)---\left(12\right)$

In the formula, the parameter vector that needs to estimate is $\stackrel{\→}{x}=\left(\begin{array}{ccc}{f}_c& k& \mathrm{\ψ}\end{array}\right);$

Be provided with function:

$f_x\left(\stackrel{\→}{x}\right)=f_c(\frac{n_1}{n_3}+\mathrm{\ψ}\frac{n_2}{n_3})(1+{\mathrm{kr}}^2)$

$f_y\left(\stackrel{\→}{x}\right)=f_c(-\mathrm{\ψ}\frac{n_1}{n_3}+\frac{n_2}{n_3})(1+{\mathrm{kr}}^2)---\left(13\right)$

Here f _xAnd f _yBe nonlinear function, adopt the non-linear least square alternative manner to come the estimated parameter vector, suppose

Be vectorial estimated bias, it is residual that Δ x and Δ y are respectively the calibration deviation;

$\mathrm{\Δx}={\stackrel{\‾}{x}}_d-{\tilde{x}}_d\≈\mathrm{A\Δ}\stackrel{\→}{x}$

$\mathrm{\Δy}={\stackrel{\‾}{y}}_d-{\tilde{y}}_d\≈\mathrm{B\Δ}\stackrel{\→}{x}---\left(14\right)$

In the formula, A, B are respectively the partial differential sensitive matrix, utilize least square method to calculate parameter vector

2.4, estimate outside installation deviation angle;

Work as principal point, focal length after the calibration of inner parameters such as distortion factor, utilizes the installation pitching of 1 pair of star sensor of data set Ω on turntable, and driftage and lift-over deviation angle are estimated;

According to formula (5), (6), (7), pitch deviation angle and lift-over deviation angle are estimated at first, imaging model is:

$x_d=f_c(1+{\mathrm{kr}}^2)\frac{f_1}{f_3}$

$y_d=f_c(1+{\mathrm{kr}}^2)\frac{f_2}{f_3}---\left(15\right)$

Utilization asks the method for partial derivative that offset is carried out modeling to be had:

The initial value of given pitching earlier and lift-over deviation angle is 0, utilizes the method for least square to carry out iterative computation then, obtains pitch deviation angle and lift-over deviation angle estimated value.

Advantage of the present invention is:

The first, owing to utilize Zero deflection band to carry out calibrated focal length and coefficient of radial distortion, having eliminated outside installation deviation may be to inner parameter estimation effect;

The second, this method model is simple, and calculated amount is little;

The 3rd, be specially adapted in the star sensor calibration based on radial distortion.

Description of drawings

Fig. 1 is that the star sensor calibration system is formed synoptic diagram.

Fig. 2 is a collecting method synoptic diagram in the existing calibration steps.

Fig. 3 is the sampling deviation synoptic diagram of star sensor after on the 2 dimension turntables pitching and driftage deviation having taken place.Having shown among the figure has one for the insensitive Zero deflection band of outside installation deviation zone on the target surface.

Fig. 4 is a turntable initial position coordinate system N synoptic diagram.

Fig. 5 is a star sensor perspective imaging synoptic diagram.

Embodiment

Below the present invention is described in further details.

The Zero deflection band definition.

According to studies show that, when sampling, a zone is arranged on the target surface for the insensitive zone of outside installation deviation as the dot matrix method of sampling of Fig. 2, be called " Zero deflection band " here, this regional data deviation is less than noise level.As shown in Figure 3, the sampling deviation synoptic diagram of star sensor after on the 2 dimension turntables pitching and driftage deviation having taken place.

When y=0, very little as can be seen along the estimated bias of x direction, common level less than sampling noiset.This is to rotate (rotation axis of turntable inside casing will rotate with housing) because the rotations of 2 dimension turntable housings belong to stationary shaft, and when inside casing was in 0 position housing rotation, the star sensor sampling error caused for less installation deviation is insensitive.So can in this deviation band, sample, the inner parameter of star sensor is calibrated.

The star sensor imaging model.

As shown in Figure 4, the coordinate system N that sets up according to the initial position of turntable is O-Xn-Yn-Zn, and it is the Xn axle with the rotation axis of inside casing, and the housing rotation axis is the Yn axle, and Xn axle and Yn axle intersect at lens of star sensor centre of perspectivity's point O point, and 0 is coordinate origin.Crossing the O point is the Zn axle of coordinate system along the star sensor boresight direction.

Being located at the turntable initial coordinate is among the N, and the starlight vector that starlight analog device takes place is:

v _n＝[n ₁ n ₂ n ₃] ^T (1)

Here, n ₁, n ₂, n ₃Be vector v _n3 coordinate components in coordinate system N.In addition, this starlight direction can represent also that in turntable coordinate system N these two angles are respectively around housing axle Ny and rotate the α angle with two angles of rotation, rotates the β angle around inner axis Nx, so the starlight vector can be expressed as:

Can represent common vector with the turntable operation angle like this.

In the star sensor installation process of reality, inevitably will introduce installation deviation.The installation deviation of star sensor on turntable can be represented by 3 angles of rotation, is respectively turntable housing rotation direction deviation angle (pitch deviation angle) θ, inside casing rotational variations angle (driftage deviation angle) φ and around the lift-over deviation angle ψ of the star sensor optical axis.So the transformational relation from turntable coordinate system N to star sensor coordinate system F is:

v _f＝R _fnv _n (3)

When adjusting starlight analog device and star sensor and be in the autocollimation state, promptly the starlight direction is consistent with the star sensor boresight direction, then α=-θ, β=-φ.

Fig. 5 is a star sensor perspective imaging synoptic diagram, and the figure areal coordinate that hits is that Σ is O '-X-Y, and its O ' is the intersection point of the star sensor optical axis and target surface, parallel respectively X and the Y direction with target surface with Y-axis of X.Star sensor coordinate system F is O-Xf-Yf-Zf, and its O point is a camera lens centre of perspectivity point, Xf and target surface coordinate system X and Y-axis parallel with Yf, and the Zf axle is the star sensor optical axis.

If the starlight vector in star sensor coordinate system F is:

v _f＝[f ₁ f ₂ f ₃]T (5)

So the perspective imaging model of star sensor is:

$\mathrm{\λ}\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_c& 0& x_c\\ 0& f_c& x_c\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]\left[\begin{array}{c}{n}_1\\ n_2\\ n_3\end{array}\right]---\left(6\right)$

λ is an arbitrary parameter, f _cBe focal length, x, y be for being the asterism image coordinate of unit with the millimeter, x _c, y _cBe principal point image coordinate, r ₁₁～r ₃₃Corresponding R _Fn9 parameters.

Because the existence of lens of star sensor distortion makes and only adopts the linear projection model can not reach very high calibration accuracy.If actual spot of measurement is (x _d, y _d), the linear model estimation point be (x, y), then the radial distortion model is:

dx＝x _d-x＝kx(x ²+y ²)

(7)

dy＝x _d-y＝ky(x ²+y ²)

The parametric calibration process.

1) data acquisition.

Collecting method such as Fig. 2, rotating table, 0.5 degree is a collection position, a station acquisition n secondary data, finally makes the asterism imaging spread all over target surface.Formula is:

$\tilde{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i$

$\tilde{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i---\left(8\right)$

If n=100, then the barycenter noise level order of magnitude that can descend.

Suppose that the star sensor visual field is 12 ° * 12 °, then can gather the asterism number this moment is 625 data points, is designated as data acquisition Ω 1.

Carry out high-density acquisition at Zero deflection band then: along the y=0 axis, revolution moved 0.1 degree and gathered a data point, gathered 120 data points altogether, was designated as data acquisition Ω 2.

2) self-collimation measurement of principal point position.

Adjust turntable, make starlight and star sensor target surface that starlight analog device sends be in the autocollimation state, and note image coordinate point and the revolving table position of this moment, be principal point coordinate (x _c, y _c).Write down revolving table position simultaneously, housing α angle and inside casing β angle.Simultaneously, with measurement point (x _c, y _c) be transformed into principal point (x _c, y _c) be in the new target surface coordinate system at center, have:

${\stackrel{\‾}{x}}_d=x_d-x_c$

${\stackrel{\‾}{y}}_d=y_d-y_c---\left(9\right)$

Here,

Be the asterism measurement coordinate system after the conversion.

3) focal length deviation, coefficient of radial distortion and installation lift-over deviation angle are estimated.

According to the data acquisition Ω 2 in the Zero deflection band, can utilize least square method to estimate the focal length deviation, coefficient of radial distortion and installation lift-over deviation angle.After the principal point position was determined, the relational expression of installation lift-over deviation angle in the target surface coordinate system of star sensor was:

$\left[\begin{array}{c}{\tilde{x}}_d\\ {\tilde{y}}_d\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\ψ}& \sin \mathrm{\ψ}\\ -\sin \mathrm{\ψ}& \cos \mathrm{\ψ}\end{array}\right]\left[\begin{array}{c}{x}_r\\ y_r\end{array}\right]---\left(10\right)$

Here, (x _r, y _r) be that the preceding target surface asterism coordinate of lift-over takes place,

For the target surface asterism coordinate after the generation lift-over, be right

Estimation.Because the lift-over deviation angle is less usually, so we can simplify following formula is:

$\left[\begin{array}{c}{\tilde{x}}_d\\ {\tilde{y}}_d\end{array}\right]=\left[\begin{array}{cc}1& \mathrm{\ψ}\\ -\mathrm{\ψ}& 1\end{array}\right]\left[\begin{array}{c}{x}_r\\ y_r\end{array}\right]---\left(11\right)$

Owing to needn't consider driftage and pitching installation deviation angle, according to formula (5) and (6), we can obtain imaging formula and are:

${\tilde{x}}_d=f_c(\frac{n_1}{n_3}+\mathrm{\ψ}\frac{n_2}{n_3})\left(1+{\mathrm{kr}}^2\right)$

${\tilde{y}}_d=f_c(-\mathrm{\ψ}\frac{n_1}{n_3}+\frac{n_2}{n_3})(1+{\mathrm{kr}}^2)---\left(12\right)$

Here, need the parameter vector of estimation to be $\stackrel{\→}{x}=\left(\begin{array}{ccc}{f}_c& k& \mathrm{\ψ}\end{array}\right),$ Be provided with function:

$f_x\left(\stackrel{\→}{x}\right)=f_c(\frac{n_1}{n_3}+\mathrm{\ψ}\frac{n_2}{n_3})(1+{\mathrm{kr}}^2)$

$f_y\left(\stackrel{\→}{x}\right)=f_c(-\mathrm{\ψ}\frac{n_1}{n_3}+\frac{n_2}{n_3})(1+{\mathrm{kr}}^2)---\left(13\right)$

Here f _xAnd f _yBe nonlinear function, adopt the non-linear least square alternative manner to come the estimated parameter vector.Suppose

Be vectorial estimated bias, it is residual that Δ x and Δ y are respectively the calibration deviation.

$\mathrm{\Δx}={\stackrel{\‾}{x}}_d-{\tilde{x}}_d\≈\mathrm{A\Δ}\stackrel{\→}{x}$

$\mathrm{\Δy}={\stackrel{\‾}{y}}_d-{\tilde{y}}_d\≈\mathrm{B\Δ}\stackrel{\→}{x}---\left(14\right)$

Here, A, B are respectively the partial differential sensitive matrix, utilize least square method just can calculate parameter vector

4) outside installation deviation angle estimation.

Work as principal point, focal length after the calibration of inner parameters such as distortion factor, can utilize the installation pitching of 1 pair of star sensor of data set Ω on turntable, and driftage and lift-over deviation angle are estimated.

Because the driftage deviation angle can not cause evaluated error, can only cause the skew at " Zero deflection band " center.Therefore the calibration of this parameter can be ignored, and obvious influence can be do not caused the work of star sensor.

According to formula (5) (6) (7), can estimate that at first imaging model is to pitch deviation angle and lift-over deviation angle:

$x_d=f_c(1+{\mathrm{kr}}^2)\frac{f_1}{f_3}$

$y_d=f_c(1+{\mathrm{kr}}^2)\frac{f_2}{f_3}---\left(15\right)$

Utilization asks the method for partial derivative that offset is carried out modeling to be had:

Can first given driftage and the initial value of lift-over deviation angle be 0, utilize the method for least square to carry out iterative computation then.

Emulation and interpretation of result.

The star sensor basic parameter of emulation is:

Visual field: 12 ° * 12 °;

Pel array: 1024 * 1024;

Pixel Dimensions: 0.015mm * 0.015mm;

Focal length: 73.6059mm

Suppose that asterism barycenter noise is 0 average, standard deviation is the Gaussian noise of 0.05 pixel, each collection position times of collection n=100, an order of magnitude, i.e. 0.005 pixel so the expectation value of noise level can descend.At this moment main error sources will be from turntable, and the precision that turntable is 0.5 rad is about as much as 0.01 pixel.

Suppose that picture centre is principal point position, that is: x ₀=512 * 0.015mm, y ₀=512 * 0.015mm,

The starlight direction that single star optical simulator takes place is that coordinate among the N is in the turntable initial coordinate:

Installation crab angle θ=0.7854 °,

Installation angle of pitch φ=0.52 36 °,

Casing and target surface installation roll angle ψ=0.5 °

The focal length deviation is 0.2mm,

Radial distortion parameter k=-0.0003

Before carrying out calculation of parameter, at first provide the initial estimate of parameter, suppose that respectively initial value is:

Deflection angle theta=0 ° is installed,

Installation angle of pitch φ=0 °,

Casing and target surface installation roll angle ψ=0 °

Initial focal length is 73.8059mm,

The radial distortion parameter is k=0,

For verification algorithm, at first do not add noise, utilize Zero deflection band focusing, distortion factor and roll angle to estimate, can obtain through 5 iterative computation:

Iterations	1	2	3	4	5
						f c/mm	0	0.20272	0.2	0.2	0.2
k	0	-0.00029756	-0.00030002	-0.0003	-0.0003
						ψ/degree	0	0.48611	0.49285	0.49282	0.49282

As can be seen from the above table, when not having noise,, can obtain the accurate estimated value of focal length and distortion factor, and the lift-over deviation makes lift-over estimation of deviation precision have error to exist owing to the driftage deviation angle certain coupling is arranged through 5 iteration.Below pitch deviation angle and lift-over deviation angle are estimated:

Iterations	1	2	3	4	5
						ψ/degree	0	0.49279	0.49282	0.49282	0.49282
θ/degree	0	0.77877	0.78474	0.78531	0.78536

Estimated value has deviation slightly as can be seen, and this is because the influence of driftage deviation angle causes.

Do not having under the situation of noise effect, last x, y loadstar point coordinate calibration offset is approximately 0, has obtained desirable calibration result.

And then consider the introducing of noise in the actual alignment process, and suppose that the barycenter residual noise level through repeatedly sampling after averaging is 0 average, mean square deviation is the white Gaussian noise of 0.005 pixel.Simulation result is as follows:

Iterations	1	2	3	4	5
						f c/mm	0	0.20239	0.19967	0.19967	0.19967
k	0	0.00029767	0.00030013	0.00030011	0.00030011
						ψ/degree	0	0.48612	0.49286	0.49283	0.49283

Be to add the pitching mounting shift angle behind the noise and the estimation procedure of lift-over mounting shift angle below.

Iterations	1	2	3	4	5
						ψ/degree	0	0.49274	0.49277	0.49277	0.49277
θ/degree	0	0.77928	0.78552	0.78611	0.78617

Under 0.05 pixel noise level, verify at last to show, x, y loadstar point coordinate calibration offset is respectively 0.0537 and 0.0542 pixel.The result shows and has obtained good calibration effect, can satisfy the high-precision requirement of star sensor.

Claims (1)

1, a kind of star sensor ground surface calibration method based on Zero deflection band uses by hover platform, and the calibration system that single star optical simulator, star sensor, the 2 axial turntables of dimension and data handling machine are formed is characterized in that,

1.1, set up the star sensor imaging model; Its step is as follows:

1.1.1, to be located at the turntable initial coordinate be among the N, the starlight vector that starlight analog device takes place is:

v _n＝[n ₁ n ₂ n ₃] ^T (1)

In the formula, n ₁, n ₂, n ₃Be vector v _n3 coordinate components in coordinate system N;

This starlight vector can also be expressed with formula (2):

In the formula, α is the angle of rotation around housing axle Ny, and β is the angle of rotation around inner axis Nx;

1.1.3, the installation deviation of star sensor on turntable represent by 3 angles of rotation, they are respectively that turntable housing rotation direction deviation angle is pitch deviation angle θ, and deviation angle φ and around the lift-over deviation angle φ of the star sensor optical axis promptly goes off course at inside casing rotational variations angle;

1.1.4, the transformational relation from turntable coordinate system N to star sensor coordinate system F is:

v _f＝R _fn v _n (3)

In the formula, v _fStarlight vector under the expression star sensor coordinate system, R _FnExpression turntable coordinate is tied to the transition matrix of star sensor coordinate system;

When adjusting starlight analog device and star sensor and be in the autocollimation state, promptly the starlight direction is consistent with the star sensor boresight direction, then α=-θ, β=-φ;

1.1.5, set up target surface coordinate system ∑, target surface coordinate system ∑ is 0 '-X-Y, 0 ' is the intersection point of the star sensor optical axis and target surface, parallel respectively X and the Y direction with target surface of X and Y-axis;

1.1.6, set up star sensor coordinate system F, star sensor coordinate system F is 0-Xf-Yf-Zf, 0 is camera lens centre of perspectivity point, Xf and Yf are parallel to target surface coordinate system X and Y-axis, the Zf axle is the star sensor optical axis;

1.1.7, set up the perspective imaging model of star sensor;

If the starlight vector in star sensor coordinate system F is:

v _f＝[f ₁ f ₂ f ₃] ^T (5)

Here, f1, f2, f3 are 3 coordinate components of starlight vector under the star sensor coordinate system;

So the perspective imaging model of star sensor is:

$\mathrm{\λ}\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_c& 0& x_c\\ 0& f_c& x_c\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]\left[\begin{array}{c}{n}_1\\ n_2\\ n_3\end{array}\right]---\left(6\right)$

In the formula, λ is an arbitrary parameter, f _cBe focal length, x, y be for being the asterism image coordinate of unit with the millimeter, x _c, y _cBe principal point image coordinate, r ₁₁～r ₃₃Be corresponding R _Fn9 parameters;

1.1.8, set up the radial distortion model, establish actual spot of measurement for (x _d, y _d), the linear model estimation point be (x, y), then the radial distortion model is:

dx＝x _d-x＝kx(x ²+y ²)

dy＝x _d-y＝ky(x ²+y ²)； (7)

1.2, parametric calibration, its step is as follows:

1.2.1, data acquisition;

1.2.1.1, rotating table, with 0.5 the degree be a collection position, in each station acquisition n secondary data, finally make the asterism imaging spread all over target surface, formula is:

$\tilde{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i$

$\tilde{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i---\left(8\right)$

N can get 10～100 times; The data of gathering are designated as data acquisition Ω 1;

1.2.1.2, carry out high-density acquisition at Zero deflection band; Along the y=0 axis, revolution moved 0.1 degree as a collection position, each station acquisition n time, and n can get 10～100 times.The data of gathering are designated as data acquisition Ω 2;

1.2.2, the self-collimation measurement of principal point position;

Adjust turntable, make starlight and star sensor target surface that starlight analog device sends be in the autocollimation state, and note image coordinate point and the revolving table position of this moment, be principal point coordinate (x _c, y _c), record revolving table position, housing α angle and inside casing β angle; Simultaneously, with measurement point (x _d, y _d) be transformed into principal point (x _c, y _c) be in the new target surface coordinate system at center, have:

${\stackrel{\‾}{x}}_d=x_d-x_c$

${\stackrel{\‾}{y}}_d=y_d-y_c---\left(9\right)$

In the formula,

Be the asterism measurement coordinate system after the conversion;

1.2.3, estimate focal length deviation, coefficient of radial distortion and installation lift-over deviation angle;

According to the data acquisition Ω 2 in the Zero deflection band, utilize least square method to estimate the focal length deviation, coefficient of radial distortion and installation lift-over deviation angle; After the principal point position was determined, the relational expression of installation lift-over deviation angle in the target surface coordinate system of star sensor was:

$\left[\begin{array}{c}{\tilde{x}}_d\\ {\tilde{y}}_d\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\ψ}& \sin \mathrm{\ψ}\\ -\sin \mathrm{\ψ}& \cos \mathrm{\ψ}\end{array}\right]\left[\begin{array}{c}{x}_r\\ y_r\end{array}\right]---\left(10\right)$

In the formula, (x _r, y _r) be that the preceding target surface asterism coordinate of lift-over takes place,

For the target surface asterism coordinate after the generation lift-over, be right

Estimation;

Because the lift-over deviation angle is less usually, so formula (10) is reduced to:

$\left[\begin{array}{c}{\tilde{x}}_d\\ {\tilde{y}}_d\end{array}\right]=\left[\begin{array}{cc}1& \mathrm{\ψ}\\ -\mathrm{\ψ}& 1\end{array}\right]\left[\begin{array}{c}{x}_r\\ y_r\end{array}\right]---\left(11\right)$

According to formula (5) and (6), obtain imaging formula and be:

${\tilde{x}}_d=f_c(\frac{n_1}{n_3}+\mathrm{\ψ}\frac{n_2}{n_3})(1+k{r}^2)$

${\tilde{y}}_d=f_c(-\mathrm{\ψ}\frac{n_1}{n_3}+\frac{n_2}{n_3})(1+k{r}^2)---\left(12\right)$

In the formula, the parameter vector that needs to estimate is $\stackrel{\→}{x}=\left(f_c\mathrm{k\ψ}\right);$

Be provided with function:

$f_c\left(\stackrel{\→}{x}\right)=f_c(\frac{n_1}{n_3}+\mathrm{\ψ}\frac{n_2}{n_3})(1+k{r}^2)$

$f_y\left(\stackrel{\→}{x}\right)=f_c(-\mathrm{\ψ}\frac{n_1}{n_3}+\frac{n_2}{n_3})(1+k{r}^2)---\left(13\right)$

Here f _xAnd f _yBe nonlinear function, adopt the non-linear least square alternative manner to come the estimated parameter vector, suppose Be vectorial estimated bias, it is residual that Δ x and Δ y are respectively the calibration deviation;

$\mathrm{\Δx}={\stackrel{\‾}{x}}_d-{\tilde{x}}_d\≈\mathrm{A\Δ}\stackrel{\→}{x}---\left(14\right)$

$\mathrm{\Δy}={\stackrel{\‾}{y}}_d-{\tilde{y}}_d\≈\mathrm{B\Δ}\stackrel{\→}{x}$

In the formula, A, B are respectively the partial differential sensitive matrix, utilize least square method to calculate parameter vector

1.2.4, estimate outside installation deviation angle;

Work as principal point, focal length after the calibration of inner parameters such as distortion factor, utilizes the installation pitching of 1 pair of star sensor of data set Ω on turntable, and driftage and lift-over deviation angle are estimated;

According to formula (5), (6), (7), pitch deviation angle and lift-over deviation angle are estimated at first, imaging model is:

$x_d=f_c(1+k{r}^2)\frac{f_1}{f_3}$

$y_d=f_c(1+k{r}^2)\frac{f_2}{f_3}---\left(15\right)$

Utilization asks the method for partial derivative that offset is carried out modeling to be had:

The initial value of given pitching earlier and lift-over deviation angle is 0, utilizes the method for least square to carry out iterative computation then, obtains pitch deviation angle and lift-over deviation angle estimated value.

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