CN104406607A - Multi-visual field composite optical sensor calibration device and method - Google Patents

Abstract

The invention provides a multi-visual field composite optical sensor calibration device and method. The multi-visual field composite optical sensor calibration device comprises a three-shaft high precision turntable, a single starlight simulator, a marble platform used for supporting the single starlight simulator, a data processing computer and a multi-visual field composite optical sensor. According to the multi-visual field composite optical sensor calibration device and method provided by the invention, a die of starlight incidence vector, starlight reflection vector and perspective projection imaging of the multi-visual field composite optical sensor is established, and a single sensor and a composite optical sensor are respectively calibrated by utilizing a two-step method. With the adoption of measuring device and method, various parameters and mounting parameters of an optical system of the multi-visual field composite optical sensor can be measured.

Description

The caliberating device of a kind of many visual fields complex optics sensor and method

Technical field

The invention provides caliberating device and the method for a kind of many visual fields complex optics sensor, belong to aerospace measurement technology.

Background technology

Many visual fields complex optics sensor is a kind of novel aerospace measurement instrument, and it utilizes multiple virtual visual field simultaneously to near-Earth object (as the earth, the moon) and fixed star imaging, for spacecraft provides attitude and positional information.General autonomous astronomical navigation system is locus and the attitude that the mode combined by multiple optical sensor (as star sensor, sun sensor, infrared horizon, ultraviolet moon sensor) determines spacecraft.These sensors based on same optical principle are functionally carried out compound by many visual fields complex optics sensor, achieve " one is quick multiplex ".The specific implementation of this sensor is shown in patent " a kind of many visual fields complex optics sensor calibration apparatus and method (patent No. ZL201310631365.X) ".Its specific implementation principle is: the optical system of many visual fields complex optics sensor is made up of four prisms and lens, according to optical reflection principle, cmos imaging face is divided into nonoverlapping multiple imaging region, fictionalize multiple observation visual field thus, and respectively to fixed star and near-Earth object imaging; Then the Image semantic classification program through system can obtain the information such as asterism barycenter and earth edge; Data handling system utilizes these information to carry out importance in star map recognition and navigation clearing, calculates the navigation information of spacecraft.Its principle schematic as shown in Figure 1.

Optical sensor must measure its inside and outside parameter before being taken into use, is referred to as the demarcation of optical sensor.Many visual fields complex optics sensor is similar to the star sensor with four virtual visual fields on structural principle, so its demarcation can adopt the scaling method of star sensor.The scaling method of tradition star sensor adopts the standardization based on two-axis platcform and single star simulator usually, it mainly make use of the feature that starlight is directional light, carry out unified Modeling to the parameter of star sensor, its concrete calibration process is shown in patent ' element correcting method (patent No. ZL2005101125537) ' inside and outside a kind of star sensor.

This method is widely used in demarcation and the accuracy test of traditional star sensor now, but for novel many visual fields complex optics sensor, this traditional scaling method is no longer applicable, its main cause have following some:

(1) four virtual optical axis of novel many visual fields complex optics sensor are towards four different directions, light inlet and optical axis are bordering on plumbness, cannot install under diaxon status condition, and two-axle rotating table cannot according to calibration request motion make asterism linear be covered with whole visual field.

(2) optical system of many visual fields complex optics sensor comprises optical prism, lens and image device, and its parameter is more complicated.Because prism parameters and sensor installation parameter, lens parameter are coupled similar, adopt traditional scaling method carry out unified Modeling calculate time, computation process can be caused to restrain or fitting precision extremely low.

Due to the restriction of device, modeling and computing method, traditional star sensor scaling method based on two-axis platcform is not suitable for the demarcation of novel many visual fields complex optics sensor.

Summary of the invention

Technology of the present invention is dealt with problems: for the demarcation Problems existing of many visual fields complex optics sensor, caliberating device and the method for a kind of novel many visual fields complex optics sensor are provided, single sensor calibration and complex optics sensor integral calibrating two parts are divided into many visual fields complex optics sensor, and carry out difference Modeling Calculation, utilize non-linear fitting method iteration to go out the best estimate of parameter.

Technical scheme of the present invention is: the caliberating device of a kind of many visual fields complex optics sensor, comprise three axle high precision turntable, for support single star optical simulator marble platform, for simulating single star optical simulator of starlight incidence, many visual fields complex optics sensor and data handling machine.Wherein single star optical simulator level is arranged in marble platform, many visual fields complex optics sensor is arranged on three-dimensional high-precision turntable, the optical axis of complex optics sensor is parallel to the interior axle of three axle high precision turntable, and the starlight direction that single star optical simulator sends is perpendicular to the axis of three axle high precision turntable.

A scaling method for many visual fields complex optics sensor, carries out in two steps, is respectively single sensor calibration and composite sensing device integral calibrating, and described single sensor refers to the part of many visual fields complex optics sensor removing optical prism; After carrying out first step list sensor calibration, obtain installation parameter and the inner parameter of single sensor, result substituted in second step composite sensing device integral calibrating and participate in iterative computation, utilize Non-linear least-square curve fitting to go out prism parameters, implementation step is as follows:

(1) demarcation of single sensor

Utilize three-axle table to demarcate single sensor, carrying out the timing signal of first step list sensor unit, many visual fields optical sensor does not install optical prism (being referred to as single sensor), adjustment three-axle table axis, make the optical axis of single sensor parallel with single star simulator starlight incident direction, the alignment error matrix of single sensor can be obtained by traditional scaling method, focal length, optics principal point and distortion coefficients of camera lens parameter, detailed process is see " inside and outside a kind of star sensor element correcting method " (patent No. ZL2005101125537).

(2) integral calibrating of many visual fields complex optics sensor

On the basis of step (1), keep the installation site of single sensor constant and correct installation optics four prism, adjustment three-axle table makes the starlight incident direction of the optical axis of complex optics sensor and single star simulator perpendicular, and demarcates as follows;

(2.1) surving coordinate system is set up

Set up sensor coordinate system and three-axle table zero-bit coordinate system, the angle that the transformational relation wherein between sensor coordinate system and three-axle table zero-bit coordinate system can be turned over by three-axle table is determined;

Sensor coordinate system M is defined as: initial point O _mfor the optical centre of many visual fields complex optics sensor lens, X _mparallel with imageing sensor line direction, Y _mparallel with imageing sensor column direction, Z _malong the optical axis direction of lens of star sensor, determined by the right-hand rule, be denoted as: O _m-X _my _mz _m;

Turntable zero-bit coordinate system N is defined as: the coordinate system determined by rotation of rotary table axle under zero-bit state, and initial point is the centre of gyration of turntable, X _rfor the rotating shaft of three-axle table inner axis, Y _rfor the rotating shaft of turntable center axle, Z _rbe that three axle axle turntable housing axle rotating shafts are determined, be denoted as: O _r-X _ry _rz _r;

(2.2) prism incidence Vector Modeling

Define and to send and the starlight vector incided optics four prism surface is prism incidence vector V from single star optical simulator ₁.The factor affecting prism incidence vector mainly comprises starlight vector initial alignment deviation V ₀, sensor installation deviation R _wwith turntable transition matrix R _r, between them, pass is:

V ₁＝R _r*R _w*V ₀

Order $V_1=\left[\begin{array}{c}{v}_{11}\\ v_{12}\\ v_{13}\end{array}\right],$ Can obtain as calculated:

v ₁＝z ₀cosαcosβcosω ₂+z ₁sinαcosβcosω ₂+z ₂sinβcosω ₂+z ₃cosαcosβcosω ₁sinω ₂

+z ₄sinαcosβcosω ₁sinω ₂+z ₅sinβcosω ₁sinω ₂+z ₆cosαcosβsinω ₁sinω ₂

+z ₇sinαcosβsinω ₁sinω ₂+z ₈sinβsinω ₁sinω ₂

v ₂＝-z ₀cosα ₁cosβsinω ₂-z ₁sinαcosβsinω ₂-z ₂sinβsinω ₂+z ₃cosα ₁cosβcosω ₁cosω ₂

+z ₄sinαcosβcosω ₁cosω ₂+z ₅sinβcosω ₁cosω ₂+z ₆cosαcosβsinω ₁cosω ₂

+z ₇sinαcosβsinω ₁cosω ₂+z ₈sinβsinω ₁cosω ₂

v ₃＝-z ₃cosαcosβsinω ₁-z ₄sinαcosβsinω ₁-z ₅sinβsinω ₁+z ₆cosαcosβcosω ₁

+z ₇sinαcosβcosω ₁+z ₈sinβcosω ₁

Wherein α, β are the class right ascension of starlight vector in coordinate system N and class declination; z ₀~ z ₈for R _wmatrix is from upper left to the element of bottom right, and its value is demarcated can obtain through (1) step; ω ₁for turntable is from the rotation angle of zero-bit state around axis, ω ₂for turntable is from the rotation angle of zero-bit around outer shaft.

(2.3) prismatic reflection Vector Modeling

Define through four prism surfaces reflections laggard enter the vector of optical lens be prismatic reflection vector V _r.The factor affecting prismatic reflection vector mainly comprises the normal vector N of corresponding edge mirror plane ₁(being assumed to be visual field 1), prism incidence vector V ₁.

According to the pass that plane reflection principle can obtain between them be:

$V_r=V_1-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{N}_1$

Order $V_r=\left[\begin{array}{c}{r}_1\\ r_2\\ r_3\end{array}\right],$ Can obtain as calculated:

r ₁＝sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂+cosαcosβ(z ₀cosω ₂+z ₃cosω ₁sinω ₂+

z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₁+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)-cosφcosγ(2sinφ

(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁)+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))

+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ(z ₃cosω ₁cosω ₂

-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂+z ₇cosω ₂sinω ₁))

+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂)+cosαcosβ(z ₀cosω ₂

+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₂+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)))

r ₂＝sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ(z ₃cosω ₁cosω ₂-z ₀sinω ₂+

z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₄-z ₁sinω ₂+z ₇cosω ₂sinω)-cosφsinγ

(2sinφ(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃cosω ₂+cosβsinα(z ₇cosω ₁-

z ₄sinω ₁))+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ

(z ₃cosω ₁cosω ₂-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂+z ₇cosω ₂sinω ₁))

+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂)+cosαcosβ

(z ₀cosω ₂+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₂+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)))

r ₃＝sinβ(z ₈cosω ₁-z ₅sinω ₁)-sinγ(2sinφ(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁)

+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+

cosαcosβ(z ₃cosω ₁cosω ₂-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂

+z ₇cosω ₂sinω ₁))+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂)+z ₈sinω ₁sinω ₂)+

cosαcosβ(z ₀cosω ₂+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+sinαcosβ(z ₁cosω ₂+z ₄cosω ₁sinω ₂

+z ₇sinω ₁sinω ₂)))+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))

(2.4) perspective projection imaging modeling

Reflection vector light enters the imaging process of lens on imageing sensor target surface can regard perspective projection as, and its imaging point position is:

$\left\{\begin{array}{c}x=-f\frac{v_{11}}{v_{13}}\frac{1}{\mathrm{Dx}}+X_0+\stackrel{\‾}{x}(q_1{r}^2+q_2{r}^4)+[p_1(r^2+2{\stackrel{\‾}{x}}^2)+2p_2\stackrel{\‾}{\mathrm{xy}}]\\ y=-f\frac{v_{12}}{v_{13}}\frac{1}{\mathrm{Dy}}+Y_0+\stackrel{\‾}{y}(q_1{r}^2+q_2{r}^4)+[p_2(r^2+2{\stackrel{\‾}{y}}^2)+2p_1\stackrel{\‾}{\mathrm{xy}}]\end{array}\right.$

$\left\{\begin{array}{c}\stackrel{\‾}{x}=x^{\′}-X_0\\ \stackrel{\‾}{y}=y^{\′}-Y_0\\ r^2={\stackrel{\‾}{x}}^2+{\stackrel{\‾}{y}}^2\end{array}\right.$

Wherein, f is lens focus, and unit is mm; (X ₀, Y ₀) be optics principal point, unit is pixel; p ₁, p ₂, q ₁, q ₂for distortion coefficients of camera lens, above-mentioned each value all can be demarcated by (1) step and be obtained.(Dx, Dy) is pixel dimension, and unit is mm.

(2.5) data acquisition and data processing

Above model establishes turntable angle position, composite sensing device parameters states the corresponding relation with asterism image coordinate, by gathering the asterism image coordinate under different revolving table position, utilizes nonlinear least square method can simulate the parameters of sensor.

(2.5.1)

Rotating table outer shaft and interior axle, be asterism linear be covered with whole visual field, a station acquisition n secondary data, n gets 100 ~ 1000, and records turntable coordinate position at that time simultaneously,

Formula is:

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

$\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i$

(2.5.2)

The turntable coordinate utilizing (2.5.1) to record, calculates prism incidence vector corresponding to different turntable coordinate, namely by turntable angle (θ according to prism incidence vector model (2.2) ₁, θ ₂, θ ₃) calculate prism incidence vector $V_1=\left[\begin{array}{c}{v}_{11}\\ v_{12}\\ v_{13}\end{array}\right].$

The asterism image coordinate utilizing (2.5.1) to obtain, calculates prismatic reflection vector corresponding to different asterism coordinate according to perspective projection imaging model (2.4).Namely by asterism position calculate prismatic reflection vector ${\stackrel{\‾}{V}}_r=\left[\begin{array}{c}\stackrel{\‾}{r_1}\\ \stackrel{\‾}{r_2}\\ \stackrel{\‾}{r_3}\end{array}\right].$

(2.5.3)

The second step that two-step approach demarcates complex optics sensor mainly contains 4 parameters, with vector represent that these parameters are: can obtain according to above-mentioned 2.4 joint prismatic reflection models:

$V_r=V_1-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{N}_1=F\left(\stackrel{\→}{x}\right)$

That is: $r_1=v_{11}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{11}=F_{r_1}\left(\stackrel{\→}{x}\right)$

$r_2=v_{12}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{12}=F_{r_2}\left(\stackrel{\→}{x}\right)$

$r_3=v_{13}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{13}=F_{r_3}\left(\stackrel{\→}{x}\right)$

Wherein $N_1=\left[\begin{array}{c}{n}_{11}\\ n_{12}\\ n_{13}\end{array}\right].$

Suppose that the estimated value of the reflection vector calculated according to model is ${\hat{V}}_r=\left[\begin{array}{c}{\hat{r}}_1\\ {\hat{r}}_2\\ {\hat{r}}_3\end{array}\right],$ Due to be nonlinear function, non-linear least square alternative manner can be adopted to carry out estimated parameter vector if for vectorial estimated bias, then have:

$\mathrm{\Δ}{r}_1=\stackrel{\‾}{r_1}-{\hat{r}}_1=\mathrm{A\Δ}\stackrel{\→}{x}$

$\mathrm{\Δ}{r}_2=\stackrel{\‾}{r_2}-{\hat{r}}_2=\mathrm{B\Δ}\stackrel{\→}{x}$

$\mathrm{\Δ}{r}_3=\stackrel{\‾}{r_3}-{\hat{r}}_3=\mathrm{C\Δ}\stackrel{\→}{x}$

$A=(\frac{\∂F_{r_1}}{\∂\mathrm{\α}},\frac{\∂F_{r_1}}{\∂\mathrm{\β}},\frac{\∂F_{r_1}}{\∂\mathrm{\γ}},\frac{\∂F_{r_1}}{\∂\mathrm{\φ}})$

$B=(\frac{\∂F_{r_2}}{\∂\mathrm{\α}},\frac{\∂F_{r_2}}{\∂\mathrm{\β}},\frac{\∂F_{r_2}}{\∂\mathrm{\γ}},\frac{\∂F_{r_2}}{\∂\mathrm{\φ}})$

$C=(\frac{\∂F_{r_3}}{\∂\mathrm{\α}},\frac{\∂F_{r_3}}{\∂\mathrm{\β}},\frac{\∂F_{r_3}}{\∂\mathrm{\γ}},\frac{\∂F_{r_3}}{\∂\mathrm{\φ}})$

Here A, B are sensitive matrix, suppose that participating in calculating asterism number is m, order

$P=\left(\begin{array}{c}\mathrm{\Δ}{r}_{11}\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{r}_{1m}\\ \mathrm{\Δ}{r}_{21}\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{r}_{2m}\\ \mathrm{\Δ}{r}_{31}\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{r}_{3m}\end{array}\right),M=\left(\begin{array}{c}{A}_1\\ \·\\ \·\\ \·\\ A_m\\ B_1\\ \·\\ \·\\ \·\\ B_m\\ C_1\\ \·\\ \·\\ \·\\ C_m\end{array}\right)$

Here the vector that is made up of the offset on three directions of P, M is the overall sensitive matrix of A, B, C tri-sensitive matrixs compositions,

Then there is iterative equation:

$\mathrm{\Δ}{\stackrel{\→}{x}}^{(k+1)}=\mathrm{\Δ}{\stackrel{\→}{x}}^{\left(k\right)}-{\left(M_k^T{M}_k\right)}^{-1}{M}_k^T{P}^{\left(k\right)}$

Wherein k is iteration sequence number, the stationary value after iteration terminates, and is the parameter calibration result of second step.The result of the comprehensive first step and second step, just can obtain the calibration value of all parameters, completes the demarcation to complex optics sensor.

Many visual fields complex optics sensor due to its measuring principle and composition structure and general star sensor different, use traditional star sensor scaling method and device cannot complete demarcation task.The present invention adopts the two step scaling methods based on three-axle table, establishes the measurement model of many visual fields complex optics sensor, uses Non-linear least-square curve fitting to go out the parameters of sensor.Compared to traditional scaling method, the present invention has the following advantages.

(1) adopt new caliberating device, calibration process is more simple and reliable.Because novel many visual fields complex optics sensor has towards the virtual visual field of four different directions, and the virtual optical axis and the main optical axis form an angle, utilize traditional two-axle rotating table to carry out timing signal, sensor is installed complicated, and the picture point obtained becomes nonlinear Distribution, greatly reduces the precision of demarcation.The present invention adopts high precision three-axle table, single star optical simulator and test computer as caliberating device, decreases installation alignment procedures complicated in demarcation, and can obtain linear test asterism by turntable motion, scaling method is more simple and reliable.

(2) establish the measurement model of many visual fields complex optics sensor, adopt two step scaling methods, decrease the coupling between parameter, improve stated accuracy.The optical system of novel many visual fields complex optics sensor comprises lens, optics four prism and imager chip, and its parameter is more complicated.Because the installation parameter of four prism parameters, sensor, lens parameter attribute are similar, when utilizing classic method to carry out overall estimation, the phenomenon be coupled can be there is.The present invention adopts two step scaling methods, demarcates respectively, the fit procedure of four prism parameters separated, avoid the introducing between different parameters error, improve stated accuracy single sensor and complex optics sensor complete machine.

Accompanying drawing explanation

Fig. 1 is many visual fields complex optics sensor measuring principle schematic diagram;

Fig. 2 is the present invention many visual fields complex optics sensor calibration device;

Fig. 3 is list sensor calibration schematic diagram of the present invention;

Fig. 4 is the present invention many visual fields complex optics sensor surving coordinate system;

Fig. 5 is prismatic reflection Vector Modeling of the present invention;

Fig. 6 is invention mirror reflective relation schematic diagram;

Fig. 7 is asterism acquisition mode in the present invention;

Fig. 8 is solution process schematic diagram.

Embodiment

The principle schematic of many visual fields complex optics sensor as shown in Figure 1, with traditional star sensor unlike.The optical system of many visual fields complex optics sensor is made up of four prisms 7 and lens 8, according to optical reflection principle, cmos imaging face is divided into nonoverlapping multiple imaging region, fictionalizes multiple observation visual field thus respectively to fixed star and near-Earth object imaging.Autonomous astronomical navigation can be realized by subsequent algorithm.

Two step caliberating devices of a kind of many visual fields of the present invention complex optics sensor are by three axle high precision turntable 1, and for supporting the marble platform 3 of single star simulator, single star optical simulator 2, many visual fields complex optics sensor 5 and data handling machine 4 form.Wherein single star optical simulator is arranged in marble platform 3, and many visual fields complex light sensor 5 is arranged on the inside casing of three-axle table, and concrete mounting means as shown in Figure 2.Wherein single star optical simulator 5 level is arranged in marble platform 3, many visual fields complex optics sensor 5 is arranged on three-dimensional high-precision turntable 1, the optical axis of many visual fields complex optics sensor 5 is parallel to the interior axle of three axle high precision turntable 1, and the starlight direction that single star optical simulator 5 sends is perpendicular to the axis of three axle high precision turntable 1.

The demarcation of many visual fields complex optics sensor is carried out by the present invention in two steps, be respectively single sensor calibration and composite sensing device integral calibrating, installation parameter and the inner parameter of single sensor can be obtained after carrying out first step demarcation, its result is substituted into second step and participates in iterative computation, significantly can weaken the coupling between parameter like this, final acquisition is reliable result accurately.

1. the demarcation of single sensor

Many visual fields complex optics sensor utilizes optical prism to fictionalize multiple visual field, realizes a quick multiplex function, and the part of its removing optical prism can be regarded as single sensor, and the scaling method of traditional star sensor can be adopted to demarcate its relevant parameters.The first step of two-step approach utilizes three-axle table to demarcate single sensor part.

Carrying out the timing signal of first step list sensor unit, many visual fields optical sensor does not install optical prism, is referred to as single sensor 6, and assembling mode as shown in Figure 3.Utilize patent ZL2005101125537 " inside and outside a kind of star sensor element correcting method " described demarcation mode, the alignment error matrix of single sensor can be obtained, focal length, the parameters such as optics principal point and distortion coefficients of camera lens.Through the first step demarcate after available major parameter and meaning as shown in the table:

Table 1 first step calibrating parameters and meaning

Parameter	Meaning
		f	Lens focus
(X 0,Y 0)	Optics principal point
		p 1、p 2、q 1、q 2	Distortion coefficients of camera lens
R w	Sensor installation deviation matrix

2. the integral calibrating of more than visual field complex optics sensor

The second step that two-step approach is demarcated is the integral calibrating of many visual fields complex optics sensor.On the basis of the first step, keep the installation site of sensor constant and assemble prism, the center of adjustment three-axle table, to shown in Fig. 2, makes the starlight incident direction of the optical axis of complex optics sensor and single star simulator perpendicular, and demarcates as follows:

2.1 set up surving coordinate system

Two-stage calibration method adopts the definition of unified coordinate system, mainly contains sensor coordinate system and three-axle table zero-bit coordinate system, and the angle that wherein between the coordinate system of the first step and second step coordinate system, relation is turned over by turntable is determined.

Sensor coordinate system M is defined as: initial point O _mfor the optical centre of many visual fields complex optics sensor lens, X _mparallel with imageing sensor line direction, Y _mparallel with imageing sensor column direction, Z _malong the optical axis direction of lens of star sensor, determined by the right-hand rule, see Fig. 4.Be denoted as: O _m-X _my _mz _m.

Turntable zero-bit coordinate system N is defined as: the coordinate system determined by rotation of rotary table axle under zero-bit state, and initial point is the centre of gyration of turntable, X _rfor the rotating shaft of three-axle table inner axis, Y _rfor the rotating shaft of turntable center axle, Z _rbe that three axle axle turntable housing axle rotating shafts are determined, be denoted as: O _r-X _ry _rz _r.Specifically as shown in Figure 4.

2.2 prism incidence Vector Modelings

Define and to send and the starlight vector incided optics four prism surface is prism incidence vector V from single star optical simulator ₁.The factor affecting prism incidence vector mainly comprises starlight vector initial alignment deviation V ₀, sensor installation deviation R _wwith turntable transition matrix R _r

Starlight vector initial alignment deviation V ₀being the direction vector of starlight under turntable zero-bit coordinate system N that starlight analog device sends, is the normalized vector of 3 × 1.

$V_0=\left[\begin{array}{c}\cos \mathrm{\α}\cos \mathrm{\β}\\ \sin \mathrm{\α}\cos \mathrm{\β}\\ \sin \mathrm{\β}\end{array}\right]$

Turntable transition matrix R _rbe turntable from zero-bit state around X _raxle rotates θ ₁, around Z _raxle rotates θ ₂corresponding rotation matrix, is expressed as:

$R_r=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_2& 0& -{\sin \mathrm{\θ}}_2\\ 0& 1& 0\\ \sin {\mathrm{\θ}}_2& 0& \cos {\mathrm{\θ}}_2\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\θ}}_1& \sin {\mathrm{\θ}}_1\\ 0& -\sin {\mathrm{\θ}}_1& \cos {\mathrm{\θ}}_1\end{array}\right]$

According to above-mentioned model, then the direction vector V of starlight vector under sensor coordinate M ₁be expressed as:

V ₁＝R _r*R _w*V ₀

Order $V_1=\left[\begin{array}{c}{v}_{11}\\ v_{12}\\ v_{13}\end{array}\right],$ Can obtain as calculated:

v ₁₁＝z ₀cosαcosβcosω ₂+z ₁sinαcosβcosω ₂+z ₂sinβcosω ₂+z ₃cosαcosβcosω ₁sinω ₂

+z ₄sinαcosβcosω ₁sinω ₂+z ₅sinβcosω ₁sinω ₂+z ₆cosαcosβsinω ₁sinω ₂

+z ₇sinαcosβsinω ₁sinω ₂+z ₈sinβsinω ₁sinω ₂

v ₁₂＝-z ₀cosα ₁cosβsinω ₂-z ₁sinαcosβsinω ₂-z ₂sinβsinω ₂+z ₃cosα ₁cosβcosω ₁cosω ₂

+z ₄sinαcosβcosω ₁cosω ₂+z ₅sinβcosω ₁cosω ₂+z ₆cosαcosβsinω ₁cosω ₂

+z ₇sinαcosβsinω ₁cosω ₂+z ₈sinβsinω ₁cosω ₂

v ₁₃＝-z ₃cosαcosβsinω ₁-z ₄sinαcosβsinω ₁-z ₅sinβsinω ₁+z ₆cosαcosβcosω ₁

+z ₇sinαcosβcosω ₁+z ₈sinβcosω ₁

2.3 prismatic reflection Vector Modelings

Define through the reflection of optics four prism surface laggard enter the vector of optical lens be prismatic reflection vector V _r.The factor affecting prismatic reflection vector mainly comprises the normal vector N of corresponding edge mirror plane ₁(being assumed to be visual field 1), prism incidence vector V ₁.

Optics four prism has four reflectings surface, and the present invention takes the method for demarcating respectively, is introduced here for the reflecting surface of visual field 1 correspondence, and other reflectings surface are demarcated can adopt same method.As shown in Figure 5, timing signal is being carried out to the prism planes of visual field 1 correspondence, supposing that the normal vector of this this plane of reflection under global coordinate system is N ₁:

$N_1=\left[\begin{array}{c}\cos \mathrm{\φ}\cos \mathrm{\γ}\\ \cos \mathrm{\φ}\sin \mathrm{\γ}\\ \sin \mathrm{\φ}\end{array}\right]$

Wherein φ, γ class right ascension of normal vector under global coordinate system and class declination for this reason.

Incident vector incides four prism surfaces, through reflecting to form prismatic reflection vector V _r.As shown in Figure 6, according to mirror-reflection relation, prism incidence vector V ₁, prismatic reflection vector V _rwith visual field 1 planar process vector N ₁number take advantage of and can form isosceles triangle ABC:

$\mathrm{\λ}{\stackrel{\→}{N}}_1={\stackrel{\→}{V}}_r-{\stackrel{\→}{V}}_1$

In Δ ABC, according to the cosine law

$\begin{array}{c}{\mathrm{BC}}^2={\mathrm{\λ}}^2={\mathrm{AB}}^2+{\mathrm{AC}}^2-2\mathrm{AB}*\mathrm{AC}*\cos {\mathrm{\θ}}_1\\ ={\left|{\stackrel{\→}{V}}_1\right|}^2+{\left|{\stackrel{\→}{V}}_r\right|}^2-2\left|{\stackrel{\→}{V}}_1\right|\left|{\stackrel{\→}{V}}_r\right|\cos \mathrm{\θ}\end{array}$

According to angular relationship:

θ ₁＝π-2θ ₂

For vector N ₁with V ₁angle:

${\mathrm{\θ}}_3=\arccos \frac{{\stackrel{\→}{V}}_2*{\stackrel{\→}{N}}_1}{\left|{\stackrel{\→}{V}}_2\right|\left|{\stackrel{\→}{N}}_1\right|}$

According to angular relationship:

θ ₂＝π-θ ₃

More than simultaneous variously can to obtain:

$V_r=V_1-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{N}_1$

If $V_r=\left[\begin{array}{c}{r}_1\\ r_2\\ r_3\end{array}\right],$ $N_1=\left[\begin{array}{c}{n}_{11}\\ n_{12}\\ n_{13}\end{array}\right],$ Then have:

$r_1=v_{11}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{11}$

$r_2=v_{12}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{12}$

$r_3=v_{13}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{13}$

Calculate:

r ₁＝sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂+cosαcosβ(z ₀cosω ₂+z ₃cosω ₁sinω ₂+

z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₁+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)-cosφcosγ(2sinφ

(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁)+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))

+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ(z ₃cosω ₁cosω ₂

-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂+z ₇cosω ₂sinω ₁))

+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂)+cosαcosβ(z ₀cosω ₂

+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₂+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)))

r ₂＝sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ(z ₃cosω ₁cosω ₂-z ₀sinω ₂+

z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₄-z ₁sinω ₂+z ₇cosω ₂sinω)-cosφsinγ

(2sinφ(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃cosω ₂+cosβsinα(z ₇cosω ₁-

z ₄sinω ₁))+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ

(z ₃cosω ₁cosω ₂-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂+z ₇cosω ₂sinω ₁))

+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂)+cosαcosβ

(z ₀cosω ₂+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₂+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)))

r ₃＝sinβ(z ₈cosω ₁-z ₅sinω ₁)-sinγ(2sinφ(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁)

+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+

cosαcosβ(z ₃cosω ₁cosω ₂-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂

+z ₇cosω ₂sinω ₁))+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂)+z ₈sinω ₁sinω ₂)+

cosαcosβ(z ₀cosω ₂+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+sinαcosβ(z ₁cosω ₂+z ₄cosω ₁sinω ₂

+z ₇sinω ₁sinω ₂)))+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))

2.4 perspective projection imaging modelings

According to Fig. 4, reflection vector light enters the imaging process of lens on imageing sensor target surface can be divided into linear process and non-linear process, and wherein linear process is perspective projection imaging process, and non-linear process is lens distortion imaging.The principal element affecting subpoint position in imaging process has optics principal point, lens focus f and distortion coefficients of camera lens, and these parameters obtain in the calibration process of first step list sensor, and its main meaning is as follows:

A. (X ₀, Y ₀) be optics principal point, be the optical axis of sensor lens combination and the intersection point of image device imaging surface;

B.f is lens focus, and unit is mm, i.e. the effective focal length of optical system of star sensor;

C. (p ₁, p ₂, q ₁, q ₂) be distortion coefficients of camera lens, in order to describe the distortion model of optical system of star sensor; Wherein q ₁, and q ₂the coefficient of radial distortion on 1 rank and 2 rank respectively, p ₁and p ₂1 rank and 2 rank decentering distortion coefficients;

D. (Dx, Dy) is pixel dimension, and unit is mm.

$\left\{\begin{array}{c}{x}^{\′}=-f\frac{v_{11}}{v_{13}}\frac{1}{\mathrm{Dx}}+X_0\\ y^{\′}=-f\frac{v_{12}}{v_{13}}\frac{1}{\mathrm{Dy}}+Y_0\end{array}\right.$

$\left\{\begin{array}{c}x=x^{\′}+\mathrm{\δx}\\ y=y^{\′}+\mathrm{\δy}\end{array}\right.$

The second order distortion model adopted is:

$\left\{\begin{array}{c}\mathrm{\δx}=\stackrel{\‾}{x}(q_1{r}^2+q_2{r}^4)+[p_1(r^2+2{\stackrel{\‾}{x}}^2)+2p_2\stackrel{\‾}{\mathrm{xy}}]\\ \mathrm{\δy}=\stackrel{\‾}{y}(q_1{r}^2+q_2{r}^4)+[p_2(r^2+2{\stackrel{\‾}{y}}^2)+2p_1\stackrel{\‾}{\mathrm{xy}}]\end{array}\right.$

Wherein:

$\left\{\begin{array}{c}\stackrel{\‾}{x}=x^{\′}-X_0\\ \stackrel{\‾}{y}=y^{\′}-Y_0\\ r^2={\stackrel{\‾}{x}}^2+{\stackrel{\‾}{y}}^2\end{array}\right.$

According to above-mentioned model, can by image asterism calculate reflection vector ${\stackrel{\‾}{V}}_r=\left[\begin{array}{c}\stackrel{\‾}{r_1}\\ \stackrel{\‾}{r_2}\\ \stackrel{\‾}{r_3}\end{array}\right].$

2.5 data acquisitions and data processing

By above modeling process, establish turntable angle position (θ ₁, θ ₂, θ ₃) to the corresponding relation of asterism image coordinate (x, y).By gathering many group turntable angles and image coordinate, utilize nonlinear least square method can simulate the prism parameters of sensor.

2.5.1

When image data, according to rule shown in Fig. 7, the outer shaft from-6 to+6 rotating three-axle table is spent, and axis, from 0 to 12 degree, at interval of being once a collection position, and gathers n secondary data at each collection position.N desirable 20 ~ 200, records revolving table position at that time simultaneously, and order rotation turntable makes imaging point be covered with visual field, then using its mean value as current asterism position data.

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

$\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i$

Wherein, x _i, y _ifor collecting the imager coordinate of asterism at every turn, for the mean value after n collection.

2.5.2

After collection many groups turntable and asterism data, need to calculate prism incidence vector and reflection vector.Overall calculation process as shown in Figure 8.

The turntable coordinate utilizing (2.5.1) to record, can calculate prism incidence vector corresponding to different turntable coordinate, namely by turntable angle (θ according to prism incidence vector model (2.2) ₁, θ ₂, θ ₃) calculate prism incidence vector $V_1=\left[\begin{array}{c}{v}_{11}\\ v_{12}\\ v_{13}\end{array}\right].$

The asterism image coordinate utilizing (2.5.1) to obtain, calculates prismatic reflection vector corresponding to different asterism coordinate according to perspective projection imaging model (2.4).Namely by asterism position calculate prismatic reflection vector ${\stackrel{\‾}{V}}_r=\left[\begin{array}{c}\stackrel{\‾}{r_1}\\ \stackrel{\‾}{r_2}\\ \stackrel{\‾}{r_3}\end{array}\right].$

2.5.3

The second step that two-step approach demarcates complex optics sensor mainly contains 4 parameters, with vector represent that these parameters are: can obtain according to above-mentioned 2.4 joint prismatic reflection models:

$V_r=V_1-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{N}_1=F\left(\stackrel{\→}{x}\right)$

That is: $r_1=v_{11}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{11}=F_{r_1}\left(\stackrel{\→}{x}\right)$

$r_2=v_{12}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{12}=F_{r_2}\left(\stackrel{\→}{x}\right)$

$r_3=v_{13}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{13}=F_{r_3}\left(\stackrel{\→}{x}\right)$

Wherein $N_1=\left[\begin{array}{c}{n}_{11}\\ n_{12}\\ n_{13}\end{array}\right].$

Suppose that the estimated value of the reflection vector calculated according to model is ${\hat{V}}_r=\left[\begin{array}{c}{\hat{r}}_1\\ {\hat{r}}_2\\ {\hat{r}}_3\end{array}\right],$ Due to be nonlinear function, non-linear least square alternative manner can be adopted to carry out estimated parameter vector if for vectorial estimated bias, then have:

$\mathrm{\Δ}{r}_1=\stackrel{\‾}{r_1}-{\hat{r}}_1=\mathrm{A\Δ}\stackrel{\→}{x}$

$\mathrm{\Δ}{r}_2=\stackrel{\‾}{r_2}-{\hat{r}}_2=\mathrm{B\Δ}\stackrel{\→}{x}$

$\mathrm{\Δ}{r}_3=\stackrel{\‾}{r_3}-{\hat{r}}_3=\mathrm{C\Δ}\stackrel{\→}{x}$

$A=(\frac{\∂F_{r_1}}{\∂\mathrm{\α}},\frac{\∂F_{r_1}}{\∂\mathrm{\β}},\frac{\∂F_{r_1}}{\∂\mathrm{\γ}},\frac{\∂F_{r_1}}{\∂\mathrm{\φ}})$

$B=(\frac{\∂F_{r_2}}{\∂\mathrm{\α}},\frac{\∂F_{r_2}}{\∂\mathrm{\β}},\frac{\∂F_{r_2}}{\∂\mathrm{\γ}},\frac{\∂F_{r_2}}{\∂\mathrm{\φ}})$

$C=(\frac{\∂F_{r_3}}{\∂\mathrm{\α}},\frac{\∂F_{r_3}}{\∂\mathrm{\β}},\frac{\∂F_{r_3}}{\∂\mathrm{\γ}},\frac{\∂F_{r_3}}{\∂\mathrm{\φ}})$

Here A, B are sensitive matrix, suppose that participating in calculating asterism number is m, order

$P=\left(\begin{array}{c}\mathrm{\Δ}{r}_{11}\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{r}_{1m}\\ \mathrm{\Δ}{r}_{21}\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{r}_{2m}\\ \mathrm{\Δ}{r}_{31}\\ \·\\ \·\\ \·\\ \mathrm{\Δ}{r}_{3m}\end{array}\right),M=\left(\begin{array}{c}{A}_1\\ \·\\ \·\\ \·\\ A_m\\ B_1\\ \·\\ \·\\ \·\\ B_m\\ C_1\\ \·\\ \·\\ \·\\ C_m\end{array}\right)$

Here the vector that is made up of the offset on three directions of P, M is the overall sensitive matrix of A, B, C tri-sensitive matrixs compositions,

Then there is iterative equation:

$\mathrm{\Δ}{\stackrel{\→}{x}}^{(k+1)}=\mathrm{\Δ}{\stackrel{\→}{x}}^{\left(k\right)}-{\left(M_k^T{M}_k\right)}^{-1}{M}_k^T{P}^{\left(k\right)}$

Wherein k is iteration sequence number, the stationary value after iteration terminates, and is the parameter calibration result of second step.The result of the comprehensive first step and second step, just can obtain the calibration value of all parameters, completes the demarcation to complex optics sensor.

Emulation and interpretation of result

The present invention adopt the basic parameter of many visual fields complex optics sensor as follows:

Visual field:

Pixel array: 1024 × 102 ∠

Pixel dimension: 0.0055mm × 0.0055mm

Focal length: 16mm

First traditional scaling method is adopted to carry out the demarcation of first step list sensor parameter, asterism number 100, each asterism station acquisition 100 secondary data.The parametric results obtained is demarcated as shown in table 1 through the first step.

Table 1 first step calibrating parameters result

In above-mentioned parameter, ψ ₁, ψ ₂for the starlight vector initial alignment deviation in first step calibration process, be respectively sensor and prolong turntable zero-bit coordinate system X _raxle, Y _raxle, Z _ralignment error on its axle, p ₁, p ₂, q ₁, q ₂for distortion coefficients of camera lens.

Then utilize above-mentioned data, second step calibration process is emulated.Bring above each parameter value into prism incidence vector model and perspective projection model, each numerical value needed for second step can be obtained.When second step emulates, emulation asterism number 169, the starlight direction that setting single file starlight analog device occurs turning the coordinate under initial coordinate system N is:

α＝-90°

β＝0°

The normal vector direction of prism first reflecting surface:

γ＝-45°

φ＝-135°

The result that final emulation obtains is as shown in table 2 below.

Table 2 second step calibrating parameters result

When not adding noise, the iterative process of parameter is as shown in table 3 below:

Solution process under table 3 noise-free case

Iterations	α	β	γ	φ
					1	-90.4829282170376	7.65589048154405	-45.8232671708237	-135.038766847946
2	-89.9868738731705	3.79852865739226	-48.0968931961025	-134.987051625700
					3	-89.9998128035864	1.81910651865815	-49.0890586095482	-134.999806050946
4	-89.9999984302528	0.807849932575455	-49.5954606570209	-134.999998344193
					5	-89.9999999933001	0.326847344511042	-49.8363278357344	-134.999999992827
6	-89.9999999999871	0.126899373289438	-49.9364537551969	-134.999999999986
					7	-90.0000000000000	0.0488737763154895	-49.9755259026622	-135.000000000000
8	-90	0.0188033614024913	-49.9905840002326	-135
					9	-90	0.00723375273135167	-49.9963776144894	-135
10	-90	0.00278292405861988	-49.9986064184489	-135
					11	-90	0.00107064605555464	-49.9994638615386	-135
12	-90	0.000411901718484022	-49.9997937354233	-135
					13	-90	0.000158468356804821	-49.9999206451268	-135
14	-90	6.09666033977422e-05	-49.9999694702641	-135
					15	-90	2.34553348794335e-05	-49.9999882544682	-135
16	-90	9.02383927195226e-06	-49.9999954812075	-135
					17	-90	3.47169044910738e-06	-49.9999982615106	-135

As seen from the above table under noise-free case, comparatively accurate result can be obtained through 17 iteration, substantially identical with emulation setting value.

Need to consider the introducing of noise in actual alignment process, its generation mainly contains two kinds of modes, and a kind of is picture noise because imaging and asterism center coordination cause, and another kind of noise is that turntable precision causes.At emulation generation 169 points, reflection vector adds that average is 0, and standard deviation is the white Gaussian noise of 1 rad, and for simulating actual noise, computation process is as shown in table 4 below:

Table 4 adds solution process under noise situations

Iterations	α	β	γ	φ
					1	-90.1630594012960	1.99580258626777	-48.9308417881941	-135.027433380954
2	-89.9990527093928	0.912700067667111	-49.5428548350697	-134.998730256157
					3	-89.9998208190054	0.379594845002274	-49.8099000062779	-134.999703028728
4	-89.9998252772507	0.152384726648931	-49.9236777381909	-134.999707996842
					5	-89.9998251598955	0.0620151329065337	-49.9689312712840	-134.999707902778
6	-89.9998251105641	0.0266031973187102	-49.9866641949034	-134.999707862658
					7	-89.9998250913154	0.0127550328605804	-49.9935988222272	-134.999707847051
8	-89.9998250837905	0.00734036644275169	-49.9963102791897	-134.999707840954
					9	-89.9998250808480	0.00522312443447393	-49.9973705127551	-134.999707838570
10	-89.9998250796974	0.00439521357833227	-49.9977850987614	-134.999707837638
					11	-89.9998250792474	0.00407146843371694	-49.9979472179164	-134.999707837273
12	-89.9998250790715	0.00394487076850668	-49.9980106131732	-134.999707837131
					13	-89.9998250790027	0.00389536575076853	-49.9980354033881	-134.999707837075

Numerical value about tends towards stability through 13 iterative process.Can find out that the method still can well restrain under noise situations according to above-mentioned simulation result, estimated value and the actual value deviation of the minute surface normal vector obtained based on least square method are very little.

The Accuracy Assessment adopted in emulation is: bring the estimated value calculated into model, the corresponding one group of turntable corner of each reflection vector, and the turntable corner calculated by contrast simulation and actual turntable corner, can calculate the RMS angle error of demarcation.This scaling method stated accuracy is 2.36 ＂ to utilize above-mentioned Accuracy Assessment to draw, suitable with the Gaussian noise levels introduced.Stated accuracy of the present invention meets the demands as can be seen here, is applicable to the demarcation of many visual fields complex optics sensor.

There is provided above embodiment to be only used to describe object of the present invention, and do not really want to limit the scope of the invention.Scope of the present invention is defined by the following claims.Do not depart from spirit of the present invention and principle and the various equivalent substitutions and modifications made, all should contain within the scope of the present invention.

Claims (2)

1. a caliberating device for the complex optics sensor of visual field more than, is characterized in that comprising: three axle high precision turntable, single star optical simulator, for supporting the marble platform of single star simulator, data handling machine and many visual fields complex optics sensor; Wherein single star optical simulator level is arranged in marble platform, many visual fields complex optics sensor is arranged on three-dimensional high-precision turntable, the main optical axis of complex optics sensor is parallel to the interior axle of three axle high precision turntable, and the starlight direction that single star optical simulator sends is perpendicular to the axis of three axle high precision turntable.

2. the scaling method of the sensor of visual field complex optics more than a kind, it is characterized in that: the demarcation of many visual fields complex optics sensor is carried out in two steps, be respectively single sensor calibration and composite sensing device integral calibrating, described single sensor refers to the part of many visual fields complex optics sensor removing optical prism; Installation parameter and the inner parameter of single sensor is obtained after carrying out first step list sensor calibration, result is substituted in second step composite sensing device integral calibrating and participate in iterative computation, utilize Non-linear least-square curve fitting to go out prism parameters, specific implementation step is as follows:

(1) demarcation of single sensor

Utilize three-axle table to demarcate single sensor, carrying out first step timing signal, many visual fields optical sensor does not install optical prism, is referred to as single sensor.Adjustment three-axle table axis, makes the optical axis of single sensor parallel with single star simulator starlight incident direction, utilizes the scaling method of star sensor to obtain the alignment error matrix of single sensor, focal length, the parameters such as optics principal point and distortion coefficients of camera lens;

(2) integral calibrating of many visual fields complex optics sensor

On the basis of step (1), keep the installation site of single sensor constant and correct installation optics four prism, adjustment three-axle table makes the starlight incident direction of the optical axis of complex optics sensor and single star simulator perpendicular, and demarcates as follows;

(2.1) surving coordinate system is set up

Set up sensor coordinate system and three-axle table zero-bit coordinate system, the angle that the transformational relation wherein between sensor coordinate system and three-axle table zero-bit coordinate system is turned over by three-axle table is determined;

Sensor coordinate system M is defined as: initial point O _mfor the optical centre of many visual fields complex optics sensor lens, X _mparallel with imageing sensor line direction, Y _mparallel with imageing sensor column direction, Z _malong the optical axis direction of lens of star sensor, determined by the right-hand rule, be denoted as: O _m-X _my _mz _m;

Turntable zero-bit coordinate system N is defined as: the coordinate system determined by rotation of rotary table axle under zero-bit state, and initial point is the centre of gyration of turntable, X _rfor the rotating shaft of three-axle table inner axis, Y _rfor the rotating shaft of turntable center axle, Z _rfor the rotating shaft of three-axle table housing axle is determined, be denoted as: O _r-X _ry _rz _r;

(2.2) prism incidence Vector Modeling

Define and to send and the starlight vector incided optics four prism surface is prism incidence vector V from single star optical simulator ₁.The factor affecting prism incidence vector comprises starlight vector initial alignment deviation V ₀, sensor installation deviation R _wwith turntable transition matrix R _r, between them, pass is:

V ₁＝R _r*R _w*V ₀

Order $V_1=\left[\begin{array}{c}{v}_{11}\\ v_{12}\\ v_{13}\end{array}\right],$ Can obtain as calculated:

v ₁₁＝z ₀cosαcosβcosω ₂+z ₁sinαcosβcosω ₂+z ₂sinβcosω ₂+z ₃cosαcosβcosω ₁sinω ₂

+z ₄sinαcosβcosω ₁sinω ₂+z ₅sinβcosω ₁sinω ₂+z ₆cosαcosβsinω ₁sinω ₂

+z ₇sinαcosβsinω ₁sinω ₂+z ₈sinβsinω ₁sinω ₂

v ₁₂＝-z ₀cosα ₁cosβsinω ₂-z ₁sinαcosβsinω ₂-z ₂sinβsinω ₂+z ₃cosα ₁cosβcosω ₁cosω ₂

+z ₄sinαcosβcosω ₁cosω ₂+z ₅sinβcosω ₁cosω ₂+z ₆cosαcosβsinω ₁cosω ₂

+z ₇sinαcosβsinω ₁cosω ₂+z ₈sinβsinω ₁cosω ₂

v ₁₃＝-z ₃cosαcosβsinω ₁-z ₄sinαcosβsinω ₁-z ₅sinβsinω ₁+z ₆cosαcosβcosω ₁

+z ₇sinαcosβcosω ₁+z ₈sinβcosω ₁

Wherein α, β are the class right ascension of starlight vector in coordinate system N and class declination; z ₀~ z ₈for R _wmatrix is from upper left to the element of bottom right, and its value is demarcated through (1) step and obtained; ω ₁for turntable is from the rotation angle of zero-bit state around axis, ω ₂for turntable is from the rotation angle of zero-bit around outer shaft;

(2.3) prismatic reflection Vector Modeling

Define through four prism surfaces reflections laggard enter the vector of optical lens be prismatic reflection vector V _r, the factor affecting prismatic reflection vector comprises the normal vector N of corresponding edge mirror plane ₁, be set to visual field 1, prism incidence vector V ₁,

According to the pass that plane reflection principle obtains between them be:

$V_r=V_1-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{N}_1$

Order $V_r=\left[\begin{array}{c}{r}_1\\ r_2\\ r_3\end{array}\right],$ Can obtain as calculated:

r ₁＝sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂+cosαcosβ(z ₀cosω ₂+z ₃cosω ₁sinω ₂+

z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₁+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)-cosφcosγ(2sinφ

(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁)+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))

+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ(z ₃cosω ₁cosω ₂

-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂+z ₇cosω ₂sinω ₁))

+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂)+cosαcosβ(z ₀cosω ₂

+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₂+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)))

r ₂＝sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ(z ₃cosω ₁cosω ₂-z ₀sinω ₂+

z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₄-z ₁sinω ₂+z ₇cosω ₂sinω)-cosφsinγ

(2sinφ(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃cosω ₂+cosβsinα(z ₇cosω ₁-

z ₄sinω ₁))+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+cosαcosβ

(z ₃cosω ₁cosω ₂-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂+z ₇cosω ₂sinω ₁))

+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂+z ₈sinω ₁sinω ₂)+cosαcosβ

(z ₀cosω ₂+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+cosβsinα(z ₁cosω ₂+z ₄cosω ₁sinω ₂+z ₇sinω ₁sinω ₂)))

r ₃＝sinβ(z ₈cosω ₁-z ₅sinω ₁)-sinγ(2sinφ(sinβ(z ₈cosω ₁-z ₅sinω ₁)+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁)

+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))+2cosφsinγ(sinβ(z ₅cosω ₁cosω ₂-z ₂sinω ₂+z ₈cosω ₂sinω ₁)+

cosαcosβ(z ₃cosω ₁cosω ₂-z ₀sinω ₂+z ₆cosω ₂sinω ₁)+cosβsinα(z ₄cosω ₁cosω ₂-z ₁sinω ₂

+z ₇cosω ₂sinω ₁))+2cosφcosγ(sinβ(z ₂cosω ₂+z ₅cosω ₁sinω ₂)+z ₈sinω ₁sinω ₂)+

cosαcosβ(z ₀cosω ₂+z ₃cosω ₁sinω ₂+z ₆sinω ₁sinω ₂)+sinαcosβ(z ₁cosω ₂+z ₄cosω ₁sinω ₂

+z ₇sinω ₁sinω ₂)))+cosαcosβ(z ₆cosω ₁-z ₃sinω ₁+cosβsinα(z ₇cosω ₁-z ₄sinω ₁))

(2.4) perspective projection imaging modeling

Reflection vector light enters the imaging process of lens on imageing sensor target surface and regards perspective projection as, and its imaging point position is:

$\left\{\begin{array}{c}x=-f\frac{v_{11}}{v_{13}}\frac{1}{\mathrm{Dx}}+X_0+\stackrel{\‾}{x}(q_1{r}^2+q_2{r}^4)+[p_1(r^2+2{\stackrel{\‾}{x}}^2)+2p_2\stackrel{\‾}{\mathrm{xy}}]\\ y=-f\frac{v_{12}}{v_{13}}\frac{1}{\mathrm{Dy}}+Y_0+\stackrel{\‾}{y}(q_1{r}^2+q_2{r}^4)+[p_2(r^2+2{\stackrel{\‾}{y}}^2)+2p_1\stackrel{\‾}{\mathrm{xy}}]\end{array}\right.$

$\left\{\begin{array}{c}\stackrel{\‾}{x}=x^{\′}-X_0\\ \stackrel{\‾}{y}=y^{\′}-Y_0\\ r^2={\stackrel{\‾}{x}}^2+{\stackrel{\‾}{y}}^2\end{array}\right.$

Wherein, f is lens focus, (X ₀, Y ₀) be optics principal point, unit is pixel; (Dx, Dy) is pixel dimension; p ₁, p ₂, p ₃, p ₄for distortion coefficients of camera lens;

(2.5) data acquisition and data processing

Above model establishes turntable angle position, composite sensing device parameters states the corresponding relation with asterism image coordinate, by gathering the asterism image coordinate under different revolving table position, utilizes nonlinear least square method can simulate the parameters of sensor;

(2.5.1)

Rotating table outer shaft and interior axle, be asterism linear be covered with whole visual field, a station acquisition n secondary data, n gets 100 ~ 1000, and records turntable coordinate position at that time simultaneously,

Formula is:

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

$\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i$

(2.5.2)

The turntable coordinate utilizing (2.5.1) to record, calculates prism incidence vector corresponding to different turntable coordinate, namely by turntable angle (θ according to prism incidence vector model (2.2) ₁, θ ₂, θ ₃) calculate prism incidence vector $V_1=\left[\begin{array}{c}{v}_{11}\\ v_{12}\\ v_{13}\end{array}\right];$

The asterism image coordinate utilizing (2.5.1) to obtain, calculates prismatic reflection vector corresponding to different asterism coordinate, namely by asterism position according to perspective projection imaging model (2.4) calculate prismatic reflection vector ${\stackrel{\‾}{V}}_r=\left[\begin{array}{c}\stackrel{\‾}{r_1}\\ \stackrel{\‾}{r_2}\\ {\stackrel{\‾}{r}}_3\end{array}\right];$

(2.5.3)

The second step that two-step approach demarcates complex optics sensor mainly contains 4 parameters, with vector represent that these parameters are: obtain according to above-mentioned (2.4) prismatic reflection model:

$V_r=V_1-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{N}_1=F\left(\stackrel{\→}{x}\right)$

That is: $r_1=v_{11}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{11}=F_{r_1}\left(\stackrel{\→}{x}\right)$

$r_2=v_{12}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{12}=F_{r_2}\left(\stackrel{\→}{x}\right)$

$r_3=v_{13}-2\frac{V_1*{N_1}^T}{\left|V_1\right|*\left|N_1\right|}{n}_{13}=F_{r_3}\left(\stackrel{\→}{x}\right)$

Wherein $N_1=\left[\begin{array}{c}{n}_{11}\\ n_{12}\\ n_{13}\end{array}\right],$

Suppose that the estimated value of the reflection vector calculated according to model is ${\hat{V}}_r=\left[\begin{array}{c}{\hat{r}}_1\\ {\hat{r}}_2\\ {\hat{r}}_3\end{array}\right],$ Due to be nonlinear function, adopt non-linear least square alternative manner to carry out estimated parameter vector if for vectorial estimated bias, then have:

${\mathrm{\Δr}}_1=\stackrel{\‾}{r_1}-{\hat{r}}_1=\mathrm{A\Δ}\stackrel{\→}{x}$

${\mathrm{\Δr}}_2=\stackrel{\‾}{r_2}-{\hat{r}}_2=\mathrm{B\Δ}\stackrel{\→}{x}$

${\mathrm{\Δr}}_3=\stackrel{\‾}{r_3}-{\hat{r}}_3=\mathrm{C\Δ}\stackrel{\→}{x}$

$A=(\frac{{\∂F}_{r_1}}{\∂\mathrm{\α}},\frac{{\∂F}_{r_1}}{\∂\mathrm{\β}},\frac{{\∂F}_{r_1}}{\∂\mathrm{\γ}},\frac{{\∂F}_{r_1}}{\∂\mathrm{\φ}})$

$B=(\frac{{\∂F}_{r_2}}{\∂\mathrm{\α}},\frac{{\∂F}_{r_2}}{\∂\mathrm{\β}},\frac{{\∂F}_{r_2}}{\∂\mathrm{\γ}},\frac{{\∂F}_{r_2}}{\∂\mathrm{\φ}})$

$A=(\frac{{\∂F}_{r_3}}{\∂\mathrm{\α}},\frac{{\∂F}_{r_3}}{\∂\mathrm{\β}},\frac{{\∂F}_{r_3}}{\∂\mathrm{\γ}},\frac{{\∂F}_{r_3}}{\∂\mathrm{\φ}})$

Here A, B are sensitive matrix, suppose that participating in calculating asterism number is m, order

$P=\left(\begin{array}{c}{\mathrm{\Δr}}_{11}\\ .\\ .\\ .\\ {\mathrm{\Δr}}_{1m}\\ {\mathrm{\Δr}}_{21}\\ .\\ .\\ .\\ {\mathrm{\Δr}}_{2m}\\ {\mathrm{\Δr}}_{31}\\ .\\ .\\ .\\ {\mathrm{\Δr}}_{3m}\end{array}\right),M=\left(\begin{array}{c}{A}_1\\ .\\ .\\ .\\ A_m\\ B_1\\ .\\ .\\ .\\ B_m\\ C_1\\ .\\ .\\ .\\ C_m\end{array}\right)$

Here the vector that is made up of the offset on three directions of P, M is the overall sensitive matrix of A, B, C tri-sensitive matrixs compositions,

Then there is iterative equation:

$\mathrm{\Δ}{\stackrel{\→}{x}}^{(k+1)}={\mathrm{\Δ}\stackrel{\→}{x}}^{\left(k\right)}-{\left(M_k^T{M}_k\right)}^{-1}{M}_k^T{P}^{\left(k\right)}$

Wherein k is iteration sequence number, the stationary value after iteration terminates, and is the parameter calibration result of second step, the result of the comprehensive first step and second step, just can obtains the calibration value of all parameters, complete the demarcation to complex optics sensor.