CN102519471A - Imaging type earth sensor earth oblateness compensation method based on trigonometric function fitting - Google Patents

Abstract

The invention relates to an imaging type earth sensor earth oblateness compensation method based on trigonometric function fitting. First, geocentric direction measurement of the imaging type earth sensor is modeled; the influence of earth oblateness is not considered; the geocentric direction is calculated according to the geometrical center coordinate of an earth imaging border point on a CCD plane. When the influence of the earth oblateness is considered, an actual image point of geocentre imaging is deviated from the geometrical center, such that a geocentre measuring vector is deviated from an actual vector; the deviation is decomposed into a rolling error angle and a pitch error angle; with a trigonometric function, the rolling error angle and the pitch error angle are fitted, such that a coefficient corresponding to the trigonometric function is obtained; with the calculation result of the trigonometric function, the geometrical center coordinate is compensated; and a geocentric direction is calculated with the compensated coordinate. The method is advantaged in simple operation method. With the method, more precise geocentric direction measurement information can be provided.

Description

Imaging-type earth sensor compression of the earth compensation method based on the trigonometric function match

Technical field

The invention belongs to the aerospace optical remote sensing technical field, relate to the compensation method of a kind of imaging-type earth sensor compression of the earth, particularly a kind of imaging-type earth sensor compression of the earth compensation method based on the trigonometric function match.

Background technology

Carrying out independent navigation based on imaging-type earth sensor and star sensor is a kind of typical astronomical navigation method.Earth sensor can be confirmed the rolling and the pitch attitude of spacecraft through the measurement to the earth's core vector; Star sensor obtains the inertia attitude to star observation; The two combines just can confirm the position of spacecraft.

Usually think that the earth is the spheroid of standard in the measurement model of earth sensor, and the true form of the earth is approximately the spheroid of little ellipticity, the existence of compression of the earth makes the earth sensor measured value have systematic error.At present; The compression of the earth modification method mainly is to the scan-type earth sensor; Paper " based on the correction algorithm of the infrared earth sensor measured value of earth ellipsoid characteristic " as Li Jie delivers on the Aerospace Control of 1997 the 15th the 4th phases of volume adopts the single order correction algorithm that the compression of the earth error is revised.

The basic functional principle of imaging-type earth sensor is according to the marginal point set of imaging imaging center to be carried out match.Often ignore compression of the earth in the former studies,, think that the geometric center after the match is exactly the picture point of ground ball center on the CCD plane, utilize this point to calculate the earth's core direction vector with standard round or standard ellipse model as edge fitting.Because the figure of the earth is not the spheroid of standard, when considering compression of the earth, earth imaging is complicated more, is not simple quafric curve, so the vector that directly utilizes the geometric center after the match to calculate not necessarily overlaps with true the earth's core vector.Because the imaging-type earth sensor is different with scan-type earth sensor principle of work, so the compensation method of compression of the earth also is very different.At present also as yet not relevant for the compensation method of imaging-type earth sensor compression of the earth.

Summary of the invention

Technology of the present invention is dealt with problems and is: the deficiency that overcomes prior art; A kind of imaging-type earth sensor compression of the earth compensation method based on the trigonometric function match is provided; Effectively overcome the influence that compression of the earth is measured the earth's core; Improve the earth's core orientation measurement precision, further improved accuracy of navigation systems.

Technical solution of the present invention is: based on the imaging-type earth sensor compression of the earth compensation method of trigonometric function match, step is following:

The first step is carried out modeling to imaging-type earth sensor the earth's core orientation measurement, and formula is following

$u_s=\frac{1}{\sqrt{x_s^2+y_s^2+f}}\left[\begin{array}{c}{-x}_s\\ -y_s\\ f\end{array}\right]---\left(1\right)$

Second step; Do not consider earlier compression of the earth; Utilize the coordinate Calculation of marginal point on imaging-type earth sensor CCD plane of earth imaging to obtain the marginal point geometric center, think the coordinate of the earth's core to this geometric center point, calculate the earth's core direction u according to modeling formula (1) on the CCD plane _s

Wherein, f is the focal length of imaging-type earth sensor lens, (x _s, y _s) be the coordinate of the earth's core in the CCD plane coordinate system;

The 3rd step, consider the compression of the earth influence, must arrive the earth's core and be imaged on the true picpointed coordinate (x in CCD plane _e, y _e), will measure the earth's core direction and true the earth's core direction ratio, utilize formula (2) structure roll error angle

With pitch error angle θ _m:

The 4th the step, through trigonometric function formula (3) to above-mentioned roll error angle

With pitch error angle θ _mCarry out match, obtain trigonometric function coefficient A ₁, A ₂And C ₁, C ₂,

Wherein u is argument of perigee and true anomaly sum,

And θ _aBe trigonometric function value;

The 5th goes on foot, and utilizes the result of calculation of formula (3)

And θ _a, edge point geometry centre coordinate is compensated, utilize formula (4) to obtain the closer true picpointed coordinate (x of the heart _e, y _e)

The 6th step is by compensation back coordinate (x _e, y _e) calculate according to modeling formula (1), obtain more accurate the earth's core direction u _e

$u_e=\frac{1}{\sqrt{x_e^2+y_e^2+f}}\left[\begin{array}{c}{-x}_e\\ -y_e\\ f\end{array}\right]---\left(5\right)$

The present invention's advantage compared with prior art is: the present invention is reduced to compression of the earth the difference of the true picpointed coordinate of geometric center coordinate and the earth's core of earth imaging marginal point to the influence of imaging-type earth sensor the earth's core orientation measurement; To measure the earth's core direction and true the earth's core direction ratio; Roll error angle and pitch error angle have been constructed; Carry out match with trigonometric function and obtain the trigonometric function coefficient; With trigonometric function result of calculation the geometric center coordinate is compensated again, thereby obtain the closer coordinate of the true picture point of the heart, can obtain more accurate the earth's core orientation measurement; Effectively overcome the influence that compression of the earth is measured the earth's core, further improved navigation accuracy; And simple to operate, be easy to realize.

Description of drawings

Fig. 1 is the process flow diagram of the inventive method;

Fig. 2 is an imaging-type earth sensor measurement coordinate system synoptic diagram;

Fig. 3 is earth ellipsoid face and Horizon floor map;

Fig. 4 is the earth sensor imaging geometry;

Fig. 5 is the synoptic diagram at roll angle sum of errors pitch error angle;

Fig. 6 is the coordinate comparison diagram of imaging geometry center and the true picture point in the earth's core before and after the compensation;

Fig. 7 is navigation filtering error comparison diagram before and after the compensation.

Embodiment

As shown in Figure 1, concrete implementation procedure of the present invention is following:

(1) definition coordinate system: geocentric inertial coordinate system (O-X _iY _iZ _i), initial point is positioned at earth centroid, and the XY face overlaps with the equatorial plane, X _iThe axle positive axis is pointed to the first point of Aries, Z _iAxle with the directed north direction for just, Y _iAxle becomes right-handed coordinate system with XZ.Imaging-type earth sensor measurement coordinate system (O-X _sY _sZ _s), initial point is positioned at the center of perfect optics lens, Z _sAxle is along sensor optical axis direction, X _sAxle is perpendicular to optical axis and consistent with the CCD direction of line scan, Y _sAxle is consistent with CCD column scan direction, and constitutes right-handed coordinate system.CCD plane coordinate system (O-X _CCDY _CCDZ _CCD), initial point is positioned at center, CCD focal plane, and X axle, Y axle are parallel to the X and the Y axle of sensor coordinate system, and are unit measurement coordinate size with the pixel.

(2) imaging-type earth sensor the earth's core orientation measurement is carried out modeling, Fig. 2 is an imaging-type earth sensor measurement coordinate system synoptic diagram, by the coordinate (x of the earth's core in the CCD plane coordinate system _s, y _s), can calculate the expression of the earth's core direction under the sensor measurement coordinate system:

$u_s=\frac{1}{\sqrt{x_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HSA00000633149300032.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="y\; s"\; filenames="HSA00000633149300032.png"\; state="\{\{state\}\}">y</figure-callout>}}_s^{}+f}}\left[\begin{array}{c}{-x}_s\\ -y_s\\ f\end{array}\right]$

Wherein, f is the focal length of imaging-type earth sensor lens, (x _s, y _s) be the coordinate of the earth's core in the CCD plane coordinate system;

(3) figure of the earth is described as the rotation ellipsoid around the formation of earth pole axis, the equation of its surperficial E in the inertial system of equator, the earth's core does

$f(x,y,z)=x^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000633149300032.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+z^2(1+2\mathrm{\&epsiv;})-R_u^2=0$

Wherein ε is a compression of the earth, R _uBe earth ellipsoid radius under the line, x, y, z are respectively the coordinate figure of earth surface point at inertial system X, Y, Z.

If satellite S is respectively (u at the coordinate figure of earth inertial system X, Y, Z; V; W); Draw tangent line vector

from S to the earth and be tangential on P (x with the E curved surface; Y; Z) point; Surface normal vector

quadrature at and P point place obtains the Horizon plane equation, and note is made plane П

$g(x,y,z)=\mathrm{ux}+\mathrm{vy}+(1+2\mathrm{\&epsiv;})\mathrm{wz}-R_u^2=0$

As shown in Figure 3, the intersection of П plane and E curved surface is the earth outline line that observes on the satellite, and the point on the outline line is exactly the former picture point of earth imaging.The picpointed coordinate of point in the CCD plane by on the outline line utilizes the edge fitting algorithm to obtain the geometric center coordinate.When ignoring compression of the earth and think that the earth is standard ball, the earth is imaged as standard circular under the zero attitude, and geometric center overlaps with the true picture point in the earth's core.

(4) do not consider earlier compression of the earth; Utilize the coordinate Calculation of marginal point on imaging-type earth sensor CCD plane of earth imaging to obtain the marginal point geometric center; Think the coordinate of the earth's core to this geometric center point, calculate the earth's core direction u according to modeling formula (1) on the CCD plane _s

(5) consider the compression of the earth influence, must arrive the earth's core and be imaged on the true picpointed coordinate (x in CCD plane _e, y _e), not overlapping with imaging marginal point geometric center, the geometric relationship of sensor imaging is as shown in Figure 4.

If (x _s, y _s) be the geometric center of match, (x _e, y _e) being imago point truly, f is the focal length of sensor lens, will measure the earth's core direction and true the earth's core direction ratio, utilizes formula 2 structure roll error angles

With pitch error angle θ _m

(6)

θ _mChange curve be approximately trigonometric function, utilize trigonometric function to above-mentioned roll error angle

With pitch error angle θ _mTwo error angles carry out match, and trigonometric function is a formula 3

Wherein u is argument of perigee and true anomaly sum.

(7) utilize the result of calculation of formula (3)

And θ _a, edge point geometry centre coordinate is compensated, utilize formula (4) to obtain the closer true picpointed coordinate (x of the heart _e, y _e)

(8) by compensation back coordinate (x _e, y _e) calculate according to modeling formula (1), obtain more accurate the earth's core direction u _eBy coordinate Calculation the earth's core, compensation back direction

$u_e=\frac{1}{\sqrt{x_e^2+y_e^2+f}}\left[\begin{array}{c}{-x}_e\\ -y_e\\ f\end{array}\right]$

Embodiment

For the clearer advantage that shows this method, carry out mathematical simulation at this.Simulated conditions: satellite flight is on the circular orbit of about 500km.Satellite is zero attitude over the ground.Fig. 5 a is the roll error angle that the true roll angle error angle that causes of compression of the earth and trigonometric function match obtain; Fig. 5 b is the difference at the roll error angle of true roll error angle and trigonometric function match; Fig. 5 c is the pitch error angle that the true angle of pitch error angle that causes of compression of the earth and trigonometric function match obtain, and Fig. 5 d is the difference at the pitch error angle of true pitch error angle and trigonometric function match.Utilize trigonometric function result of calculation to compensate to calculating marginal point geometric center coordinate; Fig. 6 a for the X axial coordinate error ratio between geometric center and the true picture point in the earth's core before and after the compensation; Fig. 6 b for the Y axial coordinate error ratio between geometric center and the true picture point in the earth's core before and after the compensation, can find out that the geometric center after over-compensation obviously reduces with the error of coordinate of imago point truly.Fig. 7 a for the site error result that utilizes the earth's core direction before and after the compensation to be used for to navigate filtering relatively, Fig. 7 b for the velocity error result that utilizes the earth's core direction before and after the compensation to be used for to navigate filtering relatively.Can find out that from simulation result figure employing the inventive method has effectively improved the measuring accuracy of the earth's core direction after imaging-type earth sensor compression of the earth is compensated, thereby improves the satellite navigation precision.

The content of not doing to describe in detail in the instructions of the present invention belongs to those skilled in the art's known technology.

Claims (1)

1. based on the imaging-type earth sensor compression of the earth compensation method of trigonometric function match, it is characterized in that step is following:

The first step is carried out modeling to imaging-type earth sensor the earth's core orientation measurement, and formula is following

$u_s=\frac{1}{\sqrt{x_s^2+y_s^2+f}}\left[\begin{array}{c}{-x}_s\\ -y_s\\ f\end{array}\right]---\left(1\right)$

Second step; Do not consider earlier compression of the earth; Utilize the coordinate Calculation of marginal point on imaging-type earth sensor CCD plane of earth imaging to obtain the marginal point geometric center, think the coordinate of the earth's core to this geometric center point, calculate the earth's core direction u according to modeling formula (1) on the CCD plane _s

Wherein, f is the focal length of imaging-type earth sensor lens, (x _s, y _s) be the coordinate of the earth's core in the CCD plane coordinate system;

The 3rd step, consider the compression of the earth influence, must arrive the earth's core and be imaged on the true picpointed coordinate (x in CCD plane _e, y _e), will measure the earth's core direction and true the earth's core direction ratio, utilize formula (2) structure roll error angle

With pitch error angle θ _m:

The 4th the step, through trigonometric function formula (3) to above-mentioned roll error angle

With pitch error angle θ _mCarry out match, obtain trigonometric function coefficient A ₁, A ₂And C ₁, C ₂,

Wherein u is argument of perigee and true anomaly sum,

And θ _aBe trigonometric function value;

The 5th goes on foot, and utilizes the result of calculation of formula (3) And θ _a, edge point geometry centre coordinate is compensated, utilize formula (4) to obtain the closer true picpointed coordinate (x of the heart _e, y _e)

The 6th step is by compensation back coordinate (x _e, y _e) calculate according to modeling formula (1), obtain more accurate the earth's core direction u _e

$u_e=\frac{1}{\sqrt{x_e^2+y_e^2+f}}\left[\begin{array}{c}{-x}_e\\ -y_e\\ f\end{array}\right]---\left(5\right).$

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