CN1804659A - Method for capturing and tracing extended beacon for deep space optical communication - Google Patents

Abstract

The invention relates to a deep space optical communication expand sighting target capture tracing method, which relates to a processing method of expand sighting target picture. It attaches Gauss white noise on the noise justified approximation of the real sighting target picture and adopts least square method to capture the sighting target picture, ascertains the center location of the sighting target picture, makes the system to enter into the tracing model, and uses dissimilar Fourier transformation method and maximum likelihood method to compute the rotating angle and the moving value of the sighting target picture, then it can compute the center of the sighting target picture by the moving value and the rotating angle and update the optical communication end wire direction by the center location.

Description

A kind of method for capturing and tracing extended beacon for deep space optical communication

Technical field

The present invention relates to extended beacon treatment of picture method.

Background technology

Carrying out the passback of survey of deep space science data with laser is the developing direction of deep space communication, carrying out the severe challenge that the remote information transmission of deep space faces with laser is accurately to alignment request, existing deep space optical communication system based on the satellite optical communication system design with ground-launched up laser beam as beacon, but with up laser beam as beacon, not only need to adopt powerful laser instrument, and be vulnerable to the influence of atmosphere and the restriction of weather, can not satisfy the requirement of deep space optical communication link round-the-clock running, therefore, we consider to adopt nature celestial image (visual image or infrared image) as beacon.Because link is in operational process, optic terminal is always aimed at the ground direction of bowl on the aircraft, and therefore the most normal natural celestial body of selecting for use is the earth and near celestial body thereof.Because the imaging on the beacon detector of these celestial bodies always expands to a plurality of pixels, therefore, we are referred to as extended beacon.Adopt the nature celestial image as beacon, need not ground surface launching up light beam as alignment fiducials, therefore can make optic terminal on the aircraft keep the independence of relative up-link, make on the aircraft optic terminal avoid the influence of atmosphere and the restriction of weather, adopt the expansion celestial image as beacon simultaneously, its light intensity is relatively stable, and higher following rate can be provided.Owing to adopt the expansion celestial image, traditional will no longer adapt to this programme as the method for capturing and tracing of beacon based on up laser beam as beacon.

Adopt earth image as beacon, usually base area soccer star's ephemeris and aircraft ephemeris are determined the initial alignment direction, because aircraft ephemeris and earth ephemeris error, on the aircraft oligodynamics environment and surroundings influence, always there are certain error in initial alignment direction and actual aligning direction, therefore need be after the initial alignment direction be determined, earth image is caught and followed the tracks of, and the key of catching and following the tracks of earth image is to determine the center of earth image accurately, according to the relation of earth picture centre position and land station, determine the sighted direction of optical communication terminal receiving antenna on the aircraft.In this process, be wherein key problem to the research with track algorithm of catching of earth image.Classic method is always directly calculated and is obtained its center according to recording real image, does like this that error is very big, precision is low.

Summary of the invention

In order to solve the problem that precision was low, error is big when classic method was caught and followed the tracks of extended beacon, the invention provides a kind of method for capturing and tracing extended beacon for deep space optical communication.Extended beacon for deep space optical communication catch the foundation that is used for the deep space optical communication link, to catching of extended beacon, adopt antenna scanning to carry out the search of beacon in conjunction with the mode of picture element scan, the tracking of extended beacon is used for communication process and keeps the deep space optical communication link not interrupt.

Method for capturing and tracing extended beacon for deep space optical communication of the present invention carries out according to the following steps:

One, catches the extended beacon position according to the following steps:1. in the process of deep-space laser communication link establishment and operation, determine optical communication terminal initial alignment direction under the inertial coordinates system according to natural celestial body and aircraft ephemeris, this direction is pointed to the extended beacon that will catch; 2. the sighted direction vector in the above-mentioned inertial coordinates system is transformed on the star in the pitching coordinate system by coordinate transform, makes on the star that is controlled at aircraft of described communication beam and carry out in the pitching coordinate system; 3. according to the correlation technique parameter of spacecraft, determine planar field of view angle, uncertain region in conjunction with Principle of Statistics; 4. in above-mentioned uncertain region, carry out antenna scanning according to the predetermined angle interval; In scanning process; Antenna each location point on track while scan is stayed for some time; The regional imaging of beacon detector to aiming at; Then the true extension beacon image that obtains and the two-dimensional matrix that is pre-stored in intrasystem standard extended beacon image are carried out first respectively Fourier-Mellin transform and get the two magnitude matrix; The recycling quadratic interpolation is transformed into log-polar system with the magnitude matrix of the two; And calculate the error coefficient of said two devices magnitude matrix by following formula (1)

$L=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{[M_s(i,j)-M_F(i,j)]}^2---\left(1\right)$

In the following formula, L is the error coefficient of said two devices magnitude matrix, and M is the line number that is interpolated into matrix in the log-polar system, and N is for being interpolated into matrix column number in the log-polar system, M _S(i j) is the amplitude of the Fourier-Mellin transform of above-mentioned standard extended beacon image in log-polar system, M _F(i j) is the amplitude of the Fourier-Mellin transform of actual beacon image in log-polar system; Position when 5. the above-mentioned error coefficient of optical communication terminal antenna alignment of control detector is got minimum value is so finish acquisition procedure;

Two, the tracing process that after above-mentioned acquisition procedure finishes, enters extended beacon, the concrete steps of following the tracks of are as follows: I, the first time are when following the tracks of, with above-mentioned be pre-stored in intrasystem standard extended beacon image or above-mentioned catch finish after the beacon image of tracing process initial time as the reference picture of this secondary tracking, utilize detector to obtain to have taken place this moment the measuring image of the extended beacon of relative motion then; II, calculate in rectangular coordinate system measuring image with respect to the rotation angle of reference picture: A, regard measuring image as reference picture and additive gaussian white noise sum according to the following steps, real image and the reference picture that tracking is detected carries out discrete Fourier transform (DFT) and delivery respectively then, obtains the amplitude spectrum of above-mentioned two images; B, utilize quadratic interpolation to be transformed into the amplitude spectrum of real image and reference picture to obtain the magnitude matrix of above-mentioned two images under polar coordinate system under the polar coordinate system, and be by the magnitude matrix of following formula (2) calculating additive gaussian white noise under polar coordinate system,

G(m，n)＝M _R(m，n)-M ₁(m，n-k) (2)

In the following formula, (m n) is the amplitude two-dimensional matrix of additive gaussian white noise in polar coordinate system, M to G _R(m n) is the magnitude matrix of measuring image in the polar coordinate system, M ₁(m n-k) is the magnitude matrix of reference picture in the polar coordinate system, k be in the polar coordinate system measuring image with respect to reference picture angle translational movement (translation of angle shows in the rectangular coordinate to be the angle rotation in the polar coordinate system); It is that 0 Gaussian distribution and each spot noise figure are separate that each pixel of C, the definition magnitude matrix of above-mentioned additive gaussian white noise under polar coordinate system is obeyed average, and the maximum likelihood that calculates described angle translational movement k by following formula (3) is estimated then,

$\hat{k}=-\frac{N}{2\mathrm{\π}}\·\frac{\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\left|\mathrm{\ω}(m,n)\right|\mathrm{\ξ}}{\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}{n}^2\left|\mathrm{\ω}(m,n)\right|}---\left(3\right)$

In the following formula,

For the maximum likelihood of described angle translational movement k is estimated, | and ω (m, n) | be above-mentioned M _R(m, discrete Fourier transform (DFT) n) and above-mentioned M ₁(m, the mould that conjugation discrete Fourier transform (DFT) n-k) multiplies each other, ξ are ω (m, Fourier phase angle n); D, calculate in the rectangular coordinate real image with respect to the reference picture rotation angle by following formula (4),

${\mathrm{\θ}}_0=\frac{2\mathrm{\π}}{N}\·\hat{k}---\left(4\right)$

In the following formula, θ ₀Be the rotation angle of measuring image in the rectangular coordinate system with respect to reference picture, N is the image array columns after the interpolation, and its value is consistent with the N in the formula (1); III, calculate in the rectangular coordinate system measuring image with respect to the translational movement of reference picture: a, with above-mentioned rotation angle θ according to the following steps ₀The following formula of substitution (5) calculates the two-dimensional matrix of postrotational reference picture,

s ₂(m, n)=s (mcos θ ₀+ nsin θ ₀-x ₀,-msin θ ₀+ ncos θ ₀-y ₀) in (5) following formula, s ₂(m n) is the reference picture two-dimensional matrix after rotating, and (m n) is the initial reference image two-dimensional matrix to s, x ₀Be the horizontal ordinate translational movement of measuring image in the rectangular coordinate system with respect to reference picture, y ₀Be the ordinate translational movement of measuring image in the rectangular coordinate system with respect to reference picture; B, calculate in the rectangular coordinate system measuring image with respect to the horizontal ordinate translational movement and the ordinate translational movement of reference picture according to following formula (6),

$\left\{\begin{array}{c}-\frac{1}{2\mathrm{\π}}\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\left|\mathrm{\υ}(m,n)\right|\mathrm{\β}(m,n)=x_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\frac{m}{M}\left|\mathrm{\υ}(m,n)\right|+y_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\frac{n}{N}\left|\mathrm{\υ}(m,n)\right|\\ -\frac{1}{2\mathrm{\π}}\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\left|\mathrm{\υ}(m,n)\right|\mathrm{\β}(m,n)=x_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\frac{m}{M}\left|\mathrm{\υ}(m,n)\right|+y_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\frac{n}{N}\left|\mathrm{\υ}(m,n)\right|\end{array}\right.---\left(6\right)$

In the following formula, υ (m n) is conjugate matrices long-pending of the Fourier transform of postrotational reference picture and measuring image, | and υ (m, n) | ((m n) is υ (m, Fourier phase angular moment battle array n) to β for m, mould n) for υ; IV, according to the anglec of rotation and translational movement, determine the center of measuring image by following formula (7),

x _t＝x′cosθ ₀+y′sinθ ₀-x ₀ (7)

y _t＝-x′sinθ ₀+y′cosθ ₀-y ₀

In the following formula, (x ', y ') be the center of the used reference picture of this secondary tracking, (x _t, y _t) be the center of measuring image; V, with the center of the optical communication terminal antenna alignment of detector measuring image this moment, so just finished tracing process for the first time; VI, when following the tracks of next time, the extended beacon measuring image the surveyed reference picture as this secondary tracking will be followed the tracks of for the first time, utilize detector to obtain to have taken place this moment the measuring image of the extended beacon of relative motion then, repeat II to IV again and go on foot, and with the center of this secondary tracking measuring image of optical communication terminal antenna alignment of detector; All follow the tracks of the reference picture of the measuring image of acquisition in VII, the each tracing process afterwards, and adjust the aligning direction of detector optical communication terminal antenna according to the center of this secondary tracking measuring image that obtains as this secondary tracking with the last time.

Principle of work: the present invention is according to the vehicle technology parameter, determined the planar field of view angle, uncertain region of scanning in conjunction with Principle of Statistics, and utilize least square method to calculate the error coefficient L of reference picture and actual measurement image, after antenna scanning is finished, control antenna is aimed at the location point of L minimum, and at this moment, the beacon image enters detector field of view, determine the center of actual beacon image can think to capture this beacon image according to the reference picture that prestores in the system.In log-polar system, flexible and the rotation of image can be regarded in log-polar system the translation on two axles as, so character by Fourier transform, coordinate translation only influences the variation of its Fourier transform phase place, and do not influence the variation of its amplitude, therefore, its amplitude should have unchangeability, so for reference picture and measuring image, the amplitude of Fourier transform should have maximum correlation in log-polar system.After catching of beacon finished, system entered tracing mode, and at tracking phase, the groundwork of system is the sensing of adjusting antenna according to the motion of beacon, so the main task of tracing process is that motion to beacon compensates.The image that the present invention detects the beacon detector is regarded the form of reference picture and white Gaussian noise sum as, and the real image of surveying has certain translational movement and rotation angle with respect to reference picture, so when following the tracks of, must calculate translational movement and rotation angle between them respectively for the center of determining real image, at this moment the present invention introduces the angle translational movement k in the polar coordinate system, and utilizes statistical method and Fourier transform to calculate above-mentioned translational movement and rotation angle.

The invention effect: 1) method of the present invention is by dwindling detector field of view, improve measuring accuracy, adopting antenna scanning to carry out extended beacon in conjunction with the method for picture element scan to catch, save capture time, and the successful acquisition probability of beacon is more than 98%; 2) the present invention can control the tracking error of optical antenna in 5%.

Description of drawings

Fig. 1 is the reference beacon image of embodiment acquisition procedure, and Fig. 2 is the actual measurement beacon image of embodiment acquisition procedure, and Fig. 3 is the reference picture of embodiment tracing process, and Fig. 4 is the actual measurement beacon image of embodiment tracing process.

Embodiment

This embodiment serves as the extended beacon that will survey with the natural celestial body earth, and according to the following steps it is carried out acquisition and tracking:the position of, catching the earth according to the following steps:1. in the process of deep-space laser communication link establishment and operation, determine optical communication terminal initial alignment direction under the inertial coordinates system according to natural celestial body and aircraft ephemeris, this direction is pointed to the extended beacon that will catch; 2. the sighted direction vector in the above-mentioned inertial coordinates system is transformed on the star in the pitching coordinate system by coordinate transform, makes on the star that is controlled at aircraft of described communication beam and carry out in the pitching coordinate system; 3. according to the correlation technique parameter of spacecraft, determine planar field of view angle, uncertain region in conjunction with Principle of Statistics; 4. in above-mentioned uncertain region, carry out antenna scanning according to the predetermined angle interval; In scanning process; Antenna each location point on track while scan is stayed for some time; The regional imaging of beacon detector to aiming at; The actual earth image that then will obtain carries out first respectively Fourier-Mellin transform with the two-dimensional matrix that is pre-stored in intrasystem Standard Earth (SE) image and gets the magnitude matrix of the two; The recycling quadratic interpolation is transformed into log-polar system with the magnitude matrix of the two; And calculate the error coefficient of said two devices magnitude matrix by following formula (1)

$L=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{[M_s(i,j)-M_F(i,j)]}^2---\left(1\right)$

In the following formula, L is the error coefficient of said two devices magnitude matrix, and M is the line number that is interpolated into matrix in the log-polar system, and N is for being interpolated into matrix column number in the log-polar system, M _S(i j) is the amplitude of the Fourier-Mellin transform of above-mentioned Standard Earth (SE) image in log-polar system, M _F(i j) is the amplitude of the Fourier-Mellin transform of actual earth image in log-polar system; Position when 5. the above-mentioned error coefficient of optical communication terminal antenna alignment of control detector is got minimum value, so finish acquisition procedure, dwindle then the beacon detector the visual field, improve measuring accuracy, obtain the real image of earth this moment, and the center of pressing following formula (8) and (9) calculating earth image of surveying

$x=\frac{\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}m\·S(m,n)}{\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}S(m,n)}---\left(8\right)$

$y=\frac{\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}n\·S(m,n)}{\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}S(m,n)}---\left(9\right)$

In the following formula, (m n) is above-mentioned Standard Earth (SE) image to S, and x is the horizontal ordinate of the actual earth image center that detects, and y is the ordinate of the actual earth image center that detects;

Two, the tracing process that after above-mentioned acquisition procedure finishes, enters extended beacon, the concrete steps of following the tracks of are as follows: I, the first time are when following the tracks of, with above-mentioned catch finish after the earth image of tracing process initial time as the reference picture of this secondary tracking, utilize detector to obtain to have taken place this moment the earth measuring image of relative motion then; II, calculate in the rectangular coordinate system measuring image with respect to the rotation angle of reference picture: A, regard measuring image as reference picture and additive gaussian white noise sum according to the following steps, real image and the reference picture that tracking is detected carries out discrete Fourier transform (DFT) and delivery respectively then, obtains the amplitude spectrum of above-mentioned two images; B, utilize quadratic interpolation to be transformed into the amplitude spectrum of real image and reference picture to obtain the magnitude matrix of above-mentioned two images under polar coordinate system under the polar coordinate system, and be by the magnitude matrix of following formula (2) calculating additive gaussian white noise under polar coordinate system,

G(m，n)＝M _R(m，n)-M ₁(m，n-k) (2)

In the following formula, (m n) is the amplitude two-dimensional matrix of additive gaussian white noise in polar coordinate system, M to G _R(m n) is the magnitude matrix of measuring image in the polar coordinate system, M ₁(m n-k) is the magnitude matrix of reference picture in the polar coordinate system, k be in the polar coordinate system measuring image with respect to reference picture angle translational movement (translation of angle shows in the rectangular coordinate to be the angle rotation in the polar coordinate system); It is that 0 Gaussian distribution and each spot noise figure are separate that each pixel of C, the definition magnitude matrix of above-mentioned additive gaussian white noise under polar coordinate system is obeyed average, and the maximum likelihood that calculates described angle translational movement k by following formula (3) is estimated then,

$\hat{k}=-\frac{N}{2\mathrm{\π}}\·\frac{\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\left|\mathrm{\ω}(m,n)\right|\mathrm{\ξ}}{\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}{n}^2\left|\mathrm{\ω}(m,n)\right|}---\left(3\right)$

In the following formula, For the maximum likelihood of described angle translational movement k is estimated, | and ω (m, n) | be above-mentioned M _R(m, discrete Fourier transform (DFT) n) and above-mentioned M ₁(m, the mould that conjugation discrete Fourier transform (DFT) n-k) multiplies each other, ξ are ω (m, Fourier phase angle n); D, calculate in the rectangular coordinate real image with respect to the reference picture rotation angle by following formula (4),

${\mathrm{\θ}}_0=\frac{2\mathrm{\π}}{N}\·\hat{k}---\left(4\right)$

In the following formula, θ ₀Be the rotation angle of measuring image in the rectangular coordinate system with respect to reference picture, N is the image array columns after the interpolation, and its value is consistent with the N in the formula (1); III, calculate in the rectangular coordinate system measuring image with respect to the translational movement of reference picture: a, with above-mentioned rotation angle θ according to the following steps ₀The following formula of substitution (5) calculates the two-dimensional matrix of postrotational reference picture,

s ₂(m，n)＝s(m·cosθ ₀+n·sinθ ₀-x ₀，-m·sinθ ₀+n·cosθ ₀-y ₀) (5)

In the following formula, s ₂(m n) is the reference picture two-dimensional matrix after rotating, and (m n) is the initial reference image two-dimensional matrix to s, x ₀Be the horizontal ordinate translational movement of measuring image in the rectangular coordinate system with respect to reference picture, y ₀Be the ordinate translational movement of measuring image in the rectangular coordinate system with respect to reference picture; B, calculate in the rectangular coordinate system measuring image with respect to the horizontal ordinate translational movement and the ordinate translational movement of reference picture according to following formula (6),

$\left\{\begin{array}{c}-\frac{1}{2\mathrm{\π}}\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\left|\mathrm{\υ}(m,n)\right|\mathrm{\β}(m,n)=x_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\frac{m}{M}\left|\mathrm{\υ}(m,n)\right|+y_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\frac{n}{N}\left|\mathrm{\υ}(m,n)\right|\\ -\frac{1}{2\mathrm{\π}}\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\left|\mathrm{\υ}(m,n)\right|\mathrm{\β}(m,n)=x_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\frac{m}{M}\left|\mathrm{\υ}(m,n)\right|+y_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\frac{n}{N}\left|\mathrm{\υ}(m,n)\right|\end{array}\right.---\left(6\right)$

In the following formula, υ (m n) is conjugate matrices long-pending of the Fourier transform of postrotational reference picture and measuring image, | and υ (m, n) | ((m n) is υ (m, Fourier phase angular moment battle array n) to β for m, mould n) for υ; IV, according to the anglec of rotation and translational movement, determine the center of measuring image by following formula (7),

x _t＝x′cosθ ₀+y′sinθ ₀-x ₀

y _t＝x′sinθ ₀+y′cosθ ₀-y ₀ (7)

In the following formula, (x ', y ') is the center of the used reference picture of this secondary tracking, i.e. the center position of the actual earth image that is calculated by above-mentioned formula (8) and (9), (x _t, y _t) be the center of measuring image; V, with the center of the optical communication terminal antenna alignment of detector measuring image this moment, so just finished tracing process for the first time; VI, when following the tracks of next time, the extended beacon measuring image the surveyed reference picture as this secondary tracking will be followed the tracks of for the first time, utilize detector to obtain to have taken place this moment the measuring image of the extended beacon of relative motion then, repeat II to IV again and go on foot, and with the center of this secondary tracking measuring image of optical communication terminal antenna alignment of detector; All follow the tracks of the reference picture of the measuring image of acquisition in VII, the each tracing process afterwards, and adjust the aligning direction of detector optical communication terminal antenna according to the center of this secondary tracking measuring image that obtains as this secondary tracking with the last time.

3. above-mentioned go on foot according to the vehicle technology parameter, the method of determining planar field of view angle, uncertain region in conjunction with Principle of Statistics is: described communication beam direction in the pitching coordinate system on star can be represented with the position angle and the angle of pitch, earlier the error of the above-mentioned position angle of definition and the angle of pitch obeys all that average is 0, variance is the Gaussian distribution of σ, and variances sigma can be determined according to the technical parameter of aircraft; Calculate the probability of successfully catching in the uncertain region by following formula (10) again,

$P={\∫}_{-\frac{{\mathrm{\θ}}_u}{2}}^{\frac{{\mathrm{\θ}}_u}{2}}{\∫}_{-\frac{{\mathrm{\θ}}_u}{2}}^{\frac{{\mathrm{\θ}}_u}{2}}f({\mathrm{\ϵ}}_h,{\mathrm{\ϵ}}_v)d{\mathrm{\ϵ}}_h{\mathrm{d\ϵ}}_v---\left(10\right)$

In the following formula, P is the probability that link is successfully set up in the uncertain region, ε _hBe azimuthal error, ε _vBe the error of the angle of pitch, f (ε _h, ε _v) be the joint probability density of above-mentioned position angle and angle of pitch error, θ _uBe field angle; Calculate the field angle θ of link is successfully set up in the uncertain region in the above-mentioned formula (10) probability P 〉=98% o'clock then _u, be planar field of view angle, uncertain region.

In image beacon acquisition procedure, visual field scanning requires to cover whole uncertain region, and therefore, the angular spacing d of adjacent two positions must satisfy

$d\≤{\mathrm{\θ}}_{\mathrm{fov}}/\sqrt{2}---\left(11\right)$

In the following formula, θ _FovIt is the visual field of beacon detector.

In catching the process of the earth, as shown in Figure 1, the reference beacon image that prestores is one 257 * 250 an earth image profile; As shown in Figure 2, one 512 * 512 the actual earth image that detects is an above-mentioned reference picture and an additive gaussian white noise sum, and the noise independent same distribution on each pixel of image, its average are 0, and variance is σ, and signal to noise ratio (S/N ratio) is 1.Following table 1 is the earth image center of calculating according to diverse ways.

Table 1

Actual beacon picture centre (pixel)		The picture centre (pixel) that acquisition algorithm calculates		Direct picture centre (pixel) according to the beacon image calculation
						x	y	x	y	x	y
251.05	254.27	251.05	254.27	250.78	254.75

According to last table as can be seen, the present invention adopts least-squares algorithm that the beacon image is caught, can determine the center of beacon image accurately, its error is very small, be almost 0, and directly adopt actual beacon image to calculate its center, because of the influence of additive gaussian white noise, its error is bigger, about 0.5 pixel.Behind the center of accurate definite beacon image, can accurately determine the antenna direction of optical communication terminal according to the relativeness of land station and earth image center.

At tracking phase, need the rotation and the translation motion of earth image be compensated.Reference picture as shown in Figure 3, post exercise actual measurement earth image is as shown in Figure 4.It is as shown in table 2 that the tracking that combines discrete Fourier transform (DFT) and maximum likelihood algorithm according to the present invention is obtained the translational movement and the rotation angle of actual beacon image.

Table 2

Actual translational movement (pixel)		Translational movement calculated value (pixel)		The actual anglec of rotation (°)	The rotation angle calculated value (°)
						x	y	x 0	y 0	θ	θ 0
-3.00	-4.00	-2.92	-3.87	5.00	5.04

According to last table as can be seen, the shift value of the beacon image that calculates and the anglec of rotation and actual value differ very little, at directions X, error only is 2.7%, in the Y direction, its error is 3.3%, and anglec of rotation error only is 0.8%, can satisfy the requirement that the deep-space laser communication light beam is accurately aimed at fully.According to translational movement that calculates and rotation angle, as shown in table 3 by can the move center of back beacon image of formula (7),

Table 3

Reference beacon picture centre (pixel)		Calculate the center (pixel) of the actual beacon image of the post exercise of surveying
				x	y	x t	y t
124.05	123.27	137.32	115.77

As seen from the above table,, can determine the center of beacon image accurately, thereby upgrade the sensing of optical communication terminal antenna dynamically according to the calculated value of the translational movement and the anglec of rotation.

Claims (3)

1, a kind of method for capturing and tracing extended beacon for deep space optical communication is characterized in that:

One, catch the extended beacon position according to the following steps:

1. in the process of deep-space laser communication link establishment and operation, determine optical communication terminal initial alignment direction under the inertial coordinates system according to natural celestial body and aircraft ephemeris, this direction is pointed to the extended beacon that will catch;

2. the sighted direction vector in the above-mentioned inertial coordinates system is transformed on the star in the pitching coordinate system by coordinate transform, makes on the star that is controlled at aircraft of described communication beam and carry out in the pitching coordinate system;

3. according to the correlation technique parameter of spacecraft, determine planar field of view angle, uncertain region in conjunction with Principle of Statistics;

4. in above-mentioned uncertain region, carry out antenna scanning according to the predetermined angle interval; In scanning process; Antenna each location point on track while scan is stayed for some time; The regional imaging of beacon detector to aiming at; Then the true extension beacon image that obtains and the two-dimensional matrix that is pre-stored in intrasystem standard extended beacon image are carried out first respectively Fourier-Mellin transform and get the two magnitude matrix; The recycling quadratic interpolation is transformed into log-polar system with the magnitude matrix of the two; And calculate the error coefficient of said two devices magnitude matrix by following formula (1)

$L=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{[M_s(i,j)-M_F(i,j)]}^2---\left(1\right)$

In the following formula, L is the error coefficient of said two devices magnitude matrix, and M is the line number that is interpolated into matrix in the log-polar system, and N is for being interpolated into matrix column number in the log-polar system, M _S(i j) is the amplitude of the Fourier-Mellin transform of above-mentioned standard extended beacon image in log-polar system, M _F(i j) is the amplitude of the Fourier-Mellin transform of actual beacon image in log-polar system;

Position when 5. the above-mentioned error coefficient of optical communication terminal antenna alignment of control detector is got minimum value is so finish acquisition procedure;

Two, the tracing process that after above-mentioned acquisition procedure finishes, enters extended beacon, the concrete steps of tracking are as follows:

I, the first time are when following the tracks of, with above-mentioned be pre-stored in intrasystem standard extended beacon image or above-mentioned catch finish after the beacon image of tracing process initial time as the reference picture of this secondary tracking, utilize detector to obtain to have taken place this moment the measuring image of the extended beacon of relative motion then;

II, calculate in rectangular coordinate system measuring image with respect to the rotation angle of reference picture according to the following steps:

A, regard measuring image as reference picture and additive gaussian white noise sum, real image and the reference picture that tracking is detected carries out discrete Fourier transform (DFT) and delivery respectively then, obtains the amplitude spectrum of above-mentioned two images;

B, utilize quadratic interpolation to be transformed into the amplitude spectrum of real image and reference picture to obtain the magnitude matrix of above-mentioned two images under polar coordinate system under the polar coordinate system, and be by the magnitude matrix of following formula (2) calculating additive gaussian white noise under polar coordinate system,

G(m，n)＝M _R(m，n)-M ₁(m，n-k) (2)

In the following formula, (m n) is the amplitude two-dimensional matrix of additive gaussian white noise in polar coordinate system, M to G _R(m n) is the magnitude matrix of measuring image in the polar coordinate system, M ₁(m n-k) is the magnitude matrix of reference picture in the polar coordinate system, k be in the polar coordinate system measuring image with respect to reference picture angle translational movement;

It is that 0 Gaussian distribution and each spot noise figure are separate that each pixel of C, the definition magnitude matrix of above-mentioned additive gaussian white noise under polar coordinate system is obeyed average, and the maximum likelihood that calculates described angle translational movement k by following formula (3) is estimated then,

$\hat{k}=-\frac{N}{2\mathrm{\π}}\·\frac{\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\left|(\mathrm{\ωm},n)\right|\mathrm{\ξ}}{\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}{n}^2\left|\mathrm{\ω}(m,n)\right|}---\left(3\right)$

In the following formula,

For the maximum likelihood of described angle translational movement k is estimated, | and ω (m, n) | be above-mentioned M _R(m, discrete Fourier transform (DFT) n) and above-mentioned M ₁(m, the mould that conjugation discrete Fourier transform (DFT) n-k) multiplies each other, ξ are ω (m, Fourier phase angle n);

D, calculate in the rectangular coordinate real image with respect to the reference picture rotation angle by following formula (4),

${\mathrm{\θ}}_0=\frac{2}{N}\·\hat{k}---\left(4\right)$

In the following formula, θ ₀Be the rotation angle of measuring image in the rectangular coordinate system with respect to reference picture, N is the image array columns after the interpolation, and its value is consistent with the N in the formula (1);

III, calculate in the rectangular coordinate system measuring image with respect to the translational movement of reference picture according to the following steps:

A, with above-mentioned rotation angle θ ₀The following formula of substitution (5) calculates the two-dimensional matrix of postrotational reference picture,

s ₂(m，n)＝s(m·cosθ ₀+n·sinθ ₀-x ₀，-m·sinθ ₀+n·cosθ ₀-y ₀) (5)

In the following formula, s ₂(m n) is the reference picture two-dimensional matrix after rotating, and (m n) is the initial reference image two-dimensional matrix to s, x ₀Be the horizontal ordinate translational movement of measuring image in the rectangular coordinate system with respect to reference picture, y ₀Be the ordinate translational movement of measuring image in the rectangular coordinate system with respect to reference picture;

B, calculate in the rectangular coordinate system measuring image with respect to the horizontal ordinate translational movement and the ordinate translational movement of reference picture according to following formula (6),

$\left\{\begin{array}{c}-\frac{1}{2\mathrm{\π}}\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\left|\mathrm{\υ}(m,n)\right|\mathrm{\β}(m,n)=x_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\frac{m}{M}\left|\mathrm{\υ}(m,n)\right|+y_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}m\frac{n}{N}\left|\mathrm{\υ}(m,n)\right|\\ -\frac{1}{2\mathrm{\π}}\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\left|\mathrm{\υ}(m,n)\right|\mathrm{\β}(m,n)=x_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\frac{m}{M}\left|\mathrm{\υ}(m,n)\right|+y_0\underset{m=0}{\overset{M}{\mathrm{\Σ}}}\underset{n=0}{\overset{N}{\mathrm{\Σ}}}n\frac{n}{N}\left|\mathrm{\υ}(m,n)\right|\end{array}\right.---\left(6\right)$

In the following formula, υ (m n) is conjugate matrices long-pending of the Fourier transform of postrotational reference picture and measuring image, | and υ (m, n) | ((m n) is υ (m, Fourier phase angular moment battle array n) to β for m, mould n) for υ; IV, according to the anglec of rotation and translational movement, determine the center of measuring image by following formula (7),

x _t＝x′cosθ ₀+y′sinθ ₀-x ₀ (7)

y _t＝-x′sinθ ₀+y′cosθ ₀-y ₀

In the following formula, (x ', y ') be the center of the used reference picture of this secondary tracking, (x _t, y _t) be the center of measuring image;

V, with the center of the optical communication terminal antenna alignment of detector measuring image this moment, so just finished tracing process for the first time;

VI, when following the tracks of next time, the extended beacon measuring image the surveyed reference picture as this secondary tracking will be followed the tracks of for the first time, utilize detector to obtain to have taken place this moment the measuring image of the extended beacon of relative motion then, repeat II to IV again and go on foot, and with the center of this secondary tracking measuring image of optical communication terminal antenna alignment of detector;

All follow the tracks of the reference picture of the measuring image of acquisition in VII, the each tracing process afterwards, and adjust the aligning direction of detector optical communication terminal antenna according to the center of this secondary tracking measuring image that obtains as this secondary tracking with the last time.

2, a kind of method for capturing and tracing extended beacon for deep space optical communication according to claim 1, it is characterized in that described communication beam direction in the pitching coordinate system on star can represent with the position angle and the angle of pitch, earlier the error of the above-mentioned position angle of definition and the angle of pitch obeys all that average is 0, variance is the Gaussian distribution of σ, and variances sigma can be determined according to the technical parameter of aircraft; Calculate the probability of successfully catching in the uncertain region by following formula (10) again,

$P={\∫}_{-\frac{{\mathrm{\θ}}_u}{2}}^{\frac{{\mathrm{\θ}}_u}{2}}{\∫}_{-\frac{{\mathrm{\θ}}_u}{2}}^{\frac{{\mathrm{\θ}}_u}{2}}f({\mathrm{\ϵ}}_h,{\mathrm{\ϵ}}_v)d{\mathrm{\ϵ}}_{h}d{\mathrm{\ϵ}}_v---\left(10\right)$

In the following formula, P is the probability that link is successfully set up in the uncertain region, ε _hBe azimuthal error, ε _vBe the error of the angle of pitch, f (ε _h, ε _v) be the joint probability density of above-mentioned position angle and angle of pitch error, θ _uBe field angle; Calculate the field angle θ of link is successfully set up in the uncertain region in the above-mentioned formula (10) probability P 〉=98% o'clock then _u, be planar field of view angle, uncertain region.

3, a kind of method for capturing and tracing extended beacon for deep space optical communication according to claim 1 is characterized in that the predetermined angle of carrying out antenna scanning must satisfy following formula (11) at interval,

$d\≤{\mathrm{\θ}}_{\mathrm{fov}}/\sqrt{2}---\left(11\right)$

In the following formula, θ _FovBe the visual field of beacon detector, d is described predetermined angle interval.