CN104123461A - Lighting visual relation calculating method for photometric analysis of space object - Google Patents

Abstract

The invention belongs to the field of foundation photoelectric observation and discloses a lighting visual relation calculating method for photometric analysis of a space object. The method comprises the following steps of performing orbit calculation to obtain the position and a velocity vector of the space object; establishing an orbital coordinate system based on the position and the velocity vector; introducing a posture parameter to establish a space object body coordinate system; calculating a light vector and an observation vector. By adopting the method, the defect that traditionally, a phase angle (an included angle formed by the space object, an observation station and the sun) is used for representing for the light visual relation of the space object is overcome, simplified particle motion is popularized to orbital motion and posture motion with outline structures, the satiation of the space object lighted by the sun in a space and observed by an observation device is specifically described, and the method is directly at the service of luminosity feature study of the space object.

Description

A kind of illumination visible relation computing method for space object photometric analysis

Technical field

The invention belongs to ground photoelectric observation field, relate to a kind of illumination visible relation computing method for space object photometric analysis.

Background technology

When space object moves in space, self is not luminous, and the luminosity information spinner that ground observation obtains will be from the sunshine of its reflection.Ground observer relatively, space object and main lighting source (sun) are not actionless, the existing rotation of the attitude with respect to stable axis of space object (rotation), the position motion (around revolution of earth) of also having living space; Due to earth rotation and revolving around the sun, the relative ground observer of the sun also has short-period diurnal variation and changes for macrocyclic year.Complicated relative position changes, and has brought complicated illumination condition and conditioned reflex to change.

In current space object photometric property is described, often use phasing degree (space angle of the sun-target-survey station) to explain the illuminated and visible relation of space object, the motion of space object is considered as particle movement by such description system, do not consider himself shape and attitude motion, and change with the year of sun relative position.In order more properly to describe the illuminated and visible relation of space object, by its inverting, emulation, determine that the attitude of space object changes, be luminosity calibration and the feature extraction service of space object, need to set up the more accurate illumination visible relation of one computing method.

Summary of the invention

This method has overcome traditional deficiency that characterizes space object illumination visible relation with phasing degree (angle between space object-survey station-sun), the particle movement of simplification is generalized in the orbital motion and attitude motion of contour structures, describe more specifically the situation of space object tested station equipment observation after space is by solar illumination, directly serve the photometric property research of space object.

Said method comprising the steps of:

Step 1: calculate position, the velocity obtained under current true equator epoch coordinate system on true equinox with

(1) utilize SGP4 or SDP4 model to carry out the extrapolation forecast calculation of space object Tle orbital tracking, obtain position and velocity under current epoch of orbital coordinate system;

(2) space object current epoch orbital coordinate system upper/lower positions and velocity be converted to position, the velocity under current true equator epoch coordinate system on true equinox with

(3) obtain light source (sun) and the survey station position vector at current true equator epoch coordinate system on true equinox simultaneously with

Step 2: position and velocity under current true equator epoch coordinate system on true equinox based on space object are set up orbital coordinate system;

Space object orbit plane is coordinate plane, z ₀axle points to the earth's core by barycenter, x ₀axle is in orbit plane and z ₀the vertical also pointing space object speed direction of axle, y ₀axle and x ₀, z ₀the axle right hand orthogonal and with orbit plane normal parallel, conventionally claim x ₀, y ₀, z ₀axle is respectively rolling, pitching and yaw axis.

Step 3: introduce attitude parameter and set up space object body coordinate system;

Introduce three Eulerian angle-crab angle ψ, pitching angle theta and the roll angle φ of space object status, the mapping relations of structure space object body coordinate system and orbital coordinate system.

Three Eulerian angle are defined as follows:

crab angle ψ: the space object axis of rolling (pointing space object speed direction) projection and track on local level the angle of axle;

pitching angle theta: the space object axis of rolling the angle of the projection with it on local level;

roll angle space object pitch axis the angle of the projection with it on local level.

Step 4: the calculating of the vector of throwing light on measurement vector.

The coordinate mapping relations of setting up according to step 3, by the position vector of the sun and survey station with be converted to the vector that throws light under body coordinate system and measurement vector and convert position angle and elevation angle to.

Technical scheme of the present invention compared with prior art has following technique effect:

(1) this method is included the formal parameter of space object and attitude parameter in the computing method of illumination visible relation in, can each facade of directviewing description irradiation visible relation in time.

(2) existing system is described illumination visible relation with a parameter-phasing degree, and the corresponding multiple actual irradiations of same phasing degree possibility can be optionally, and this method is described light source with four parameters and irradiated and survey station visible relation, more accurate also more unique.

Brief description of the drawings

Fig. 1 is space object illumination visible relation calculation flow chart of the present invention;

Fig. 2 is space object orbital coordinate system schematic diagram of the present invention;

Fig. 3 is space object body coordinate system schematic diagram of the present invention.

Embodiment

The illumination visible relation computing method of space object photometric analysis of the present invention, specific implementation process is as follows:

Step 1: calculate position, the velocity obtained under current true equator epoch coordinate system on true equinox with

(1) utilize SGP4 or SDP4 model to carry out the extrapolation forecast calculation of space object Tle orbital tracking, obtain the coordinate vector under current epoch of orbital coordinate system;

Utilize SGP4 (Simplified General Perturbations Satellite Orbit Model4) or SDP4 (Simplified Deep Space Perturbations Satellite Orbit Model4) to carry out the forecast calculation of Tle (Two-Line Element) data.

According to the Tle radical of space object, according to the cycle difference of space object, call respectively SGP4 or SDP4 model calculates, obtain position and the velocity information of the space object under Tle coordinate system (current epoch orbital coordinate system).

(2) space object current epoch orbital coordinate system upper/lower positions and velocity be converted to position, the velocity under current true equator epoch coordinate system on true equinox with

The coordinate system of Tle data is orbital coordinate systems of its epoch in data moment, and the position of calculating and velocity information are also under current epoch of orbit coordinate, can obtain current epoch of orbital coordinate system upper/lower positions and velocity with extremely vector under current true equator epoch coordinate system on true equinox transformational relation,

$\stackrel{\→}{r}={R_z}^T(\mathrm{\μ}+\mathrm{\Δ\μ}){\stackrel{\→}{r}}^{\′}---\left(1\right)$

$\stackrel{\→}{v}={R_z}^T(\mathrm{\μ}+\mathrm{\Δ\μ}){\stackrel{\→}{v}}^{\′}---\left(2\right)$

The μ here and Δ μ are precession in right ascension and nutating; R _zreferring to formula (11).

(3) obtain light source (sun) and the survey station position vector in current true equator epoch coordinate system on true equinox with

utilize sun mean element to calculate sun coordinate vector under current true equator epoch coordinate system on true equinox;

Position of sun utilizes mean element to calculate and obtains, and the median orbital elements of the sun in J2000 celestial coordinate system epoch is:

Wherein d and T be respectively by the standard Julian date that J2000.0 starts at epoch and century number, specific formula for calculation is as follows:

$\left\{\begin{array}{c}d=\mathrm{JD}\left(t\right)-2451545.0\\ T=\frac{d}{36525.0}\end{array}\right.---\left(4\right)$

Obtained after the orbital tracking in t moment by the mean element computing formula of the sun, can obtain the coordinate vector of the sun by the conversion formula of orbital tracking and position vector, formula is as follows:

${\stackrel{\→}{r}}_1=\left(\begin{array}{c}x\\ y\\ z\end{array}\right)=a(\cos E-e)\·\stackrel{\→}{P}+a\sqrt{1-e^2}\sin E\·\stackrel{\→}{Q}---\left(5\right)$

Wherein: a, e are respectively semi-major axis, the excentricity of solar orbit, the eccentric anomaly that E is solar orbit.

$\begin{array}{c}\stackrel{\→}{P}=\left(\begin{array}{c}\cos \mathrm{\Ω}\cos \mathrm{\ω}-\sin \mathrm{\Ω}\sin \mathrm{\ω}\cos i\\ \sin \mathrm{\Ω}\cos \mathrm{\ω}+\cos \mathrm{\Ω}\sin \mathrm{\ω}\cos i\\ \sin \mathrm{\ω}\sin i\end{array}\right)\\ \stackrel{\→}{Q}=\left(\begin{array}{c}-\cos \mathrm{\Ω}\sin \mathrm{\ω}-\sin \mathrm{\Ω}\cos \mathrm{\ω}\cos i\\ -\sin \mathrm{\Ω}\sin \mathrm{\ω}+\cos \mathrm{\Ω}\cos \mathrm{\ω}\cos i\\ \cos \mathrm{\ω}\sin i\end{array}\right)\end{array}---\left(6\right)$

${\stackrel{\→}{R}}_{\mathrm{sun}}=\left(\mathrm{GR}\right){\stackrel{\→}{r}}_1---\left(7\right)$

Wherein: the transition matrix that (GR) is tied to instantaneous true equator and feels concerned about for J2000 celestial coordinates epoch.

calculate survey station coordinate vector under current true equator epoch coordinate system on true equinox;

${\stackrel{\→}{R}}_{\mathrm{station}}={\left(\mathrm{ER}\right)}^T{\left(\mathrm{ER}\right)}^T{\stackrel{\→}{R}}_0---\left(10\right)$

Wherein: wherein λ, respectively geographic longitude, the geographic latitude of survey station.A _ebe the equatorial radius of reference ellipsoid, f is the ellipticity a of reference ellipsoid _e=6378.136km, f=0.00335281, (ER) ^tfor pseudo body-fixed system to instantaneous true equator the transition matrix felt concerned about, (EP) ^tfor body-fixed coordinate system is tied to the transition matrix between pseudo body-fixed system.

Each rotation matrix R _x(θ) ... computing formula be

$\left\{\begin{array}{c}{R}_x\left(\mathrm{\θ}\right)=\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\θ}& \sin \mathrm{\θ}\\ 0& -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right)\\ R_y\left(\mathrm{\θ}\right)=\left(\begin{array}{ccc}\cos \mathrm{\θ}& 0& -\sin \mathrm{\θ}\\ 0& 1& 0\\ \sin \mathrm{\θ}& 0& \cos \mathrm{\θ}\end{array}\right)\\ R_z\left(\mathrm{\θ}\right)=\left(\begin{array}{ccc}\cos \mathrm{\θ}& \sin \mathrm{\θ}& 0\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}& 0\\ 0& 0& 1\end{array}\right)\end{array}\right.---\left(11\right)$

Rotation matrix R _x(θ) ... be orthogonal matrix, have step 2: position and velocity under current true equator epoch coordinate system on true equinox based on space object are set up orbital coordinate system;

Orbital coordinate system is conventional space object body coordinate system, and the attitude of the three-axis stabilization space object (as remote sensing space object, communication space object) of absolute orientation is just defined in this coordinate system.It is taking space object orbit plane as coordinate plane, z ₀axle points to the earth's core by barycenter, x ₀axle is in orbit plane and z ₀the vertical also pointing space object speed direction of axle, y ₀axle and x ₀, z ₀the axle right hand orthogonal and with orbit plane normal parallel, as Fig. 3, this coordinate system rotates in space.Conventionally claim x ₀, y ₀, z ₀for rolling, pitching and yaw axis.

Utilize position and the velocity of space object orbital motion, the unit vector of each coordinate axis of orbital coordinate system can be expressed as:

$\begin{array}{c}{\stackrel{\→}{x}}_0={\stackrel{\→}{y}}_0\×{\stackrel{\→}{z}}_0\\ {\stackrel{\→}{y}}_0=\frac{\stackrel{\→}{v}\×\stackrel{\→}{r}}{|\stackrel{\→}{v}\×\stackrel{\→}{r}|}\\ {\stackrel{\→}{z}}_0=-\frac{\stackrel{\→}{r}}{\left|\stackrel{\→}{r}\right|}\end{array}---\left(12\right)$

with form right-handed helix system, wherein with for position and the velocity of target.

Step 3: introduce attitude parameter and set up space object body coordinate system;

Orbital coordinate system is a kind of reference frame, the description of attitude is embodied to the physical quantity of celestial body at this coordinate system change in coordinate axis direction, be called attitude parameter, introduce three Eulerian angle-crab angle ψ, pitching angle theta and the roll angle φ of space object status, the mapping relations of structure body coordinate system and orbital coordinate system.

Three Eulerian angle are defined as follows:

crab angle ψ: the space object axis of rolling (pointing space object speed direction) projection and track on local level the angle of axle;

pitching angle theta: the space object axis of rolling the angle of the projection with it on local level;

roll angle space object pitch axis the angle of the projection with it on local level.

Being expressed as follows of transformational relation between orbital coordinate system and body coordinate system--attitude matrix:

$\left[\begin{array}{c}{x}_b\\ y_b\\ z_b\end{array}\right]=\stackrel{\→}{A}\left[\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right]---\left(13\right)$

Step 4: the calculating of the vector of throwing light on measurement vector.

The coordinate mapping relations of setting up according to step 3, by the position vector of the sun and survey station with be converted to position angle and elevation angle under body coordinate system.(referring to formula 16)

According to vector calculus law, can obtain any one current true equator epoch coordinate system on true equinox vector be transformed into vector in body coordinate system mapping relations, specific as follows:

${\stackrel{\→}{r}}_1=\left(\begin{array}{c}{x}_1\\ y_1\\ z_1\end{array}\right)=A\·{\stackrel{\→}{R}}_0---\left(15\right)$

The computing formula that is converted to position angle A and elevation angle h is as follows:

$\left\{\begin{array}{c}\mathrm{rp}=\sqrt{{x_1}^2+{y_1}^2}\\ h=a\tan (z_1/\mathrm{rp})\\ A=360-a\tan 2(y_1/z_1,x_1/z_1)\end{array}\right.---\left(6\right)$

On the basis of above-mentioned coordinate transformation relation, set up the body coordinate system of space object, the survey station vector that research is related to solar vector as in substitution formula (15), carry out coordinate conversion respectively, be transformed into measurement vector in body coordinate system with illumination vector carry out again the calculating of position angle and elevation angle, so just can obtain to shine upon and be related to A _sun, h _sunvisible relation A with survey station _station, h _station, utilize these four parameters to characterize space object and shined upon and survey station visible relation, analyze its visual condition over time.

Technique effect of the present invention is that the formal parameter of space object and attitude parameter are included in the computing method of illumination visible relation, can each facade of directviewing description irradiation visible relation in time; Existing system is described illumination visible relation with a parameter-phasing degree, and the corresponding multiple actual irradiations of same phasing degree possibility can be optionally, and this method is described light source with four parameters and irradiated and survey station visible relation, more accurate also more unique.

Claims (5)

1. for illumination visible relation computing method for space object photometric analysis, it is characterized in that, described method comprises the steps:

Step 1: calculate position, the velocity obtained under current true equator epoch coordinate system on true equinox with

Step 2: position and velocity under current true equator epoch coordinate system on true equinox based on space object are set up orbital coordinate system;

Step 3: introduce attitude parameter and set up space object body coordinate system, the mapping relations of structure body coordinate system and orbital coordinate system;

Step 4: the calculating of the vector that throws light on (sun-satellite vector) and measurement vector (survey station-satellite vector).

2. illumination visible relation computing method according to claim 1, is characterized in that, described step 1 specifically comprises:

1) utilize SGP4 or SDP4 model to carry out the extrapolation forecast calculation of space object Tle orbital tracking, obtain position and velocity under current epoch of orbital coordinate system;

2) by space object current epoch orbital coordinate system upper/lower positions and velocity be converted to position, the velocity under current true equator epoch coordinate system on true equinox with

3) obtain light source (sun) and the position vector of survey station in this coordinate system simultaneously with

3. illumination visible relation computing method according to claim 1, is characterized in that, the x of described step 2 middle orbit coordinate system ₀, y ₀, z ₀axle is respectively rolling, pitching and yaw axis.

4. illumination visible relation computing method according to claim 1, it is characterized in that, in described step 3, attitude parameter is: three Eulerian angle-crab angle ψ, pitching angle theta and the roll angle φ of space object status, for constructing the mapping relations of body coordinate system and orbital coordinate system; The wherein crab angle ψ representation space object axis of rolling (pointing space object speed direction) projection and track on local level the angle of axle; Pitching angle theta represents the object axis of rolling the angle of the projection with it on local level; Roll angle represent object pitch axis the angle of the projection with it on local level.

5. illumination visible relation computing method according to claim 1, is characterized in that, the concrete grammar of step 4 is: the coordinate mapping relations of setting up according to step 3, and by the position vector of the sun and survey station with be converted to the vector that throws light under body coordinate system and measurement vector and the position angle converting to and elevation angle, obtain and shine upon A thus _sun, h _sunwith survey station A _station, h _stationthe visible relation characterizing.