CN113361163B - Satellite attitude estimation method for correcting earth reflected light - Google Patents

Satellite attitude estimation method for correcting earth reflected light Download PDF

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CN113361163B
CN113361163B CN202110619180.1A CN202110619180A CN113361163B CN 113361163 B CN113361163 B CN 113361163B CN 202110619180 A CN202110619180 A CN 202110619180A CN 113361163 B CN113361163 B CN 113361163B
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CN113361163A (en
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汪夏
黎吉顺
张雅声
徐灿
李智
方宇强
贺俊
李鹏举
程文华
刁华飞
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Peoples Liberation Army Strategic Support Force Aerospace Engineering University
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Abstract

The invention provides a satellite attitude estimation method for correcting terrestrial reflected light, which comprises the following steps: dividing the earth surface into a plurality of surface elements according to longitude and latitude grids, and screening effective surface elements; according to the inverse proportion law of the radiation illumination and the square of the distance, calculating the radiation illumination of the sunlight visible light wave band at each effective surface element, and according to the Lambert reflection principle, calculating the radiation illumination of the effective surface elements at the target satellite; according to the radiation illumination generated by the effective surface elements at the target satellite, calculating the radiation illumination of the target satellite to the detector by taking each effective surface element as a light source according to the Lambert reflection principle; adding the radiation illumination of the target satellite to the detector to obtain the radiation illumination of the target satellite to the detector when the earth is used as a light source; subtracting the real-time radiation illumination of the target satellite to the detector when the earth is used as a light source from the real-time radiation illumination of the target satellite to the detector obtained from the target satellite, and obtaining corrected observation data of the radiation illumination of the satellite to the detector when only the sun is used as the light source; and performing attitude estimation on the satellite by using a tasteless Kalman filtering method to obtain the correction data of the earth reflected light. The invention accurately calculates the illumination of the earth reflected light to the satellite and the illumination of the satellite under the condition, and the satellite attitude estimation based on the illumination can greatly improve the estimation precision.

Description

Satellite attitude estimation method for correcting terrestrial reflected light
Technical Field
The invention belongs to the technical field of optical characteristic identification, and particularly relates to calculation of influence of earth reflected light on optical observation of medium and high orbit satellites.
Background
Ground-based optical observation is an important means for acquiring satellite characteristic information. The sun acts as a constant light source, and the emitted radiation rays enter the entrance pupil of the detector after being reflected by the surface of the satellite. According to the principle that the incident light intensity is unchanged and light transmission is combined, the optical information received by the detector is changed due to the fact that the shape, the posture and the surface material of the satellite are different. Therefore, based on this principle, information such as the shape, size, operating state, etc. of the satellite can be recognized by the acquired satellite photometric information. However, in real-world observation, there are other stray light sources besides the sun, so that the light signal received by the detector is a mixed light obtained by reflecting incident light from a satellite at multiple angles.
The main stray light source known at present is the earth, which is a relatively special light source, and the earth does not have the ability of emitting light by itself, but reflects the light emitted by the sun so as to illuminate a satellite. Since the sun can illuminate only half of the earth at the same time, the indirect solar radiation intensity received by the satellite has an inseparable relationship with the geometric position relationship of the sun, the earth and the satellite.
In the early days of the study, researchers generally accepted that they had negligible effect on satellite optical observations, based on the relatively low albedo of the earth, and therefore focused only on direct irradiation by the sun. However, with the development of observation technology and the intensive research, some unreasonable phenomena appear in the daily satellite observation, and after multi-phase optical observation is performed on different satellites, the change trends of the luminosity curves of the different satellites at a large phase angle are found to be flat, which indicates that the contribution of the earth reflected light to the satellite luminosity at the large phase angle is larger than that of the sun. In addition, most satellites are irregular in shape and material, so that optical signals received by the detector are extremely sensitive to the observation geometric position relationship (the relative position relationship among the light source, the target satellite and the detector), and the relative position relationship among the sun, the earth, the satellite and the detector needs to be considered at the same time.
In recent years, people have become aware of the non-negligible effect of indirect solar radiation on satellite optical observations. Based on the existing celestial body reflection model, the influence of the earth reflected light on satellite observation is analyzed. However, most researchers have investigated to verify the feasibility of using the earth's reflected light to perform satellite observation during the day. They focused on the spectral shape of the composite light and analyzed the target reflected light signal at a single time or at several times. And the influence degree of the earth reflected light relative to the direct solar radiation illumination at different times is not compared in detail, and a quantitative standard is not given to the possibility of neglecting indirect radiation. Therefore, in practical applications, uncorrected satellite observation data will result in a decrease in satellite state estimation accuracy.
Disclosure of Invention
The invention provides a satellite attitude estimation method for correcting earth reflected light, which solves the technical problems of quantitative calculation of the earth reflected light and low accuracy of traditional satellite attitude estimation based on photometric data. In the process of researching the optical characteristics of the satellite, the brightness of the satellite detected by the detector is changed by the existence of the earth reflected light, and the satellite characteristic analysis is greatly influenced. The method accurately calculates the influence of the earth reflected light in different time periods, corrects the satellite observation data based on the calculation result, and improves the estimation precision after the attitude estimation is carried out by the odorless Kalman filtering method.
In order to achieve the above object, the present invention provides a method for estimating satellite attitude by correcting terrestrial reflected light, comprising the following steps:
the method comprises the following steps: dividing the earth surface into a plurality of surface elements according to a longitude and latitude grid, and calculating the surface element area; screening effective surface elements based on the shielding relation among the sun, the earth and a target satellite;
step two: according to an inverse proportion law of the radiation illumination and the square of the distance, calculating the radiation illumination of the solar visible light wave band at each effective surface element, and according to a Lambert reflection principle, calculating the radiation illumination generated by the effective surface elements at a target satellite;
step three: according to the radiation illumination generated by the effective surface elements at the target satellite, calculating the radiation illumination of the target satellite to the detector by taking each effective surface element as a light source according to the Lambert reflection principle; adding the radiation illumination of the target satellite to the detector to obtain the radiation illumination of the target satellite to the detector when the earth is used as a light source;
step four: subtracting the radiation illuminance of the target satellite to the detector when the earth is used as a light source from the real-time radiation illuminance of the target satellite to the detector obtained from the target satellite to obtain corrected observation data of the radiation illuminance of the target satellite to the detector when only the sun is used as the light source;
step five: and based on the corrected observation data, performing attitude estimation on the target satellite by using an odorless Kalman filtering method to obtain the earth reflected light correction data.
In the first step, the method for dividing the earth surface into a plurality of surface elements according to the longitude and latitude grids comprises the following steps: based on a longitude and latitude grid on the earth surface, the center of a surface element is located at a longitude and latitude point, and the length and the width are respectively a latitude distance and a longitude distance.
The method for calculating the surface element area comprises the following steps: each ground surface element is l in length j ＝2πR E A/360; surface element at latitude i, width d i ＝2πR E cosi/360; the surface area of the ground surface is s ij ＝l j d i (ii) a Wherein l j Is the length of the surface element at longitude j, d i Is the width, s, of the ground surface element at latitude i ij Is the surface area, R E I, j represent latitude and longitude, respectively, for the radius of the earth.
The method for screening the effective surface element comprises the following steps:
Figure BDA0003099037250000031
wherein, theta in Is the incident zenith angle, theta, of sunlight to the ground surface element out Is a reflection zenith angle.
In the second step, the method for calculating the irradiance of the solar visible light wave band at each effective surface element comprises the following steps: according to the inverse law that the radiation illumination is in inverse proportion to the square of the distance, under the condition that sunlight is not shielded, the radiation illumination of a solar visible light wave band at each effective surface element is obtained:
Figure BDA0003099037250000032
wherein R is 0 Is the average distance of the day and the ground within one year; q 0 Is at a distance R from the sun 0 And the radiation illumination of a visible light wave band (0.4-0.7 mu m) part, wherein R is the distance from a ground surface element to the sun, and Q is the radiation illumination of the visible light wave band (0.4-0.7 mu m) at an effective surface element away from the sun.
The method for calculating the radiation illumination generated by the effective surface element at the target satellite according to the Lambert reflection principle to obtain the radiation illumination of a single ground surface element suffered by the target satellite comprises the following steps: the illumination of the solar radiation on the earth surface is as follows:
Figure BDA0003099037250000041
wherein R is 0 Is the average distance between the day and the ground in a year, R se Distance of the sun from the earth, Q se Irradiance, Q, of the sun at the earth's surface 0 To be at a distance R from the sun 0 The radiation illumination of a visible light wave band;
the radiant brightness of the ground surface element generated in each direction is as follows:
Figure BDA0003099037250000042
wherein, theta in Is the incident zenith angle, Q, of sunlight to the ground surface element se cosθ in The total average albedo value of the illuminance of the solar radiation received by the surface elements of the earth and the surface atmosphere is
Figure BDA0003099037250000043
L ij The radiation brightness generated by the ground surface element to each direction;
a single ground surface element (i, j) is at
Figure BDA0003099037250000044
The radiation illuminance generated at the directional target satellite is:
Figure BDA0003099037250000045
wherein,
Figure BDA0003099037250000046
is the direction vector of the bin pointing to the target satellite,
Figure BDA0003099037250000047
the ground surface element forming a solid angle, s, with respect to the target satellite ij Is the area of the ground surface element with longitude and latitude located in (i, j),
Figure BDA0003099037250000048
is the distance, Q, from the ground surface element to the target satellite ij For a single ground surface element (i, j) in
Figure BDA0003099037250000049
The radiation illuminance generated at the directional target satellite.
In the third step, according to the radiation illuminance generated by the effective surface element at the target satellite, the method for calculating the radiation illuminance of the target satellite to the detector by using each effective surface element as a light source according to the lambertian reflection principle comprises the following steps:
Figure BDA00030990372500000410
wherein the vector of the sun pointing to the target, i.e. the incident light vector, is lambda S (ii) a The vector of the target pointing to the detector, i.e. the observation vector, is lambda F (ii) a The normal vector of a certain surface element of the target satellite is n; the included angle between the incident vector and the normal vector of the surface element is the incident zenith angle and is recorded as theta S The included angle between the observation vector and the normal vector of the surface element is the observation zenith angle and is recorded as theta F (ii) a According to incident zenith angle theta S Observing the zenith angle theta F Judging whether the detector can receive the reflected light of the target satellite or not according to the size relation;
the order received by the ith element of the target satelliteThe irradiance of each ground surface element is: q ls (i)＝Q ls ·cos(θ S (i) ); wherein Q is ls Represents the irradiance of the light source at the target satellite as theta S (i) The angle of incidence of the ray representing the ith ground element, Q ls (i) Irradiance of a single ground surface element received by an ith element on the target satellite;
according to a radiation illumination transfer formula, the radiation illumination of the detector by the ith bin of the target satellite is as follows:
Figure BDA0003099037250000051
wherein alpha is i Is the reflectivity of the ith element, S (i) is the area of the ith element, R sf Distance of target satellite from detector, Q sf (i) Irradiance of the detector for the ith bin of the target satellite, theta F (i) Observing a zenith angle; the discrimination coefficient eta of the shielding of the bin of the target satellite is as follows:
Figure BDA0003099037250000052
wherein, theta S At the incident zenith angle, theta F To observe the zenith angle.
The radiation illumination of the target satellite to the detector when a single earth effective surface element is taken as a unique light source is as follows:
Figure BDA0003099037250000053
wherein Q is sf (i) The radiation illumination of the ith surface element of the target satellite to the detector is obtained, eta (i) is the shielding judgment coefficient of the ith surface element of the target satellite, n is the total surface element number of the target satellite, and Q is sf Is the total irradiance of the target satellite to the detector.
In the third step, the radiation illuminance of the target satellite to the detector is obtained by adding the radiation illuminance of the target satellite to the detector when the earth is used as a light source, and the third step includes: according to the radiation illumination of the detector by the target satellite when a single effective surface element is used as a unique light source, the radiation illumination of the target satellite based on the whole earth reflected light can be obtained by superposing all the effective surface elements
Figure BDA0003099037250000054
S Is effective Is the effective surface area.
In the fourth step, the correction method for correcting the observation data includes:
Figure BDA0003099037250000055
wherein the real-time radiation illumination of the target satellite obtained from the target satellite to the detector is Q A Correcting the observed data to Q J When the earth is used as a light source, the radiation illumination of the target satellite to the detector is
Figure BDA0003099037250000061
In the fifth step, the attitude estimation method of the target satellite comprises the following steps: state vector
Figure BDA0003099037250000062
Wherein δ p represents an error rodgerge parameter; omega is the rolling angular velocity of the target satellite, and the target attitude refers to the attitude of the target specimen system relative to the earth inertial coordinate system; the state vector is subjected to tasteless transformation to obtain 2n +1 sigma points, and the expression is as follows:
Figure BDA0003099037250000063
Figure BDA0003099037250000064
wherein λ ═ α 2 (n + κ) -n, which is a scaling factor, typically κ ═ 3-n;
Figure BDA0003099037250000065
the sigma (i) is the ith sigma point of the current state quantity; filtering value at k time
Figure BDA0003099037250000066
As the current mean value sigmPoint a, is marked as
Figure BDA0003099037250000067
Figure BDA0003099037250000068
A filtering value of the state covariance matrix at the moment k; by P i Represents the ith column of the matrix P; chol (P) represents the cholesky decomposition of the matrix P, with the corresponding weights:
Figure BDA0003099037250000069
where n is the dimension of the state vector, W mean Denotes the mean value, W cov Represents the covariance, alpha is the coefficient controlling the degree of sigma point spread, and the range is usually [10 ] -4 ,1](ii) a Beta is a weight value adjustment coefficient, and is usually 2; λ ═ α 2 (n + κ) -n, which is a scaling factor, typically κ ═ 3-n; the sigma of the error quaternion is obtained,
Figure BDA0003099037250000071
Figure BDA0003099037250000072
wherein, a is 1, f is 2(a +1),
Figure BDA0003099037250000073
representing the first three components of a quaternion
Figure BDA0003099037250000074
Fourth component representing quaternion
Figure BDA0003099037250000075
Representing a quaternion error component; then the conversion from the error quaternion to the quaternion is carried out,
Figure BDA0003099037250000076
wherein,
Figure BDA0003099037250000077
represents the mean of the current quaternion sigma point,
Figure BDA0003099037250000078
the error quaternion representing the ith sigma point is a quaternion value obtained by multiplying and converting the quaternion,
Figure BDA0003099037250000079
representing an error quaternion of the ith sigma point; the quaternion multiplication is defined as follows,
Figure BDA00030990372500000710
wherein,
Figure BDA00030990372500000711
for the three-dimensional vector a, [ a ] a-]A matrix of cross-product of vectors is represented,
Figure BDA00030990372500000712
q a and q is b Represents any two quaternions; quaternion sigma point and angular velocity sigma point,
Figure BDA00030990372500000713
wherein,
Figure BDA00030990372500000714
Δ t is the detector sampling time interval; r (omega) k ) Discretizing in time domain by a kinetic equation; based on the transmitted quaternion sigma point, the conversion of error Rodrigue parameter point is carried out,
Figure BDA00030990372500000715
wherein, the conjugated quaternary elementNumber q of -1 Is defined as
Figure BDA0003099037250000081
In turn, the user can then,
Figure BDA0003099037250000082
wherein, a is 1, f is 2(a + 1). Let its mean value sigma point
Figure BDA0003099037250000083
The sigma point of the state vector after transfer is obtained as
Figure BDA0003099037250000084
Finally, the state updating and the covariance updating are carried out in a weighted summation mode,
Figure BDA0003099037250000085
in the formula, Q k+1 Process noise covariance as discrete time; the observation predicted value of each sigma point can be calculated by an observation equation,
Figure BDA0003099037250000086
h represents an observation equation;
Figure BDA0003099037250000087
the observation predicted value corresponding to the sigma point is obtained; and then obtaining an observation prediction mean value, a measurement covariance and a cross covariance by weighted summation:
Figure BDA0003099037250000088
Figure BDA0003099037250000089
R k+1 to represent
Figure BDA00030990372500000810
The measured covariance is represented as a function of the measured covariance,
Figure BDA00030990372500000811
the cross-covariance is expressed as a cross-covariance,
Figure BDA00030990372500000812
representing the observation predicted value of the k +1 step; the calculation of the Kalman gain is carried out,
Figure BDA00030990372500000813
K k+1 the Kalman gain of the (k +1) th filtering is represented; a state update and a covariance update,
Figure BDA00030990372500000814
in the formula,
Figure BDA00030990372500000815
for the device observation at time k +1, i.e. corrected target satellite observation data Q J (ii) a Converting the error rodgerge parameter in the state filtered value into a quaternion and zeroing the error rodgerge parameter before the next filtering is started, i.e.
Figure BDA00030990372500000816
Figure BDA00030990372500000817
Represents the state vector at the time of the (k +1) th filtering, 0 3×1 A zero matrix of 3 rows and 1 column is shown.
The invention has the following beneficial effects:
1. the invention accurately calculates the illumination of the earth reflected light to the satellite and the total illumination of the satellite received by the detector by carrying out gridding processing on the earth model, and the model considers the influence of the volume of the earth and the orbit height factor of the satellite on the simulation result in detail.
2. The brightness change of the satellite caused by earth reflected light in one year is simulated, and the following two situations are considered: first, sunlight cannot reach the earth due to lunar obstruction. And secondly, the satellite is in the earth shadow area and cannot be irradiated by the earth reflected light. And thirdly, shielding relation among surface elements of the satellite.
3. Based on the established earth reflection light model, the obtained satellite observation data can be corrected, and the corrected data is input into the odorless Kalman filter, so that the estimation precision of the satellite attitude can be greatly improved.
4. On the other hand, the ratio of the influence of the earth reflected light on satellite observation at different moments is given, for example, observation can be carried out at a moment with weaker influence in order to reduce the influence, and the method has certain guiding significance for the research of satellite observers.
Drawings
Fig. 1 is a schematic flow chart of a method for estimating satellite attitude through terrestrial reflected light correction according to the present invention.
FIG. 2 is a schematic diagram of the surface of the earth divided into a plurality of bins by a grid of latitudes and longitudes.
FIG. 3 is a schematic diagram of the floor surface element (i, j) length and width calculations.
Fig. 4 is a schematic diagram of ground surface element reflection.
Fig. 5 is a schematic diagram of a detector receiving satellite reflected light.
Fig. 6-1 is a front view of an effective surface element.
Fig. 6-2 is a top view of an effective surface element.
Fig. 7 shows the illuminance of the GEO satellite on the detector within a year when the earth reflects light.
FIG. 8 is a plot of the effect of earth reflected light on GEO satellite observations at different times of the year.
FIG. 9-1 is an uncorrected satellite Euler angle θ 1 And filtering the estimation graph.
FIG. 9-2 is an uncorrected satellite Euler angle θ 2 And filtering the estimation graph.
FIG. 9-3 is an uncorrected satellite Euler angle θ 3 And filtering the estimation graph.
FIG. 10-1 is a corrected satellite Euler angle θ 1 And filtering the estimation graph.
FIG. 10-2 is a corrected satellite Euler angle θ 2 And filtering the estimation graph.
FIG. 10-3 is a graph of corrected satellite Euler angles θ 3 And filtering the estimation graph.
Detailed Description
In the embodiment of the present invention, the first and second substrates,the GEO satellite is observed by assuming that the detector is positioned on the earth surface (75.5966 DEG E,30.0386 DEG N,0m) and taking one year as the observation time (1 Jan 202100: 00:00.000 UTCG-1 Jan 202200: 00:00.000UTCG) and 60s as the observation interval. Setting satellite size to 5 × 5 × 5m 3 Attitude is unstable rolling, initial angular velocity [ 0-0.10 ]]The quaternion of initial state is [ -0.6469240.401929-0.3330140.555917 ]]. The observation noise was set to 0.05m in standard deviation 2 Is zero mean white noise. The reflectivity of each face of the satellite was 0.3. As shown in fig. 1, the invention discloses a satellite attitude estimation method for correcting terrestrial reflected light, which comprises the following steps:
the method comprises the following steps: dividing the earth surface into a plurality of surface elements according to a longitude and latitude grid, and calculating the area of the surface elements; screening effective surface elements based on the shielding relation among the sun, the earth and a target satellite;
as shown in fig. 2, the earth surface is divided into grid surface elements according to a longitude and latitude grid, the surface element center is located at a longitude and latitude point (i, j) (i, j ∈ N), and the length and the width are respectively a latitude distance and a longitude distance.
As shown in FIG. 3, the radius of the earth is R E Each surface element can be regarded as a rectangular plane with the center located at a longitude and latitude point (i, j) (i, j ∈ N), and the length and width are respectively a latitude distance and a longitude distance, and the length of each surface element is: l. the j ＝2πR E A/360; a ground surface element at latitude i, with a width of: d i ＝2πR E cosi/360; the area of the ground surface element is: s is ij ＝l j d i (ii) a Wherein l j Is the length of the surface element at longitude j, d i Is the width, s, of the ground surface element at latitude i ij Is the surface area, R E I, j represent latitude and longitude, respectively, for the radius of the earth.
As shown in fig. 4, the screening method for screening effective surface elements includes: the incident zenith angle of sunlight on the ground surface element is theta in The reflection zenith angle is theta out The method for screening the effective surface element comprises the following steps:
Figure BDA0003099037250000111
wherein, theta in The angle of incidence zenith, θ, of sunlight on a ground element out Is a reflection zenith angle.
Step two: according to a radiation illumination transfer rule, namely an inverse proportion law of radiation illumination and distance square, calculating the radiation illumination of a solar visible light wave band at each effective surface element, and calculating the radiation illumination of the effective surface elements generated at a target satellite according to a Lambert reflection principle, the method comprises the following steps: according to the inverse law of the radiation illumination and the square of the distance, under the condition that sunlight is not shielded, the radiation illumination of a solar visible light waveband at each effective surface element is obtained:
Figure BDA0003099037250000112
wherein R is 0 Is the average distance of the day and the ground within one year; q 0 Is at a distance R from the sun 0 Wherein, the irradiance of visible light wave band (0.4-0.7 μm) part, R is the distance from the ground surface element to the sun, and Q is the irradiance of visible light wave band (0.4-0.7 μm) at the effective surface element of R distance from the sun.
For example: suppose the average distance R of the day and the ground within one year 0 Is 1.495 x 10 8 km, then at distance R 0 The irradiance Q integrated in the visible light band (0.4-0.7 μm) 0 Is 438.894W/m 2 . According to the fact that the solar irradiance is inversely proportional to the square of the distance, the irradiance of the solar visible light wave band at any position can be expressed as the irradiance of the sunlight in the condition that the sunlight is not shielded
Figure BDA0003099037250000113
In the second step, the method for calculating the radiation illumination generated by the effective surface element at the target satellite to obtain the radiation illumination of a single ground surface element on the satellite comprises the following steps: the illumination of the solar radiation on the earth surface is as follows:
Figure BDA0003099037250000114
wherein R is 0 Is the average distance between the day and the ground in a year, R se Distance of the sun from the earth, Q se Is a Chinese character ofIrradiance, Q, of sun on the earth's surface 0 To be at a distance R from the sun 0 The radiation illumination of a visible light wave band; assuming that the total average albedo value of the earth's surface and the earth's surface atmosphere is
Figure BDA0003099037250000115
The radiance generated by the surface element for each direction can be calculated as:
Figure BDA0003099037250000116
wherein, theta in Is the incident zenith angle, Q, of sunlight to the ground surface element se cosθ in Illuminance of solar radiation received for a ground surface element; a single ground surface element (i, j) is at
Figure BDA0003099037250000121
The radiation illuminance generated at the directional target satellite is:
Figure BDA0003099037250000122
wherein,
Figure BDA0003099037250000123
is the direction vector of the bin pointing to the target satellite,
Figure BDA0003099037250000124
the ground surface element forming a solid angle, s, with respect to the target satellite ij Is the area of the ground surface element with longitude and latitude located in (i, j),
Figure BDA0003099037250000125
is the distance, Q, from the ground surface element to the target satellite ij For a single ground surface element (i, j) at
Figure BDA0003099037250000126
The radiation illuminance generated at the directional target satellite.
Step three: according to the radiation illumination generated by the effective surface elements at the target satellite, calculating the radiation illumination of the target satellite to the detector by taking each effective surface element as a light source according to the Lambert reflection principle; will be provided withAdding the radiation illumination of the target satellite to the detector to obtain the radiation illumination of the target satellite to the detector when the earth is used as a light source; the method for calculating the radiation illumination of the detector by the satellite by using each effective surface element as a light source according to the radiation illumination of the effective surface element generated at the target satellite by using the Lambert reflection principle comprises the following steps: the satellite reflection model is shown in FIG. 5, taking a cube star with a side length of 5m as an example, and the vector of the sun pointing to the target, i.e. the incident light vector, is set to be lambda S (ii) a Let the vector of the target pointing to the detector, i.e. the observation vector, be λ F (ii) a The normal vector of a certain surface element of the satellite is n; defining the included angle between the incident vector and the normal vector of the surface element as the incident zenith angle, and recording the angle as theta S Defining the included angle between the observation vector and the normal vector of the surface element as the observation zenith angle, and recording as theta F . The expression is as follows:
Figure BDA0003099037250000127
according to incident zenith angle theta S And observing the zenith angle theta F The size relationship of (2) determines whether the detector can receive the satellite reflected light.
The irradiance of the single ground surface element received by the ith element on the target satellite is as follows:
Q ls (i)＝Q ls ·cos(θ S (i) ); wherein Q is ls Represents the irradiance of the light source at the satellite as theta S (i) Representing the angle of incidence of the ray of the ith ground element. According to a radiation illumination transfer formula, the radiation illumination of the detector by the ith bin of the satellite is as follows:
Figure BDA0003099037250000128
wherein alpha is i Is the reflectivity of the ith element, S (i) is the area of the ith element, R sf Distance of the satellite from the detector, Q sf (i) Irradiance, theta, of the detector for the ith element of the satellite F (i) To observe the zenith angle. The satellite surface element shielding discrimination coefficient eta is as follows:
Figure BDA0003099037250000131
wherein, theta S At the incident zenith angle, theta F To observe zenith angles.
The radiation illumination of the detector by the satellite when a single effective surface element of the earth is taken as a unique light source is as follows:
Figure BDA0003099037250000132
wherein Q is sf (i) The radiation illumination of the detector is represented by the ith bin of the satellite, eta (i) is the shielding discrimination coefficient of the ith bin of the satellite, n is the total bin number of the satellite, and Q sf Is the total irradiance of the satellite to the detector.
In the third step, when the obtained radiation illumination is superposed to obtain the radiation illumination of the detector by the satellite when the whole earth is used as a light source, the method comprises the following steps: according to the radiation illumination of the detector by the satellite when a single effective surface element is used as a unique light source, the radiation illumination of the satellite based on the whole earth reflected light can be obtained by superposing all effective surface elements
Figure BDA0003099037250000133
S Is effective The active surface area is shown in fig. 6-1 and 6-2.
Step four: subtracting the radiation illuminance of the target satellite to the detector when the earth is used as a light source from the real-time radiation illuminance of the target satellite to the detector obtained from the target satellite to obtain corrected observation data of the radiation illuminance of the target satellite to the detector when only the sun is used as the light source;
and according to the processes of the first step, the second step and the third step, calculating the radiation illumination of the GEO orbit satellite to the detector when the earth is used as the only light source by taking one year as simulation time. Fig. 7 shows simulation results when GEO-orbiting satellites are used as objects of study, and fig. 8 shows the influence of different earth reflected lights on satellite observation results.
In the fourth step, the method for correcting the observation data of the target satellite for correcting the radiation illuminance of the detector when only the sun is used as the light source comprises the following steps:
Figure BDA0003099037250000134
wherein the real-time radiation illumination of the target satellite obtained from the target satellite to the detector is Q A Correcting the observed data to Q J When the earth is used as a light source, the radiation illumination of the target satellite to the detector is
Figure BDA0003099037250000135
Step five: and based on the corrected observation data, performing attitude estimation on the target satellite by using an odorless Kalman filtering method to obtain the earth reflected light correction data. For example: and selecting the observation data of the observation station from 40 points at 1 month, 1 day, evening and 16 hours to 18 hours and 40 points for posture estimation. The calculated ratio of the influence of the earth reflected light is 0.1-0.2. In order to avoid the possible singular value problem in the process of calculating the three-component parameter, the invention selects the quaternion with relative linearity of operation as the description parameter. Quaternion is defined as q ═ epsilon T q 4 ] T ，ε T Being a three-dimensional vector, q 4 Is a scalar quantity and satisfies a constraint q T q is 1. The attitude motion equation and the angular velocity dynamic equation expressed by the quaternion are as follows:
Figure BDA0003099037250000141
in the formula,
Figure BDA0003099037250000142
E 3×3 denotes a 3 × 3 identity matrix, ω (t) ═ ω x ω y ω z ] T Representing the angular velocity of the target in the system, pi (t) is the sum of the external moment applied to the target and the self-control force, and J is the moment of inertia of the target. w (t) and v (t) are process noise and observation noise, respectively, and are replaced by white gaussian noise with an average value of 0. For the three-dimensional vector a, [ a ] a]A matrix of cross-product of vectors is represented,
Figure BDA0003099037250000143
the quaternion attitude transfer matrix is: a (q) xi (q) T Ψ (q); in the formula,
Figure BDA0003099037250000144
the observation equation is established as:
Figure BDA0003099037250000145
wherein k is the observation time, Q 0 Is the sun constant, R sf Distance of satellite from detector, theta i (k) The incident zenith angle theta of the ith bin of the satellite at the kth moment r (k) The observation zenith angle of the ith surface element at the kth moment is shown, eta (k) is a surface element shielding judgment coefficient at the kth moment, S (i) is the area of the ith surface element of the satellite, n is the total number of the surface elements of the satellite, and 6 is taken here. State vector
Figure BDA0003099037250000146
Wherein δ p represents an error rodgerge parameter; omega is the rolling angular velocity of the satellite, and the target attitude refers to the attitude of the eye specimen system relative to the earth inertial coordinate system; the state vector is subjected to tasteless transformation to obtain 2n +1 sigma points, and the expression is as follows:
Figure BDA0003099037250000151
wherein λ ═ α 2 (n + κ) -n, which is a scaling factor, typically κ ═ 3-n;
Figure BDA0003099037250000152
the sigma (i) is the ith sigma point of the current state quantity; filtering value at k time
Figure BDA0003099037250000153
As the current mean sigma point, is recorded as
Figure BDA0003099037250000154
Figure BDA0003099037250000155
A filtering value of the state covariance matrix at the moment k; with P i Represents the ith column of the matrix P; chol (P) represents the cholesky decomposition of the matrix P, with the corresponding weights:
Figure BDA0003099037250000156
where n is the dimension of the state vector, W mean Denotes the mean value, W cov Represents the covariance, alpha is the coefficient controlling the degree of sigma point spread, and the value range is usually [10 ] -4 ,1](ii) a Beta is a weight adjustment coefficient, and is usually 2; λ ═ α 2 (n + k) -n, which is a scaling factor, is usually 3-n. The sigma of the error quaternion is obtained,
Figure BDA0003099037250000157
wherein a is 1, f is 2(a +1),
Figure BDA0003099037250000158
the first three components of the quaternion are represented,
Figure BDA0003099037250000159
fourth component representing quaternion
Figure BDA00030990372500001510
Representing a quaternion error component; then the conversion from the error quaternion to the quaternion is carried out,
Figure BDA00030990372500001511
wherein,
Figure BDA00030990372500001512
represents the mean of the current quaternion sigma point,
Figure BDA00030990372500001513
error quaternion representing ith sigma pointAccording to the quaternion value obtained by quaternion multiplication conversion,
Figure BDA00030990372500001514
representing an error quaternion of the ith sigma point;
the quaternion multiplication may be defined as follows,
Figure BDA0003099037250000161
wherein,
Figure BDA0003099037250000162
for the three-dimensional vector a, [ a ] a]A matrix of cross-product of vectors is represented,
Figure BDA0003099037250000163
q a and q is b Representing any two quaternions.
Quaternion sigma point and angular velocity sigma point,
Figure BDA0003099037250000164
wherein,
Figure BDA0003099037250000165
Δ t is the detector sampling time interval; Γ (ω [. omega. ]) k ) Discretizing in a time domain by a kinetic equation;
based on the transmitted quaternion sigma point, the conversion of error Rodrigue parameter point is carried out,
Figure BDA0003099037250000166
wherein, the conjugate quaternion q -1 Is defined as
Figure BDA0003099037250000167
In turn, the user can then,
Figure BDA0003099037250000168
wherein, a is 1, f is 2(a + 1). Let its mean value sigma point
Figure BDA0003099037250000169
The sigma point of the state vector after transfer is obtained as
Figure BDA00030990372500001610
Finally, the state updating and the covariance updating are carried out in a weighted summation mode,
Figure BDA00030990372500001611
in the formula, Q k+1 Is the process noise covariance in discrete time. The observation predicted value of each sigma point can be calculated by an observation equation,
Figure BDA0003099037250000171
h denotes an observation equation.
Figure BDA0003099037250000172
The observation predicted value corresponding to the sigma point is obtained; and then obtaining an observation prediction mean value, a measurement covariance and a cross covariance by weighted summation:
Figure BDA0003099037250000173
Figure BDA0003099037250000174
R k+1 to represent
Figure BDA0003099037250000175
The measured covariance is represented as a function of the measured covariance,
Figure BDA0003099037250000176
the cross-covariance is expressed as a cross-covariance,
Figure BDA0003099037250000177
and (4) representing the observed predicted value of the step (k + 1).
And (3) calculating the Kalman gain,
Figure BDA0003099037250000178
K k+1 the kalman gain of the (k +1) th filtering is shown. A state update and a covariance update,
Figure BDA0003099037250000179
in the formula,
Figure BDA00030990372500001710
for the device observation at time k +1, i.e. corrected satellite observation data Q J . Finally, the error rodgerge parameter in the state filtering value is converted into quaternion, and the error rodgerge parameter is set to zero before the next filtering is started, namely
Figure BDA00030990372500001711
The resulting pose estimation results are shown in fig. 9-1, 9-2, and 9-3.
As a comparative experiment, uncorrected satellite observation data Q A As observed data in the non-odor filter, i.e., in the equation in the state update in step five,
Figure BDA00030990372500001712
the estimation results are shown in FIG. 10-1, FIG. 10-2, and FIG. 10-3. As can be seen from the result graph, the attitude estimation is performed based on the corrected satellite observation data, and the estimation accuracy and the convergence rate can be obtained more quickly. Therefore, the invention has great application value.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (10)

1. A method for estimating the attitude of a satellite corrected by terrestrial reflected light is characterized by comprising the following steps:
the method comprises the following steps: dividing the earth surface into a plurality of surface elements according to a longitude and latitude grid, and calculating the area of the surface elements; screening effective surface elements based on the shielding relation among the sun, the earth and a target satellite;
step two: according to an inverse proportion law of the radiation illumination and the square of the distance, calculating the radiation illumination of the solar visible light wave band at each effective surface element, and calculating the radiation illumination of the effective surface elements at the target satellite according to a Lambert reflection principle;
step three: according to the radiation illumination generated by the effective surface elements at the target satellite, calculating the radiation illumination of the target satellite to the detector when each effective surface element is taken as a light source through a Lambert reflection principle; adding the radiation illumination of the target satellite to the detector to obtain the radiation illumination of the target satellite to the detector when the earth is used as a light source;
step four: subtracting the radiation illuminance of the target satellite to the detector when the earth is used as a light source from the real-time radiation illuminance of the target satellite to the detector obtained from the target satellite to obtain corrected observation data of the radiation illuminance of the target satellite to the detector when only the sun is used as the light source;
step five: and based on the corrected observation data, performing attitude estimation on the target satellite by using an odorless Kalman filtering method to obtain the earth reflected light correction data.
2. The method for estimating the attitude of an earth-reflected-light-corrected satellite according to claim 1, wherein in the first step, the method for dividing the surface of the earth into a plurality of bins according to a graticule comprises: based on a longitude and latitude grid on the earth surface, the center of a surface element is located at a longitude and latitude point, and the length and the width are respectively a latitude distance and a longitude distance.
3. The method for estimating an attitude of an earth-reflected-light-corrected satellite according to claim 1 or 2, wherein in step one, the method for calculating the bin area comprises:
each ground surfaceThe element length is: l j ＝2πR E /360；
A ground surface element at latitude i, with a width of: d i ＝2πR E cosi/360；
The area of the ground surface element is: s is ij ＝l j d i ；
Wherein l j Is the length of the surface element at longitude j, d i Is the width, s, of the ground surface element at latitude i ij Is the area of the surface element, R E I, j represent latitude and longitude, respectively, for the radius of the earth.
4. A method of estimating an attitude of an earth-reflected light corrected satellite according to any one of claims 1-3, wherein in step one, the method of screening for effective bins comprises:
Figure FDA0003099037240000021
wherein, theta in Is the incident zenith angle, theta, of sunlight to the ground surface element out Is a reflection zenith angle.
5. The method for estimating satellite attitude based on correction of terrestrial reflected light according to claim 1, wherein in the second step, the method for calculating the irradiance of the visible light band of the sun at each effective bin comprises:
according to the inverse law that the radiation illumination is in inverse proportion to the square of the distance, under the condition that sunlight is not shielded, the radiation illumination of a solar visible light wave band at each effective surface element is obtained:
Figure FDA0003099037240000022
wherein R is 0 Is the average distance of the day and the ground within one year; q 0 Is at a distance R from the sun 0 The irradiance of visible light (0.4-0.7 μm), R is the distance from ground surface element to sun, and Q is the distance from ground surface element to sunAnd (3) the radiation illumination of a visible light wave band (0.4-0.7 mu m) at the effective surface area from the sun R.
6. The method for estimating satellite attitude based on terrestrial reflected light correction according to claim 1 or 5, wherein in step two, the method for calculating the irradiance of the target satellite with the effective bin according to the lambertian reflection principle to obtain the irradiance of the target satellite with a single terrestrial surface element comprises:
the illumination of the solar radiation on the earth surface is as follows:
Figure FDA0003099037240000031
wherein R is 0 Is the average distance between the day and the ground in a year, R se Distance of sun to earth, Q se Irradiance, Q, of the sun at the earth's surface 0 To be at a distance R from the sun 0 The radiation illumination of a visible light wave band;
the radiant brightness of the ground surface element generated in each direction is as follows:
Figure FDA0003099037240000032
wherein, theta in Is the incident zenith angle, Q, of sunlight to the ground surface element se cosθ in The total average albedo value of the illuminance of the solar radiation received by the surface elements of the earth and the surface atmosphere is
Figure FDA0003099037240000033
L ij The radiation brightness generated by the ground surface element to each direction;
a single ground surface element (i, j) is at
Figure FDA0003099037240000034
The radiation illuminance generated at the directional target satellite is:
Figure FDA0003099037240000035
wherein,
Figure FDA0003099037240000036
is the direction vector of the bin pointing to the target satellite,
Figure FDA0003099037240000037
the ground surface element forming a solid angle, s, with respect to the target satellite ij Is the area of the ground surface element with longitude and latitude located in (i, j),
Figure FDA0003099037240000038
is the distance, Q, from the ground surface element to the target satellite ij For a single ground surface element (i, j) in
Figure FDA0003099037240000039
The radiation illuminance generated at the directional target satellite.
7. The method for estimating satellite attitude through terrestrial reflected light correction according to claim 1, wherein in step three, the method for calculating the irradiance of the target satellite on the detector by using lambertian reflection principle according to the irradiance of the target satellite generated by the effective surface elements in the target satellite, and when each effective surface element is taken as a light source, the method comprises the following steps:
Figure FDA00030990372400000310
wherein the vector of the sun pointing to the target, i.e. the incident light vector, is lambda S (ii) a The vector of the target pointing to the detector, i.e. the observation vector, is lambda F (ii) a The normal vector of a certain surface element of the target satellite is n; the included angle between the incident vector and the normal vector of the surface element is the incident zenith angle and is recorded as theta S The included angle between the observation vector and the normal vector of the surface element is the observation zenith angle and is recorded as theta F (ii) a According to incident zenith angle theta S Observing the zenith angle theta F Whether the detector can receive the data is judged according to the magnitude relation of the dataReflecting light by the target satellite;
the irradiance of the single ground surface element received by the ith element on the target satellite is as follows:
Q ls (i)＝Q ls ·cos(θ S (i))；
wherein Q is ls Represents the irradiance of the light source at the target satellite as theta S (i) The angle of incidence of the ray representing the ith ground element, Q ls (i) Irradiance of a single ground surface element received by an ith element on the target satellite; according to a radiation illumination transfer formula, the radiation illumination of the detector by the ith bin of the target satellite is as follows:
Figure FDA0003099037240000041
wherein alpha is i Is the reflectivity of the ith element, S (i) is the area of the ith element, R sf Distance of target satellite from detector, Q sf (i) Irradiance of the detector for the ith bin of the target satellite, theta F (i) To observe zenith angles; the target satellite surface element shielding judgment coefficient eta is as follows:
Figure FDA0003099037240000042
wherein, theta S Is incident zenith angle, theta F To observe zenith angles;
the radiation illumination of the target satellite to the detector when a single earth effective surface element is taken as a unique light source is as follows:
Figure FDA0003099037240000043
wherein Q is sf (i) The radiation illumination of the detector is the ith surface element of the target satellite, eta (i) is the shielding discrimination coefficient of the ith surface element of the target satellite, n is the total surface element number of the target satellite, and Q is sf The total irradiance of the target satellite to the detector.
8. The method for estimating satellite attitude through terrestrial reflected light correction according to claim 1 or 7, wherein in the third step, the irradiance of the target satellite on the detector when the light source is the earth is obtained by adding the irradiance of the target satellite on the detector, and the method comprises:
according to the radiation illumination of the target satellite to the detector when a single effective surface element is used as a unique light source, the radiation illumination of the target satellite based on the whole earth reflected light can be obtained by superposing all the effective surface elements
Figure FDA0003099037240000051
S Is effective Is the effective surface area.
9. The method for estimating satellite attitude based on earth reflected light correction according to claim 1, wherein in the fourth step, the method for correcting observation data includes:
Figure FDA0003099037240000052
wherein the real-time radiation illumination of the target satellite obtained from the target satellite to the detector is Q A Corrected observation data is Q J When the earth is used as a light source, the radiation illumination of the target satellite to the detector is
Figure FDA0003099037240000053
10. The method as claimed in claim 1, wherein the method for estimating the attitude of the target satellite in the fifth step comprises:
state vector
Figure FDA0003099037240000054
Wherein δ p represents an error rodger parameter; omega is the rolling angular velocity of the target satellite, and the target attitude indicates the system phase of the eye specimenAttitude to the earth inertial coordinate system;
the state vector is subjected to tasteless transformation to obtain 2n +1 sigma points, and the expression is as follows:
Figure FDA0003099037240000055
wherein λ ═ α 2 (n + κ) -n, which is a scaling factor, typically κ ═ 3-n;
Figure FDA0003099037240000061
the sigma (i) is the ith sigma point of the current state quantity; filtering value at k time
Figure FDA0003099037240000062
As the current mean sigma point, record
Figure FDA0003099037240000063
A filtering value of the state covariance matrix at the moment k; by P i Represents the ith column of the matrix P; chol (P) represents the cholesky decomposition of the matrix P, with the corresponding weights:
Figure FDA0003099037240000064
where n is the dimension of the state vector, W mean Denotes the mean value, W cov Represents the covariance, alpha is the coefficient controlling the degree of sigma point spread, and the value range is usually [10 ] -4 ,1](ii) a Beta is a weight value adjustment coefficient, and is usually 2; λ ═ α 2 (n + κ) -n, which is a scaling factor, typically κ ═ 3-n; the sigma of the error quaternion is obtained,
Figure FDA0003099037240000065
Figure FDA0003099037240000066
wherein a is 1, f is 2(a +1),
Figure FDA0003099037240000067
representing the first three components of a quaternion
Figure FDA0003099037240000068
Fourth component representing quaternion
Figure FDA0003099037240000069
Representing a quaternion error component; then the conversion from the error quaternion to the quaternion is carried out,
Figure FDA00030990372400000610
wherein,
Figure FDA00030990372400000611
represents the mean of the current quaternion sigma point,
Figure FDA00030990372400000612
expressing the quaternion value obtained by the quaternion multiplication conversion of the error quaternion of the ith sigma point,
Figure FDA00030990372400000613
representing an error quaternion of the ith sigma point; the quaternion multiplication is defined as follows,
Figure FDA00030990372400000614
wherein,
Figure FDA0003099037240000071
for the three-dimensional vector a, [ a ] a-]Representing a vector cross product matrix，
Figure FDA0003099037240000072
q a And q is b Represents any two quaternions;
quaternion sigma point and angular velocity sigma point,
Figure FDA0003099037240000073
wherein,
Figure FDA0003099037240000074
Δ t is the detector sampling time interval; Γ (ω [. omega. ]) k ) Discretizing in a time domain by a kinetic equation; based on the transmitted quaternion sigma point, the conversion of error Rodrigue parameter point is carried out,
Figure FDA0003099037240000075
wherein, the conjugate quaternion q -1 Is defined as
Figure FDA0003099037240000076
In turn, the user can then,
Figure FDA0003099037240000077
wherein, a is 1, f is 2(a + 1). Let its mean value sigma point
Figure FDA0003099037240000078
The sigma point of the state vector after transfer is obtained as
Figure FDA0003099037240000079
Finally, the state updating and the covariance updating are carried out in a weighted summation mode,
Figure FDA00030990372400000710
in the formula, Q k+1 Process noise covariance as discrete time; the observation predicted value of each sigma point can be calculated by the observation equation,
Figure FDA0003099037240000081
h represents an observation equation;
Figure FDA0003099037240000082
the observation predicted value corresponding to the sigma point is obtained; and then obtaining an observation prediction mean value, a measurement covariance and a cross covariance by weighted summation:
Figure FDA0003099037240000083
Figure FDA0003099037240000084
R k+1 to represent
Figure FDA0003099037240000085
The measured covariance is represented as a function of the measured covariance,
Figure FDA0003099037240000086
the cross-covariance is expressed as a cross-covariance,
Figure FDA0003099037240000087
representing the observation predicted value of the k +1 step; the calculation of the Kalman gain is carried out,
Figure FDA0003099037240000088
K k+1 the Kalman gain of the (k +1) th filtering is represented;
a state update and a covariance update,
Figure FDA0003099037240000089
in the formula,
Figure FDA00030990372400000810
for the device observation at the k +1 th time, i.e. corrected target satellite observation data Q J (ii) a Converting the error rodgerge parameter in the state filtered value into a quaternion and zeroing the error rodgerge parameter before the next filtering is started, i.e.
Figure FDA00030990372400000811
Represents the state vector at the time of the (k +1) th filtering, 0 3×1 Representing a zero matrix of 3 rows and 1 column.
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