CN112013874B - Satellite-borne laser altimeter on-orbit calibration method based on laser footprint prior coordinate - Google Patents
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Abstract
The invention relates to an on-orbit calibration method of a satellite-borne laser altimeter based on a laser footprint priori coordinate, which comprises the steps of taking observation parameters of the satellite-borne laser altimeter and a satellite platform and the laser footprint priori coordinate as input, taking a zenith angle and an azimuth angle of a laser pointing vector and a system error of a laser ranging value as variables, constructing a distance offset model of the laser footprint, solving a first-order partial derivative of each system error variable by the distance offset square sum on the basis of the minimization of the square sum of a plurality of distance offsets to establish an error equation set, and realizing the on-orbit calibration of the system error of the laser pointing zenith angle and azimuth angle and the laser ranging value by simultaneous solution of the error equation set. The method is not only suitable for on-orbit calibration of the satellite-borne laser altimeter without attitude maneuvering capability, but also can realize calibration of system errors of laser pointing and laser ranging at the same time.
Description
Technical Field
The invention belongs to the field of laser remote sensing, and particularly relates to an on-orbit calibration method for a satellite-borne laser altimeter, which is suitable for on-orbit calibration of laser pointing direction and distance of the satellite-borne laser altimeter under the condition that the geometric coordinates of a laser footprint are known.
Background
The satellite-borne laser altimeter is a new type of earth observation equipment carried on satellite platform, and can accurately obtain the distance between satellite and ground targetThe distance of (c). And high-precision calculation of the laser footprint geometric positioning coordinate can be realized by combining the information such as the position, the attitude, the laser pointing direction and the like of the satellite platform. The principle of the geometrical positioning of the laser footprint of the satellite-borne laser altimeter is shown in fig. 1, which is the fusion result of data acquired by three sensors, namely the satellite-borne laser altimeter, a satellite positioning system and a satellite attitude determination system. According to the principle of vector superposition, the laser footprint has coordinate vectors in the world coordinate
Can be expressed as:
in the formula,
representing satellite platform position vectors acquired by a satellite positioning system,
representing the satellite positioning system to laser altimeter offset vector,
and the laser ranging vector is determined by the ranging value of the laser altimeter and the laser pointing vector, wherein the laser pointing vector can be expressed by a zenith angle and an azimuth angle under an international terrestrial coordinate system.
The solution of the laser footprint geometric positioning coordinates involves a variety of coordinate frames: 1) the laser altimeter carrier coordinate system takes a laser emission reference point as an original point, the z axis points downwards to the normal direction of the optical platform, the x axis points to the flight direction of the satellite, and the y axis meets the right-hand rule; 2) the satellite platform coordinate system takes the antenna phase center of a GPS or BDS as an origin, the z axis points to the earth mass center (geocentric), the x axis points to the satellite flight direction, and the y axis meets the right-hand rule; 3) the attitude platform coordinate system takes a platform reference center as an original point, a z axis points to the normal direction of the inertial platform downwards, an x axis points to the flight direction of the satellite, and a y axis meets the right-hand rule; 4) an international celestial coordinate system (ICRF) takes the geocenter as an origin, the z axis is vertical to the average equatorial plane of the J2000.0 epoch and faces upwards, the x axis points to the dynamics vernalization point of the J2000.0 epoch, and the y axis meets the right-hand rule; 5) an international earth coordinate system (ITRF) takes the earth center as an origin, a z axis points to the direction of a protocol earth pole (CTP), an x axis points to the intersection point of a Greenwich mean meridian plane and the equator of the CTP, and a y axis meets the right-hand rule.
The laser footprint geometric positioning precision mainly depends on the positioning precision of a satellite platform, the measurement precision of the offset from a satellite positioning system to a laser altimeter and the measurement precision of a laser ranging vector. The positioning precision of a satellite platform can be improved by adopting a high-precision satellite orbit determination technology, a satellite positioning system and a laser altimeter are arranged to be in rigid connection, and offset errors caused by satellite vibration and temperature change can be reduced, so that the core factor influencing the geometric positioning precision of a laser footprint is the measurement precision of a laser ranging vector, and the laser ranging vector is comprehensively determined by a laser ranging value and a laser pointing vector. The on-orbit calibration of the satellite-borne laser altimeter aims to eliminate the system errors of laser ranging and laser pointing and improve the geometric positioning precision of a laser footprint. Common on-orbit calibration modes of the satellite-borne laser altimeter comprise a satellite attitude maneuver method, a natural earth surface matching method and a ground footprint detector method. The ground footprint detector method is characterized in that a plurality of footprint detectors are distributed on the ground to capture the central coordinates of laser footprints, and the laser ranging values and the laser pointing information are back-calculated based on the prior coordinates of the laser footprints. The calibration method is expensive, but the calibration precision is highest.
At present, there are few published reports on an on-orbit calibration method of a satellite-borne laser altimeter based on laser footprint prior coordinates, and the known reports include: 1. an on-track calibration method for realizing laser pointing angle errors based on the difference between 'real laser footprint coordinates' captured by a ground detector and 'actual laser footprint coordinates' measured by a laser altimeter (Magruder, L.A., Webb, C.E., Urban, T.J., et al.ICESat timing data product verification at White fields Space Harbor [ J ]. IEEE Transactions on geometry and remove Sensing,2007,45(1), 147) 155), which can calibrate the on-track calibration result of the laser pointing angle without providing angle system errors of the laser pointing vector under a specific Space coordinate system; 2. the method can obtain the system error of the direction cosine angle of the laser pointing vector under a specific space coordinate system, but requires the satellite to have attitude maneuvering capability, so that the incident angle of the laser emitted by the laser altimeter on the ground detector can be continuously changed. Thus, for satellites without attitude maneuver capability, the in-orbit calibration method cannot be applied.
Disclosure of Invention
The invention mainly solves the problems of the existing on-orbit calibration method of the satellite-borne laser altimeter based on the prior coordinate of the laser footprint: the method comprises the steps of taking observation parameters of a satellite-borne laser altimeter and a satellite platform and prior coordinates of a laser footprint as input, taking zenith and azimuth angles of a laser pointing vector and system errors of laser ranging values as variables, constructing a distance offset model of the laser footprint, solving a first-order partial derivative of the distance offset square sum on each system error variable to establish an error equation set by taking the square sum of a plurality of distance offsets as a principle of minimizing, and realizing on-orbit calibration of the system errors of the laser pointing zenith and azimuth angles and the laser ranging values by simultaneous solution of the error equation set.
The technical problem of the invention is mainly solved by the following technical scheme:
an on-orbit calibration method of a satellite-borne laser altimeter based on laser footprint prior coordinates comprises the following steps: (1) firstly, according to initial parameters of on-orbit calibration of a satellite-borne laser altimeter, (2) calculating a zenith angle and an azimuth angle of a laser pointing vector under an international celestial coordinate system; (3) then calculating the coordinate deviation between the laser footprint coordinate measured by the satellite-borne laser altimeter and the laser footprint prior coordinate; (4) secondly, constructing a distance offset equation of the laser footprint; (5) respectively solving a first-order partial derivative of the system error variables by the distance offset sum of squares to establish an error equation set; (6) and finally, solving an error equation set to obtain a zenith angle and an azimuth angle of the laser pointing vector and a system error of the laser ranging value.
In the above on-orbit calibration method for a satellite-borne laser altimeter based on laser footprint prior coordinates, the initial parameters of the on-orbit calibration of the satellite-borne laser altimeter include:
observing parameters of the satellite-borne laser altimeter: and the zenith angle and the azimuth angle of the laser ranging value and the laser pointing vector under the laser altimeter carrier coordinate system.
Observing parameters of a satellite platform sensor: three attitude angles (roll angle, pitch angle and course angle) of the satellite attitude system and positioning coordinates of the satellite positioning system under an international terrestrial coordinate system.
Other parameters: offset vector from a satellite positioning system to a laser altimeter under an international terrestrial coordinate system, prior coordinate of a laser footprint, and a conversion matrix between an international celestial sphere and an international terrestrial coordinate system.
In the above on-orbit calibration method for a satellite-borne laser altimeter based on laser footprint prior coordinates, the zenith angle and azimuth angle of the laser pointing vector under the international celestial coordinate system are calculated, and the method comprises the following substeps:
step 2.1, calculating the laser pointing vector under the international celestial coordinate system
Wherein,
indicating the laser pointing direction under the coordinate system of the height indicator carrier,
representing the attitude transformation matrix. Phi is akAnd εkRespectively representing the zenith angle and the azimuth angle omega of the laser vector under the coordinate system of the altimeter carrierk、
And thetakThree attitude angles, namely roll, pitch and heading are indicated, respectively, and subscript k is 1,2,3, … N, N being the total number of measurements.
Step 2.2 directing the laser to the vector
Normalizing to obtain laser pointing vector
Wherein,
indicating laser pointing vector
The die of (1).
Step 2.3 calculating laser pointing vector
Zenith angle alpha under international celestial coordinate systemkAnd azimuth angle betak：
In the formula,
and
are respectively vectors
1 and 3.
In the above on-orbit calibration method for the satellite-borne laser altimeter based on the laser footprint prior coordinate, the method for calculating the coordinate deviation between the laser footprint coordinate measured by the satellite-borne laser altimeter and the laser footprint prior coordinate comprises the following substeps:
3.1 calculating the laser footprint coordinate (x) measured by the satellite-borne laser altimeter under the international terrestrial coordinate systemk，yk，zk)：
Wherein, (xg)k，ygk，zgk) Is the positioning coordinate of the satellite positioning system under the international terrestrial coordinate system,
is the offset vector, rho, from the satellite positioning system to the laser altimeter in the international terrestrial coordinate systemkIs the laser distance measuring value, T, measured by a laser altimetertThe transformation matrix from the international celestial coordinate system to the international terrestrial coordinate system can be obtained by inputting the on-orbit calibration time and inquiring from the international terrestrial rotation service website.
3.2 calculating the coordinate deviation (delta x) between the laser footprint coordinate measured by the satellite-borne laser altimeter and the laser footprint prior coordinatek，Δyk，Δzk)：
In the formula,
is TtInverse matrix of (X)k，Yk，Zk) Is the prior coordinate of the laser footprint under the international terrestrial coordinate system.
In the on-orbit calibration method of the satellite-borne laser altimeter based on the prior coordinate of the laser footprint, a distance offset equation of the laser footprint is constructed, and the method comprises the following substeps:
4.1 constructing an error model (delta u) of the laser footprint geometric coordinate under the international celestial coordinate system by using the zenith angle and azimuth angle of the laser pointing vector and the system error of the laser ranging valuek，Δvk，Δwk)：
In the formula, Δ α, Δ β, and Δ ρ are respectively the zenith angle and azimuth angle of the laser pointing vector and the system error of the laser ranging value.
4.2 distance offset Δ d for building laser footprintkModel:
in the above on-orbit calibration method for the satellite-borne laser altimeter based on the laser footprint prior coordinate, the distance offset sum of squares is used to calculate the first-order partial derivative of the system error variable to establish an error equation set:
in the above on-orbit calibration method for the satellite-borne laser altimeter based on the laser footprint prior coordinate, an error equation set is solved, and the zenith angle and the azimuth angle of the laser pointing vector and the system error of the laser ranging value are obtained, which comprises the following substeps:
6.1 neglecting the error of the laser ranging system, simultaneously solving a first equation and a second equation of the error equation set to obtain the systematic error of the zenith angle and the azimuth angle of the laser pointing vector.
And 6.2 substituting the zenith angle and azimuth angle system error results of the laser pointing vector into a third equation of the error equation set, and resolving the third equation to obtain the system error of the laser ranging.
The invention has the following advantages: the coordinate deviation between the laser footprint and the prior laser footprint measured by the laser altimeter is used as an input quantity, a distance offset model of the laser footprint is constructed, the sum of squares of the distance offsets of a plurality of laser footprints is used for conducting first-order derivation on the system errors of laser pointing and laser ranging respectively, an error equation set with the system errors as variables is established, and the zenith angle and the azimuth angle of the laser pointing vector and the system errors of laser ranging values are obtained through simultaneous calculation of the error equation set. The on-orbit calibration method (the specific implementation process is shown in figure 2) is not only suitable for on-orbit calibration of a satellite-borne laser altimeter without attitude maneuvering capability, but also can simultaneously realize calibration of system errors of laser pointing and laser ranging.
Drawings
FIG. 1 is a geometric positioning principle of a laser footprint of a satellite-borne laser altimeter.
FIG. 2 is a flow for realizing an on-orbit calibration method of a satellite-borne laser altimeter based on laser footprint prior coordinates.
FIG. 3 is the coordinate deviation between the laser footprint coordinate measured by the satellite-borne laser altimeter and the prior coordinate of the laser footprint before calibration in the embodiment.
FIG. 4 is the coordinate deviation between the laser footprint coordinate measured by the satellite-borne laser altimeter after calibration and the prior coordinate of the laser footprint in the embodiment.
FIG. 5 is a distance offset distribution before and after calibration for 20 sets of laser footprints using the cross-validation method in an example.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
Example (b):
firstly, a specific method flow of the present invention is introduced, which mainly comprises the following steps:
1. inputting initial parameters of on-orbit calibration of a satellite-borne laser altimeter, comprising the following processes:
(1.1) observing parameters of a satellite-borne laser altimeter: and the zenith angle and the azimuth angle of the laser ranging value and the laser pointing vector under the laser altimeter carrier coordinate system.
(1.2) observing parameters of a satellite platform sensor: three attitude angles (roll angle, pitch angle and course angle) of the satellite attitude system and positioning coordinates of the satellite positioning system under an international terrestrial coordinate system.
(1.3) other parameters: offset vector from a satellite positioning system to a laser altimeter under an international terrestrial coordinate system, prior coordinate of a laser footprint, and a conversion matrix between an international celestial sphere and an international terrestrial coordinate system.
2. Calculating the zenith angle and the azimuth angle of the laser pointing vector under the international celestial coordinate system, and the method comprises the following processes:
(2.1) calculating the laser pointing vector under the international celestial coordinate system
Wherein,
indicating the laser pointing direction under the coordinate system of the height indicator carrier,
representing the attitude transformation matrix. Phi is akAnd εkRespectively representing the zenith angle and the azimuth angle omega of the laser vector under the coordinate system of the altimeter carrierk、
And thetakThree attitude angles, namely roll, pitch and heading, are indicated, respectively, and subscript k is 1,2,3, … 20.
(2.2) directing the laser light at a vector
Normalizing to obtain laser pointing vector
Wherein,
indicating laser pointing vector
The die of (1).
(2.3) calculating laser pointing vector
Zenith angle alpha under international celestial coordinate systemkAnd azimuth angle betak：
Wherein,
and
are respectively vectors
1 and 3.
3. The method for calculating the coordinate deviation between the laser footprint coordinate measured by the satellite-borne laser altimeter and the laser footprint prior coordinate comprises the following steps:
(3.1) calculating the laser footprint coordinate measured by the satellite-borne laser altimeter under the international terrestrial coordinate system
Wherein, (xg)k，ygk，zgk) Is the positioning coordinate of the satellite positioning system under the international terrestrial coordinate system,
is the offset vector, rho, from the satellite positioning system to the laser altimeter in the international terrestrial coordinate systemkIs the laser distance measuring value, T, measured by a laser altimetertIs a conversion matrix from an international celestial coordinate system to an international terrestrial coordinate system.
(3.2) calculating the coordinate deviation between the laser footprint coordinate measured by the satellite-borne laser altimeter and the laser footprint prior coordinate
Wherein,
is TtInverse matrix of (X)k，Yk，Zk) Is the prior coordinate of the laser footprint under the international terrestrial coordinate system.
4. Constructing a distance offset equation of the laser footprint, comprising the following processes:
(4.1) constructing an error model of the geometric coordinates of the laser footprint under an international celestial coordinate system:
and respectively carrying out zenith angle and azimuth angle of the laser pointing vector and the system error of the laser ranging value by using the delta alpha, the delta beta and the delta rho.
(4.2) distance offset Δ d for building laser footprintkModel:
5. respectively solving the first-order partial derivatives of the distance offset square sum on the system error variables to establish an error equation system:
6. solving an error equation set to obtain a zenith angle and an azimuth angle of a laser pointing vector and a system error of a laser ranging value, and the method comprises the following processes:
and (6.1) neglecting the error of the laser ranging system, and simultaneously solving a first equation and a second equation of the error equation set to obtain the systematic error of the zenith angle and the azimuth angle of the laser pointing vector.
And (6.2) substituting the system errors of the zenith angle and the azimuth angle of the laser pointing vector into a third equation of the error equation set, and resolving the third equation to obtain the system errors of the laser ranging.
Secondly, the following is a specific embodiment of the method of the invention:
1. inputting initial parameters of on-orbit calibration of the satellite-borne laser altimeter, including a laser ranging value of the satellite-borne laser altimeter, a laser zenith angle and an azimuth angle under a carrier coordinate system of the laser altimeter, an attitude angle and a positioning coordinate of a satellite platform, an offset vector from a satellite positioning system to the laser altimeter under an international terrestrial coordinate system, a prior coordinate of a laser footprint, a conversion matrix between the international celestial sphere and the international terrestrial coordinate system and the like, wherein parameter names, symbols and numerical values are shown in table 1;
TABLE 1 initial parameters for on-orbit calibration of satellite-borne laser altimeter
In this embodiment, it is assumed that the errors of the zenith angle and the azimuth angle of the laser pointing are respectively Δ φk20+ rand (") and Δ εk30+2rand ("), laser range error Δ ρk2+0.2rand (m), wherein rand represents a random number of 0-1, and the prior coordinate of the laser footprint in the international terrestrial coordinate system can be represented as:
in the formula,
representing the error in the a priori coordinates of the laser footprint.
2. Calculating to obtain the pointed zenith angle alpha of the laser under the international celestial coordinate systemkAnd the azimuth angle beta is respectively equal to the zenith angle phi under the carrier coordinate system of the laser altimeterkAnd azimuth angle εk；
3. Firstly, calculating the laser footprint coordinate (x) measured by a satellite-borne laser altimeter under an international terrestrial coordinate systemk，yk，zk) Combined with the prior coordinate (X) of the laser footprintk，Yk，Zk) And calculating to obtain coordinate deviation (delta x) between the twok，Δyk，Δzk) The distribution is shown in fig. 3.
4. And constructing a distance offset model of the laser footprint under the international celestial coordinate system by taking the zenith angle and the azimuth angle of the laser pointing vector and the system error of the laser ranging value as variables.
5. And respectively solving the first-order partial derivatives of the distance offset square sum and the system error variable to establish an error equation system.
6. Firstly, neglecting the error of a laser ranging system, simultaneously solving a first equation and a second equation of an error equation set, and obtaining the system errors of the zenith angle and the azimuth angle of a laser pointing vector which are respectively 20.48 'and 48.12'; and then substituting the system errors of the zenith angle and the azimuth angle of the laser pointing vector into a third equation of the error equation set, and solving the third equation to obtain the system error of the laser ranging of 2.08 m.
Thirdly, verification and analysis:
and respectively comparing the laser ranging value with the system errors of the zenith angle and the azimuth angle of the laser pointing vector with the initial system error of the prior coordinate of the laser footprint, and obtaining that the residual quantity of the laser ranging system error is only 0.08m, the residual quantity of the laser pointing zenith angle system error is only 0.48 'and the residual quantity of the laser pointing azimuth angle system error reaches 18.12'. In fact, there is no strict constraint relation between the positioning error of the laser footprint and the systematic error of the laser pointing azimuth angle. Respectively substituting the zenith angle and the azimuth angle of the laser pointing vector and the system error of the laser ranging value into the laser footprint geometric positioning model, and resolving to obtain the coordinate deviation between the laser footprint geometric positioning coordinate and the laser footprint prior coordinate after on-orbit calibration, as shown in fig. 4. Comparing the coordinate deviation results before the on-track calibration (as shown in fig. 3), it is found that the maximum value of the absolute value of the coordinate deviation is reduced from (11.13, 48.99, 1.05) m to (1.45, 1.47, 0.19) m.
Meanwhile, a cross validation mode is adopted to evaluate the calibration method in the patent. Firstly, 40 groups of initial parameters (shown in table 1) of on-orbit calibration of the satellite-borne laser altimeter are input, wherein the front 20 groups of data are used for resolving the laser pointing angle and the laser ranging system error, and the rear 20 groups of data are used for evaluating the calibration accuracy of the laser footprint geometric positioning. The distance offset distribution of the rear 20 groups of laser footprints before and after calibration is obtained by calculation based on the calibration method of the patent, and is shown in figure 5. From the results in fig. 5, it can be seen that the average values of the distance offsets of the last 20 groups of laser footprints before and after calibration are 49.55m and 1.34m respectively, and the distance offsets are rapidly reduced, which indicates that the method of the present invention can well eliminate the systematic errors of the laser pointing angle and the laser ranging, and greatly improve the geometric positioning accuracy of the laser footprints.
Claims (6)
1. An on-orbit calibration method of a satellite-borne laser altimeter based on laser footprint prior coordinates is characterized by comprising the following steps:
step 1, acquiring initial parameters of on-orbit calibration of a satellite-borne laser altimeter;
step 2, calculating zenith angles and azimuth angles of the laser pointing vectors under the international celestial coordinate system; the method comprises the following substeps:
step 2.1, calculating the laser pointing vector under the international celestial coordinate system
Wherein,
indicating the laser pointing direction under the coordinate system of the height indicator carrier,
represents the attitude transformation matrix, phikAnd εkRespectively representing the zenith angle and the azimuth angle omega of the laser vector under the coordinate system of the altimeter carrierk、
And thetakThree attitude angles, namely a roll angle, a pitch angle and a heading angle are respectively expressed, subscript k is 1,2,3, … N, and N is the total number of times of measurement;
step 2.2, directing the laser to the vector
Normalizing to obtain laser pointing vector
Wherein,
indicating laser pointing vector
The mold of (4);
step 2.3, calculating the laser pointing vector
Zenith angle alpha under international celestial coordinate systemkAnd azimuth angle betak：
In the formula,
and
are respectively vectors
1 and 3 elements of (a);
step 3, resolving coordinate deviation between the laser footprint coordinate measured by the satellite-borne laser altimeter and the laser footprint prior coordinate;
step 4, constructing a distance offset equation of the laser footprint;
step 5, respectively solving a first-order partial derivative of the system error variables by the distance offset sum of squares to establish an error equation set;
and 6, resolving an error equation set, and acquiring a zenith angle and an azimuth angle of the laser pointing vector and a system error of the laser ranging value.
2. The on-orbit calibration method for the satellite-borne laser altimeter based on the prior coordinates of the laser footprint of claim 1, which is characterized in that: the initial parameters of the on-orbit calibration of the satellite-borne laser altimeter in the step 1 comprise,
observing parameters of the satellite-borne laser altimeter: the laser ranging value, the zenith angle and the azimuth angle of the laser pointing vector under the laser altimeter carrier coordinate system;
observing parameters of a satellite platform sensor: three attitude angles of a satellite attitude system, namely a roll angle, a pitch angle and a course angle, and a positioning coordinate of the satellite positioning system under an international terrestrial coordinate system;
other parameters: offset vector from a satellite positioning system to a laser altimeter under an international terrestrial coordinate system, prior coordinate of a laser footprint, and a conversion matrix between an international celestial sphere and an international terrestrial coordinate system.
3. The on-orbit calibration method for the satellite-borne laser altimeter based on the prior coordinates of the laser footprint of claim 1, which is characterized in that: and 3, resolving the coordinate deviation between the laser footprint coordinate measured by the satellite-borne laser altimeter and the laser footprint prior coordinate, which comprises the following substeps:
step 3.1, calculating laser footprint coordinates (x) measured by the satellite-borne laser altimeter under the international terrestrial coordinate systemk,yk,zk)：
Wherein, (xg)k,ygk,zgk) Is the positioning coordinate of the satellite positioning system under the international terrestrial coordinate system,
is the offset vector, rho, from the satellite positioning system to the laser altimeter in the international terrestrial coordinate systemkIs the laser distance measuring value, T, measured by a laser altimetertThe conversion matrix from the international celestial coordinate system to the international terrestrial coordinate system is obtained by inputting the on-orbit calibration time and inquiring from the international terrestrial rotation service website;
step 3.2, calculating the coordinate deviation (delta x) between the laser footprint coordinate measured by the satellite-borne laser altimeter and the laser footprint prior coordinatek,Δyk,Δzk)：
In the formula,
is TtInverse matrix of (X)k,Yk,Zk) Is the prior coordinate of the laser footprint under the international terrestrial coordinate system.
4. The on-orbit calibration method for the satellite-borne laser altimeter based on the prior coordinates of the laser footprint of claim 3, which is characterized in that: the step 4 of constructing a distance offset equation of the laser footprint comprises the following substeps,
step 4.1, constructing an error model (delta u) of the laser footprint geometric coordinate under the international celestial coordinate system by using the zenith angle and azimuth angle of the laser pointing vector and the system error of the laser ranging valuek,Δvk,Δwk)：
In the formula, the delta alpha, the delta beta and the delta rho respectively indicate the zenith angle and the azimuth angle of a laser pointing vector and the system error of a laser ranging value;
step 4.2, constructing a distance offset equation delta d of the laser footprintk：
5. The on-orbit calibration method for the satellite-borne laser altimeter based on the prior coordinates of the laser footprint as claimed in claim 4, wherein: in step 5, the distance offset sum of squares is used for respectively solving a first order partial derivative of the system error variable to establish an error equation set:
wherein N is the total number of measurements.
6. The on-orbit calibration method for the satellite-borne laser altimeter based on the prior coordinates of the laser footprint as claimed in claim 5, wherein: the specific implementation of step 6 comprises the following sub-steps,
step 6.1, neglecting the error of the laser ranging system, and simultaneously resolving an equation I and an equation II of an error equation set to obtain the systematic error of the zenith angle and the azimuth angle of the laser pointing vector;
and 6.2, substituting the system error results of the zenith angle and the azimuth angle of the laser pointing vector into a third equation of the error equation set, and resolving the third equation to obtain the system error of the laser ranging.
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