CN112013874B - Satellite-borne laser altimeter on-orbit calibration method based on laser footprint prior coordinate - Google Patents

Abstract

The invention relates to an on-orbit calibration method of a spaceborne laser altimeter based on a priori coordinates of laser footprints. The zenith angle and azimuth angle of the pointing vector and the systematic error of the laser ranging value are used as variables, and the distance offset model of the laser footprint is constructed. The squared sum of the shifts calculates the first-order partial derivatives of each systematic error variable to establish the error equation system. Through the simultaneous solution of the error equation system, the system error of the laser pointing zenith angle and azimuth angle and the laser ranging value can be calculated. Orbit calibration. The method is not only suitable for the on-orbit calibration of the spaceborne laser altimeter without attitude maneuvering ability, but also can realize the calibration of the system error of laser pointing and laser ranging at the same time.

Description

An on-orbit calibration method of spaceborne laser altimeter based on prior coordinates of laser footprints

technical field

The invention belongs to the field of laser remote sensing, and in particular relates to an on-orbit calibration method of a spaceborne laser altimeter, which is suitable for the on-orbit calibration of the laser pointing and distance of a spaceborne laser altimeter when the geometric coordinates of the laser footprint are known. .

Background technique

可以表示为：The spaceborne laser altimeter is a new type of earth observation equipment mounted on the satellite platform, which can accurately obtain the distance between the satellite and the ground target. Combined with the position, attitude and laser pointing information of the satellite platform, the high-precision solution of the geometric positioning coordinates of the laser footprint can be realized. The geometric positioning principle of the laser footprint of the spaceborne laser altimeter is shown in Figure 1. It is the fusion result of the data collected by the three sensors of the spaceborne laser altimeter, the satellite positioning system and the satellite attitude determination system. According to the principle of vector superposition, the coordinate vector of the laser footprint in the international earth coordinates

It can be expressed as:

代表卫星定位系统所获取的卫星平台位置矢量，

代表卫星定位系统到激光测高仪的偏移矢量，

代表由激光测高仪测距值和激光指向矢量确定的激光测距矢量，其中的激光指向矢量可以采用国际地球坐标系下的天顶角和方位角来表示。In the formula,

represents the position vector of the satellite platform obtained by the satellite positioning system,

represents the offset vector from the satellite positioning system to the laser altimeter,

Represents the laser ranging vector determined by the ranging value of the laser altimeter and the laser pointing vector, where the laser pointing vector can be represented by the zenith angle and azimuth angle in the international earth coordinate system.

The calculation of the geometric positioning coordinates of the laser footprint involves a variety of coordinate frames: 1) The laser altimeter carrier coordinate system is based on the laser emission reference point as the origin, the z-axis points down to the normal direction of the optical platform, and the x-axis points to the satellite flight direction , the y-axis satisfies the right-hand rule; 2) The satellite platform coordinate system is based on the GPS or BDS antenna phase center as the origin, the z-axis points to the earth's center of mass (geocenter), the x-axis points to the satellite flight direction, and the y-axis satisfies the right-hand rule; 3) The attitude platform coordinate system is based on the platform reference center as the origin, the z-axis points down to the normal direction of the inertial platform, the x-axis points to the satellite flight direction, and the y-axis satisfies the right-hand rule; 4) The international celestial coordinate system (ICRF) is based on the center of the earth The origin, the z-axis is perpendicular to the mean equator of the J2000.0 epoch, and the x-axis points to the dynamic equinox at the J2000.0 epoch, and the y-axis satisfies the right-hand rule; 5) The International Earth Coordinate System (ITRF) takes the center of the earth as the The origin, the z-axis points in the direction of the Protocol Earth Pole (CTP), the x-axis points to the intersection of the Greenwich mean meridian plane and the CTP equator, and the y-axis satisfies the right-hand rule.

The geometric positioning accuracy of the laser footprint mainly depends on the positioning accuracy of the satellite platform, the measurement accuracy of the offset from the satellite positioning system to the laser altimeter and the measurement accuracy of the laser ranging vector. Among them, the use of high-precision satellite orbit determination technology can improve the positioning accuracy of the satellite platform, and the rigid connection between the satellite positioning system and the laser altimeter can reduce the offset error caused by satellite vibration and temperature changes. Therefore, The core factor affecting the geometrical positioning accuracy of the laser footprint is the measurement accuracy of the laser ranging vector, and the laser ranging vector is determined comprehensively by the laser ranging value and the laser pointing vector. The purpose of the on-orbit calibration of the spaceborne laser altimeter is to eliminate the systematic errors of laser ranging and laser pointing, and to improve the geometric positioning accuracy of the laser footprint. Common on-orbit calibration methods of spaceborne laser altimeter include satellite attitude maneuver method, natural surface matching method and ground footprint detector method. Among them, the ground footprint detector method captures the center coordinates of laser footprints by arranging several footprint detectors on the ground, and calculates the laser ranging value and laser pointing information based on the prior coordinates of these laser footprints. This calibration method is more expensive, but its calibration accuracy is the highest.

Up to now, there are few public reports on the on-orbit calibration method of the spaceborne laser altimeter based on the prior coordinates of the laser footprint. The known reports include: 1. Based on the "true laser footprint coordinates" captured by the ground detector and The difference between the "actual laser footprint coordinates" measured by the laser altimeter realizes the on-orbit calibration method of the laser pointing angle error (Magruder, L.A., Webb, C.E., Urban, T.J., et al.ICES at altimetry data product verification at White Sands Space Harbor[J].IEEE Transactions on Geoscience and RemoteSensing,2007,45(1),147-155), this method can check the on-orbit calibration results of the laser pointing angle but cannot provide the laser pointing vector Angle system error in a specific space coordinate system; 2. On-orbit calibration method of laser pointing angle error based on laser pointing vector and pointing angle residual model obtained by ground detectors (Yi Hong, Li Song, Ma Yue, Huang Ke et al. On-orbit calibration of laser altimeter based on footprint detection [J]. Acta Physica Sinica, 2017, 66(13), 134206-134206), this method can obtain the direction cosine of the laser pointing vector in a specific space coordinate system However, it requires the satellite to have attitude maneuverability, so that the incident angle of the laser emitted by the laser altimeter on the ground detector can be continuously changed. Therefore, for satellites without attitude maneuverability, this on-orbit calibration method cannot be applied.

SUMMARY OF THE INVENTION

The invention mainly solves the problems existing in the existing on-orbit calibration method of the spaceborne laser altimeter based on the prior coordinates of the laser footprint: proposes an observation parameter and laser footprint based on the spaceborne laser altimeter and the satellite platform. The a priori coordinates of , as input, take the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value as the variables to construct the distance offset model of the laser footprint, and use the square of the multiple distance offsets as variables. According to the principle of minimizing the sum of the distance and the offset, the first-order partial derivative of each system error variable is calculated to establish the error equation system, and the laser pointing zenith angle and azimuth angle and On-orbit calibration of systematic errors of laser ranging values.

The above-mentioned technical problems of the present invention are mainly solved by the following technical solutions:

A method for on-orbit calibration of a spaceborne laser altimeter based on a priori coordinates of laser footprints, including the following processes: (1) first, according to the initial parameters of the on-orbit calibration of the spaceborne laser altimeter, (2) calculating a laser pointing vector The zenith angle and azimuth angle in the international celestial coordinate system; (3) Then calculate the coordinate deviation between the coordinates of the laser footprint measured by the spaceborne laser altimeter and the prior coordinates of the laser footprint; (4) Second Construct the distance offset equation of the laser footprint; (5) calculate the first-order partial derivatives of the system error variables by summing the squares of the distance offsets to establish the error equation system; (6) finally solve the error equation system to obtain the laser The zenith and azimuth angles of the pointing vector and the systematic error of the laser ranging values.

In the above-mentioned on-orbit calibration method of a spaceborne laser altimeter based on the prior coordinates of laser footprints, the initial parameters of the on-orbit calibration of the spaceborne laser altimeter include:

Observation parameters of the spaceborne laser altimeter: laser ranging value, zenith angle and azimuth angle of the laser pointing vector in the laser altimeter carrier coordinate system.

Satellite platform sensor observation parameters: three attitude angles (roll angle, pitch angle and heading angle) of the satellite attitude system and the positioning coordinates of the satellite positioning system in the international earth coordinate system.

Other parameters: the offset vector from the satellite positioning system to the laser altimeter in the international earth coordinate system, the a priori coordinates of the laser footprint, the conversion matrix between the international celestial sphere and the international earth coordinate system.

In the above-mentioned on-orbit calibration method of a spaceborne laser altimeter based on the prior coordinates of laser footprints, calculating the zenith angle and azimuth angle of the laser pointing vector in the international celestial coordinate system includes the following sub-steps:

Step 2.1 Calculate the laser pointing vector in the international celestial coordinate system

表示测高仪载体坐标系下的激光指向，in,

Indicates the laser pointing in the coordinate system of the altimeter carrier,

和θ_k分别表示三个姿态角，即侧滚角、俯仰角和航向角，下标k＝1，2，3，…N，N为测量的总次数。Represents the pose transformation matrix. φ _k and ε _k represent the zenith angle and azimuth angle of the laser vector in the altimeter carrier coordinate system, respectively, ω _k ,

and θ _k represent three attitude angles, namely roll angle, pitch angle and heading angle, respectively, and the subscript k=1, 2, 3, ... N, where N is the total number of measurements.

进行归一化处理得到激光指向矢量

其中，

表示激光指向矢量

的模。Step 2.2 Point the laser at the vector

Perform normalization to get the laser pointing vector

in,

Represents the laser pointing vector

's model.

在国际天球坐标系下的天顶角α_k和方位角β_k：Step 2.3 Calculate the laser pointing vector

Zenith angle α _k and azimuth angle β _k in the international celestial coordinate system:

和

分别为矢量

的第1和第3个元素。In the formula,

and

respectively as vectors

The 1st and 3rd elements of .

In the above-mentioned on-orbit calibration method of the spaceborne laser altimeter based on the prior coordinates of the laser footprint, the coordinates between the coordinates of the laser footprint measured by the spaceborne laser altimeter and the prior coordinates of the laser footprint are calculated. Deviation, including the following sub-steps:

3.1 Calculate the coordinates of the laser footprint (x _k , y _k , z _k ) measured by the spaceborne laser altimeter in the international earth coordinate system:

是在国际地球坐标系下的卫星定位系统到激光测高仪的偏移矢量，ρ_k是激光测高仪测得的激光测距值，T_t是国际天球坐标系到国际地球坐标系的转换矩阵，它可以通过输入在轨标定时间从国际地球自转服务网站查询得到。In the formula, (xg _k , yg _k , zg _k ) are the positioning coordinates of the satellite positioning system in the international earth coordinate system,

is the offset vector from the satellite positioning system to the laser altimeter in the international earth coordinate system, ρ _k is the laser ranging value measured by the laser altimeter, and T _t is the conversion from the international celestial coordinate system to the international earth coordinate system matrix, which can be obtained from the International Earth Rotation Service website by entering the on-orbit calibration time.

3.2 Calculate the coordinate deviation (Δx _k , Δy _k , Δz _k ) between the coordinates of the laser footprint measured by the spaceborne laser altimeter and the prior coordinates of the laser footprint:

是T_t的逆矩阵，(X_k，Y_k，Z_k)是国际地球坐标系下的激光足印先验坐标。In the formula,

is the inverse matrix of T _t , and (X _k , Y _k , Z _k ) are the prior coordinates of the laser footprint in the international earth coordinate system.

In the above-mentioned on-orbit calibration method of a spaceborne laser altimeter based on the prior coordinates of laser footprints, the distance offset equation of laser footprints is constructed, including the following sub-steps:

4.1 Based on the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value, the error model of the geometric coordinates of the laser footprint in the international celestial coordinate system is constructed (Δu _k , Δv _k , Δw _k ):

In the formula, Δα, Δβ and Δρ are the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value, respectively.

4.2 Build the distance offset Δd _k model of the laser footprint:

In the above-mentioned on-orbit calibration method of the spaceborne laser altimeter based on the prior coordinates of the laser footprint, the first-order partial derivatives of the system error variables are calculated by the sum of the squares of the distance offsets to establish the error equation system:

In the above-mentioned on-orbit calibration method of a spaceborne laser altimeter based on the prior coordinates of laser footprints, the error equations are solved to obtain the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value, Includes the following sub-steps:

6.1 Ignoring the laser ranging system error, solve equation 1 and equation 2 of the error equation system simultaneously to obtain the zenith angle and azimuth angle system error of the laser pointing vector.

6.2 Substitute the systematic error results of the zenith angle and azimuth angle of the laser pointing vector into Equation 3 of the error equation system, and solve the equation to obtain the systematic error of the laser ranging.

The invention has the following advantages: using the coordinate deviation between the laser footprint measured by the laser altimeter and the a priori laser footprint as the input, the distance offset model of the laser footprint is constructed, and a plurality of laser footprints are combined The first-order derivation of the system error of laser pointing and laser ranging is carried out by the sum of the squares of the distance offsets, and an error equation system with the system error as a variable is established. By solving the error equation system simultaneously, the laser pointing vector is obtained. Systematic errors in zenith and azimuth and laser ranging values. This on-orbit calibration method (the specific implementation process is shown in Figure 2) is not only suitable for the on-orbit calibration of the spaceborne laser altimeter without attitude maneuverability, but also can realize the system error of laser pointing and laser ranging at the same time. Calibration.

Description of drawings

Figure 1 shows the geometric positioning principle of the laser footprint of the spaceborne laser altimeter.

Figure 2 The realization flow of the on-orbit calibration method of the spaceborne laser altimeter based on the prior coordinates of the laser footprint.

3 is the coordinate deviation between the coordinates of the laser footprint measured by the spaceborne laser altimeter before calibration in the embodiment and the prior coordinates of the laser footprint.

FIG. 4 is the coordinate deviation between the coordinates of the laser footprint measured by the spaceborne laser altimeter after calibration in the embodiment and the prior coordinates of the laser footprint.

FIG. 5 is the distance offset distribution of 20 groups of laser footprints before and after calibration using the cross-validation method in the embodiment.

Detailed ways

The technical solutions of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

Example:

1. First introduce the specific method flow of the present invention, which mainly includes the following steps:

1. Input the initial parameters of the on-orbit calibration of the spaceborne laser altimeter, including the following process:

(1.1) Observation parameters of spaceborne laser altimeter: laser ranging value, zenith angle and azimuth angle of laser pointing vector in the laser altimeter carrier coordinate system.

(1.2) Observation parameters of satellite platform sensors: three attitude angles (roll angle, pitch angle and heading angle) of the satellite attitude system and the positioning coordinates of the satellite positioning system in the international earth coordinate system.

(1.3) Other parameters: the offset vector from the satellite positioning system to the laser altimeter in the international earth coordinate system, the prior coordinates of the laser footprint, and the conversion matrix between the international celestial sphere and the international earth coordinate system.

2. Calculate the zenith angle and azimuth angle of the laser pointing vector in the international celestial coordinate system, including the following process:

(2.1) Calculate the laser pointing vector in the international celestial coordinate system

表示测高仪载体坐标系下的激光指向，in,

Indicates the laser pointing in the coordinate system of the altimeter carrier,

和θ_k分别表示三个姿态角，即侧滚角、俯仰角和航向角，下标k＝1，2，3，…20。Represents the pose transformation matrix. φ _k and ε _k represent the zenith angle and azimuth angle of the laser vector in the altimeter carrier coordinate system, respectively, ω _k ,

and θ _k respectively represent three attitude angles, namely roll angle, pitch angle and heading angle, and the subscript k=1, 2, 3, . . . 20.

进行归一化处理得到激光指向矢量

其中，

表示激光指向矢量

的模。(2.2) Point the laser to the vector

Perform normalization to get the laser pointing vector

in,

Represents the laser pointing vector

's model.

在国际天球坐标系下的天顶角α_k和方位角β_k：

其中，

和

分别为矢量

的第1和第3个元素。(2.3) Calculate the laser pointing vector

Zenith angle α _k and azimuth angle β _k in the international celestial coordinate system:

in,

and

respectively as vectors

The 1st and 3rd elements of .

3. Calculate the coordinate deviation between the laser footprint coordinates measured by the spaceborne laser altimeter and the prior coordinates of the laser footprint, including the following process:

其中，(xg_k，yg_k，zg_k)是卫星定位系统在国际地球坐标系下的定位坐标，

是在国际地球坐标系下的卫星定位系统到激光测高仪的偏移矢量，ρ_k是激光测高仪测得的激光测距值，T_t是国际天球坐标系到国际地球坐标系的转换矩阵。(3.1) Calculate the coordinates of the laser footprints measured by the spaceborne laser altimeter in the international earth coordinate system

Among them, (xg _k , yg _k , zg _k ) are the positioning coordinates of the satellite positioning system in the international earth coordinate system,

is the offset vector from the satellite positioning system to the laser altimeter in the international earth coordinate system, ρ _k is the laser ranging value measured by the laser altimeter, and T _t is the conversion from the international celestial coordinate system to the international earth coordinate system matrix.

其中，

是T_t的逆矩阵，(X_k，Y_k，Z_k)是国际地球坐标系下的激光足印先验坐标。(3.2) Calculate the coordinate deviation between the coordinates of the laser footprint measured by the spaceborne laser altimeter and the prior coordinates of the laser footprint

in,

is the inverse matrix of T _t , and (X _k , Y _k , Z _k ) are the prior coordinates of the laser footprint in the international earth coordinate system.

4. Construct the distance offset equation of the laser footprint, including the following process:

其中，Δα、Δβ和Δρ分别激光指向矢量的天顶角和方位角以及激光测距值的系统误差。(4.1) Construct the error model of the geometric coordinates of the laser footprint in the international celestial coordinate system:

Among them, Δα, Δβ and Δρ are the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value, respectively.

(4.2) Construct the distance offset Δd _k model of the laser footprint:

5. Calculate the first-order partial derivatives of the system error variables by summing the squares of the distance offsets to establish a system of error equations:

6. Solve the error equation system to obtain the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value, including the following processes:

(6.1) Neglecting the laser ranging system error, solve equation 1 and equation 2 of the error equation system simultaneously, and obtain the zenith angle and azimuth angle system error of the laser pointing vector.

(6.2) Substitute the systematic error of the zenith angle and azimuth angle of the laser pointing vector into Equation 3 of the error equation system, and solve the equation to obtain the systematic error of the laser ranging.

Two, the following is a specific embodiment of the method of the present invention:

1. Input the initial parameters of the on-orbit calibration of the spaceborne laser altimeter, including the laser ranging value of the spaceborne laser altimeter, the laser zenith angle and azimuth in the carrier coordinate system of the laser altimeter, and the attitude of the satellite platform Angle and positioning coordinates, the offset vector from the satellite positioning system under the international earth coordinate system to the laser altimeter, the a priori coordinates of the laser footprint, the conversion matrix between the international celestial sphere and the international earth coordinate system, etc. The parameter names, The symbols and values are shown in Table 1;

Table 1 Initial parameters of on-orbit calibration of spaceborne laser altimeter

In this embodiment, it is assumed that the errors of the zenith angle and azimuth angle of the laser pointing are Δφ _k =20+rand(") and Δε _k =30+2rand(") respectively, and the laser ranging error Δρ _k =2+0.2rand( m), where rand represents a random number from 0 to 1, then the prior coordinates of the laser footprint in the international earth coordinate system can be expressed as:

表示激光足印先验坐标的误差。In the formula,

Represents the error in the prior coordinates of the laser footprint.

2. The zenith angle α _k and azimuth angle β of laser pointing in the international celestial coordinate system are calculated to be equal to the zenith angle φ _k and the azimuth angle ε _k in the carrier coordinate system of the laser altimeter, respectively;

3. First calculate the laser footprint coordinates (x _k , y _k , z _k ) measured by the spaceborne laser altimeter in the international earth coordinate system, and then combine the prior coordinates of the laser footprint (X _k , Y _k , Z _k ), the coordinate deviation (Δx _k , Δy _k , Δz _k ) between the two is obtained by solving, and its distribution is shown in Figure 3.

4. Taking the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value as variables, the distance offset model of the laser footprint in the international celestial coordinate system is constructed.

5. Calculate the first-order partial derivatives of the system error variables by summing the squares of the distance offsets to establish a system of error equations.

6. First ignore the laser ranging system error, solve equation 1 and equation 2 of the error equation system simultaneously, and obtain the zenith angle and azimuth angle system errors of the laser pointing vector are 20.48" and 48.12" respectively; then the laser pointing vector The systematic error of zenith angle and azimuth angle is substituted into Equation 3 of the error equation system, and the systematic error of laser ranging is 2.08m by solving this equation.

3. Verification Analysis:

The laser ranging value and the systematic errors of the zenith and azimuth angles of the laser pointing vector are compared with the initial systematic errors of the prior coordinates of the laser footprint. The residual amount of zenith angle systematic error is only 0.48", while the residual amount of laser pointing azimuth systematic error reaches 18.12". In fact, there is no strict constraint between the positioning error of the laser footprint and the systematic error of the laser pointing azimuth. The zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value are respectively substituted into the geometric positioning model of the laser footprint, and the geometric positioning coordinates of the laser footprint and the laser footprint prior are obtained after the orbit calibration. The coordinate deviation between the coordinates is shown in Figure 4. Comparing the coordinate deviation results before the orbit calibration (as shown in Figure 3), it can be seen that the maximum absolute value of the coordinate deviation decreases from (11.13, 48.99, 1.05) m to (1.45, 1.47, 0.19) m.

At the same time, a cross-validation method is used to evaluate the calibration method in this patent. First, input 40 groups of initial parameters for on-orbit calibration of the spaceborne laser altimeter (as shown in Table 1), of which the first 20 groups of data are used to calculate the laser pointing angle and laser ranging system error, and the last 20 groups of data are used for Evaluate the calibration accuracy of the geometric localization of laser footprints. Based on the calibration method of this patent, the distance offset distribution of the last 20 groups of laser footprints before and after calibration is obtained, as shown in Figure 5. From the results in Figure 5, it can be seen that the average 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 decrease rapidly, which shows that the method of this patent can be very effective. It can eliminate the systematic errors of laser pointing angle and laser ranging, and greatly improve the geometric positioning accuracy of laser footprints.

Claims (6)

1. a space-borne laser altimeter on-orbit calibration method based on laser footprint a priori coordinates, is characterized in that, comprises the following process: Step 1, obtain the initial parameters of the on-orbit calibration of the spaceborne laser altimeter; Step 2: Calculate the zenith angle and azimuth angle of the laser pointing vector in the international celestial coordinate system; including the following sub-steps: Step 2.1, calculate the laser pointing vector in the international celestial coordinate system

in,

Indicates the laser pointing in the coordinate system of the altimeter carrier,

represents the attitude transformation matrix, φ _k and ε _k represent the zenith angle and azimuth angle of the laser vector in the altimeter carrier coordinate system, respectively, ω _k ,

and θ _k respectively represent three attitude angles, namely roll angle, pitch angle and heading angle, subscript k=1,2,3,...N, N is the total number of measurements; Step 2.2, point the laser at the vector

Perform normalization to get the laser pointing vector

in,

Represents the laser pointing vector

the model; Step 2.3, Calculate the laser pointing vector

Zenith angle α _k and azimuth angle β _k in the international celestial coordinate system:

In the formula,

and

respectively as vectors

the 1st and 3rd elements of ; Step 3: Calculate the coordinate deviation between the coordinates of the laser footprint measured by the spaceborne laser altimeter and the prior coordinates of the laser footprint; Step 4, construct the distance offset equation of the laser footprint; Step 5: Calculate the first-order partial derivatives of the system error variables by summing the squares of the distance offsets to establish an error equation system; Step 6: Solve the error equation system to obtain the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value. 2. a kind of spaceborne laser altimeter on-orbit calibration method based on laser footprint prior coordinates according to claim 1, is characterized in that: the spaceborne laser altimeter on-orbit calibration described in step 1 The initial parameters include, Observation parameters of spaceborne laser altimeter: laser ranging value, zenith angle and azimuth angle of laser pointing vector in the coordinate system of laser altimeter carrier; Satellite platform sensor observation parameters: three attitude angles of the satellite attitude system, namely roll angle, pitch angle and heading angle, the positioning coordinates of the satellite positioning system in the international earth coordinate system; Other parameters: the offset vector from the satellite positioning system to the laser altimeter in the international earth coordinate system, the a priori coordinates of the laser footprint, the conversion matrix between the international celestial sphere and the international earth coordinate system. 3. a kind of spaceborne laser altimeter on-orbit calibration method based on laser footprint prior coordinates according to claim 1, is characterized in that: in step 3, solve the laser foot that spaceborne laser altimeter records. The coordinate deviation between the print coordinates and the prior coordinates of the laser footprint, including the following sub-steps: Step 3.1, calculate the laser footprint coordinates (x _k , y _k , z _k ) measured by the spaceborne laser altimeter in the international earth coordinate system:

In the formula, (xg _k , yg _k , zg _k ) are the positioning coordinates of the satellite positioning system in the international earth coordinate system,

is the offset vector from the satellite positioning system to the laser altimeter in the international earth coordinate system, ρ _k is the laser ranging value measured by the laser altimeter, and T _t is the conversion from the international celestial coordinate system to the international earth coordinate system The matrix is obtained from the International Earth Rotation Service website by entering the on-orbit calibration time; Step 3.2, calculate the coordinate deviation (Δx _k , Δy _k , Δz _k ) between the coordinates of the laser footprint measured by the spaceborne laser altimeter and the prior coordinates of the laser footprint:

In the formula,

is the inverse matrix of T _t , and (X _k , Y _k , Z _k ) are the prior coordinates of the laser footprint in the international earth coordinate system. 4. a kind of spaceborne laser altimeter on-orbit calibration method based on laser footprint prior coordinates according to claim 3, is characterized in that: in step 4, the distance offset equation of laser footprint is constructed, including following substep, Step 4.1, with the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value, construct the error model of the geometric coordinates of the laser footprint in the international celestial coordinate system (Δu _k , Δv _k , Δw _k ):

In the formula, Δα, Δβ and Δρ are the zenith angle and azimuth angle of the laser pointing vector and the systematic error of the laser ranging value, respectively; Step 4.2, construct the distance offset equation Δd _k of the laser footprint:

5. a kind of spaceborne laser altimeter on-orbit calibration method based on laser footprint a priori coordinates according to claim 4, is characterized in that: in step 5, the distance offset square sum is calculated to the system error variable respectively. First-order partial derivatives to establish the system of error equations:

where N is the total number of measurements. 6. a kind of spaceborne laser altimeter on-orbit calibration method based on laser footprint prior coordinates according to claim 5, is characterized in that: the concrete realization of step 6 comprises the following sub-steps, Step 6.1, ignoring the laser ranging system error, solve equation 1 and equation 2 of the error equation system simultaneously, and obtain the zenith angle and azimuth angle system error of the laser pointing vector; Step 6.2: Substitute the systematic error results of the zenith angle and azimuth angle of the laser pointing vector into Equation 3 of the error equation system, and solve the equation to obtain the systematic error of the laser ranging.

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