A method for correcting satellite laser footprint positioning errors in mountainous forest areas

Abstract

The invention provides a method for correcting satellite laser footprint positioning errors in mountainous forest areas, comprising: acquiring laser echo waveform data of the mountainous forest area, calculating the true laser ranging value of the mountainous forest canopy of each laser footprint; selecting points near the laser footprint as possible laser footprint points, calculating the satellite-ground integrated laser ranging value of the possible laser footprint points, and the ranging residuals between the satellite-ground integrated laser ranging value and the true laser ranging value of the mountainous forest canopy; traversing a number of continuous laser footprints, calculating the ranging residuals of the possible laser footprint points and accumulating them to obtain the ranging residual sum; iteratively calculating the ranging residual sum of the possible laser footprint points, and taking the possible laser footprint points corresponding to the minimum ranging residual sum as correction points, so as to complete the correction of the laser footprint positioning errors in the mountainous forest area without using high-precision terrain data.

Description

Technical Field

[0001] The invention relates to the technical field of laser remote sensing ranging, and in particular to a high-precision calibration method for satellite-borne single-photon laser based on a corner reflector. Background Art

[0002] Satellite lasers have shown significant advantages in large-scale forestry surveys such as forest canopy height mapping due to their good elevation measurement accuracy and excellent ground penetration capabilities. In order to improve the accuracy of large-scale forestry surveys that combine satellite lasers and multi-source remote sensing data, it is necessary to reduce the satellite laser footprint positioning error. For example, the satellite is affected by factors such as jitter and the thermal effect of long-term laser operation, which makes the satellite laser actually have a large positioning error when it is in orbit; at the same time, due to the large slope of mountainous terrain, the existing laser footprint positioning error will bring about a large elevation error, thereby reducing the accuracy of large-scale forestry surveys such as forest canopy height inversion. For example, a 10m laser footprint positioning error in a mountain with a slope of 10 degrees will bring an elevation error of 1.76m.

[0003] In the prior art, the correction methods for satellite laser footprint positioning errors in mountainous forest areas are mainly divided into correction methods based on terrain matching and correction methods based on simulation waveform matching. Among them, the correction method based on terrain matching mainly uses reference terrain data to calculate the elevation residual between the laser footprint itself and the reference terrain data at different positions on the ground, and then corrects the laser footprint positioning error based on the elevation residuals of multiple laser footprints and the minimum principle. The correction accuracy is directly related to the accuracy of the reference terrain data, and requires a large number of laser points to participate in the solution at the same time, relying on high-precision reference terrain data such as long strips and large-scale airborne LiDAR point clouds. However, this type of data is difficult to obtain in mountainous forest areas, expensive, and difficult to obtain on a large scale. In addition, the inconsistency between the reference terrain data and the laser time will also bring uncertainty to the results.

[0004] The correction method based on simulation waveform matching requires echo simulation around the initial position of the laser footprint, and calculates the similarity between the simulated waveforms at different positions and the laser's own recorded waveforms, and finds the best position of the laser footprint on the ground based on the principle of the highest similarity between the two. This method also relies on high-precision reference terrain data, which needs to be used for echo simulation; in addition, due to the similar spatial structure of forest areas and the high similarity of simulated waveforms at different positions, this method is prone to fall into the local optimal solution, reducing the correction accuracy. In addition, due to the obstruction of forest branches and leaves, the measurement accuracy of laser data in or under the forest is low, which brings uncertainty to the correction method and reduces the accuracy. Summary of the invention

[0005] The purpose of the present invention is to provide a method for correcting satellite laser footprint positioning errors in mountainous forest areas, which can complete the laser footprint positioning error correction without high-precision terrain data in mountainous forest areas, and use forest canopy data with better measurement accuracy for correction, thereby improving the correction accuracy.

[0006] To solve the above problems, the present invention provides a method for correcting satellite laser footprint positioning errors in mountainous forest areas, comprising: acquiring laser echo waveform data of mountainous forest areas, and calculating the true laser ranging value of the mountainous forest canopy for each laser footprint; selecting points near the laser footprint as possible laser footprint points, and calculating the satellite-ground integrated laser ranging value of the possible laser footprint points, as well as the ranging residual between the satellite-ground integrated laser ranging value and the true laser ranging value of the mountainous forest canopy; traversing a number of consecutive laser footprints, calculating the ranging residuals of the possible laser footprint points and accumulating them to obtain the ranging residual sum; iteratively calculating the ranging residual sum of the possible laser footprint points, and taking the possible laser footprint point corresponding to the minimum ranging residual sum as a correction point.

[0007] Furthermore, the above-mentioned mountain forest satellite laser footprint positioning error correction method selects points near the laser footprint as possible laser footprint points, calculates the satellite-ground integrated laser ranging value of the possible laser footprint point, and the ranging residual between the satellite-ground integrated laser ranging value and the mountain forest canopy laser true ranging value, including: constructing a search area with the laser footprint as the center, and selecting a number of evenly distributed possible laser footprint points in the search area; iteratively calculating the ranging residual sum of the possible laser footprint points, and taking the possible laser footprint points corresponding to the minimum ranging residual sum as correction points, including: taking the laser footprint as the initial position and assigning coordinates to each possible laser footprint point; constructing a three-dimensional discrete point set using the ranging residual sum of the possible laser footprint points and the coordinates of the possible laser footprint points; fitting the three-dimensional discrete point set into a spatial surface, regarding all points on the spatial surface as possible laser footprint points, calculating the minimum value of the spatial surface, and taking the possible laser footprint points corresponding to the minimum value as correction points.

[0008] Furthermore, the search area described in the above-mentioned mountain forest area satellite laser footprint positioning error correction method covers a square area centered on the initial position and with a side length greater than or equal to 4 times the laser footprint positioning error.

[0009] Furthermore, the search area in the above-mentioned mountain forest satellite laser footprint positioning error correction method is a square area, and evenly distributed possible laser footprint points are selected in the square area; taking the initial position as the origin, the plane coordinate set of each possible laser footprint point is: .

[0010] Furthermore, the calculation formula of the sum of the ranging residuals in the above-mentioned mountain forest area satellite laser footprint positioning error correction method is:

[0011]

[0012] in, For the The laser footprint may be traversed The residual error after laser footprints is For the The laser footprint may traverse the first The satellite-ground integrated laser ranging value when the laser footprint is For the The true laser distance measurement value of the mountain forest canopy of the laser footprint, is the absolute value symbol.

[0013] Furthermore, in the above-mentioned mountain forest area satellite laser footprint positioning error correction method, all the possible laser footprint points are traversed, and the ranging residual sum of all the possible laser footprint points is collected as a ranging residual sum set, and the expression of the ranging residual sum set is:

[0014]

[0015] in, is the number of possible points of the laser footprint, ;in, is the side length of the search area, is the side length of the possible points of the laser footprint; the coordinates of the three-dimensional discrete point set are: .

[0016] Furthermore, the surface equation of the space surface in the above-mentioned mountain forest area satellite laser footprint positioning error correction method is:

[0017]

[0018] in, are the plane coordinates of possible points of the laser footprint; and are the parameters of the fitted surface equation; the Lagrange multiplier method is used to solve the minimum value of the fitted space surface, and the x and y coordinates corresponding to the minimum point are the correction values ​​of the laser footprint positioning error ; Add the coordinates of the initial position to the laser footprint positioning error correction , complete the laser footprint positioning error correction.

[0019] Furthermore, in the above-mentioned mountain forest area satellite laser footprint positioning error correction method, the laser echo waveform data is waveform decomposed, and the forest canopy echo is extracted, and the laser emission time and the laser return time are calculated respectively, and the laser initial ranging value is calculated in combination with the laser ranging self-offset. The calculation formula of the laser initial ranging value is:

[0020]

[0021] in, is the initial laser distance measurement value, is the laser return time, is the laser emission time, is the speed of light, is the laser ranging offset itself;

[0022] The air pressure value and precipitation at the initial position are obtained and the atmospheric delay error of the laser ranging is calculated. The actual laser ranging value of the mountain forest canopy is calculated according to the initial laser ranging value and the atmospheric delay error of the laser ranging. The calculation formula of the actual laser ranging value of the mountain forest canopy is:

[0023]

[0024] in, is the actual laser distance measurement value of the mountain forest canopy; is the initial laser ranging value; is the atmospheric delay error of laser ranging;

[0025] By extracting the forest canopy echo from the laser echo waveform data, the laser return time is calculated and the laser emission time .

[0026] Furthermore, the calculation formula of the satellite-ground integrated laser ranging value in the above-mentioned mountain forest area satellite laser footprint positioning error correction method is:

[0027]

[0028] in, It is the satellite-ground integrated laser ranging value; is the two-norm; The ground coordinates of possible points of the laser footprint; The three-dimensional coordinates of the satellite centroid at the moment of laser emission;

[0029] The three-dimensional coordinates of the satellite centroid at the time of laser emission It is calculated based on the three-dimensional coordinates of the satellite's center of mass and the offset from the satellite's laser emission point to the satellite's center of mass. The calculation formula is as follows:

[0030] (7)

[0031] in, is the three-dimensional coordinate of the satellite center of mass, is the offset from the satellite laser light-emitting point to the satellite mass center. The calculation formula of the three-dimensional coordinates of the satellite mass center is as follows:

[0032]

[0033] in, is the three-dimensional coordinate of the satellite's center of mass; is the three-dimensional coordinates of the satellite GNSS position; is the offset from the satellite GNSS position to the satellite center of mass.

[0034] The present invention uses forest canopy data to correct the laser footprint positioning error. Since the forest canopy is unobstructed, the satellite laser measurement accuracy is better, thereby improving the correction accuracy of the laser footprint positioning error in the mountainous forest area. In addition, the present invention does not require high-precision terrain data in the mountainous forest area. It uses the satellite DSM data that is relatively easy to obtain to achieve laser footprint correction in the mountainous forest area, saving the cost of obtaining high-precision terrain data, and also reducing the difficulty of correcting the laser footprint positioning error in the mountainous forest area, improving applicability. The corrected satellite laser data combined with optical and other multi-source remote sensing data can effectively improve the accuracy of large-scale forest canopy height inversion, forest aboveground biomass estimation and other large-scale forestry surveys. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of a flow chart of an embodiment of the present invention;

[0036] Figure 2 It is a schematic diagram of a calculation model for the true laser distance measurement value of a mountain forest canopy according to an embodiment of the present invention;

[0037] Figure 3 It is a schematic diagram of a satellite-ground integrated laser ranging value calculation model according to an embodiment of the present invention;

[0038] Figure 4 is a schematic diagram of a search area in an embodiment of the present invention;

[0039] Figure 5 is a schematic diagram of the ranging residual and possible points of each laser footprint in the search area of ​​the embodiment of the present invention;

[0040] Figure 6 is a schematic diagram of a three-dimensional discrete point set of distance measurement residuals and possible point coordinates of laser footprints according to an embodiment of the present invention;

[0041] Figure 7 Schematic diagram of a three-dimensional discrete point set fitting spatial surface according to an embodiment of the present invention;

[0042] Figure 8 It is the Gaussian component extraction result of the complex waveform of beam 1 laser point 292680916.33 in Pu'er area according to the embodiment of the present invention;

[0043] Fig. 9 It is the Gaussian component extraction result of the complex waveform of beam 1 laser point 292680921.00 in Pu'er area according to the embodiment of the present invention;

[0044] Fig.10 It is the Gaussian component extraction result of the complex waveform of beam 2 laser point 292680904.67 in Pu'er area according to the embodiment of the present invention;

[0045] Fig.11 It is the Gaussian component extraction result of the complex waveform of beam 2 laser point 292680911.00 in Pu'er area according to the embodiment of the present invention;

[0046] Fig.12 is a two-dimensional surface of the residual sum of the laser ranging of beam 1 in an embodiment of the present invention;

[0047] Fig.13 is a two-dimensional surface of the residual sum of the laser ranging of beam 2 in an embodiment of the present invention;

[0048] Fig.14 is a fitting surface of the residual sum of the laser ranging of beam 1 in an embodiment of the present invention;

[0049] Fig.15 It is the fitting surface of the residual sum of beam 2 laser ranging in the embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0051] The following is a description of a method for correcting satellite laser footprint positioning errors in mountainous forest areas shown in an embodiment of the present invention.

[0052] In order to facilitate the subsequent description of this embodiment, how to calculate the mountain forest canopy laser real distance measurement value and the satellite-ground integrated laser distance measurement value is first described.

[0053] First, the calculation of the true laser distance measurement value of the mountain forest canopy is explained. Figure 2The laser echo waveform in mountain forest areas is very complex, showing multiple peaks. However, according to the satellite laser echo forming principle, the first peak of the laser echo is the forest canopy echo.

[0054] The laser echo waveform data of the mountain forest area is obtained, and the waveform is decomposed after preprocessing such as denoising and smoothing. That is, the forest canopy echo is extracted, and the laser emission time and laser return time are calculated respectively. The laser initial ranging value is calculated by using the laser emission time and laser return time combined with the laser ranging's own offset.

[0055] Satellite laser waveforms are usually Gaussian waveforms, so in this embodiment, a Gaussian mixture model is used to decompose the satellite laser echo waveform in the mountain forest area to obtain the Gaussian components of the laser echo waveform, and extract the first Gaussian component of the laser echo waveform. The Gaussian mixture model is shown in the following formula:

[0056] (1)

[0057] in, is the expected laser echo waveform; is the echo waveform data per frame, ,in Is Gaussian function generation; is the mean of the Gaussian components; is the standard deviation of the Gaussian component.

[0058] The peak moment of the laser emission pulse is extracted as the laser emission time, and the peak moment of the first Gaussian component in the laser echo waveform data obtained by waveform decomposition is calculated as the laser return time. Combined with the laser ranging offset itself, the initial laser ranging value can be calculated. The calculation formula is as follows:

[0059] (2)

[0060] in, is the laser return time, is the laser emission time, is the speed of light, It is the offset of laser ranging itself.

[0061] When satellite lasers penetrate the atmosphere, they are affected by atmospheric refraction and scattering, which causes the laser transmission time to be prolonged and a laser ranging delay error to occur. This error needs to be corrected and is mainly related to air pressure and humidity.

[0062] In this embodiment, the global public meteorological data released by the National Centers for Environmental Prediction (NCEP) of the United States is used to extract the air pressure value and precipitation at the laser footprint location. Then, the laser ranging atmospheric delay error is calculated according to the satellite laser atmospheric delay correction model, and the calculation formula is as follows:

[0063] (3)

[0064] In the formula, is the laser nadir angle The mapping function of is the dry-term delay error related to air pressure; is the wet term delay error associated with precipitation.

[0065] Next, we will calculate the true laser distance measurement value of the mountain forest canopy, referring to Figure 2 , the true laser distance measurement value of the mountain forest canopy is directly related to the initial laser distance measurement value and the laser distance measurement atmospheric delay error. Therefore, the calculation formula for the true laser distance measurement value of the mountain forest canopy is:

[0066] (4)

[0067] in, is the true laser distance measurement value of the mountain forest canopy; is the initial laser distance measurement value; is the atmospheric delay error of laser ranging.

[0068] The following is an explanation of the calculation of the satellite-ground integrated laser ranging value. Figure 3 Then, a satellite-ground integrated triangle is constructed based on the satellite centroid point A at the time of laser emission, the satellite laser light-emitting point B at the time of laser emission, and the possible point C of the ground laser footprint. The distance between the satellite laser light-emitting point B at the time of laser emission and the possible point C of the ground laser footprint is calculated, that is, the satellite-ground integrated laser ranging value. The calculation formula is as follows:

[0069] (5)

[0070] in, It is the satellite-ground integrated laser ranging value; is the two-norm; are the ground coordinates of possible points of the laser footprint; It is the three-dimensional coordinates of the satellite light point at the moment of laser emission.

[0071] The three-dimensional coordinates of the satellite light point at the time of laser emission It can be obtained by calculating the three-dimensional coordinates of the satellite's centroid and the offset from the satellite's laser emission point to the satellite's centroid. The specific steps are as follows:

[0072] The GNSS (Global Navigation Satellite System) data of several moments before and after the laser emission is obtained. In this embodiment, the GNSS data of four moments before and after is obtained, and then the Lagrange interpolation method is used to calculate the three-dimensional coordinates of the satellite space at the time of laser emission. Then, according to the offset from the satellite GNSS position to the satellite center of mass, the three-dimensional coordinates of the satellite center of mass at the time of laser emission are calculated. The calculation formula is as follows:

[0073] (6)

[0074] in, is the three-dimensional coordinate of the satellite's center of mass; is the three-dimensional coordinates of the satellite GNSS position; is the offset from the satellite GNSS position to the satellite center of mass.

[0075] Satellite lasers are usually installed on satellite platforms in a fixed manner, that is, the offset from the laser light-emitting point to the satellite's center of mass is usually accurately measured on the ground, so the three-dimensional coordinates of the satellite laser light-emitting point are:

[0076] (7)

[0077] in, is the three-dimensional coordinate of the satellite laser light-emitting point, It is the offset from the satellite laser light-emitting point to the satellite mass center.

[0078] Since the correction point of the laser footprint is near the laser footprint, and the ranging residual between the satellite-ground integrated laser ranging value of the correction point and the true ranging value of the mountain forest canopy laser is the smallest, it is only necessary to select points near the laser footprint as possible laser footprint points, and iteratively calculate the ranging residuals of the possible laser footprint points. The possible laser footprint points with the smallest ranging residuals are selected as correction points to complete the error correction. However, there are random errors in a single laser footprint, so it is necessary to introduce multiple continuous laser footprints to eliminate random errors.

[0079] refer to Figure 1 The method for correcting the satellite laser footprint positioning error in mountain forest areas shown in this embodiment specifically includes the following steps:

[0080] S100: firstly obtain the laser echo waveform data of the mountain forest area, and calculate the true laser distance measurement value of the mountain forest canopy of each laser footprint.

[0081] S200: Select points near the laser footprint as possible laser footprint points, calculate the satellite-ground integrated laser ranging value of the possible laser footprint point, and the ranging residual between the satellite-ground integrated laser ranging value and the true ranging value of the mountain forest canopy laser.

[0082] S300: Iteratively calculate the sum of the ranging residuals of the possible laser footprint points, and use the possible laser footprint point corresponding to the minimum sum of the ranging residuals as the correction point.

[0083] Step S200: selecting points near the laser footprint as possible laser footprint points, calculating the satellite-ground integrated laser ranging value of the possible laser footprint points, and the ranging residual between the satellite-ground integrated laser ranging value and the true ranging value of the mountain forest canopy laser, specifically includes:

[0084] S210: constructing a search area with the laser footprint as the center, and selecting a number of evenly distributed possible laser footprint points in the search area.

[0085] To ensure that the calibration point is within the search area, the search area covers a square area centered on the laser footprint with a side length greater than or equal to 4 times the laser footprint positioning error.

[0086] Wherein step S300: iteratively calculating the distance residual sum of the possible laser footprint points, and taking the possible laser footprint point corresponding to the minimum distance residual sum as the correction point, specifically includes:

[0087] S310: using the laser footprint as the initial position, assigning coordinates to each possible point of the laser footprint;

[0088] S320: constructing a three-dimensional discrete point set by using the distance measurement residual of the possible laser footprint point and the coordinates of the possible laser footprint point;

[0089] S330: Fit the three-dimensional discrete point set into a spatial surface, regard all points on the spatial surface as possible laser footprint points, calculate the minimum value of the spatial surface, and use the possible laser footprint point corresponding to the minimum value as the correction point. Figure 4 , taking the laser footprint as the initial position, constructing a square search grid with the initial position as the center as the search area, assuming that the laser footprint positioning error is , the extent of the square search grid is set to: , thus ensuring that the true location of the laser footprint is within the constructed square search grid. Grid spacing of the square search grid The setting is related to the resolution of the ground reference terrain data DSM (Digital Surface Model). In this embodiment, the grid spacing Set to the same resolution as the DSM, the center of each pixel is used as the possible point of the laser footprint, so the square search grid can be evenly divided into The possible points of the laser footprint are taken as the initial position, and the plane coordinate set of the possible points of the laser footprint is: , the elevation of each possible point of the laser footprint can be interpolated from the DSM.

[0090] refer to Figure 5 , for the square search grid possible laser footprint points, and calculate the distance residual of each possible laser footprint point , will The laser footprint may be within The ranging residuals are accumulated to obtain the ranging residuals and Finally, the entire square search grid is traversed to obtain the ranging residuals and sets of all possible points of the laser footprint , the expression is as follows:

[0091] (8)

[0092] in, is the number of possible points of the laser footprint, calculated as: , For the Laser footprint possible points traversal The residual error after laser footprints is For the The laser footprint may traverse the first The satellite-ground integrated laser ranging value when the laser footprint is For the The true laser distance measurement value of the mountain forest canopy of the laser footprint, is the absolute value symbol.

[0093] refer to Figure 6 , and then the plane coordinate set of possible points of the laser footprint With the ranging residual and the set The coordinates of constructing a three-dimensional discrete point set are: Then, according to the principle of least squares method, the surface equation is used to fit the three-dimensional discrete points to fit the space surface. The surface equation is as follows:

[0094] (9)

[0095] in, are the plane coordinates of possible points of the laser footprint; and are the fitting surface equation parameters.

[0096] The obtained fitting space surface is as follows Figure 7 As shown in the figure, the closer the laser footprint is to the calibration point, the smaller the residual error will be. Therefore, the Lagrange multiplier method is used to solve the minimum value of the fitted space surface. The coordinates corresponding to the minimum point are the correction value of the laser footprint positioning error. Then the laser footprint positioning error correction Together with its initial coordinates, the laser footprint positioning error correction can be completed.

[0097] The following is an explanation with reference to specific examples. Taking the full waveform laser of my country's GF7-01 satellite as an example, 35 laser points of beam 1 and beam 2 of the 19326th track of GF7-01 satellite passing through Pu'er area on April 11, 2023 are selected as experimental data, and the ground reference terrain data is selected from the 2.5m DSM data generated by the stereo image pair of the 19326th track of GF7-01 satellite on April 11, 2023. The present invention is implemented based on the above data.

[0098] First, all the laser echo waveforms of beam 1 and beam 2 in Pu'er area of ​​the 19326th track of GF7-01 satellite were obtained, and the pre-processed waveforms were obtained through waveform denoising and smoothing. Then, the Gaussian mixture model was used to decompose each pre-processed waveform to obtain all Gaussian components of each laser echo waveform in the mountainous forest area. The results are shown in the figure. Figure 8 As shown, there are two more complex laser echo waveforms in beams 1 and 2 of GF7-01 star in Pu'er area, where (a) and (b) are beam 1 laser points 292680916.33 and 292680921.00 respectively; (c) and (d) are beam 2 laser points 292680904.67 and 292680911.00 respectively.

[0099] Then, according to the laser emission pulse of GF7-01 and the first peak of the laser echo extracted by waveform decomposition, the laser emission time and laser return time are calculated respectively. Combined with the offset of the laser ranging of GF7-01, the initial laser ranging value of GF7-01 is calculated based on formula (2). Among them, the initial ranging values ​​of the laser points 292680916.33 and 292680921.00 of beam 1 and the laser points 292680904.67 and 292680911.00 of beam 2 are shown in Table 1.

[0100] Table 1

[0101]

[0102] According to the laser emission time, the NCEP data of the same time period is obtained, and then the air pressure value and precipitation at the laser footprint are obtained by the spatiotemporal interpolation method according to the laser footprint position. Finally, the atmospheric delay error of the GF7-01 laser ranging is calculated using formula (3). Among them, the atmospheric delay errors of the laser ranging of beam 1 laser points 292680916.33 and 292680921.00 and beam 2 laser points 292680904.67 and 292680911.00 are shown in Table 2.

[0103] Table 2

[0104]

[0105] According to the GF7-01 laser initial ranging value and laser ranging atmospheric delay error calculated in the above steps, the precise satellite laser ranging value of the mountain forest canopy is calculated using formula (4). Among them, the precise laser ranging values ​​of beam 1 laser points 292680916.33 and 292680921.00 and beam 2 laser points 292680904.67 and 292680911.00 are shown in Table 3.

[0106] Table 3

[0107]

[0108] Then, a search area with a side length of 100 m was constructed with each laser footprint of the GF7-01 satellite in Pu'er as the center, and the grid spacing was set to 2.5 m. The actual plane coordinates of the possible points of the laser footprint in each search grid were jointly allocated by the initial position coordinates of the laser footprint and the grid spacing, and the ground elevation of the possible points of the laser footprint was obtained by interpolation of the 2.5 m DSM of the GF7-01 satellite.

[0109] For all possible laser footprint points in the laser footprint ground search grid, the ranging residual between the satellite-ground integrated laser ranging and its true ranging value is first calculated for each laser footprint. Then, the 35 laser ranging residuals of the possible laser footprint points are accumulated to obtain the ranging residual sum. Finally, the entire search grid is traversed to obtain the laser ranging residual sum set of all possible laser footprint points, and it is plotted as a two-dimensional surface, such as Fig.12 and Fig.13 shown.

[0110] Then use Formula 9 to fit the two-dimensional surface to a spatial surface, such as Fig.14 and Fig.15 shown.

[0111] The Lagrange multiplier method is used to directly solve the minimum value of the fitting surface, and the coordinates corresponding to the minimum point are obtained, so the correction amount of the laser footprint positioning error is obtained. The results are shown in the following table:

[0112] Table 4

[0113]

[0114] It should be understood that the above specific embodiments of the present invention are only used to illustrate or explain the principles of the present invention, and do not constitute a limitation of the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc. made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. In addition, the appended claims of the present invention are intended to cover all changes and modifications that fall within the scope and boundaries of the appended claims, or the equivalent forms of such scope and boundaries.

Claims

1. A method for correcting satellite laser footprint positioning errors in mountainous forest areas, characterized in that: include: Obtain laser echo waveform data in mountain forest areas and calculate the true laser distance measurement value of the mountain forest canopy for each laser footprint; Selecting points near the laser footprint as possible laser footprint points, calculating the satellite-ground integrated laser ranging value of the possible laser footprint point, and the ranging residual between the satellite-ground integrated laser ranging value and the true ranging value of the mountain forest canopy laser; Traversing a number of continuous laser footprints, calculating the ranging residuals of possible points of the laser footprints and accumulating them to obtain a ranging residual sum; The calculation formula of the ranging residual sum is: , in, For the The laser footprint may be traversed The residual error after laser footprints is For the The laser footprint may traverse the first The satellite-ground integrated laser ranging value when the laser footprint is For the The actual laser distance measurement value of the mountain forest canopy when the laser footprint is is the absolute value symbol; The distance measurement residual sum of the possible laser footprint points is iteratively calculated, and the possible laser footprint point corresponding to the minimum distance measurement residual sum is used as a correction point.

2. The method for correcting satellite laser footprint positioning errors in mountainous forest areas according to claim 1, characterized in that: The step of selecting points near the laser footprint as possible laser footprint points, calculating the satellite-ground integrated laser ranging value of the possible laser footprint point, and the ranging residual between the satellite-ground integrated laser ranging value and the true ranging value of the mountain forest canopy laser, includes: Constructing a search area with the laser footprint as the center, and selecting a number of evenly distributed possible laser footprint points within the search area; The iterative calculation of the distance measurement residual sum of the possible laser footprint points, and taking the possible laser footprint point corresponding to the minimum distance measurement residual sum as the correction point, comprises: Using the laser footprint as an initial position, assigning coordinates to each possible point of the laser footprint; Construct a three-dimensional discrete point set by combining the distance measurement residual of the possible laser footprint point and the coordinates of the possible laser footprint point; The three-dimensional discrete point set is fitted into a spatial surface, all points on the spatial surface are regarded as possible laser footprint points, the minimum value of the spatial surface is calculated, and the possible laser footprint point corresponding to the minimum value is used as the correction point.

3. The method for correcting satellite laser footprint positioning errors in mountainous forest areas according to claim 2, characterized in that: The search area covers a square area centered at the initial position and with a side length greater than or equal to 4 times the laser footprint positioning error.

4. The method for correcting satellite laser footprint positioning errors in mountainous forest areas according to claim 3, characterized in that: The search area is a square area, and evenly distributed possible points of the laser footprint are selected in the square area; Taking the initial position as the origin, the plane coordinate set of each possible point of the laser footprint is: .

5. The method for correcting satellite laser footprint positioning errors in mountainous forest areas according to claim 4, characterized in that: Traverse all the possible points of the laser footprint, collect the ranging residual sums of all the possible points of the laser footprint into a ranging residual sum set, and the expression of the ranging residual sum set is: , in, is the number of possible points of the laser footprint, ,in, is the side length of the search area, is the side length of the possible points of the laser footprint; The coordinates of the three-dimensional discrete point set are: .

6. The method for correcting satellite laser footprint positioning errors in mountainous forest areas according to claim 5, characterized in that: The surface equation of the space surface is: , in, are the plane coordinates of possible points of the laser footprint; and are the parameters of the fitted surface equation; The Lagrange multiplier method is used to solve the minimum value of the fitted space surface. The x and y coordinates corresponding to the minimum point are the correction values ​​of the laser footprint positioning error. ; Add the coordinates of the initial position to the laser footprint positioning error correction , complete the laser footprint positioning error correction.

7. The method for correcting satellite laser footprint positioning errors in mountainous forest areas according to claim 2, characterized in that: The laser echo waveform data is decomposed, and the forest canopy echo is extracted. The laser emission time and the laser return time are calculated respectively, and the laser initial ranging value is calculated in combination with the laser ranging offset. The calculation formula of the laser initial ranging value is: , in, is the initial laser distance measurement value, is the laser return time, is the laser emission time, is the speed of light, is the laser ranging offset itself; The air pressure value and precipitation at the initial position are obtained and the atmospheric delay error of the laser ranging is calculated. The actual laser ranging value of the mountain forest canopy is calculated according to the initial laser ranging value and the atmospheric delay error of the laser ranging. The calculation formula of the actual laser ranging value of the mountain forest canopy is: , in, is the actual laser distance measurement value of the mountain forest canopy; is the initial laser ranging value; is the atmospheric delay error of laser ranging; By extracting the forest canopy echo from the laser echo waveform data, the laser return time is calculated and the laser emission time .

8. The method for correcting satellite laser footprint positioning errors in mountainous forest areas according to claim 1, characterized in that: The calculation formula of the satellite-ground integrated laser ranging value is: , in, is the satellite-ground integrated laser ranging value; is the two-norm; The ground coordinates of possible points of the laser footprint; The three-dimensional coordinates of the satellite light source at the moment of laser emission; The three-dimensional coordinates of the satellite light-emitting point at the time of laser emission are based on the three-dimensional coordinates of the satellite centroid The offset from the satellite laser emission point to the satellite center of mass is calculated as follows: （7）， in, is the three-dimensional coordinate of the satellite center of mass, is the offset from the satellite laser light-emitting point to the satellite center of mass. The calculation formula of the three-dimensional coordinates of the satellite center of mass is as follows: , in, is the three-dimensional coordinate of the satellite's center of mass; is the three-dimensional coordinates of the satellite GNSS position; is the offset from the satellite GNSS position to the satellite center of mass.

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