Satellite-borne lidar echo simulation method and device based on point cloud data

Abstract

The application provides a spaceborne laser radar echo simulation method and device based on point cloud data, which can realize fast and high-precision simulation of bare ground target and vegetation target echo with absolute radiation characteristics. The method comprises the following steps: step 1, input initial parameters; step 2, calculate the average pulse interval of the point cloud data and the normal vector of each point target; step 3, calculate the corrected intensity of each point target in the laser footprint range and the reflectivity correction factor corresponding to the radiation calibration area, so as to correct the influence of the laser ranging value and the laser incidence angle on the point cloud intensity, and obtain the reflectivity value corresponding to each point target; step 4, based on the average pulse interval and the reflectivity value, calculate the slope and the reflection power of each point target, and then calculate the response echo function of each point target in the footprint range; and step 5, based on the response echo function, calculate the target overall response signal sequence, and perform convolution on the sequence and the spaceborne laser radar transmission pulse waveform sequence to obtain the simulation echo.

Description

Technical Field

[0001] This invention belongs to the field of laser remote sensing technology, specifically relating to a method and device for simulating the echo of a spaceborne lidar based on point cloud data. Background Technology

[0002] A full-waveform spaceborne lidar is an active remote sensing device that uses laser as its radiation source. It continuously emits laser pulses towards the target and, through processing and analysis of the reflected echoes within the laser footprint range, quantitatively retrieves the target's geometric and physical characteristics. Full-waveform spaceborne lidar features wide coverage, high measurement resolution, and all-weather operation, and is widely used in forest biomass estimation, polar glacier change, global topographic mapping, and lake hydrological monitoring. The received echoes from the spaceborne lidar are the fundamental data for target information retrieval, and their waveform distribution is closely related to the morphological characteristics of the target and the hardware parameters of the spaceborne lidar. Therefore, before launching a spaceborne lidar, a dedicated waveform simulator is typically developed to simulate the echo data and evaluate its performance in different application scenarios.

[0003] Target topography data is the core input of the waveform simulator, and its types mainly include target models with preset geometric distributions and digital surface models under real-world conditions. Since airborne LiDAR point cloud data can generate high-precision and high-resolution digital surface models, point cloud data has become one of the most widely used input data for spaceborne LiDAR waveform simulators. Airborne LiDAR point cloud data is generally stored in LAS file format, encompassing target point cloud location information and point cloud intensity information. The point cloud location is the three-dimensional coordinate of the target point within the projected coordinate frame, and the point cloud intensity is the relative intensity value of the target's reflected signal. Typically, point cloud intensity information is affected by various factors such as the true reflectivity of the target being measured, the emission energy of the airborne LiDAR, the laser scanning angle, and the laser ranging value. Therefore, point cloud intensity information cannot represent the true reflectivity of the target being measured. Often, it is necessary to conduct radiometric calibration of the airborne LiDAR on a Lambertian reflective surface with known reflectivity, such as an asphalt road surface, to convert the point cloud intensity information into target reflectivity data.

[0004] To date, spaceborne lidar echo simulation methods based on point cloud data can be divided into three categories. The first category involves NASA processing point cloud data into triangular meshes, calculating the target reflection energy and reflection time within each triangular mesh, and combining this with the measurement principles of spaceborne lidar to simulate accurate ground target echoes (Filin S, Csatho B. An efficient algorithm for the synthesis of laser altimetry waveforms [R]. Byrd Polar Research Center, The Ohio State University, 2000.). The first type of waveform simulation method has low computational efficiency and is only suitable for simulating reflected echoes from targets on bare ground. It is difficult to simulate target echoes in vegetated areas. The second type is the waveform simulation method based on the Discrete Anisotropic Radiative Transfer Model (DART) (Gastellu-Etchegorry JP, Yin T, Lauret N, et al. Simulation of satellite, airborne and terrestrial LiDAR with DART(I): Waveform simulation with quasi-Monte Carlo ray tracing[J]. Remote Sensing of Environment, 2016, 184: 418-435.). By modeling the target in three dimensions, the radiative transfer model is used to simulate the interaction between the laser pulse and the target, so as to achieve accurate simulation of target echoes, including targets on bare ground and those in vegetation. These waveform simulation methods cannot directly use point cloud data as input; the point cloud data must undergo complex processing to extract the structural parameters of the land surface contour and forest vegetation. The third type is a waveform simulation method based on the accumulation of point cloud data (Hancock S, Armston J, Hofton M, et al. The GEDI simulator: A large-footprint waveform lidar simulator for calibration and validation of spaceborne missions[J]. Earth and Space Science, 2019, 6(2): 294-310.), which treats the response waveform of each point target as an impulse function and accumulates it in the target elevation direction to generate a pseudo echo, without considering the changes in the radiation characteristics of the laser pulse during transmission. This type of waveform simulation method has high computational efficiency, but it cannot obtain the absolute amplitude information of the target echo.Therefore, the above three types of spaceborne lidar echo simulation methods based on point cloud data cannot meet the requirements for rapid and high-precision simulation of echoes from bare surface targets and vegetated targets. Summary of the Invention

[0005] This invention is made to solve the above-mentioned problems, and aims to provide a method and device for simulating the echo of a spaceborne lidar based on point cloud data. It can achieve rapid and high-precision simulation of the echoes of bare surface targets and vegetation targets with absolute radiation characteristics by using the radiation calibration of point cloud data and the radiation correction of the laser pulse transmission process of the spaceborne lidar.

[0006] To achieve the above objectives, the present invention employs the following solution:

[0007] <Method>

[0008] This invention provides a method for simulating the echo of a spaceborne lidar based on point cloud data, comprising the following steps:

[0009] Step 1: Input the initial parameters for the spaceborne lidar echo simulation;

[0010] Step 2: Select the airborne lidar point cloud data within the footprint range of the spaceborne lidar, and calculate the average pulse spacing and the normal vector of each point target in the point cloud data.

[0011] Step 3: Based on the normal vector of each point target, calculate the correction intensity of each point target within the laser footprint range and calculate the reflectivity correction factor corresponding to the radiation calibration area. In this way, correct the influence of laser ranging value and laser incident angle on the point cloud intensity and obtain the reflectivity value corresponding to each point target.

[0012] Step 4: Based on the average pulse spacing and reflectivity value, calculate the slope γ of each target point within the laser footprint range. i and reflected power P i This allows us to obtain the response echo width T for each point target. i Then according to T i Calculate the response echo function h of each target point within the laser footprint range. i (q):

[0013]

[0014] In the formula, This indicates a width of 2T. i Rectangular function, sgn represents the step function, τ i τ represents the beam propagation time corresponding to the i-th point target. i =2R i / c, Δt represents the spaceborne lidar echo sampling time interval, and q represents the time sampling sequence;

[0015] Step 5: Based on the response echo function, calculate the overall response signal sequence of the target, and convolve it with the transmitted pulse waveform sequence of the spaceborne lidar to obtain the simulated echo.

[0016] Preferably, the spaceborne lidar echo simulation method based on point cloud data provided by the present invention includes the following sub-steps in step 2:

[0017] Step 2.1, selecting airborne lidar point cloud data within the footprint range of the spaceborne lidar, mainly includes the following process:

[0018] (2.1.1) The footprint geographic coordinates (X) of the spaceborne lidar under the international geodetic coordinate framework f Y f Z f ) and the geographic coordinates (X) of the satellite platform location s Y s Z s Transform the coordinates to the same projected coordinate frame as the airborne lidar point cloud:

[0019] (x f y f , z f ) T =R t ·(X f Y f Z f ) T , (x s y s , z s ) T =R t ·(X s Y s Z s ) T

[0020] In the formula, R t This represents the transformation matrix between the International Geodetic Frame and the Projected Geodetic Frame, (x f y f , z f ) and (x s y s , z s () represent the footprint of the spaceborne lidar and the geographical coordinates of the platform location under the projected coordinate frame, respectively;

[0021] (2.1.2) The satellite ray vector corresponding to the i-th point target in the computer-borne lidar point cloud data With the pointing vector of the spaceborne lidar The angle between

[0022]

[0023] In the formula, Among them, (x i y i , z i () represents the three-dimensional coordinates of the i-th target point, with subscripts i = 1, 2, ... N. pt N pt This indicates the total number of point targets in the airborne lidar point cloud data.

[0024] (2.1.3) Select the airborne lidar point cloud data within the laser footprint range, whose point target indices satisfy:

[0025]

[0026] In the formula, This represents the root mean square laser divergence angle of the spaceborne lidar.

[0027] Step 2.2: Calculate the average pulse spacing d of the point cloud data within the laser footprint range. sc It mainly includes the following processes:

[0028] (2.2.1) Count the number of emission pulses N corresponding to the point cloud data within the laser footprint area. ps :

[0029] N ps =Length[Unique(F)]

[0030] In the formula, F = {Q} i |i∈Ω} represents the set of emission pulse numbers within the laser footprint range, where Q i This represents the emission pulse number corresponding to the i-th point target. The Length function calculates the array length, and the Unique(F) function calculates the array of distinct elements in set F.

[0031] (2.2.2) Calculate the average pulse spacing d corresponding to the point cloud data within the laser footprint range. sc :

[0032]

[0033] In the formula, S f This represents the area of ​​the laser footprint on the geoid. Where H represents the satellite orbital altitude, and α represents the laser pointing zenith angle;

[0034] Step 2.3: Calculate the normal vector of each target point within the laser footprint range. It mainly includes the following processes:

[0035] (2.3.1) Calculate the distance between the i-th point target and other points within the footprint range of the spaceborne lidar.

[0036]

[0037] In the formula, (x j ,y j ,z j () represents the coordinates of the j-th target point within the footprint area;

[0038] (2.3.2) will Sort the values ​​from smallest to largest, and select the target coordinates corresponding to the first 6 smallest values. The set of extreme coordinates N that constitutes the target at point i i ;

[0039] (2.3.3) Calculate the extreme value coordinate set N i offset vector matrix M i :

[0040]

[0041] In the formula, and M respectively i Vector components in the x, y, and z directions;

[0042] (2.3.4) Calculate the offset vector matrix M i The covariance matrix A i :

[0043]

[0044] In the formula, For vectors with vector The covariance function can be expressed as: Among them, a k and b k Representing vectors respectively with vector The k-th element in and Representing vectors respectively sum vector The average value of the elements;

[0045] (2.3.5) Calculate the covariance matrix Ai eigenvalue set λ i :

[0046] |A i -λ i E|=0,i∈Ω

[0047] In the formula, E is a 3×3 identity matrix;

[0048] (2.3.6) Select the eigenvalue set λ i Minimum eigenvalue λ min Calculate the normal vector of the point target.

[0049]

[0050] Preferably, in the spaceborne lidar echo simulation method based on point cloud data provided by the present invention, step 3 includes the following sub-steps:

[0051] Step 3.1: Calculate the airborne laser incident angle θ for each point target within the laser footprint range. i :

[0052]

[0053] In the formula, This represents the airborne ray vector corresponding to the i-th point target. Among them, (u i ,v i ,w i () represents the platform position coordinates when the airborne lidar measures the i-th point target; The normal vector representing the point target;

[0054] Step 3.2: Calculate the laser ranging value r corresponding to each point target within the laser footprint range. i :

[0055]

[0056] In the formula, the symbol || represents the modulo operation;

[0057] Step 3.3: Correct the influence of laser incident angle and laser ranging value on point cloud intensity, and calculate the corrected intensity I′ of each point target within the laser footprint range. i :

[0058]

[0059] In the formula, I i This represents the input intensity of the target at point i;

[0060] Step 3.4, calculate the reflectivity value of each target point within the laser footprint range, which mainly includes the following process:

[0061] (3.4.1) The point cloud data (Cx) of the airborne lidar in the radiation calibration area m Cy m ,Cz m ), replacing the point cloud data (x) within the laser footprint area in step 2.2. i ,y i ,z i ), calculate the normal vector of each target point in the radiation calibration area. Where m = 1, 2, ... N pc N pc This indicates the total number of point targets in the radiation calibration area;

[0062] (3.4.2) Calculate the airborne laser incident angle β for each point target within the radiation calibration area. m :

[0063]

[0064] In the formula, This represents the airborne ray vector corresponding to the m-th point target within the radiation calibration area. Among them, (Cu m ,Cv m ,Cw m () represents the platform position coordinates when the airborne lidar measures the m-th point target in the radiation calibration area;

[0065] (3.4.3) Calculate the laser ranging value Cr corresponding to each point target within the radiation calibration area. m :

[0066]

[0067] (3.4.4) Calculate the reflectivity correction factor γ ref :

[0068]

[0069] In the formula, CI m This represents the input intensity of the m-th target point within the radiation calibration area;

[0070] (3.4.5) Obtain the reflectivity value ρ corresponding to each point target within the laser footprint range. i :

[0071] ρ i =I′ i γ ref ρ ref,i∈Ω

[0072] In the formula, ρ ref The true reflectance of the target in the radiation calibration area.

[0073] Preferably, in the spaceborne lidar echo simulation method based on point cloud data provided by the present invention, step 4 includes the following sub-steps:

[0074] Step 4.1: Calculate the reflected power P of each target point within the laser footprint range. i It mainly includes the following processes:

[0075] (4.1.1) Calculate the distance R between the i-th point target within the laser footprint range and the spaceborne lidar platform. i :

[0076]

[0077] In the formula, Among them, (x i ,y i ,z i () represents the three-dimensional coordinates of the i-th target point, with subscripts i = 1, 2, ..., N. pt N pt This represents the total number of point targets in the airborne lidar point cloud data; (x s ,y s ,z s () represents the geographic coordinates of the platform location within the projected coordinate frame;

[0078] (4.1.2) Calculate the incident angle φ of the spaceborne laser corresponding to the i-th point target within the laser footprint range. i :

[0079]

[0080] In the formula, The normal vector representing the point target;

[0081] (4.1.3) Calculate the area weight S of the i-th point target. i :

[0082]

[0083] In the formula, γ i Let be the slope of the i-th target point within the laser footprint range. d sc The average pulse spacing of the point cloud data within the laser footprint area;

[0084] (4.1.4) Calculate the reflected power P of each point target within the laser footprint range. i :

[0085]

[0086] In the formula, T a η is the atmospheric one-way attenuation coefficient. r For the optical transmittance of the spaceborne lidar system, A r ρ is the area of ​​the receiving telescope of the spaceborne lidar. i This represents the reflectance value corresponding to each target point within the footprint area;

[0087] Step 4.2, calculate the response echo function of each target point within the laser footprint range, mainly including the following process:

[0088] (4.2.1) Calculate the response echo width T of each point target within the laser footprint range. i :

[0089]

[0090] In the formula, c is the speed of light in a vacuum;

[0091] (4.2.2) Calculate the response echo function h of each point target within the laser footprint range. i (q):

[0092]

[0093] In the formula, This indicates a width of 2T. i Rectangular function, sgn represents the step function, τ i Let τ be the beam propagation time corresponding to the i-th point target. i =2R i / c, Δt represents the sampling time interval of the spaceborne lidar echo, q represents the time sampling sequence, q is an integer, and its value ranges from floor{min[(τ i -T i ) / Δt]} to ceil{max[(τ i +T i ) / Δt]}, where floor and ceil functions represent floor and ceil operations, respectively.

[0094] Preferably, in the spaceborne lidar echo simulation method based on point cloud data provided by the present invention, step 5 includes the following sub-steps:

[0095] Step 5.1: Calculate the response echo function h of all point targets within the laser footprint range. i (q) are superimposed to obtain the overall target response signal sequence h. sc (q):

[0096]

[0097] Step 5.2, combine the overall target response signal sequence with the spaceborne lidar emitted pulse sequence P. f (q) Perform convolution to obtain the simulated echo P rec (q):

[0098] P rec (q)=P f (q)*h sc (q).

[0099] Preferably, in the point cloud data-based spaceborne lidar echo simulation method provided by the present invention, the initial parameters for the spaceborne lidar echo simulation in step 1 include:

[0100] Parameter 1: Parameters of the spaceborne lidar system, including: satellite orbital altitude, root mean square laser divergence angle, receiving telescope area, echo sampling time interval, and system optical transmittance;

[0101] Parameter 2: Observation parameters of the spaceborne lidar, including: laser pointing zenith angle, emitted laser pulse waveform sequence, geographic coordinates of the laser footprint, and geographic coordinates of the satellite platform location;

[0102] Parameter 3: Airborne LiDAR point cloud parameters, including: three-dimensional coordinate data and intensity data of the point cloud in the spaceborne LiDAR echo simulation area and the airborne LiDAR radiation calibration area;

[0103] Parameter 4. Other auxiliary parameters, including: the position coordinates of the airborne lidar platform and the sequence number of the emitted pulse, the true reflectivity of the target within the radiation calibration area, the atmospheric attenuation coefficient, and the transformation matrix between the international geodetic coordinate frame and the projected coordinate frame.

[0104] <device>

[0105] Furthermore, the present invention also provides a spaceborne lidar echo simulation device based on point cloud data capable of automatically implementing the above-mentioned <method>, characterized in that it includes:

[0106] Initialization section: Input the initial parameters for the spaceborne lidar echo simulation;

[0107] The spacing and vector calculation unit selects point cloud data of airborne lidar within the footprint range of the spaceborne lidar, and calculates the average pulse spacing of the point cloud data and the normal vector of each point target.

[0108] The reflectivity acquisition unit calculates the correction intensity of each point target within the laser footprint range based on the normal vector of each point target and calculates the reflectivity correction factor corresponding to the radiation calibration area. This corrects the influence of laser ranging value and laser incident angle on the point cloud intensity and obtains the reflectivity value corresponding to each point target.

[0109] The response echo calculation unit calculates the slope γ of each target point within the laser footprint range based on the average pulse spacing and reflectivity value. i and reflected power P i This allows us to obtain the response echo width T for each point target. i Then according to T i Calculate the response echo function h of each target point within the laser footprint range. i (q):

[0110]

[0111] In the formula, This indicates a width of 2T. i Rectangular function, sgn represents the step function, τ i τ represents the beam propagation time corresponding to the i-th point target. i =2R i / c, Δt represents the spaceborne lidar echo sampling time interval, and q represents the time sampling sequence;

[0112] The simulated echo acquisition unit calculates the overall target response signal sequence based on the response echo function, and convolves it with the transmitted pulse waveform sequence of the spaceborne lidar to obtain the simulated echo.

[0113] The control unit is communicatively connected to the initialization unit, the spacing and vector calculation unit, the reflectivity acquisition unit, the response echo calculation unit, and the simulation echo acquisition unit, and controls their operation.

[0114] Preferably, the spaceborne lidar echo simulation device based on point cloud data provided by the present invention further includes: an input display unit, which is communicatively connected to the control unit, allowing the operator to input operation commands and displaying corresponding information according to the operation commands.

[0115] Preferably, in the spaceborne lidar echo simulation device based on point cloud data provided by the present invention, the input display unit can statically or dynamically display the input and output data and processing procedures of the basic data acquisition unit, monitoring data acquisition unit, model construction unit, and operation unit in the form of text, data tables, two-dimensional or three-dimensional images according to the operation instructions.

[0116] Preferably, in the spaceborne lidar echo simulation device based on point cloud data provided by the present invention, the reflectivity acquisition unit acquires the reflectivity value corresponding to each point target using the following sub-steps 3.1 to 3.4:

[0117] Step 3.1: Calculate the airborne laser incident angle θ for each point target within the laser footprint range. i :

[0118]

[0119] In the formula, This represents the airborne ray vector corresponding to the i-th point target. Among them, (u i ,v i ,w i () represents the platform position coordinates when the airborne lidar measures the i-th point target; The normal vector representing the point target;

[0120] Step 3.2: Calculate the laser ranging value r corresponding to each point target within the laser footprint range. i :

[0121]

[0122] In the formula, the symbol || represents the modulo operation;

[0123] Step 3.3: Correct the influence of laser incident angle and laser ranging value on point cloud intensity, and calculate the corrected intensity I′ of each point target within the laser footprint range. i :

[0124]

[0125] In the formula, I i This represents the input intensity of the target at point i;

[0126] Step 3.4, calculate the reflectivity value of each target point within the laser footprint range, including the following process:

[0127] (3.4.1) The point cloud data (Cx) of the airborne lidar in the radiation calibration area m Cy m ,Cz m ), replacing the point cloud data within the laser footprint range (x i ,y i ,z i ), calculate the normal vector of each target point in the radiation calibration area. Where m = 1, 2, ... N pc N pc This indicates the total number of point targets in the radiation calibration area;

[0128] (3.4.2) Calculate the airborne laser incident angle β for each point target within the radiation calibration area. m :

[0129]

[0130] In the formula, This represents the airborne ray vector corresponding to the m-th point target within the radiation calibration area. Among them, (Cu m ,Cv m ,Cw m () represents the platform position coordinates when the airborne lidar measures the m-th point target in the radiation calibration area;

[0131] (3.4.3) Calculate the laser ranging value Cr corresponding to each point target within the radiation calibration area. m :

[0132]

[0133] (3.4.4) Calculate the reflectivity correction factor γ ref :

[0134]

[0135] In the formula, CI m This represents the input intensity of the m-th target point within the radiation calibration area;

[0136] (3.4.5) Obtain the reflectivity value ρ corresponding to each point target within the laser footprint range. i :

[0137] ρ i =I′ i γ ref ρ ref ,i∈Ω

[0138] In the formula, ρ ref The true reflectance of the target in the radiation calibration area.

[0139] The role and effect of invention

[0140] (1) The radiation characteristics of the simulated echo are accurately described by combining the radiation calibration of the point cloud intensity of the airborne lidar with the radiation calibration of the target slope and the laser incident angle.

[0141] (2) A rectangular function is used instead of the impulse function as the response echo function of the point target to eliminate the influence of the target area on the simulated echo and accurately describe the shape distribution of the simulated echo.

[0142] (3) Rapid and high-precision simulation of echoes from bare ground targets and vegetation targets with absolute radiation characteristics has been achieved. Attached Figure Description

[0143] Figure 1 This is a flowchart of a spaceborne lidar echo simulation method based on point cloud data, as described in an embodiment of the present invention.

[0144] Figure 2 This is a waveform diagram of the laser pulse emitted by a spaceborne lidar according to an embodiment of the present invention;

[0145] Figure 3 This is a diagram showing the three-dimensional coordinates and intensity data of the point cloud in the simulated area of ​​the spaceborne lidar echo involved in an embodiment of the present invention;

[0146] Figure 4 This is a point cloud three-dimensional coordinate and intensity data diagram of the radiation calibration area of ​​the airborne lidar involved in the embodiments of the present invention;

[0147] Figure 5 This is a point cloud data map of the footprint range of the spaceborne lidar obtained by screening in an embodiment of the present invention;

[0148] Figure 6 This is a normal vector diagram of point targets within the footprint range of a spaceborne lidar according to an embodiment of the present invention;

[0149] Figure 7 This is a point cloud reflectance map of the footprint range of a spaceborne lidar after radiometric correction, as described in an embodiment of the present invention.

[0150] Figure 8 This is a sequence diagram of the overall response signal of the target within the footprint range of the spaceborne lidar involved in the embodiments of the present invention;

[0151] Figure 9 This is a simulated echo map within the footprint range of a spaceborne lidar involved in an embodiment of the present invention;

[0152] Figure 10 This is a comparison diagram of the simulated echo obtained by the DART software in the embodiments of the present invention and the simulated echo obtained by the method of the present invention.

[0153] Figure 11 This is a normalized comparison chart of the simulated echo obtained by the point cloud accumulation method involved in the embodiments of the present invention, the simulated echo obtained by the method of the present invention, and the simulated echo of DART software. Detailed Implementation

[0154] The following describes in detail, with reference to the accompanying drawings, the specific implementation scheme of the spaceborne lidar echo simulation method and device based on point cloud data involved in this invention.

[0155] <Example 1>

[0156] In this embodiment, the Global Ecosystem Dynamics Survey (GEDI) lidar developed by NASA is used as an example. Based on the point cloud data of airborne lidar in vegetated areas generated by DART software, the technical solution of the present invention will be specifically explained.

[0157] I. For example Figure 1 As shown in this embodiment, the spaceborne lidar echo simulation method based on point cloud data includes the following:

[0158] Step 1: Input the initial parameters for the spaceborne lidar echo simulation, mainly including:

[0159] Parameters of a spaceborne lidar system include: satellite orbital altitude, emitted laser pulse energy, root mean square laser divergence angle, receiving telescope area, echo sampling time interval, and system optical transmittance.

[0160] Observation parameters of spaceborne lidar include the laser pointing zenith angle, the waveform sequence of the emitted laser pulse, the geographic coordinates of the laser footprint, and the geographic coordinates of the satellite platform location.

[0161] Airborne lidar point cloud parameters: including the three-dimensional coordinate data and intensity data of the point cloud in the spaceborne lidar echo simulation area and the airborne lidar radiation calibration area.

[0162] Other auxiliary parameters include the airborne lidar platform's position coordinates and emitted pulse number, the target's true reflectivity within the radiation calibration area, the atmospheric attenuation coefficient, and the transformation matrix between the international geodetic coordinate frame and the projected coordinate frame.

[0163] For a detailed description of all parameters, please refer to Table 1.

[0164] Table 1 Initial parameters for spaceborne lidar echo simulation

[0165]

[0166] Step 2: Select point cloud data from the airborne lidar within the footprint range of the spaceborne lidar, and calculate the average pulse spacing and normal vector of each point target. This includes the following sub-steps:

[0167] Step 2.1, selecting airborne lidar point cloud data within the footprint range of the spaceborne lidar, mainly includes the following process:

[0168] (2.1.1) Transform the footprint geographic coordinates (30,30,0) of the spaceborne lidar and the geographic coordinates (30,-44114,420000) of the satellite platform location under the international geodetic coordinate framework to the same projected coordinate framework as the airborne lidar point cloud coordinates:

[0169] (x f y f , z f ) T =(30, 30, 0) T , (x s y s , z s ) T = (30, -44114, 420000) T

[0170] In the formula, (x f y f , z f ) and (x s y s , z s ) represent the footprint of the spaceborne lidar and the geographical coordinates of the platform location under the projected coordinate frame, respectively.

[0171] (2.1.2) The satellite ray vector corresponding to the i-th point target in the computer-borne lidar point cloud data With the pointing vector of the spaceborne lidar The angle between

[0172]

[0173] In the formula, Among them, (x i y i , z i () represents the three-dimensional coordinates of the i-th target point, with subscripts i = 1, 2, ..., 65150.

[0174] (2.1.3) Select the airborne lidar point cloud data within the laser footprint range, whose point target indices satisfy:

[0175]

[0176] In this embodiment, the point cloud data within the range of the footprint light spot obtained through screening is as follows: Figure 5 As shown.

[0177] Step 2.2, calculating the average pulse spacing of the point cloud data within the laser footprint range, mainly includes the following processes:

[0178] (2.2.1) Count the number of emission pulses N corresponding to the point cloud data within the laser footprint area. ps :

[0179] N ps =Length[unique(F)]

[0180] In the formula, F = {Q} i |i∈Ω} represents the set of emission pulse numbers within the laser footprint range, where Q i This represents the emission pulse number corresponding to the i-th point target. The Length function calculates the array length, and the Unique(F) function calculates the array of distinct elements in set F.

[0181] Based on the statistics of this embodiment Figure 5 The point cloud data within the laser footprint range shown is used to obtain the number of emitted pulses N. ps =15915.

[0182] (2.2.2) Calculate the average pulse spacing d corresponding to the point cloud data within the laser footprint range. sc :

[0183]

[0184] In the formula, S f S represents the area of ​​the laser footprint on the geoid. f =997.36m 2 .

[0185] The average pulse spacing d in this example was obtained through calculation. sc ≈0.25m.

[0186] Step 2.3: Calculate the normal vector of each target point within the laser footprint range. It mainly includes the following processes:

[0187] (2.3.1) Calculate the distance between the i-th point target and other points within the footprint range of the spaceborne lidar.

[0188]

[0189] In the formula, (x j ,y j ,z j ) represents the coordinates of the j-th target point within the footprint area.

[0190] (2.3.2) will Sort the values ​​from smallest to largest, and select the target coordinates corresponding to the first 6 smallest values. The set of extreme coordinates N that constitutes the target at point i i .

[0191] (2.3.3) Calculate the extreme value coordinate set N i offset vector matrix M i :

[0192]

[0193] In the formula, and M respectively i Vector components in the x, y, and z directions.

[0194] (2.3.4) Calculate the offset vector matrix M i covariance matrix y i :

[0195]

[0196] In the formula, For vectors with vector The covariance function can be expressed as: Among them, a k and b k Representing vectors respectively with vector The k-th element in and Representing vectors respectively sum vector The average value of the elements.

[0197] (2.3.5) Calculate the covariance matrix A i eigenvalue set λ i :

[0198] |A i -λ i E|=0,i∈Ω

[0199] In the formula, E is a 3×3 identity matrix.

[0200] (2.3.6) Select the eigenvalue set λ i Minimum eigenvalue λ min Calculate the normal vector of the point target.

[0201]

[0202] In this embodiment, the normal vector of the point target within the laser footprint range is as follows: Figure 6 As shown.

[0203] Step 3: Correct the influence of laser incident angle and laser ranging value on point cloud intensity, and obtain the reflectivity value corresponding to each point target, including the following sub-steps:

[0204] Step 3.1: Calculate the airborne laser incident angle θ for each point target within the laser footprint range. i :

[0205]

[0206] In the formula, This represents the airborne ray vector corresponding to the i-th point target. Among them, (u i ,v i ,w i ) represents the platform position coordinates when the airborne lidar measures the i-th point target.

[0207] Step 3.2: Calculate the laser ranging value r corresponding to each point target within the laser footprint range. i :

[0208]

[0209] In the formula, the symbol "||" represents the modulo operation.

[0210] Step 3.3: Correct the influence of laser incident angle and laser ranging value on point cloud intensity, and calculate the corrected intensity I′ of each point target within the laser footprint range. i :

[0211]

[0212] In the formula, I i This represents the input intensity of the target at point i.

[0213] Step 3.4, calculate the reflectivity value of each target point within the laser footprint range, which mainly includes the following process:

[0214] (3.4.1) The point cloud data (Cx) of the airborne lidar in the radiation calibration area m Cy m ,Cz m ), replacing the point cloud data (x) within the laser footprint area in step 2.2. i ,y i ,z i ), calculate the normal vector of each target point in the radiation calibration area. Where m = 1, 2, ... 3840.

[0215] (3.4.2) Calculate the airborne laser incident angle β for each point target within the radiation calibration area. m :

[0216]

[0217] In the formula, This represents the airborne ray vector corresponding to the m-th point target within the radiation calibration area. Among them, (Cu m ,Cv m ,Cw m ) represents the platform position coordinates when the airborne lidar measures the m-th point target in the radiation calibration area.

[0218] (3.4.3) Calculate the laser ranging value Cr corresponding to each point target within the radiation calibration area. m :

[0219]

[0220] (3.4.4) Calculate the reflectivity correction factor γ ref :

[0221]

[0222] In the formula, CI m This represents the input intensity of the m-th point target within the radiation calibration area.

[0223] (3.4.5) Obtain the reflectivity value ρ corresponding to each point target within the laser footprint range. i :

[0224] ρ i =0.2I′ i γ ref ,i∈Ω

[0225] After radiometric correction, the point cloud reflectance within the laser footprint area is as follows: Figure 6 As shown.

[0226] Step 4: Calculate the response echo for each point target using the laser radiation transmission equation, including the following sub-steps:

[0227] Step 4.1: Using the laser radiation transmission equation, calculate the reflected power P of each target point within the laser footprint range. i It mainly includes the following processes:

[0228] (4.1.1) Calculate the distance R between the i-th point target within the laser footprint range and the spaceborne lidar platform. i :

[0229]

[0230] (4.1.2) Calculate the incident angle φ of the spaceborne laser corresponding to the i-th point target within the laser footprint range. i :

[0231]

[0232] (4.1.3) Calculate the area weight S of the i-th point target. i :

[0233] S i =0.25 2 / cosγ i ,i∈Ω

[0234] In the formula, γ i Let be the slope of the i-th target point within the laser footprint range.

[0235] (4.1.4) Calculate the reflected power P of each point target within the laser footprint range. i :

[0236]

[0237] Step 4.2, calculate the response echo function of each target point within the laser footprint range, mainly including the following process:

[0238] (4.2.1) Calculate the response echo width T of each point target within the laser footprint range. i :

[0239]

[0240] In the formula, c = 2.99792458 × 10 8 m / s is the speed of light in a vacuum.

[0241] (4.2.2) Calculate the response echo function h of each point target within the laser footprint range. i (q):

[0242]

[0243] In the formula, This indicates a width of 2T. i Rectangular function, sgn represents the step function, τ i Let τ be the beam propagation time corresponding to the i-th point target. i =2R i / c, Δt represents the sampling time interval of the spaceborne lidar echo, q represents the time sampling sequence, q is an integer, and its value ranges from floor{min[(τ i -T i ) / Δt]} to ceil{max[(τ i +T i ) / Δt]}, where floor and ceil functions represent floor and ceil operations, respectively.

[0244] Step 5: Calculate the overall target response signal sequence and convolve it with the transmitted pulse waveform sequence of the spaceborne lidar to obtain the simulated echo, including the following sub-steps:

[0245] Step 5.1: Superimpose the response echo functions of all point targets within the laser footprint range to obtain the overall target response signal sequence h. sc (q):

[0246]

[0247] In this embodiment, the calculated distribution of the overall target response signal sequence is as follows: Figure 8 As shown.

[0248] Step 5.2, compare the overall target response function with the transmitted pulse waveform sequence P of the spaceborne lidar. f (q) Perform convolution to obtain the simulated echo P rec (q):

[0249] P rec (q)=P f (q)*h sc (q)

[0250] In this embodiment, the obtained simulated echo of the spaceborne lidar is as follows: Figure 9 As shown.

[0251] II. The following is an accuracy verification analysis using an embodiment of the method of the present invention:

[0252] Using the DART software simulated echo as a reference, the accuracy of the simulated echo obtained by the method of this invention is evaluated from two perspectives: the radiation characteristics and the waveform geometry characteristics. First, the simulated echo of the spaceborne lidar with absolute radiation characteristics obtained in this embodiment is visually compared with the DART software simulated echo; the distribution results are as follows. Figure 10 As shown in the figure. The difference between the total energy of the simulated echo obtained by the method of this invention and the total energy of the DART simulated echo is less than 6%, which indicates that the method of this invention has high accuracy in waveform radiation characteristic simulation. Secondly, without considering the echo radiation characteristics, the simulated echo obtained by the point cloud accumulation method, the simulated echo obtained by the method of this invention, and the echo simulated by DART software are normalized according to their respective maximum waveform values. The resulting echo distribution comparison diagram is shown in the figure. Figure 11 As shown in Table 2, the correlation coefficients and root mean square errors of the simulated echoes obtained by the method of this invention and the point cloud accumulation method with the simulated echoes obtained by DART software are statistically analyzed.

[0253] Table 2 Evaluation parameters of simulated echoes from the method of this invention, the traditional method, and the point cloud accumulation method.

[0254] Evaluation parameters The method of this invention simulates echo Point cloud accumulation method for simulating echo Correlation coefficient 0.9910 0.8237 Root mean square error 0.0530 0.2489

[0255] As shown in Table 2, the method of the present invention has a higher waveform correlation coefficient and a smaller root mean square error compared to the traditional point cloud accumulation method. This indicates that the simulated echo obtained by the method of the present invention has a more accurate waveform geometry. Combining the evaluation results of both the radiation characteristics and waveform geometry characteristics of the echo, it can be concluded that the method of the present invention can accurately simulate the echo waveform of a spaceborne lidar with absolute radiation characteristics.

[0256] <Example 2>

[0257] This second embodiment provides a device for simulating spaceborne lidar echoes based on the method of the present invention. The device includes a basic data acquisition unit, a monitoring data acquisition unit, a model construction unit, an operation unit, a simulation unit, an input display unit, and a control unit.

[0258] The initialization unit can perform the steps described in step 1 above, inputting the initial parameters for the spaceborne lidar echo simulation.

[0259] The spacing and vector calculation unit can perform the work described in step 2 above, calculating the average pulse spacing of the point cloud data and the normal vector of each point target.

[0260] The reflectance acquisition unit can perform the work described in step 3 above to acquire the reflectance value corresponding to each point target.

[0261] The response echo calculation unit can perform the steps described in step 4 above, calculating the response echo function h of each point target within the laser footprint range. i (q).

[0262] The simulation echo acquisition unit can perform the work described in step 5 above and obtain the simulation echo based on the response echo function.

[0263] The input display unit allows the operator to input operation commands and displays corresponding information based on those commands. For example, the input display unit can statically or dynamically display the input and output data and processing procedures of the initialization unit, spacing and vector calculation unit, reflectivity acquisition unit, response echo calculation unit, and simulated echo acquisition unit in the form of text, data tables, or two-dimensional or three-dimensional images, based on the operation commands.

[0264] The control unit is communicatively connected to the initialization unit, spacing and vector calculation unit, reflectivity acquisition unit, response echo calculation unit, simulation echo acquisition unit, and input display unit, controlling their operation.

[0265] The above embodiments are merely illustrative examples of the technical solutions of the present invention. The spaceborne lidar echo simulation method and apparatus based on point cloud data involved in the present invention are not limited to the content described in the above embodiments, but are defined by the scope of the claims. Any modifications, additions, or equivalent substitutions made by those skilled in the art based on these embodiments are within the scope of protection claimed by the claims of the present invention.

Claims

1. A method for simulating the echo of a spaceborne lidar based on point cloud data, characterized in that, Includes the following steps: Step 1: Input the initial parameters for the spaceborne lidar echo simulation; Step 2: Select the airborne lidar point cloud data within the footprint range of the spaceborne lidar, and calculate the average pulse spacing and the normal vector of each point target in the point cloud data. Step 3: Based on the normal vector of each point target, calculate the correction intensity of each point target within the laser footprint range and calculate the reflectivity correction factor corresponding to the radiation calibration area. In this way, correct the influence of laser ranging value and laser incident angle on the point cloud intensity and obtain the reflectivity value corresponding to each point target. Step 4: Based on the average pulse spacing and reflectivity value, calculate the slope of each target point within the laser footprint range. and reflected power This allows us to obtain the response echo width for each point target. Then according to Calculate the response echo function of each target point within the laser footprint range. : In the formula, Indicates width is Rectangular function, , Represents the step function. Indicates the first The beam propagation time corresponding to each point target , This indicates the time interval for echo sampling of the spaceborne lidar. Represents a time-sampled sequence; Step 5: Based on the response echo function, calculate the overall response signal sequence of the target, and convolve it with the transmitted pulse waveform sequence of the spaceborne lidar to obtain the simulated echo.

2. The spaceborne lidar echo simulation method based on point cloud data according to claim 1, Its features are: Step 2 includes the following sub-steps: Step 2.1, selecting airborne lidar point cloud data within the footprint range of the spaceborne lidar, includes the following process: (2.1.1) The footprint geographic coordinates of the spaceborne lidar under the international geodetic coordinate framework Geographic coordinates of the satellite platform location Transform to the same projected coordinate frame as the airborne lidar point cloud coordinates: ， In the formula, This represents the transformation matrix between the International Geodetic Frame and the Projected Geodetic Frame. and These represent the footprint of the spaceborne lidar and the geographical coordinates of the platform location within the projected coordinate frame, respectively. (2.1.2) The first point cloud data of computer-borne lidar The star-borne ray vector corresponding to each point target With the pointing vector of the spaceborne lidar The angle between : In the formula, ,in, Indicates the first The three-dimensional coordinates of the target point, with subscripts , This indicates the total number of point targets in the airborne lidar point cloud data. ; (2.1.3) Select the airborne lidar point cloud data within the laser footprint range, whose point target indices satisfy: In the formula, This represents the root mean square laser divergence angle of the spaceborne lidar. Step 2.2: Calculate the average pulse spacing of the point cloud data within the laser footprint area. It includes the following processes: (2.2.1) Count the number of emission pulses corresponding to the point cloud data within the laser footprint range. : In the formula, This represents the set of emission pulse numbers within the laser footprint range, where Indicates the first The transmission pulse sequence number corresponding to each point target. The function is used to calculate the length of an array. Function to find sets An array composed of different elements; (2.2.2) Calculate the average pulse spacing corresponding to the point cloud data within the laser footprint range. : In the formula, This represents the area of ​​the laser footprint on the geoid. ,in, Indicates the satellite's orbital altitude. This indicates that the laser is pointing towards the zenith angle; Step 2.3: Calculate the normal vector of each target point within the laser footprint range. It includes the following processes: (2.3.1) Calculate the first The distance between the point target and other points within the footprint range of the spaceborne lidar : In the formula, Indicates the first footprint within the area. The coordinates of the target point; (2.3.2) will Sort the values ​​from smallest to largest, and select the target coordinates corresponding to the first 6 smallest values. , , forming the first Set of extreme coordinates of a target point ; (2.3.3) Calculate the set of extreme value coordinates offset vector matrix : In the formula, , and They represent exist , and Vector components in the direction; (2.3.4) Calculate the offset vector matrix covariance matrix : In the formula, For vectors with vector The covariance function, where, and Representing vectors respectively with vector The Middle One element, and Representing vectors respectively sum vector The average value of the elements; (2.3.5) Calculate the covariance matrix eigenvalue group : In the formula, It is a 3×3 identity matrix; (2.3.6) Selecting the eigenvalue set Minimum eigenvalue Calculate the normal vector of the point target. : 。 3. The spaceborne lidar echo simulation method based on point cloud data according to claim 1, Its features are: Step 3 includes the following sub-steps: Step 3.1: Calculate the airborne laser incident angle for each point target within the laser footprint range. : In the formula, Indicates the first The airborne ray vector corresponding to each point target ,in, Indicates the measurement of the first airborne lidar The platform's position coordinates when the target point is identified; The normal vector representing the point target; Step 3.2: Calculate the laser ranging value corresponding to each point target within the laser footprint range. : In the formula, the symbol This represents the modulo operation; Step 3.3: Correct the influence of laser incident angle and laser ranging value on point cloud intensity, and calculate the corrected intensity of each point target within the laser footprint range. : In the formula, Indicates the first Input intensity of each point target; Step 3.4, calculate the reflectivity value of each target point within the laser footprint range, including the following process: (3.4.1) The point cloud data of the airborne lidar in the radiation calibration area Replace the point cloud data within the laser footprint area in step 2.2 Calculate the normal vector of each target point in the radiation calibration area. ,in, , This indicates the total number of point targets in the radiation calibration area; (3.4.2) Calculate the airborne laser incident angle for each point target within the radiation calibration area. : In the formula, Indicates the first [unit] within the radiation calibration area The airborne ray vector corresponding to each point target ,in, This indicates that the airborne lidar measured the first [unit / item] in the radiation calibration area. The platform's position coordinates when the target point is identified; (3.4.3) Calculate the laser ranging value corresponding to each point target within the radiation calibration area. : (3.4.4) Calculate the reflectance correction factor : In the formula, Indicates the first [unit] within the radiation calibration area Input intensity of each point target; (3.4.5) Obtain the reflectivity value of each point target within the laser footprint range. : In the formula, The true reflectance of the target in the radiation calibration area.

4. The spaceborne lidar echo simulation method based on point cloud data according to claim 1, Its features are: Step 4 includes the following sub-steps: Step 4.1: Calculate the reflected power of each target point within the laser footprint range. It includes the following processes: (4.1.1) Calculate the first number within the laser footprint range The distance between a point target and the spaceborne lidar platform : In the formula, ,in, Indicates the first The three-dimensional coordinates of the target point, with subscripts , This indicates the total number of point targets in the airborne lidar point cloud data; This represents the geographical coordinates of the platform's location within the projected coordinate framework. (4.1.2) Calculate the first number within the laser footprint range. The incident angle of the satellite-borne laser corresponding to each point target : In the formula, The normal vector representing the point target; (4.1.3) Calculate the first Area weight of each point target : In the formula, ; The average pulse spacing of the point cloud data within the laser footprint area; (4.1.4) Calculate the reflected power of each point target within the laser footprint range. : In the formula, The atmospheric one-way attenuation coefficient. For the optical transmittance of the spaceborne lidar system, The area of ​​the receiving telescope for the spaceborne lidar; This represents the reflectance value corresponding to each target point within the footprint area; Step 4.2, calculate the response echo function of each target point within the laser footprint range, including the following process: (4.2.1) Calculate the response echo width of each point target within the laser footprint range. : In the formula, The speed of light in a vacuum; (4.2.2) Calculate the response echo function of each target point within the laser footprint range. ; Time sampling sequence It is an integer, and its value ranges from arrive ,in, and The functions represent rounding down and rounding up, respectively.

5. The spaceborne lidar echo simulation method based on point cloud data according to claim 1, characterized in that: in, Step 5 includes the following sub-steps: Step 5.1: Analyze the response echo functions of all point targets within the laser footprint range. By superimposing the signals, the overall target response signal sequence is obtained. : Step 5.2: Combine the overall target response signal sequence with the spaceborne lidar emission pulse sequence. Convolution is performed to obtain the simulated echo. : 。 6. The spaceborne lidar echo simulation method based on point cloud data according to claim 1, Its features are: in, In step 1, the initial parameters for the spaceborne lidar echo simulation include: Parameter 1: Parameters of the spaceborne lidar system, including: satellite orbital altitude, root mean square laser divergence angle, receiving telescope area, echo sampling time interval, and system optical transmittance; Parameter 2: Observation parameters of the spaceborne lidar, including: laser pointing zenith angle, emitted laser pulse waveform sequence, geographic coordinates of the laser footprint, and geographic coordinates of the satellite platform location; Parameter 3: Airborne LiDAR point cloud parameters, including: three-dimensional coordinate data and intensity data of the point cloud in the spaceborne LiDAR echo simulation area and the airborne LiDAR radiation calibration area; Parameter 4. Other auxiliary parameters, including: the position coordinates of the airborne lidar platform and the sequence number of the emitted pulse, the true reflectivity of the target within the radiation calibration area, the atmospheric attenuation coefficient, and the transformation matrix between the international geodetic coordinate frame and the projected coordinate frame.

7. A spaceborne lidar echo simulation device based on point cloud data, characterized in that, include: Initialization section: Input the initial parameters for the spaceborne lidar echo simulation; The spacing and vector calculation unit selects point cloud data of airborne lidar within the footprint range of the spaceborne lidar, and calculates the average pulse spacing of the point cloud data and the normal vector of each point target. The reflectivity acquisition unit calculates the correction intensity of each point target within the laser footprint range based on the normal vector of each point target and calculates the reflectivity correction factor corresponding to the radiation calibration area. This corrects the influence of laser ranging value and laser incident angle on the point cloud intensity and obtains the reflectivity value corresponding to each point target. The response echo calculation unit calculates the slope of each target point within the laser footprint range based on the average pulse spacing and reflectivity value. and reflected power This allows us to obtain the response echo width for each point target. Then according to Calculate the response echo function of each target point within the laser footprint range. : In the formula, Indicates width is Rectangular function, , Represents the step function. Indicates the first The beam propagation time corresponding to each point target , This indicates the time interval for echo sampling of the spaceborne lidar. Represents a time-sampled sequence; The simulated echo acquisition unit calculates the overall target response signal sequence based on the response echo function, and convolves it with the transmitted pulse waveform sequence of the spaceborne lidar to obtain the simulated echo. The control unit is communicatively connected to the initialization unit, the spacing and vector calculation unit, the reflectivity acquisition unit, the response echo calculation unit, and the simulation echo acquisition unit, and controls their operation.

8. The spaceborne lidar echo simulation device based on point cloud data according to claim 7, characterized in that, Also includes: The input display unit is connected to the control unit, allowing the operator to input operation commands and displaying corresponding information based on those commands.

9. The spaceborne lidar echo simulation device based on point cloud data according to claim 8, characterized in that: in, The input display unit can statically or dynamically display the input and output data and processing procedures of the initialization unit, spacing and vector calculation unit, reflectivity acquisition unit, response echo calculation unit, and simulation echo acquisition unit in the form of text, data tables, or two-dimensional or three-dimensional images, according to the operation instructions.

10. The spaceborne lidar echo simulation device based on point cloud data according to claim 7, Its features are: in, The reflectance acquisition unit uses the following sub-steps 3.1 to 3.4 to obtain the reflectance value corresponding to each point target: Step 3.1: Calculate the airborne laser incident angle for each point target within the laser footprint range. : In the formula, Indicates the first The airborne ray vector corresponding to each point target ,in, Indicates the measurement of the first airborne lidar The platform's position coordinates when the target point is identified; The normal vector representing the point target; Step 3.2: Calculate the laser ranging value corresponding to each point target within the laser footprint range. : In the formula, the symbol This represents the modulo operation; Step 3.3: Correct the influence of laser incident angle and laser ranging value on point cloud intensity, and calculate the corrected intensity of each point target within the laser footprint range. : In the formula, Indicates the first Input intensity of each point target; Step 3.4, calculate the reflectivity value of each target point within the laser footprint range, including the following process: (3.4.1) The point cloud data of the airborne lidar in the radiation calibration area Replaces point cloud data within the laser footprint range Calculate the normal vector of each target point in the radiation calibration area. ,in, , This indicates the total number of point targets in the radiation calibration area; (3.4.2) Calculate the airborne laser incident angle for each point target within the radiation calibration area. : In the formula, Indicates the first [unit] within the radiation calibration area The airborne ray vector corresponding to each point target ,in, This indicates that the airborne lidar measured the first [unit / item] in the radiation calibration area. The platform's position coordinates when the target point is identified; (3.4.3) Calculate the laser ranging value corresponding to each point target within the radiation calibration area. : (3.4.4) Calculate the reflectance correction factor : In the formula, Indicates the first [unit] within the radiation calibration area Input intensity of each point target; (3.4.5) Obtain the reflectivity value of each point target within the laser footprint range. : In the formula, The true reflectance of the target in the radiation calibration area.

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