Semi-empirical wave decomposition method for airborne laser bathymetry near-surface penetration error correction

Abstract

The present application relates to a semi-empirical waveform decomposition method for airborne laser bathymetry near-surface penetration error correction, belonging to the technical field of airborne laser bathymetry, which utilizes the time of laser reaching water surface and water bottom, echo intensity and shape adjustment parameter to construct water surface echo model and water bottom echo model, and then constructs water body backscattering model through simplifying laser radiation transmission theory, thereby forming a semi-empirical signal convolution model as a whole; the probability distribution of water body parameters in the model is estimated by using deep water waveform samples, and then the reasonable initial value and value range of the water body parameters are determined; the semi-empirical signal convolution model parameters are optimized and solved in combination with the initial value and value range of the water body parameters, the water surface signal position is determined by the model parameters, and the near-surface penetration error is corrected. The present application can reasonably model each component of the waveform, and can adapt to waveform processing under different water depths, effectively improving the detection accuracy of the water surface signal.

Description

Technical Field

[0001] This invention relates to a semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry, belonging to the field of airborne laser bathymetry technology. Background Technology

[0002] In shallow seabed topography surveying, Airborne Laser Bathymetry (ALB) leverages the advantages of airborne platforms to achieve efficient and flexible operations, effectively addressing the accessibility limitations of traditional acoustic bathymetry in shallow sea areas. ALB technology measures seabed topography by transmitting and receiving green lasers with strong water penetration, using the acquired surface and seabed echo signals. Unlike land-based lidar, ALB's laser transmission path involves both air and water media; therefore, refraction correction is necessary when calculating seabed point coordinates. The water surface is the interface between air and water; because the laser's transmission direction and speed differ in these two media, the determination of the water surface location ultimately affects the accuracy of seabed topography measurements.

[0003] The waveform received by the ALB system in water bodies consists of surface echo, backscattered water, and bottom echo. Ideally, the surface echo signal would appear as a distinct peak. However, when the waves are small and the water surface is smooth, the laser beam is almost specularly reflected at the surface, making the surface signal difficult for the receiver to detect. In this case, the weak directionality of the backscattered water will dominate the waveform and be mistakenly detected as a surface signal. This phenomenon is known as the "surface uncertainty problem." This problem is particularly significant in nearshore waters and bay areas where waves are limited by topography. The resulting error in surface signal detection is defined as near-surface penetration (NWSP) error. The NWSP error is jointly determined by the intensity of the surface echo signal and the intensity of the backscattered water. The former mainly depends on the laser incident angle and water roughness, while the latter is mainly related to the water attenuation coefficient. Therefore, the magnitude of the NWSP error varies within the same measurement area and cannot be directly corrected by single-point measurements.

[0004] Near-infrared lasers (NIWS) can be used for precise water surface measurement because they cannot penetrate water. Some ALB systems are equipped with NIWS, but it has been found that even on relatively smooth water surfaces, NIWS still cannot detect many areas. Analysis of NWSP errors using NIWS-detected water surfaces as a reference reveals regional regularities in the errors, which can be corrected through statistical analysis. Specific methods include corrections based on suspended sediment concentration and corrections based on redundant observations. The suspended sediment concentration-based method interpolates the turbidity of the entire measurement area using actual suspended sediment concentration values ​​obtained from measurements, and then establishes a statistical relationship between NWSP error and suspended sediment concentration to correct the water surface position. The redundant observation-based method involves taking two repeated observations from different angles in the measurement area, theoretically establishing a relationship between the difference between the two measurements and the NWSP error, thus retrieving the accurate water surface position.

[0005] While statistical analysis can effectively correct NWSP errors, existing methods require additional observations during actual operations, impacting measurement efficiency to some extent. The ideal approach is to correct NWSP errors solely through analysis of the original waveform. Waveform decomposition involves fitting the waveform to its components according to a model. For water waveforms acquired by the ALB system, waveform decomposition represents a combination of surface echoes, water backscattering, and bottom echoes. If the waveform decomposition method can accurately reconstruct each component, the determination of the water surface position can be independent of water backscattering, thus indirectly correcting NWSP errors. The key to waveform decomposition lies in model establishment, and in ALB, this hinges on establishing the water backscattering model. Based on model definition, existing water backscattering models can be broadly categorized into three types: geometric function models, mathematical function models, and signal convolution models. Geometric function models are based on the shape of the water backscattering waveform and are mostly represented by piecewise functions, such as triangular functions, quadrilateral functions, first-order polynomial exponential functions, and second-order polynomial exponential functions. When fitting the effect of water backscattering on depth sounding accuracy using different geometric function models, it was found that exponential functions are better suited to waveforms under different water quality and depth conditions. Mathematical function models are combinations of multiple mathematical functions. Compared to geometric function models represented by piecewise functions, mathematical function models have the advantage of continuity and can reduce the influence of local extrema when solving model parameters. Representative methods include the double exponential function model, the semi-Gaussian function model, and the multivariate Gaussian function model. The signal convolution model treats the waveform as a convolution of the target cross-section and the laser emission signal, embedding convolution operations within the model to indirectly achieve waveform fitting by fitting the target cross-section. Among the three models mentioned above, geometric function models and mathematical function models can only achieve similarity to the waveform shape, while only the signal convolution model is based on the waveform generation process, thus best conforming to the laser radiation transmission law and being closest to reality. However, existing signal convolution models use multiple shape parameters when constructing the target cross-section. These parameters are highly correlated and lack practical physical meaning. Furthermore, they lack consideration for aquatic environmental factors when setting initial values ​​for model parameters and do not constrain water-related parameters during parameter solving, resulting in randomness in waveform decomposition results. Summary of the Invention

[0006] The purpose of this invention is to provide a semi-empirical waveform decomposition method for correcting near-water surface seepage errors in airborne laser depth sounding, so as to achieve accurate reconstruction of each component of the waveform, correct near-water surface seepage errors, and improve the accuracy of water surface signal detection.

[0007] To achieve the above objectives, the present invention includes:

[0008] The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry of the present invention includes the following steps:

[0009] 1) Water surface echo model parameters are constructed based on the laser's arrival time at the water surface, water surface echo intensity, and waveform shape adjustment parameters. These parameters are then used as inputs to construct the water surface echo model through signal convolution. Similarly, water bottom echo model parameters are constructed based on the laser's arrival time at the water bottom, water bottom echo intensity, and waveform shape adjustment parameters. These parameters are also used as inputs to construct the water bottom echo model through signal convolution. Water backscattering model parameters are determined through a combination optimization of airborne laser depth sounding system parameters and water environment parameters. These parameters are then used as inputs to construct the water backscattering model through signal convolution. A semi-empirical signal convolution model describing the water body echo waveform is constructed based on the water surface echo model, water bottom echo model, and water backscattering model. The water surface echo model parameters and water bottom echo model parameters constitute depth sounding signal parameters, and the water backscattering model parameters constitute water body parameters.

[0010] 2) Determine the initial values ​​of the depth sounding signal parameters using a depth classification and adaptive threshold detection method; determine the initial values ​​and ranges of the water body parameters using deep-water waveform samples containing only surface signals and backscattered signals from the complete water body.

[0011] 3) Optimize the initial values ​​of the depth sounding signal parameters and the initial values ​​of the water body parameters. Use the range of water body parameters and the optimized initial values ​​of the depth sounding signal parameters and the initial values ​​of the water body parameters as inputs to the semi-empirical signal convolution model for solution, and calculate the coordinates of the water surface point and the bottom point.

[0012] The beneficial effects of the above technical solution are as follows: First, this invention utilizes the timing of laser arrival at the water surface and bottom, echo intensity, and shape adjustment parameters to construct surface echo models and bottom echo models, making the constructed water area model closer to the shape of the actual transmitted signal, thereby more accurately correcting the near-surface penetration error. Second, this invention uses deep-water waveforms to calculate the initial values ​​and ranges of water body parameters, and inputs these calculated initial values ​​and ranges into the constructed semi-empirical signal convolution model, making the solution to the semi-empirical signal convolution model more accurate. By constructing a model that more closely resembles actual signal transmission and using prior waveforms for constraints during the solution process, this invention effectively improves the accuracy of surface signal detection.

[0013] Furthermore, the water surface echo model is as follows:

[0014]

[0015] Among them, W S (t) represents the water surface echo model, α SLet t be the instantaneous value of the response function corresponding to the moment the laser reaches the water surface, and t be the current time. S Let σ be the instant the laser reaches the water surface. S For shape adjustment parameters, This is the waveform of the laser emission signal.

[0016] The beneficial effects of the above technical solution are as follows: The water surface echo model in this invention uses the time and shape adjustment parameters of the laser reaching the water surface at the instant, which can more closely approximate the shape of the actual transmitted signal and ensure the accuracy of the calculation results.

[0017] Furthermore, the underwater echo model is as follows:

[0018]

[0019] Among them, W B (t) represents the underwater echo model, α B Let t be the instantaneous value of the response function corresponding to the moment the laser reaches the bottom of the water, and t be the current time. B Let σ be the instant the laser reaches the bottom of the water. B For shape adjustment parameters, This is the waveform of the laser emission signal.

[0020] The beneficial effects of the above technical solution are as follows: The underwater echo model in this invention uses the time and shape adjustment parameters of the laser reaching the water surface, which can more closely approximate the shape of the actual transmitted signal and ensure the accuracy of the calculation results.

[0021] Furthermore, the water backscattering model is as follows:

[0022]

[0023] Where η0 and η1 are combinations of airborne laser bathymetry system parameters and water environment parameters, denoted as the first and second parameters of the water backscattering model, respectively, and t is the current time. S The value represents the instant the laser beam reaches the water surface; "*" indicates the convolution operation. This is the waveform of the laser emission signal.

[0024] The beneficial effects of the above technical solution are as follows: the water backscattering model in this invention adopts shape adjustment parameters, airborne laser depth sounding system parameters and water environment parameters, which can more closely approximate the shape of the actual transmitted signal and ensure the accuracy of the calculation results.

[0025] Furthermore, the semi-empirical signal convolution model is as follows:

[0026] W(t) = W S (t)+W C (t)+W B (t)

[0027] Where W(t) is a semi-empirical signal convolution model, W S (t) represents the water surface echo model, W C (t) represents the backscattering model of the water body, W B (t) represents the underwater echo model.

[0028] Further, in step 2), the initial values ​​and ranges of the water body parameters are calculated using a method for estimating the probability distribution of water body parameters. The method for estimating the probability distribution of water body parameters is as follows:

[0029] a. Obtain deep-water waveforms containing only surface signals and backscattering from a complete water body, perform maximum detection on the deep-water waveforms, and determine the location of the surface signal;

[0030] b. Remove the water surface signal from the deep water waveform based on the width of the laser emission signal to obtain the backscattered waveform of the water body to be fitted;

[0031] c. Substitute the water surface signal position from step a into the water backscattering model as a constant, and use this model to fit the water backscattering waveform from step b to calculate the probability distribution estimate of the water parameters.

[0032] The beneficial effects of the above technical solution are as follows: Considering that water backscattering has some overlap with both surface and bottom signals, making it difficult to directly determine the initial value from the waveform, this invention obtains deep-water waveform samples, uses these samples to determine the water waveform to be fitted, and solves the water backscattering model with the goal of finding the closest approximation between the water backscattering model and the water waveform to be fitted. This allows for the rapid and accurate estimation of the probability distribution of water parameters.

[0033] Furthermore, the process for determining the initial values ​​of the depth sounding signal parameters in step 2) is as follows:

[0034] The average waveform of the water body is obtained by removing the part affected by the water surface signal from the width of the transmitted signal, and the part with the stronger amplitude at the front end is recorded as the water body identification waveform.

[0035] Calculate the correlation between each frame of waveform and the water body marker waveform, and classify the waveforms into two categories, shallow water waveforms and deep water waveforms, based on the magnitude of the correlation.

[0036] For shallow water waveforms, a fixed threshold maximum detection method is used to determine the position and initial intensity of the sounding signal. For deep water waveforms, an adaptive threshold maximum detection method is used to determine the position and initial intensity of the sounding signal.

[0037] The beneficial effects of the above technical solution are as follows: By classifying and processing water depth, the present invention uses different detection methods to determine the initial values ​​of different water depth sounding signals, which can further improve the accuracy and efficiency of waveform decomposition.

[0038] Furthermore, the deep-water waveform obtained in step a consists of several frames. In step c, the water parameters of each frame of the waveform are calculated to obtain the probability distribution estimate of the water parameters. The average value is used as the initial value of the water parameters determined in step 2). The maximum and minimum values ​​in the probability distribution estimate of the second parameter are used as the upper and lower limits of the second parameter value, respectively, as the range of values ​​of the water parameters determined in step 2).

[0039] The beneficial effects of the above technical solution are as follows: after calculating the probability distribution estimates of multiple sets of water body parameters, the average value of the multiple probability distribution estimates is taken, and the average value is used as the initial value of the water body parameters and substituted into the semi-empirical signal convolution model to ensure that the coordinates of the water surface point and the bottom point calculated by the semi-empirical signal convolution model are more accurate.

[0040] Further, in step 3), the initial values ​​of the depth sounding signal parameters and the initial values ​​of the water body parameters are input into the semi-empirical signal convolution model, and the model parameters are optimized within the range of water body parameter values.

[0041] The beneficial effects of the above technical solution are: optimizing the initial values ​​of the depth sounding signal parameters and the initial values ​​of the water body parameters, making the initial values ​​of the input model more accurate, thereby ensuring the accuracy of water surface detection. Attached Figure Description

[0042] Figure 1 This is a cross-sectional diagram of the theoretical analysis of near-water surface seepage error in this invention;

[0043] Figure 2 This is a diagram showing the changes in laser incident angle and refraction angle under the Mapper5000 scanning method of this invention;

[0044] Figure 3 This is a diagram showing the horizontal error of the bottom point in this invention.

[0045] Figure 4 This is a vertical error diagram of the bottom point of the present invention;

[0046] Figure 5 This is a flowchart of the semi-empirical waveform decomposition method for airborne laser depth sounding according to the present invention;

[0047] Figure 6 This is the mean value diagram of deep-water waveform samples of the present invention;

[0048] Figure 7 This is a diagram of the test area of ​​the present invention;

[0049] Figure 8 This is the water parameter η0 distribution diagram of the present invention;

[0050] Figure 9 This is a water parameter η1 distribution diagram of the present invention;

[0051] Figure 10 This is a cross-sectional view of the water surface point cloud parallel to the route direction using the APD.

[0052] Figure 11 This is a cross-sectional view of the water surface point cloud parallel to the route direction of the RLD;

[0053] Figure 12 This is a cross-sectional view of the water surface point cloud parallel to the EW / EFSP direction;

[0054] Figure 13 This is a cross-sectional view of the water surface point cloud of the SSCM parallel to the route direction of the present invention;

[0055] Figure 14 This is a cross-sectional view of the surface point cloud perpendicular to the route direction using the APD.

[0056] Figure 15 This is a cross-sectional view of the water surface point cloud perpendicular to the route direction of the RLD;

[0057] Figure 16 This is a cross-sectional view of the water surface point cloud perpendicular to the flight path direction in EW / EFSP.

[0058] Figure 17 This is a cross-sectional view of the water surface point cloud perpendicular to the route direction of the SSCM of this invention;

[0059] Figure 18 This is a waveform processing result diagram of RLD shallow water;

[0060] Figure 19 This is a waveform processing result diagram of EW shallow water;

[0061] Figure 20 This is a diagram showing the SSCM shallow water waveform processing result of the present invention;

[0062] Figure 21 This is a waveform processing result diagram of RLD deep water;

[0063] Figure 22 This is a waveform processing result diagram of EFSP deepwater;

[0064] Figure 23 This is a waveform processing result diagram of the SSCM deep-water waveform of the present invention;

[0065] Figure 24 This is an image map showing the distribution of water surface elevation errors;

[0066] Figure 25 This is a map showing the distribution of water surface elevation errors in the RLD system.

[0067] Figure 26 This is a map showing the EW / EFSP water surface elevation error distribution.

[0068] Figure 27This is the SSCM water surface elevation error distribution map of the present invention. Detailed Implementation

[0069] The present invention will now be described in further detail with reference to the accompanying drawings.

[0070] Example:

[0071] The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry (NWSP) provided by this invention constructs a semi-empirical signal convolution model by simplifying the physical process of laser radiation transmission. This model has advantages such as a small number of unknown parameters and strong independence between parameters, which can effectively improve the accuracy of model parameter solution. In addition, a small number of seepage waveform samples are manually selected using flight track and image data to calculate the initial values ​​and selection range of water body parameters. By setting reasonable initial parameter values ​​and value ranges, the consistency between the waveform decomposition results and the actual waveform is improved, thereby achieving accurate correction of NWSP error.

[0072] To demonstrate the necessity of NWSP error correction, this invention establishes the relationship between NWSP error and underwater topographic measurement results through theoretical formula derivation. The NWSP error is analyzed within the plane containing the laser incident ray and the normal. Figure 1 As shown in the figure, the solid black line represents the actual transmission path of the laser. The laser travels from the center O of the laser along the path r. a Reaching the water surface point X′ S , at X′ S Refraction occurs at point r and then along path r w Reaching the bottom point X B The gray dashed line represents the laser transmission path calculated when NWSP error exists, i.e., the laser travels from O along path r′. a To X′ S Then from X′ S Starting along path r′ w Arrival at X′ B According to the point calculation model, the coordinates of the water surface point and the water bottom point can be expressed as:

[0073] X′ S =O+r′ a =O+(L a +c a Δt / 2)γ a

[0074] X′ B =X′ S +r′ w =O+(L a +c a Δt / 2)γ a +(L w -c w Δt / 2)γw

[0075] Among them, L a and L w These represent the actual distances the laser travels in air and water, respectively, where Δt is the bidirectional transmission time difference of the water surface signal caused by NWSP, and c is the distance traveled in air and water. a and c w c represents the propagation speed of laser light in air and water, respectively. a The projection of Δt / 2 in the vertical direction corresponds to Figure 1 Δh S This refers to the "penetration depth" of the laser on the water surface, γ. a and γ w γ represents the unit direction vector of laser propagation in air and water, respectively. a and γ w The calculation formula is:

[0076] γ a =(sinθ) a cosθ a )

[0077] γ w =(sinθ) w cosθ w )

[0078] Where, θ a and θ w Let be the angle of incidence and the angle of refraction of the laser at the water surface, respectively, which follow Snell's law, i.e.:

[0079]

[0080] Where, n a and n w These are the refractive indices of the laser in air and water, respectively.

[0081] Water surface error E S and bottom error E B They can be represented as:

[0082] E S =X′ S -X S =c a Δtγ a / 2

[0083] E B =X′ B -X B =Δt(c a γ a -c w γ w ) / 2

[0084] Therefore, the NWSP error depends on the penetration depth Δh S and laser incident angle θ a Size.

[0085] This invention specifically analyzes the error of NWSP (Neural Wave Spinning) using the domestically developed dual-frequency ALB system Mapper5000 from the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, as an example to calculate the error caused by NWSP to the coordinates of the bottom point in several directions. Mapper5000 employs a conical scanning method, where the laser incident angle changes periodically with the rotation of the scanning mirror, and the refraction angle also changes accordingly. Figure 2 As shown.

[0086] Under conditions of good water quality, the penetration depth Δh of the laser at the water surface S At approximately 10-25cm, Δh S A fixed value of 20cm is used, which, along with the laser incident angle, is substituted into the underwater error E. B From the expression, the errors of the bottom point in the horizontal and vertical directions can be obtained, such as... Figure 3 , Figure 4 As shown. Combined with Figure 3 , Figure 4 As can be seen, at a laser incident angle of approximately 13°, the error at the bottom point is smaller in the horizontal direction than in the vertical direction. The horizontal error is about one-tenth of the penetration depth, while the vertical error is about one-quarter of the penetration depth. In shallow water measurements, the required depth measurement accuracy is typically 0.3m. As water quality deteriorates, the NWSP error will continue to increase; therefore, the impact of NWSP on bottom measurements is not negligible.

[0087] The water waveforms acquired using green lasers can be used to invert water quality parameters such as suspended sediment concentration and water attenuation coefficient, indicating that water information related to NWSP can be directly obtained from the waveforms. Therefore, it is feasible to correct NWSP errors solely through waveform decomposition. Figure 5 As shown, this invention is based on the proposed semi-empirical signal convolution model (SSCM). It utilizes manually collected deep-water waveform samples with complete water backscattering to initialize and limit the range of bathymetry signal parameters and water body parameters, thus incorporating waveform priors into the waveform separation process. Then, a trust region algorithm is used to solve for the model parameters within the limited range, thereby determining the accurate location of the bathymetry signal. The proposed SSCM is a semi-empirical model combining theory and experience. On the one hand, it is simplified from a laser radiation transmission model, possessing a theoretical foundation; on the other hand, the initial values ​​and ranges of the water body parameters in the model are determined by the actual waveform, giving it empirical constraints.

[0088] The semi-empirical waveform decomposition method proposed in this invention specifically includes the following steps:

[0089] 1) Model establishment.

[0090] Based on the composition of the water echo waveform, the waveform W(t) that the SSCM can receive can be represented as a combination of its components.

[0091] W(t) = W S (t)+W C (t)+W B (t)

[0092] Among them, W S (t) represents the water surface echo model, W C (t) represents the backscattering model of the water body, W B (t) represents the underwater echo model. In the laser radiation transmission model, the system received waveform W(t) is the result of the target cross-section P(t) and the laser emission signal waveform. The convolution of P(t) can be further expressed as follows, based on the waveform composition:

[0093] P(t)=P S (t)+P C (t)+P B (t)

[0094] Among them, P S (t), P C (t), P B (t) are the response functions of the water surface, water body, and bottom, respectively.

[0095] Ideally, water surface echoes are generated by instantaneous water surface signals, i.e., P S (t) only at time t when the laser reaches the water surface S There exists a non-zero value α at this location. S ,Right now:

[0096]

[0097] In reality, the shape of water surface echoes is affected by waves. To enhance the model's adaptability, SSCM adds a shape adjustment parameter σ to the laser emission waveform. S :

[0098]

[0099] Based on this, a water surface echo model is established using signal convolution:

[0100]

[0101] In this text, "*" represents a convolution operation. Similarly, the underwater echo model can be represented as:

[0102]

[0103] Where, α B The underwater response function P B (t) at the moment t_t reaches the bottom of the water B In addition to the value at the location, since the shape of the underwater echo is affected by the underwater topography, a shape adjustment parameter σ also needs to be added. B .

[0104] According to the radiative transmission model of laser light, the intensity of water echoes gradually changes with water depth, that is:

[0105]

[0106] Where F represents parameters related to the system, atmospheric environment, and water surface environment, k is the water attenuation coefficient, z is the current water depth, and H is the flight platform altitude. For water depth z, the corresponding time delay can be expressed as:

[0107]

[0108] Since ALB technology is mainly used for shallow sea measurements, the denominator n in the formula for water echo intensity is... w The effect of z in H+z can be ignored.

[0109] Then, substituting the time delay calculation formula for the water depth z of the water body layer into the solid echo intensity, we get:

[0110]

[0111] The water response function of the SSCM is further simplified as follows:

[0112] P C (t)=exp(η0+η1(tt S )), t S <t<t B

[0113] Where η0 and η1 are combinations of system and environmental parameters, specifically expressed as:

[0114] η0=ln(F)+2ln(cosθ a )-2ln(n w H)

[0115] η1=-c w k

[0116] The backscattering model of the water body can then be obtained through signal convolution:

[0117]

[0118] 2) Determining the initial values ​​of the parameters.

[0119] According to step 2), the entire SSCM calculation process includes 8 unknown parameters:

[0120] λ=(α S ,t S ,σ S ,α B ,t B ,σ B ,η0,η1)

[0121] The first six parameters are depth sounding signal parameters, and the last two are water body parameters.

[0122] ① Determination of initial values ​​for depth sounding signal parameters.

[0123] Reliable initial values ​​can effectively improve the accuracy and efficiency of waveform decomposition. Therefore, a method for determining the initial values ​​of depth sounding signals for water depth classification and adaptive threshold detection is proposed, which includes the following steps:

[0124] A. Deep-water sample acquisition and processing. A small number of deep-water waveform samples (those from depths exceeding the system's detection capabilities) are manually collected from the dataset. All samples are unified on the time axis based on their time difference with the surface signal, and then averaged over time to obtain the mean waveform. For example... Figure 6 As shown, the average waveform ρ of the water body is obtained by removing the influence of the water surface signal based on the width of the transmitted signal. Then, the part with the stronger amplitude at the front end is extracted and recorded as the water body identification waveform ρ. C ( Figure 6 (The area selected by the dashed box).

[0125] B. Waveform Depth Classification. Because shallow water waveforms are prone to signal overlap, while deep water waveforms are susceptible to noise interference from the seabed, waveforms need to be classified according to water depth. The waveform in each frame is compared with the water body marker waveform ρ. C The correlation between the waveforms was analyzed, with shallow water waveforms showing a lower correlation and deep water waveforms showing a higher correlation. Based on the magnitude of the correlation, the waveforms were further divided into shallow water and deep water categories.

[0126] C. Waveform Preprocessing. For deep-water waveforms, the mean squared difference function is used for noise reduction. For shallow-water waveforms, the Richardson-Lucy deconvolution method is used to improve signal resolution. However, considering the long computation time of the deconvolution algorithm and the fact that subsequent waveform decomposition can also handle overlapping signals, this invention only performs mean filtering on the waveforms.

[0127] D. Signal Detection. For shallow water waveforms, the bottom signal is less affected by water attenuation, so a fixed threshold maximum detection method can be used. For deep water waveforms, the bottom signal is easily interfered with by noise, especially high-intensity noise located in the backscattered part of the water. Therefore, an adaptive threshold is constructed using ρ to improve the detection rate of the bottom signal.

[0128] The initial value t of the depth sounding signal's location and intensity can be obtained through signal detection. S0 t B0 α S0 α B0 Initial value of shape adjustment parameter σ S0 σ B0 The initial value is uniformly set to 1. For shallow water waveforms where only one signal (t0, α0) is detected, based on experience, it is usually closer to the signal location at the bottom of the water. Therefore, the initial value is set as follows: t S0 =t0-2,t B0 =t0, α S0 =α B0 =0.5×α0.

[0129] ② Determination of initial values ​​and ranges for water body parameters.

[0130] Because water backscattering partially overlaps with both surface and bottom signals, it's difficult to directly obtain initial values ​​from the wavelet data. The water parameter η0 is related to system and environmental parameters; ignoring changes in underwater light speed, η1 is only related to the water attenuation system k. For waveforms in the same measurement area, the changes in η0 and η1 are relatively small. Therefore, we can use deep-water waveform samples containing only surface signals and complete water backscattering to obtain the initial values ​​and ranges of the water parameters. The specific steps are as follows:

[0131] A. Perform maximum detection on each frame of deep-water waveform sample to determine the initial value t of the water surface signal position. S0 .

[0132] B. By removing the portion of the signal affecting the water surface based on the width of the transmitted signal, the waveform to be fitted is obtained.

[0133] C. Set initial values ​​for water parameters. Since the model is simple to construct, the initial values ​​for water parameters only need to be set within an approximately reasonable range. In this invention, η0 and η1 are set to 2 and -0.01, respectively.

[0134] D. t S0 Substitute these parameters into the water backscattering model and solve for η0 and η1 using the Levecberg-Marquardt algorithm.

[0135] E. Use the average value of the fitting results of all deep-water waveform samples as the initial value of the water body parameters.

[0136] The water parameter η0 affects the overall intensity of water backscattering and is related to the energy distribution of laser reflection at the water surface. This depends on the instantaneous state of the water surface and therefore has a certain degree of randomness; thus, its value range should not be limited in subsequent waveform decomposition. The water parameter η1 controls the rate of decrease in the intensity of the water backscattering waveform and corresponds to the water attenuation coefficient. It is a key factor affecting the shape of the water backscattering waveform and its value range needs to be constrained. Therefore, the minimum and maximum values ​​of the fitting results are used as the lower and upper bounds of η1, respectively.

[0137] 3) Optimize the solution.

[0138] Substitute the initial values ​​λ0 and η1 of the depth sounding signal parameters and water body parameters determined in step 2) into the SSCM, where the initial value λ0 consists of 6 depth sounding signal parameters: α S ,t S ,σ S ,α B ,t B ,σ B Given the initial values ​​of the water body parameter η0, the model parameter λ is optimized within a set range using the trust region algorithm, and t is used as an example. S and t B As the depth sounding signal position output, the coordinates of the water surface point and the bottom point are obtained by combining the POS and encoder data with the laser's point calculation model.

[0139] The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry provided by this invention improves the signal convolution model by adopting a semi-empirical signal convolution model, making the waveform components more closely resemble the real situation and the calculation results more accurate.

[0140] To verify the accuracy of the calculation results provided by the method of the present invention, this embodiment also analyzes and verifies the method of the present invention.

[0141] Experimental data was acquired by the Mapper5000 system near an island in China in August 2020. It includes waveform data, POS data, and encoder data from four channels. Relevant system parameter settings are shown in Table 1. The waveform data from the four channels represent one near-infrared channel (APD) and three green light channels (PMT1-PMT3). PMT1 and PMT2 are for small field-of-view reception, while PMT3 is for large field-of-view reception. PMT1 and PMT2 share a single receiving field of view, obtained through polarizer splitting. The receiving direction of PMT1 is parallel to the polarization direction of the emitted laser, while the receiving direction of PMT2 is perpendicular to the polarization direction of the emitted laser. In this embodiment, the water surface signal detected by the APD is used as a reference, and the waveform decomposition is performed using the PMT1 channel waveform, which exhibits relatively stable backscattering from the water.

[0142] Table 1 System parameter settings for obtaining measured data

[0143]

[0144] like Figure 7 As shown, the test area is located in the northwest of a certain location, with a test area size of approximately 1.7km × 1.1km. Six navigation strips, S1-S6, were deployed from west to east within the test area. The rectangular area in the figure represents the location of manually collected deep-water waveform samples. The distribution of water parameters calculated from the deep-water waveform samples is shown below. Figure 8 , Figure 9 As shown.

[0145] To verify the effectiveness of the method of this invention, the navigation zone S1, where the deep-water waveform sample is located, was selected for the experiment. The surface signal obtained by maximum detection of the APD channel waveform was used as a reference. The RLD algorithm, which can effectively improve signal resolution, was selected for comparison. Specifically, the Empirical Model (EW) was used for shallow-water waveforms, and the Second-Order Polynomial Exponential Function (EFSP) model was used for deep-water waveforms. This method has a high overall fit to the waveform. It should be noted that the method of this invention and the EW / EFSP used the same initial values ​​of the bathymetry signal for calculation in the experiment, and the calculated bathymetry signal was uniformly converted to the WGS_1984_UTM_Zone_49N coordinate system according to the point calculation model.

[0146] Four performance evaluation indicators were selected for comparative analysis of the methods, including the average water surface elevation, standard deviation, signal detection rate, and root mean square error (RMSE) of water surface elevation. The average value represents the overall level of water surface elevation; the standard deviation reflects the dispersion of the water surface point cloud to some extent; the signal detection rate is the percentage of waveforms that can simultaneously detect signals from both the water surface and the seabed; and the RMSE is the water surface elevation error calculated using the APD water surface point elevation as the true value. Table 2 shows the experimental results for flight strip S1. It can be seen that the average elevations of RLD and SSCM (in this invention) are similar and both higher than the results of EW / EFSP. The lower standard deviations of EW / EFSP and SSCM indicate a relatively concentrated distribution of the water surface point cloud. The signal detection rates of EW / EFSP and SSCM are comparable, while RLD is lower, indicating that the waveform decomposition method has a stronger depth sounding signal detection capability. Among the three methods, SSCM has the lowest RMSE, indicating that the water surface detection results of SSCM are closest to the reference results of the APD channel.

[0147] Table 2 Analysis of Water Surface Permeability Correction Capability for Single-Ship Path

[0148]

[0149] To further analyze the ability of SSCM to correct NWSP errors, two cross-sections were extracted from the water surface point cloud, one parallel to the flight path and the other perpendicular to the flight path, as shown below. Figures 10-17 As shown, where Figure 10 , Figure 11 , Figure 12 and Figure 13 These are surface point cloud profiles of APD, RLD, EW / EFSP, and SSCM parallel to the route direction, respectively. Figure 14 , Figure 15 , Figure 16 and Figure 17 These are water surface point cloud profiles perpendicular to the flight path, generated by APD, RLD, EW / EFSP, and SSCM. The dashed lines in the figures represent the trend lines of the APD reference water surface point cloud. The laser incident angle parallel to the flight path is essentially fixed, therefore the NWSP effect exhibits an overall deviation within a small area. In the direction perpendicular to the flight path, the laser incident angle is larger in the middle and smaller at the edges. Since the smaller the laser incident angle, the greater the error in the elevation direction of NWSP, the NWSP error will show a distribution pattern of smaller error in the middle and larger error at the edges. However, in the water surface point cloud generated by SSCM (… Figure 17 The fact that the above distribution pattern could not be clearly observed indicates that SSCM has greatly corrected the NWSP error.

[0150] exist Figures 10-13 The water depth in the midpoint cloud gradually increases from left to right. Comparing the shallow water waveform processing results on the left, it can be found that the RLD has a large error in detecting the water surface points at the very shallow water at the far left, indicating that the RLD has a weak signal detection capability for extremely shallow water waveforms. This is also the reason why the RLD has the lowest detection rate in Table 2. Although both EW / EFSP and SSCM can process extremely shallow water waveforms, the SSCM's water surface point cloud is more concentrated and has the highest degree of conformity with the reference trend line, indicating that the SSCM performs best in shallow water waveform processing.

[0151] like Figure 18 , Figure 19 and Figure 20 Here are examples of RLD, EW, and SSCM processing extremely shallow water waveforms. It can be seen that for waveforms with highly overlapping signals, RLD, due to the need to suppress noise, limits the number of iterations and thus cannot effectively distinguish between surface and bottom signals. EW, lacking constraints from water parameters, causes the fitting results to converge to local extrema. Although the backscattered component of water is relatively small in shallow water waveforms, SSCM, with its constraints from water parameters, allows it to find the correct surface signal location through iterative searching during the fitting process.

[0152] contrast Figures 10-13 The deep-water waveform processing results on the right show that EW / EFSP is most significantly affected by NWSP, exhibiting a clear overall deviation from the reference trend line, while SSCM is closest to the reference trend line. Figure 21 , Figure 22 and Figure 23The results show the deep-water waveform processing using RLD, EFSP, and SSCM, respectively. It can be seen that while the RLD algorithm can correct NWSP errors to some extent, the surface peak after deconvolution is still shifted backward due to varying degrees of backscattering from the water body, lacking relevant prior knowledge. EFSP, using a piecewise geometric function model, cannot flexibly adjust model parameters when NWSP errors are large (i.e., poor initial values ​​for the surface signal position), thus failing to effectively correct the surface signal position. SSCM, while maintaining high fitting accuracy, decomposes the waveform within a reasonable range of water parameters, correctly separating surface echoes, backscattered water, and bottom echoes from the overlapping signals, thereby achieving NWSP correction.

[0153] To comprehensively analyze the ability of the method of this invention to correct NWSP errors, six flight strips within the survey area were processed one by one, and the water surface elevation error and its distribution were statistically analyzed using the APD channel water surface signal as a reference. The experimental results are shown in […]. Figure 24 , Figure 25 , Figure 26 , Figure 27 And Table 3. From Figures 24-27 It can be seen that the surface elevation errors of RLD and EW / EFSP are generally higher than those of SSCM, and are most pronounced in the extremely shallow water area. The error of SSCM is relatively evenly distributed across the survey area, but there are still some areas where the NWSP error is not fully corrected, and the surface elevation is slightly lower than the reference value. As shown in Table 3, the surface elevation accuracy of SSCM is significantly improved, increasing by 44% and 51% compared to RLD and EW / EFSP, respectively. Furthermore, the surface elevation error of SSCM does not show a linear increasing trend with the increase of distance from the sample, indicating that the initial values ​​and range of water parameters obtained by collecting deep-water waveform samples are suitable for processing the waveforms of the entire survey area without the need for multiple samplings during the processing.

[0154] Table 3. Water surface elevation error in the survey area

[0155]

[0156]

[0157] In ALB waveform processing, near-surface seepage error affects the accuracy of water surface detection and indirectly impacts the accuracy of bottom measurement. Due to a lack of prior knowledge, this error typically requires auxiliary data or repeated observations to correct. To address this, this invention proposes a semi-empirical waveform decomposition method. This method extracts relevant water environment parameters from a small number of deep-water waveform samples and integrates them into a model based on laser radiative transfer theory. This provides both empirical and theoretical support for waveform decomposition, thereby achieving accurate correction of near-surface seepage error. Experiments demonstrate that this invention can reasonably model the various components of the waveform, especially water backscattering, and is adaptable to waveform processing at different water depths, effectively improving water surface detection accuracy. Compared to deconvolution algorithms and traditional waveform decomposition methods, the accuracy is improved by 44% and 51%, respectively.

Claims

1. A semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry, characterized in that, Includes the following steps: Step 1) Based on the time of laser arrival at the water surface, the water surface echo intensity, and the waveform shape adjustment parameter S, water surface echo model parameters are constructed. These parameters are used as inputs to build the water surface echo model through signal convolution. Similarly, based on the time of laser arrival at the bottom of the water, the bottom echo intensity, and the waveform shape adjustment parameter B, bottom echo model parameters are constructed. These parameters are used as inputs to build the bottom echo model through signal convolution. Water backscattering model parameters are simplified by combining airborne laser depth sounding system parameters and water environment parameters. These parameters are used as inputs to build the water backscattering model through signal convolution. A semi-empirical signal convolution model describing the water body echo waveform is constructed based on the water surface echo model, bottom echo model, and water backscattering model. The water surface echo model parameters and bottom echo model parameters constitute depth sounding signal parameters, and the water backscattering model parameters constitute water body parameters. Step 2) Determine the initial values ​​of the depth sounding signal parameters using the depth classification processing and adaptive threshold detection method. Initial values ​​and ranges of water body parameters are determined using deep-water waveform samples containing only surface signals and backscattered signals from a complete water body. Step 3) Input the initial values ​​of the depth sounding signal parameters, the initial values ​​of the water body parameters, and the range of values ​​of the water body parameters into the semi-empirical signal convolution model for solution, and calculate the coordinates of the water surface point and the bottom point.

2. The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry according to claim 1, characterized in that, The water surface echo model is as follows: in, For water surface echo model, This represents the instantaneous value of the response function corresponding to the moment the laser reaches the water surface. For the current time, The instant the laser reaches the water surface. S is the shape adjustment parameter. This is the waveform of the laser emission signal.

3. The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry according to claim 1, characterized in that, The underwater echo model is as follows: in, For underwater echo model, This represents the instantaneous value of the response function corresponding to the moment the laser reaches the bottom of the water. For the current time, The instant the laser reaches the bottom of the water. For shape adjustment parameter B, This is the waveform of the laser emission signal.

4. The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry according to claim 1, characterized in that, The water backscattering model is as follows: in, and It is a combination of airborne laser bathymetry system parameters and water environment parameters, denoted as the first and second parameters of the water backscattering model, respectively. For the current time, The instant the laser reaches the water surface, " indicates a convolution operation. This is the waveform of the laser emission signal.

5. The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry according to any one of claims 2-4, characterized in that, The semi-empirical signal convolution model is as follows: in, It is a semi-empirical signal convolution model. For water surface echo model, For water backscattering models, This is a model of underwater echoes.

6. The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry according to claim 1, characterized in that, In step 2), the initial values ​​and ranges of the water body parameters are calculated using a method for estimating the probability distribution of water body parameters. The method for estimating the probability distribution of water body parameters is as follows: Step a. Obtain deep-water waveforms containing only surface signals and backscattered data from a complete water body, perform maximum detection on the deep-water waveforms, and determine the location of the surface signal; Step b. Remove the water surface signal from the deep water waveform based on the width of the laser emission signal to obtain the backscattered waveform of the water body to be fitted; Step c. Substitute the water surface signal position from step a into the water backscattering model as a constant, and use this model to fit the water backscattering waveform from step b to calculate the probability distribution estimate of the water parameters.

7. The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry according to claim 1, characterized in that, The process for determining the initial values ​​of the depth sounding signal parameters in step 2) is as follows: The average waveform of the water body is obtained by removing the part affected by the water surface signal from the width of the transmitted signal, and the part with the stronger amplitude at the front end is recorded as the water body identification waveform. Calculate the correlation between each frame of waveform and the water body marker waveform, and classify the waveforms into two categories, shallow water waveforms and deep water waveforms, based on the magnitude of the correlation. For shallow water waveforms, a fixed threshold maximum detection method is used to determine the position and initial intensity of the sounding signal. For deep water waveforms, an adaptive threshold maximum detection method is used to determine the position and initial intensity of the sounding signal.

8. The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry according to claim 6, characterized in that, The deep-water waveform obtained in step a consists of several frames. In step c, the water parameters of each frame of the waveform are calculated to obtain the probability distribution estimate of the water parameters. Multiple sets of probability distribution estimates of the water parameters are calculated, and the average value of the multiple sets of probability distribution estimates is taken. The average value is used as the initial value of the water parameters determined in step 2). The maximum and minimum values ​​in the probability distribution estimate of the second parameter are used as the upper and lower limits of the value of the second parameter, respectively, as the range of values ​​of the water parameters determined in step 2).

9. The semi-empirical waveform decomposition method for near-surface seepage error correction in airborne laser bathymetry according to claim 1, characterized in that, In step 3), the initial values ​​of the sounding signal parameters and the initial values ​​of the water body parameters are input into the semi-empirical signal convolution model, and the model parameters are optimized within the range of water body parameter values.

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