Full waveform lidar super-resolution waveform decomposition method based on bandwidth simulation extrapolation, storage medium and equipment

Abstract

The bandwidth simulation extrapolation-based full-waveform laser radar super-resolution waveform decomposition method, storage medium and equipment belong to the technical field of full-waveform laser radar data processing. In order to solve the problem that the existing waveform decomposition method is difficult to identify the high overlap rate multi-target echo under the condition that the system resolution is limited. The echo signal is modeled as the result of the convolution of the transmitted pulse and the target scattering cross-section function and the superposition of noise; the transmitted pulse is expressed as the result of the mixed superposition of several narrow Gaussian pulses with equal standard deviation; the narrow Gaussian pulse corresponding to the maximum peak intensity is selected as the reference of the reconstructed transmitted pulse, and the received echo is reconstructed as the superposition of the echoes corresponding to the narrow Gaussian pulses, the echo signal is expressed as the discrete convolution relationship of the convolution matrix composed of the narrow Gaussian pulses, the distribution of the projection along the laser beam direction is reconstructed, the target scattering cross-section function is inverted, and the spatial distribution of the target along the laser beam direction is extracted according to the peak position.

Description

Technical Field

[0001] This invention belongs to the field of full-waveform lidar data processing technology, specifically relating to a method, storage medium, and device for super-resolution waveform decomposition of full-waveform lidar. Background Technology

[0002] In a full-waveform lidar system, the lidar emits a laser beam. After the laser beam interacts with multiple ground targets within its illumination range, the system receiver digitizes the echoes through high-frequency sampling, thus obtaining echo signals with the same sequence of interaction as the ground targets. The echo waveform records the backscattering contribution along the laser beam direction and is an important information carrier characterizing the vertical structure of the target. However, when the spacing between multiple scatterers along the laser beam direction is small, such as in cases of layered vegetation canopy, scattering between branches and leaves and nearby ground, the boundary between building facades and the ground, and slight undulations on slopes, the echo components exhibit high overlap and aliasing in the time domain. This leads to phenomena such as high overlap of multi-target echoes, waveform distortion, or weak echoes being submerged by strong echoes. The fundamental reason is that the system bandwidth and the transmitted pulse width together limit the minimum resolvable target spacing. The system impulse response and noise further reduce the resolvability of nearby components, making echo resolution significantly more difficult as the target spacing decreases. To improve the ability of full-waveform lidar to distinguish adjacent targets, super-resolution waveform decomposition processing is required to accurately extract the position information of each target from the echo signal. Summary of the Invention

[0003] This invention aims to address the problem that existing waveform decomposition methods struggle to identify high-overlapping multi-target echoes under limited system resolution, i.e., the difficulty in distinguishing targets that are close to each other.

[0004] A method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation includes:

[0005] Step 2: Echo signal Modeled as a transmitted pulse With target scattering cross-section function The result of convolution and noise superposition; representing the emitted pulse as several narrow Gaussian pulses with equal standard deviation. The result of mixing and superposition;

[0006] Step 3: Select the maximum peak intensity The corresponding narrow Gaussian pulse As a reference for reconstructing the transmitted pulse, the received echo is reconstructed as a superposition of the echoes corresponding to each narrow Gaussian pulse, thereby determining the reconstructed echo signal. ;

[0007] Step 4: Reconstruct the echo signal The discrete convolution relationship is represented as follows: , It is by The convolution matrix formed, The length of the echo sequence. Represents a constant term. To mitigate noise, the projection distribution along the laser beam direction is reconstructed. , The regularization coefficient is used.

[0008] Step 5: Solve The target scattering cross-section function is inverted, and the target spatial distribution along the laser beam direction is extracted based on the peak position.

[0009] Furthermore, the echo signal modeled in step 2 is represented as: , Indicates the transmission pulse. For echo signal, Represents a constant term. To add noise, This represents the convolution operation; This is the target scattering cross-section function.

[0010] Furthermore, the emitted pulse is represented as the result of a superposition of several narrow Gaussian pulses with equal standard deviation constraints. ,in, To have different peak positions Different amplitudes The Gaussian function, and They have a consistent standard deviation; i represents the i-th narrow Gaussian pulse; t represents time. This indicates the time corresponding to the location of the peak.

[0011] Furthermore, step 3 reconstructs the received echoes into a superposition of the corresponding echoes of the narrow Gaussian pulses, as follows:

[0012]

[0013] in Represents Gaussian components and the Gaussian component corresponding to the maximum peak value The sampling interval between them; The time series length of the transmitted pulse is represented by: ; Gaussian components Corresponding peak intensity; symbol Gaussian components and The transformation relationship matrix between them; , It is an identity matrix of size N1 and N2.

[0014] Furthermore, the reconstructed echo signal determined in step 3 ,in To reconstruct the matrix.

[0015] Furthermore, by The constructed convolution matrix It is obtained through the following steps:

[0016] Firstly by Directly generated convolution matrix , It is a vector of all zeros; express Transpose of; Indicates the length of the time sequence of the transmitted pulse;

[0017] Then in the convolution matrix Extract several consecutive rows from the data to construct a new convolution matrix that matches the length of the actual observed echo vector. This makes the new convolution matrix The diagonal position and the emitted pulse Peak positions are aligned to obtain a new convolution matrix. .

[0018] Furthermore, in transmitting the echo signal Before modeling, the transmitted pulse and echo signals need to be preprocessed. The preprocessing process includes filtered spline interpolation and noise reduction.

[0019] Furthermore, a Savitzky-Golay filter is used in the noise reduction process.

[0020] A computer storage medium storing at least one instruction, which is loaded and executed by a processor to implement the aforementioned method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation.

[0021] A super-resolution waveform decomposition device for full-waveform lidar based on bandwidth analog extrapolation is disclosed. The device includes a processor and a memory. The memory stores at least one instruction, which is loaded and executed by the processor to implement the super-resolution waveform decomposition method for full-waveform lidar based on bandwidth analog extrapolation.

[0022] Beneficial effects:

[0023] This invention proposes a super-resolution waveform decomposition method for full-waveform lidar based on bandwidth simulation extrapolation, supplementing existing full-waveform lidar waveform decomposition algorithms. First, a physical model of the echo signal is established based on the full-waveform lidar echo signal generation process. Then, a Gaussian mixture model with equal standard deviation is used to fit the transmitted pulse, decomposing the original transmitted pulse into several narrow-pulse-width Gaussian pulses. Next, based on the parameters of the transmitted pulse decomposition, the echo signal is reconstructed into a reconstructed echo signal corresponding to the Gaussian pulses according to the linear property of convolution, thus achieving bandwidth simulation extrapolation. Then, an overcomplete dictionary and sparse representation model are constructed based on the reconstructed echo signal and the narrow-pulse-width Gaussian pulses. The target scattering cross-section function representing the target position information is obtained by solving the sparse representation. Finally, the target position information is obtained using the peak position of the scattering cross-section function. This method is applicable to waveform data acquired by full-waveform lidar, is easy to implement, can effectively identify multi-target echoes with high overlap rates, improves the resolution of lidar detection of multiple targets, and can solve the problem of resolving targets at close range in full-waveform lidar. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the process for a full-waveform lidar super-resolution waveform decomposition method based on bandwidth simulation extrapolation;

[0025] Figure 2 A schematic diagram of the equivalent subpulse of a laser emission source;

[0026] Figure 3 This is a schematic diagram of super-resolution waveform decomposition. Detailed Implementation

[0027] This invention proposes a super-resolution waveform decomposition method for full-waveform lidar data acquired by full-waveform lidar based on bandwidth simulation extrapolation. This method aims to improve the resolution of echoes from highly overlapping multiple targets. First, a physical model of the echo signal is established based on the echo signal generation process of the full-waveform lidar. Then, a Gaussian mixture model with equal standard deviation is used to fit the transmitted pulse, decomposing the original transmitted pulse into several narrow-pulse-width Gaussian pulses. Next, based on the parameters of the transmitted pulse decomposition, the echo signal is reconstructed into a reconstructed echo signal corresponding to the Gaussian pulses according to the linear property of convolution, thus achieving bandwidth simulation extrapolation. Then, an overcomplete dictionary and sparse representation model are constructed based on the reconstructed echo signal and the narrow-pulse-width Gaussian pulses. The target scattering cross-section function representing the target position information is obtained by solving the sparse representation. Finally, the target position information is obtained using the peak position of the scattering cross-section function. This method is applicable to waveform data acquired by full-waveform lidar, is easy to implement, improves the resolution of lidar detection of multiple targets, and can solve the problem of short-range target resolution in full-waveform lidar. Further explanation is provided below with specific implementation details.

[0028] Specific implementation method one: Combining Figure 1 This implementation method is described below.

[0029] The full-waveform lidar super-resolution waveform decomposition method based on bandwidth analog extrapolation described in this embodiment includes the following steps:

[0030] Step 1: Preprocess the transmitted pulse and echo signals. The preprocessing process includes filtered spline interpolation and noise reduction.

[0031] When acquiring data, full-waveform lidar requires preprocessing through spline interpolation and filtering due to its low sampling rate and the presence of noise in the signal.

[0032] Spline interpolation: Due to system bandwidth limitations, full-waveform lidar typically samples analog signals and converts them into digital signals at a relatively low frequency. By performing spline interpolation on the transmitted pulse and echo signals, the ability to describe the waveform in detail can be improved.

[0033] Noise Reduction Filtering: The waveforms acquired by lidar are susceptible to interference from ambient light, inherent noise from photodiodes, and amplifier circuit noise. To improve the signal-to-noise ratio, a Savitzky-Golay (SG) filter can be used for smoothing. This filter effectively suppresses noise while maintaining the original signal shape relatively well.

[0034] Step 2: Perform bandwidth simulation extrapolation based on the transmitted pulse:

[0035] To effectively recover the target spatial structure information hidden in the waveform data of a small-spot full-waveform lidar, it is necessary to first model and analyze the physical mechanism of echo signal generation. The echo signal is usually regarded as the result of the convolution of the transmitted pulse and the target scattering cross-section function, plus noise, as shown in Equation (1).

[0036] (1)

[0037] in, Indicates the transmission pulse. For echo signal, Represents a constant term. To add noise, This represents the convolution operation; This is the target scattering cross-section function.

[0038] The smallest resolvable interval between two targets along the direction of laser beam propagation. This is called range resolution, which is essentially determined by the pulse width of the emitted laser beam. The theoretical limit of the decision can be expressed as:

[0039] (2)

[0040] Where c is the speed of light.

[0041] In practical system design, narrow pulses can directly improve range resolution, but they also require wider system bandwidth and higher sampling rates, constrained by the time-width-bandwidth product. Furthermore, narrowing the pulse reduces single-pulse energy, thus lowering the signal-to-noise ratio for long-range detection. These trade-offs are collectively governed by the Rayleigh time criterion: the minimum resolvable time delay between two overlapping echoes. The corresponding threshold must be met, as shown in the following formula.

[0042] (3)

[0043] in This refers to the system bandwidth.

[0044] This relationship reveals that range resolution is inevitably limited by inherent physical constraints when balancing pulse width, system bandwidth, and detection range. Based on the above analysis, simply compressing the emitted pulse width cannot effectively improve target resolution along the laser beam direction.

[0045] To overcome the limitation of system bandwidth on distance resolution, this invention adopts the approach of "bandwidth simulation extrapolation," the core of which lies in high-precision fitting of the transmitted pulse waveform and reconstruction of the echo signal. Specifically, the transmitted pulse is represented as the result of a superposition of several narrow Gaussian pulses with equal standard deviation constraints, which is referred to in this invention as the Equal Standard Deviation Constrained Gaussian Mixture Model (E-GMM), as shown in the following equation.

[0046] (4)

[0047] in, To have different peak positions Different amplitudes The Gaussian function, and They have a consistent standard deviation ; i represents the i-th narrow Gaussian pulse; t represents time. This indicates the time corresponding to the location of the peak.

[0048] The practical physical meaning of the equal standard deviation Gaussian mixture model lies in representing the emission source of a small-spot full-waveform lidar as an equivalent set of coaxial, co-directional propagating sub-pulses. Each sub-pulse has the same beam coverage area, i.e., a consistent spatial footprint, but differs in intensity and time delay, and is uniformly characterized using a standard Gaussian function with a narrower pulse width, such as... Figure 2As shown. Compared with traditional methods that directly use the measured transmitted pulse as the diffusion kernel for deconvolution, this method explicitly decomposes the transmitted pulse into a set of controllable sub-components through the parameterized form of E-GMM. This not only enhances the modeling adaptability to the differences in transmitted waveforms of different lidar systems, but also provides unified and flexible pulse prior information for super-resolution waveform decomposition.

[0049] Step 3: Reconstruct the echo signal using extrapolated parameters simulated by the bandwidth of the transmitted pulse.

[0050] Under ideal conditions, if the width of a narrow Gaussian pulse can be adjusted to approach zero infinitely, theoretically, infinitely high range resolution can be achieved. In this case, the target reconstruction process can be simplified to a single deconvolution operation. However, practical systems face various constraints, primarily ill-posed by noise and quantization errors during data acquisition. These factors collectively limit the infinite expansion of bandwidth, necessitating a careful trade-off between signal-to-noise ratio and bandwidth expansion. To optimize this balance, the maximum peak intensity is selected. The corresponding narrow Gaussian pulse As a reference for reconstructing the transmitted pulse, a narrow Gaussian pulse here refers to a pulse width narrower than the original pulse. This choice effectively suppresses noise amplification while maintaining a high signal strength, thereby extending the bandwidth while maintaining the reliability and stability of the echo signal.

[0051] Based on the fitting results of the arithmetic Gaussian mixture model to the transmitted pulse, the received echo is reconstructed as a superposition of the echoes corresponding to these narrow Gaussian pulses, thus achieving a finer discrimination capability on the time axis than the original pulse width. Specifically, based on the linear property of convolution operations, we have

[0052] (5)

[0053] in This represents the Gaussian component of the emitted pulse obtained according to the arithmetic Gaussian mixture model. and the Gaussian component corresponding to the maximum peak value The sampling interval between them is used Let the time sequence length of the transmitted pulse be represented, then we have , Gaussian components Corresponding peak intensity. Symbol Gaussian components With Gaussian components The transformation relationship matrix between them; As a unit array, , It is an identity matrix of size N1 and N2.

[0054] Therefore, the transmitted pulse after bandwidth simulation extrapolation Corresponding reconstructed echo signal It can be represented as

[0055] (6)

[0056] in To reconstruct the echo signal, a reconstruction matrix is ​​needed. .

[0057] Step 4: Solve the sparse representation of the reconstructed echo signal using the bandwidth-simulated extrapolated transmitted pulse:

[0058] After bandwidth simulation extrapolation, the transmitted pulse after bandwidth simulation extrapolation can be obtained. and its corresponding reconstructed echo signal Theoretically, under the same sampling rate, the length of the received echo sequence is usually greater than the length of the transmitted pulse sequence. This is mainly because the echo signal can be modeled in the time domain as a convolution operation between the transmitted pulse and the target scattering cross-section function. Since the target scattering cross-section function can be regarded as a discrete sequence with finite support, the convolution operation introduces a time broadening effect, resulting in an expansion of the echo waveform along the time axis, making its effective length exceed that of the original transmitted pulse. On the other hand, when inverting the target scattering cross-section function, it is necessary to estimate it within the distance range corresponding to the entire laser beam propagation path, even in target-free regions (where the scattering cross-section is zero), to ensure the integrity of the inversion results. Therefore, in discrete numerical implementations, the length of the target scattering cross-section function is usually set to be the same as the length of the echo time sequence. Consistent. To facilitate subsequent algorithm derivation and expression, the discrete convolution relationship is uniformly represented in the form of a convolution matrix in equation (7).

[0059] (7)

[0060] in, It is by The convolution matrix is ​​constructed. First, by... Directly generated convolution matrix The following is by get .

[0061] As shown in the following formula

[0062] (8)

[0063] in, A vector consisting of all zeros. This represents a vector consisting of 0 rows and 1 column of all zeros. Represents a vector consisting of all zeros in row K-1 and column 1; Indicates matrix transpose. express The transpose of .

[0064] In actual data acquisition using lidar systems, the recording length of echo signals has inherent limitations. Systems typically do not continuously sample for the entire propagation time after laser emission, but rather record within the expected time window of the target echo return. Sampling stops when no valid echo returns. Therefore, the actual acquired echo sequence only covers a portion of the time interval of the signal generated during the interaction between the emitted pulse and the target.

[0065] To construct an accurate mathematical model under this constraint, it is necessary to start from the convolution matrix describing the complete physical process. Extract several consecutive rows from the data to construct a new convolution matrix that matches the length of the actual observed echo vector. Since the maximum value of the echo signal usually corresponds to the maximum value of the target scattering cross-section function, and this moment should interact with the peak value of the transmitted pulse, a continuous row can be truncated around the position corresponding to the peak value of the transmitted pulse in the convolution matrix to construct the new matrix. The diagonal position and the emitted pulse Peak position alignment, i.e. , Indicates the index of a matrix element. In essence, it is... The element in the first row and first column is The peak value, the second column, the second row is The peak value of each column The peak values ​​are sequentially strung down one row, that is... The diagonal position is the transmitted pulse. Peak value.

[0066] The new convolutional matrix constructed in this way Mathematically, this is equivalent to an overcomplete dictionary consisting of reconstructed emitted pulses with different time delays. Within the unified framework of the echo signal model, the spatial structure of a series of targets distributed along the laser beam propagation path can be projected onto the direction of the laser beam. The backscattering contribution of the target in this direction can be approximately represented as a linear superposition of multiple basis vectors in this dictionary. Therefore, the contribution of each scattering center to the total echo is characterized by a reconstructed emitted pulse (i.e., a basis vector in the dictionary) with a specific time delay and amplitude scaling. The model ultimately inverts the spatial structure information of the target by solving for the weight coefficients of a series of basis vectors.

[0067] Since the target distribution along the propagation path is sparse, the reconstructed echo and reconstructed transmitted pulse are substituted into the model to establish a corresponding sparse representation model, and the projection distribution along the laser beam direction is reconstructed:

[0068] (9)

[0069] in, The regularization coefficient is used. Represents the L2 norm. This represents the L0 norm.

[0070] Step 5: Use the target scattering cross-section function obtained from the sparse solution to solve for the target location information:

[0071] By solving equation (9) to invert the target scattering cross-section function, the target spatial distribution along the laser beam direction can be extracted based on its peak position.

[0072] By combining the transmitted pulse waveform reconstructed using bandwidth extension technology, the solution of the scattering cross-section function is transformed into an optimization problem under sparse representation, thereby achieving range resolution exceeding the Rayleigh limit during the inversion process. This method effectively overcomes the resolution limitation inherent in the system's hardware bandwidth by exploiting the sparsity of the echo signal under a specific dictionary, ultimately achieving super-resolution waveform decomposition.

[0073] To verify the performance of the algorithm proposed in this invention, super-resolution waveform decomposition tests were performed on waveform data acquired by a full-waveform lidar. The experimental results are as follows: Figure 3 As shown, Figure 3 The results of super-resolution waveform decomposition are presented, verifying the effectiveness of the proposed super-resolution waveform decomposition method for full-waveform lidar based on bandwidth simulation extrapolation. Specific Implementation Method Two:

[0075] This embodiment is a computer storage medium that stores at least one instruction. The at least one instruction is loaded and executed by a processor to implement the aforementioned method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation.

[0076] It should be understood that the instructions include computer program products, software, or computerized methods corresponding to any method described in this invention; the instructions can be used to program computer systems or other electronic devices. Computer storage media may include readable media on which instructions are stored, and may include, but are not limited to, magnetic storage media, optical storage media; magneto-optical storage media include read-only memory (ROM), random access memory (RAM), erasable programmable memory (e.g., EPROM and EEPROM), and flash memory layers, or other types of media suitable for storing electronic instructions. Specific implementation method three:

[0078] This embodiment is a super-resolution waveform decomposition device for full-waveform lidar based on bandwidth analog extrapolation. The device includes a processor and a memory. It should be understood that this includes any device described in this invention that includes a processor and a memory. The device may also include other units or modules that perform display, interaction, processing, control, and other functions through signals or instructions.

[0079] The memory stores at least one instruction, which is loaded and executed by the processor to implement the aforementioned method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation.

[0080] Those skilled in the art will understand that at least one stored instruction constitutes a computer program product corresponding to a method or system. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0081] This application is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of this application, and can also be used with corresponding devices. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0082] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0083] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0084] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0085] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation, characterized in that, include: Step 2: Echo signal Modeled as a transmitted pulse With target scattering cross-section function The result of convolution and noise superposition; representing the emitted pulse as several narrow Gaussian pulses with equal standard deviation. The result of mixing and superposition; Step 3: Select the maximum peak intensity The corresponding narrow Gaussian pulse As a reference for reconstructing the transmitted pulse, the received echo is reconstructed as a superposition of the echoes corresponding to each narrow Gaussian pulse, thereby determining the reconstructed echo signal. ; Step 4: Reconstruct the echo signal The discrete convolution relationship is represented as follows: , It is by The convolution matrix formed, The length of the echo sequence. Represents a constant term. To mitigate noise, the projection distribution along the laser beam direction is reconstructed. , The regularization coefficient is used. Step 5: Solve The target scattering cross-section function is inverted, and the target spatial distribution along the laser beam direction is extracted based on the peak position.

2. The method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation according to claim 1, characterized in that, The echo signal modeled in step 2 is represented as follows: , Indicates the transmission pulse. For echo signal, Represents a constant term. To add noise, This represents the convolution operation; This is the target scattering cross-section function.

3. The method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation according to claim 1, characterized in that, The emitted pulse is represented as the result of a superposition of several narrow Gaussian pulses with equal standard deviation constraints. ,in, To have different peak positions Different amplitudes The Gaussian function, and They have a consistent standard deviation; i represents the i-th narrow Gaussian pulse; t represents time. This indicates the time corresponding to the location of the peak.

4. The method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation according to claim 3, characterized in that, Step 3 reconstructs the received echoes into a superposition of the corresponding echoes of the narrow Gaussian pulses, as follows: in Represents Gaussian components and the Gaussian component corresponding to the maximum peak value The sampling interval between them; The time series length of the transmitted pulse is represented by: ; Gaussian components Corresponding peak intensity; symbol Gaussian components and The transformation relationship matrix between them; , It is an identity matrix of size N1 and N2.

5. The method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation according to claim 4, characterized in that, The reconstructed echo signal determined in step 3 ,in To reconstruct the matrix.

6. The method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation according to claim 5, characterized in that, Depend on The constructed convolution matrix It is obtained through the following steps: Firstly by Directly generated convolution matrix , It is a vector of all zeros; express Transpose of; Indicates the length of the time sequence of the transmitted pulse; Then in the convolution matrix Extract several consecutive rows from the data to construct a new convolution matrix that matches the length of the actual observed echo vector. This makes the new convolution matrix The diagonal position and the emitted pulse Peak positions are aligned to obtain a new convolution matrix. .

7. A method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation according to any one of claims 1 to 6, characterized in that, In the echo signal Before modeling, the transmitted pulse and echo signals need to be preprocessed. The preprocessing process includes filtered spline interpolation and noise reduction.

8. The method for super-resolution waveform decomposition of full-waveform lidar based on bandwidth analog extrapolation according to claim 7, characterized in that, The noise reduction process uses a Savitzky-Golay filter.

9. A computer storage medium, characterized in that, The storage medium stores at least one instruction, which is loaded and executed by a processor to implement the full-waveform lidar super-resolution waveform decomposition method based on bandwidth analog extrapolation as described in any one of claims 1 to 8.

10. A super-resolution waveform decomposition device for full-waveform lidar based on bandwidth analog extrapolation, characterized in that, The device includes a processor and a memory, the memory storing at least one instruction, which is loaded and executed by the processor to implement the full-waveform lidar super-resolution waveform decomposition method based on bandwidth analog extrapolation as described in any one of claims 1 to 8.

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