A differential absorption laser radar signal denoising method and computer readable medium

Abstract

The application provides a differential absorption laser radar signal denoising method and a computer readable medium. The application performs multi-signal space-time average processing on a differential absorption laser radar measured signal sequence to obtain a space-time average laser radar signal sequence; acquires a to-be-decomposed radar signal sequence, obtains a plurality of to-be-decomposed radar signal forward and negative noise sequences through the to-be-decomposed radar signal sequence and a plurality of white noise sequences, and obtains a plurality of layer intrinsic mode signal sequences and a residual signal sequence through empirical mode decomposition calculation; divides the plurality of layer intrinsic mode signal sequences into each layer high-frequency and low-frequency intrinsic mode signal sequences, and respectively obtains reconstructed high-frequency and low-frequency intrinsic mode signal sequences through filtering processing; and obtains a denoised differential absorption laser radar signal sequence through residual signal sequence reconstruction calculation. The application can realize global adaptive filtering of a signal, and ensures that the signal has a high signal-to-noise ratio, a high space-time resolution, a low reconstruction error and a low distortion degree.

Description

Technical Field

[0001] This invention belongs to the field of atmospheric remote sensing technology, and particularly relates to a method for denoising differential absorption lidar signals and a computer-readable medium. Background Technology

[0002] The distribution of greenhouse gases is closely related to climate change. If the concentration of greenhouse gases in the atmosphere is too high, the greenhouse effect will harm the entire natural environment. Rising temperatures will cause the sea ice in the Arctic and Antarctic to melt, leading to rising sea levels and potentially submerging some low-lying countries. Furthermore, the permafrost in the Arctic and Antarctic stores large amounts of methane; rising temperatures will cause these regions to release even more greenhouse gases, triggering a domino effect. Therefore, effectively monitoring the distribution of greenhouse gas concentrations is essential.

[0003] Differential absorption lidar is currently the mainstream active method for greenhouse gas detection. Active detection does not have strict requirements for solar radiation and has strong resistance to cloud interference, enabling continuous 24-hour observation and obtaining greenhouse gas concentration distribution information under extreme environments. However, differential absorption lidar echo signals are susceptible to various noise interferences, such as thermal noise, dark current noise, sky background noise, and noise caused by atmospheric disturbances. More importantly, signal strength decreases exponentially with increasing detection distance, and lidar signals at high altitudes are easily submerged in noise. Furthermore, because differential calculations are required for two wavelength signals, higher signal quality is required. Therefore, noise reduction processing is necessary for differential absorption lidar.

[0004] Differential absorption lidar echo signals typically undergo multi-signal time averaging and adjacent-height signal averaging first. However, indiscriminate averaging can lead to reduced spatiotemporal resolution and over-averaging of cloud signals, thus limiting its noise reduction effect. Therefore, alternative methods are needed for further noise reduction. Wavelet Transform (WT) and Empirical Mode Decomposition (EMD) are commonly used for low-pass filtering. WT's wavelet basis can be selected based on the trend of different signals, but the non-adaptive nature of the wavelet basis means that a single wavelet basis cannot achieve global optimization. EMD can perform adaptive mode decomposition based on the signal, suitable for non-stationary and nonlinear lidar signals. However, its overshoot and edge effects can lead to significant reconstruction errors, resulting in signal distortion. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a method for denoising differential absorption lidar and a computer-readable medium to achieve denoising processing of noisy differential absorption lidar signals.

[0006] The technical solution of this invention is a method for denoising differential absorption lidar signals, characterized in that:

[0007] A new differential absorption lidar signal sequence is obtained by multi-signal time averaging, and a moving average lidar signal sequence is obtained by moving average processing.

[0008] The radar signal sequence to be decomposed is obtained. Multiple positive noise sequences and multiple negative noise sequences of the radar signal to be decomposed are obtained from the radar signal sequence to be decomposed and multiple white noise sequences. Through empirical mode decomposition and residual signal sequence calculation, multi-layer intrinsic mode signal sequence and residual signal sequence are obtained.

[0009] The multi-layer intrinsic mode signal sequence is divided into a high-frequency intrinsic mode signal sequence and a low-frequency intrinsic mode signal sequence for each layer. The reconstructed high-frequency intrinsic mode signal sequence and the reconstructed low-frequency intrinsic mode signal sequence are obtained by filtering.

[0010] The denoised differential absorption lidar signal sequence is obtained by reconstructing the residual signal sequence.

[0011] The specific steps of the method of the present invention are as follows:

[0012] Step 1: Perform multi-signal time averaging on the measured signal sequence of the differential absorption lidar to obtain a new differential absorption lidar signal sequence, and then perform moving average processing on the new differential absorption lidar signal sequence to obtain the moving average lidar signal sequence.

[0013] Step 2: After multiple moving averages, arbitrarily select one sequence from the lidar signal sequences as the radar signal sequence to be decomposed. Randomly generate multiple white noise sequences using the Rand function model. From the radar signal sequence to be decomposed and the multiple white noise sequences, obtain multiple positively and negatively noised sequences of the radar signal to be decomposed. Perform empirical mode decomposition on each positively noised sequence of the radar signal to be decomposed to obtain a multi-layered positive intrinsic mode signal sequence and a positive residual signal sequence of each radar signal to be decomposed. Perform empirical mode decomposition on each negatively noised sequence of the radar signal to be decomposed to obtain a multi-layered negative intrinsic mode signal sequence of each radar signal to be decomposed. The process involves: obtaining the state signal sequence and the negative residual signal sequence of each radar signal to be decomposed; calculating the multi-layered intrinsic mode signal sequence of each radar signal to be decomposed using the multi-layered positive intrinsic mode signal sequence and the multi-layered negative intrinsic mode signal sequence of each radar signal to be decomposed; calculating the residual signal sequence of each radar signal to be decomposed using the positive residual signal sequence and the negative residual signal sequence of each radar signal to be decomposed; calculating the multi-layered intrinsic mode signal sequence using the information from the multi-layered intrinsic mode signal sequences of multiple radar signals to be decomposed; and calculating the residual signal sequence using the residual signal sequence of multiple radar signals to be decomposed.

[0014] Step 3: Divide the multi-layer intrinsic mode signal sequence into high-frequency intrinsic mode signal sequences and low-frequency intrinsic mode signal sequences. Perform improved wavelet threshold transform filtering on each high-frequency intrinsic mode signal sequence to obtain the reconstructed high-frequency intrinsic mode signal sequence. Perform Savitzky-Golay smoothing filtering on each low-frequency intrinsic mode signal sequence to obtain the reconstructed low-frequency intrinsic mode signal sequence.

[0015] Step 4: Perform residual signal sequence reconstruction calculation using the reconstructed high-frequency intrinsic mode signal sequence and the reconstructed low-frequency intrinsic mode signal sequence to obtain the denoised differential absorption lidar signal sequence;

[0016] Preferably, each measured signal sequence of the differential absorption lidar in step 1 is defined as follows:

[0017] X k =[x k (1),x k (2),...,x k (N)]

[0018] Where N is the length of the measured signal from each differential absorption lidar, and X... k Let x represent the measured signal sequence of the k-th differential absorption lidar. k(n) represents the nth differential absorption lidar measured signal in the kth differential absorption lidar measured signal sequence, k = 1, 2, 3…K, n = 1, 2, 3…N, where K is the column number of the new differential absorption lidar signal sequence;

[0019] Step 1 involves performing multi-signal time averaging to obtain a new differential absorption lidar signal sequence, as detailed below:

[0020] Y m =[y m (1),y m (2),y m (3),...,y m (N)]

[0021]

[0022] Among them, Y m Let y represent the m-th new differential absorption lidar signal sequence, where a is the number of signal segments in a single time average, and y is the number of signal segments in a single time average. m (n) represents the nth new differential absorption lidar signal in the mth new differential absorption lidar signal sequence, M is the number of columns in the new differential absorption lidar signal sequence, N is the length of each measured differential absorption lidar signal, and m∈[1,M], n∈[1,N];

[0023] Step 1 involves performing a moving average process on the new differential absorption lidar signal sequence to obtain the moving average lidar signal sequence, as detailed below:

[0024] Z m =[z m (1),z m (2),z m (3),...,z m (N)]

[0025]

[0026] Among them, Z m Let z represent the LiDAR signal sequence after the m-th moving average. m (n) represents the nth moving average lidar signal in the mth moving average lidar signal sequence, M is the number of columns in the new differential absorption lidar signal sequence, N is the length of each differential absorption lidar measured signal, and m∈[1,M], n∈[1,N];

[0027] Preferably, the radar signal sequence to be decomposed in step 2 is specifically defined as follows:

[0028] The radar signal sequence to be decomposed is specifically defined as follows:

[0029] Z d ={z d (1), z d (2), ..., z d (N)}

[0030] Among them, Z d Let z represent the radar signal sequence to be decomposed. d (n) represents the nth radar signal to be decomposed in the radar signal sequence to be decomposed, n∈[1,N], and N is the length of each differential absorption lidar measured signal;

[0031] Step 2 involves randomly generating L white noise sequences using the Rand function model, specifically defined as follows:

[0032] W i ={w i (1),w i (2),w i (3)...w i (N)}

[0033] i∈[1,L],n∈[1,N]

[0034] Among them, W i Let w represent the generated i-th white noise sequence. i (n) represents the nth noise signal in the i-th white noise sequence. L is the number of white noise sequences generated, and N represents the number of noise signals in each white noise sequence, which is the same as the number of signals in the radar signal sequence to be decomposed.

[0035] The L forward noise-adding sequences of the radar signals to be decomposed in step 2 are specifically defined as follows:

[0036]

[0037]

[0038] i∈[1,L],n∈[1,N]

[0039] in, This represents the i-th forward noise-added sequence of the radar signal to be decomposed. This represents the nth signal in the forward noise-adding sequence of the i-th radar signal to be decomposed.

[0040] The L negative noise-adding sequences of the radar signals to be decomposed in step 2 are specifically defined as follows:

[0041]

[0042]

[0043] i∈[1,L],n∈[1,N]

[0044] in, This represents the i-th negative noise-added sequence of the radar signal to be decomposed. This represents the nth signal in the negative noise-added sequence of the i-th radar signal to be decomposed;

[0045] The multi-layered positive intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is defined as follows:

[0046]

[0047] i∈[1,L],n∈[1,N],j∈[1,J]

[0048] Where J is the number of empirical mode decomposition layers. This represents the j-th layer of the positive intrinsic mode signal sequence of the i-th radar signal to be decomposed. This represents the nth positive intrinsic mode signal in the j-th layer of the positive intrinsic mode signal sequence of the i-th radar signal to be decomposed;

[0049] The forward residual signal sequence of each radar signal to be decomposed in step 2 is defined as follows:

[0050]

[0051] i∈[1,L],n∈[1,N]

[0052] in, This represents the positive residual signal sequence of the i-th radar signal to be decomposed. This represents the nth positive residual signal in the sequence of positive residual signals of the i-th radar signal to be decomposed;

[0053] The multi-layer negative intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is defined as follows:

[0054]

[0055] i∈[1,L],j∈[1,J]

[0056] Where J is the number of empirical mode decomposition layers. This represents the j-th layer negative intrinsic mode signal sequence of the i-th radar signal to be decomposed. This represents the nth negative intrinsic mode signal in the j-th layer negative intrinsic mode signal sequence of the i-th radar signal to be decomposed;

[0057] The negative residual signal sequence of each radar signal to be decomposed in step 2 is defined as follows:

[0058]

[0059] i∈[1,L],n∈[1,N]

[0060] in, Let r represent the negative residual signal sequence of the i-th radar signal to be decomposed. i + (n) represents the nth negative residual signal in the negative residual signal sequence of the i-th radar signal to be decomposed;

[0061] The multi-layer intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is as follows:

[0062] C j,i ={c j,i (1), c j,i (2), ..., c j,i (N)}

[0063]

[0064] i∈[1,L],j∈[1,J]

[0065] Among them, C j,i Let c represent the sequence of intrinsic mode signals of the j-th layer of the i-th radar signal to be decomposed. j,i (n) represents the nth intrinsic mode signal in the j-th intrinsic mode signal sequence of the i-th radar signal to be decomposed;

[0066] The residual signal sequence for each radar signal to be decomposed in step 2 is as follows:

[0067] R i ={r i (1), r i (2), ..., r i (N)}

[0068]

[0069] i∈[1,L]

[0070] Among them, R i Let r represent the residual signal sequence of the i-th radar signal to be decomposed. i (n) represents the nth residual signal in the residual signal sequence of the i-th radar signal to be decomposed;

[0071] The multi-layer intrinsic mode signal sequence mentioned in step 2 is defined as follows:

[0072] C j ={c j (1), c j (2), ..., c j(N)}

[0073]

[0074] Among them, C j Let c represent the intrinsic mode signal sequence of the j-th layer. j (n) represents the nth intrinsic mode signal in the j-th layer intrinsic mode signal sequence;

[0075] The residual signal sequence mentioned in step 2 is defined as follows:

[0076] R={r(1), r(2),..., r(N)}

[0077]

[0078] Where R represents the residual signal sequence, and r(n) represents the nth residual signal in the residual signal sequence;

[0079] Preferably, step 3, which involves dividing the multi-layer intrinsic mode signal sequence into a high-frequency intrinsic mode signal sequence and a low-frequency intrinsic mode signal sequence, is as follows:

[0080] Step 3.1: Construct a reconstructed signal sequence after discarding each layer of intrinsic mode signals and residual sequences, and calculate the cross-correlation coefficient between the reconstructed signal sequence after discarding each layer of intrinsic mode signals and the radar signal sequence to be decomposed;

[0081] The reconstructed signal sequence after discarding the intrinsic mode sequence of each layer is defined as follows:

[0082]

[0083]

[0084] in, This represents the reconstructed signal sequence after discarding the m-layer intrinsic mode sequences. This represents the nth signal in the reconstructed signal sequence after discarding the m-layer intrinsic mode sequences;

[0085] The cross-correlation coefficient between the reconstructed signal sequence after discarding the intrinsic mode sequences of each layer and the radar signal sequence to be decomposed is defined as follows:

[0086]

[0087] Where ρ(m) represents the cross-correlation coefficient between the reconstructed signal after discarding the m-layer intrinsic mode signal sequence and the radar signal sequence to be decomposed, z d (n) represents the nth radar signal to be decomposed in the radar signal sequence to be decomposed, n∈[1,N], and N is the length of each differential absorption lidar measured signal;

[0088] Step 3.2: Let \(m\in[1,J]\), set the initial value of \(m\) to 1, with a step size of 1, and repeat Step 3.1 until \(\rho(m)\) is less than the threshold, then stop the calculation. Denote \(m = M\) at this time.

[0089] Step 3.3: Denote \(C\) M as the sequence of the boundary layers of the intrinsic mode signals. If \(j < M\), then \(C\) j is the sequence of the high-frequency intrinsic mode signals of the \(j\)-th layer. If \(M\leq j\leq J\), then \(C\) j is the sequence of the low-frequency intrinsic mode signals of the \(j\)-th layer.

[0090] The improved wavelet threshold transform filtering described in Step 3 is specifically as follows:

[0091] Select the db3 wavelet basis, perform wavelet transform on the sequence of the high-frequency intrinsic mode signals of each layer to obtain the wavelet coefficients after wavelet transform, process the wavelet coefficients using the improved soft threshold equation to obtain the wavelet coefficients after threshold processing, and through the wavelet coefficients after threshold processing and the db3 wavelet basis for reconstruction calculation, obtain the reconstructed sequence of the high-frequency intrinsic mode signals.

[0092] The wavelet coefficients after the wavelet transform are defined as follows:

[0093] A j =\({a\) j (1),a j (2),\(\cdots,a\) j (n),\(\cdots,a\) j (K j )}\)

[0094] where \(j\in[1,M]\)

[0095] Among them, \(K\) j represents the number of wavelet coefficients after wavelet transform of the sequence of the high-frequency intrinsic mode signals of the \(j\)-th layer, \(A\) j represents the sequence of wavelet coefficients after wavelet transform of the sequence of the high-frequency intrinsic mode signals of the \(j\)-th layer, and \(a\) j (n) represents the \(n\)-th coefficient of the sequence of wavelet coefficients after wavelet transform of the sequence of the high-frequency intrinsic mode signals of the \(j\)-th layer.

[0096] The wavelet coefficients obtained after the improved threshold equation processing are defined as follows:

[0097]

[0098] Among them, \(K\) j represents the number of wavelet coefficients obtained after wavelet transform and improved threshold equation processing of the sequence of the high-frequency intrinsic mode signals of the \(j\)-th layer. This represents the wavelet coefficient sequence of the j-th layer high-frequency intrinsic mode signal sequence after wavelet transform and improved threshold equation processing. It represents the nth coefficient of the wavelet coefficient sequence after the j-th layer high-frequency intrinsic mode signal sequence has been processed by wavelet transform and improved threshold equation.

[0099] The improved threshold processing equation is defined as follows:

[0100] When A j When ≤λ,

[0101] When A j When >λ, satisfy

[0102]

[0103] When A j When <λ, satisfy

[0104]

[0105] Where λ is the denoising threshold, and the threshold is selected as follows:

[0106]

[0107] Where σ is the noise standard deviation estimated from the first layer mother wavelet coefficients, and N is the length of each differential absorption lidar measured signal;

[0108] The reconstructed high-frequency intrinsic mode signal sequence described in step 3 is defined as follows:

[0109]

[0110] in, This represents the reconstructed high-frequency intrinsic mode signal sequence after wavelet transform and thresholding of the j-th layer intrinsic mode signal sequence. This represents the nth intrinsic mode signal in the reconstructed high-frequency intrinsic mode signal sequence after wavelet transformation and thresholding of the j-th intrinsic mode signal sequence.

[0111] Step 3.3 describes performing Savitzky-Golay smoothing filtering on the low-frequency intrinsic mode signal sequence to obtain the reconstructed low-frequency intrinsic mode signal sequence;

[0112] The reconstructed low-frequency intrinsic mode signal sequence described in step 3 is defined as follows:

[0113]

[0114] in, This represents the low-frequency intrinsic mode signal sequence after the j-th layer intrinsic mode signal sequence has been smoothed by Savitzky-Golay filtering. This represents the nth intrinsic mode signal in the low-frequency intrinsic mode signal sequence after the j-th layer intrinsic mode signal sequence has been smoothed by Savitzky-Golay filtering;

[0115] Preferably, the denoised differential absorption lidar signal sequence described in step 4 is defined as follows:

[0116] P = {p(1), p(2), p(3), ..., p(N)}

[0117]

[0118] Where P represents the denoised differential absorption lidar signal sequence, p(n) represents the nth denoised differential absorption lidar signal in the denoised differential absorption lidar signal sequence, J is the empirical mode decomposition level, and M is the level of the first low-frequency intrinsic mode signal sequence in the intrinsic mode signal sequence. This represents the nth intrinsic mode signal in the reconstructed high-frequency intrinsic mode signal sequence after wavelet transform and thresholding of the j-th layer intrinsic mode signal sequence. Let r(n) represent the nth intrinsic mode signal in the low-frequency intrinsic mode signal sequence after the j-th layer intrinsic mode signal sequence has been smoothed by Savitzky-Golay, and r(n) represent the nth residual signal in the residual signal sequence.

[0119] The present invention also provides a computer-readable medium storing a computer program executed by an electronic device, wherein when the computer program is run on the electronic device, it performs the steps of the differential absorption lidar signal denoising method.

[0120] The advantages of this invention are that it can achieve global adaptive filtering of the signal, and under the premise of ensuring high spatiotemporal resolution of the signal, it can remove high-frequency clutter noise while ensuring that the effective information of the signal is not lost, resulting in excellent noise reduction effect. This invention effectively improves the signal-to-noise ratio of differential absorption lidar signals, reduces reconstruction error, and reduces signal distortion, providing high-precision, low-interference echo signals for greenhouse gas profile concentration inversion. Attached Figure Description

[0121] Figure 1 : Flowchart of the method according to an embodiment of the present invention.

[0122] Figure 2 Echo signal diagram of multi-signal averaging and adjacent height averaging according to an embodiment of the present invention.

[0123] Figure 3: The intrinsic mode function diagram after complementary set empirical mode decomposition in an embodiment of the present invention.

[0124] Figure 4 : Echo signal diagram after denoising according to an embodiment of the present invention.

[0125] Figure 5 The echo signal after wavelet transform denoising is compared in the embodiments of the present invention.

[0126] Figure 6 Echo signal diagrams after empirical mode decomposition denoising in the embodiments of the present invention.

[0127] Figure 7 Echo signal diagrams after empirical mode decomposition denoising in the embodiments of the present invention. Detailed Implementation

[0128] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0129] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0130] The following is combined Figure 1-7 The technical solution of this invention is a method for denoising differential absorption lidar signals, as detailed below:

[0131] like Figure 1 The diagram shown is a flowchart of a method according to an embodiment of the present invention.

[0132] Step 1: Perform multi-signal time averaging on the measured signal sequence of the differential absorption lidar to obtain a new differential absorption lidar signal sequence, and then perform moving average processing on the new differential absorption lidar signal sequence to obtain the moving average lidar signal sequence.

[0133] Each measured signal sequence of the differential absorption lidar mentioned in step 1 is defined as follows:

[0134] X k =[x k (1),x k (2),...,x k (N)]

[0135] Where N is the length of the measured signal from each differential absorption lidar, and X... k Let x represent the measured signal sequence of the k-th differential absorption lidar. k (n) represents the nth differential absorption lidar measured signal in the kth differential absorption lidar measured signal sequence, k = 1, 2, 3…K, n = 1, 2, 3…N, K = 1000 is the column number of the differential absorption lidar measured signal sequence;

[0136] Step 1 involves performing multi-signal time averaging to obtain a new differential absorption lidar signal sequence, as detailed below:

[0137] Y m =[y m (1),y m (2),y m (3),...,y m (N)]

[0138]

[0139] Among them, Y m Let y represent the m-th new differential absorption lidar signal sequence, where a = 10 is the number of signal segments in a single time-averaged sequence. m (n) represents the nth new differential absorption lidar signal in the mth new differential absorption lidar signal sequence, M = 100 is the number of columns in the new differential absorption lidar signal sequence, N = 10000 is the length of each measured differential absorption lidar signal, and m ∈ [1, M], n ∈ [1, N];

[0140] Step 1 involves performing a moving average process on the new differential absorption lidar signal sequence to obtain the moving average lidar signal sequence, as detailed below:

[0141] Z m =[z m (1),z m (2),z m (3),...,z m (N)]

[0142]

[0143] Among them, Z m Let z represent the LiDAR signal sequence after the m-th moving average. m (n) represents the nth moving averaged lidar signal in the mth moving averaged lidar signal sequence, where M is the number of columns in the new differential absorption lidar signal sequence, and N is the length of each measured differential absorption lidar signal, and m∈[1,M], n∈[1,N]. Figure 2The image shown is an echo signal diagram of multi-signal averaging and adjacent height averaging according to an embodiment of the present invention.

[0144] Step 2: After multiple moving averages, arbitrarily select one sequence from the lidar signal sequences as the radar signal sequence to be decomposed. Randomly generate multiple white noise sequences using the Rand function model. From the radar signal sequence to be decomposed and the multiple white noise sequences, obtain multiple positively and negatively noised sequences of the radar signal to be decomposed. Perform empirical mode decomposition on each positively noised sequence to obtain a multi-layered positive intrinsic mode signal sequence and a positive residual signal sequence for each radar signal to be decomposed. Perform empirical mode decomposition on each negatively noised sequence to obtain a multi-layered negative intrinsic mode signal sequence for each radar signal to be decomposed. The signal sequence, the negative residual signal sequence of each radar signal to be decomposed; by calculating the multi-layer positive intrinsic mode signal sequence and the multi-layer negative intrinsic mode signal sequence of each radar signal to be decomposed, the multi-layer intrinsic mode signal sequence of each radar signal to be decomposed is obtained; by calculating the positive residual signal sequence and the negative residual signal sequence of each radar signal to be decomposed, the residual signal sequence of each radar signal to be decomposed is obtained; by calculating the information of the multi-layer intrinsic mode signal sequences of multiple radar signals to be decomposed, the multi-layer intrinsic mode signal sequence is obtained; by calculating the residual signal sequence of multiple radar signals to be decomposed, the residual signal sequence is obtained; such as Figure 3 The figure shown is the intrinsic mode function diagram after complementary set empirical mode decomposition according to an embodiment of the present invention.

[0145] Step 2 involves decomposing the radar signal sequence, which is specifically defined as follows:

[0146] The radar signal sequence to be decomposed is specifically defined as follows:

[0147] Z d ={z d (1), z d (2), ..., z d (N)}

[0148] Among them, Z d Let z represent the radar signal sequence to be decomposed. d (n) represents the nth radar signal to be decomposed in the radar signal sequence to be decomposed, n∈[1,N], and N is the length of each differential absorption lidar measured signal;

[0149] Step 2 involves randomly generating L white noise sequences using the Rand function model, specifically defined as follows:

[0150] W i ={w i (1),wi (2),w i (3)...w i (N)}

[0151] i∈[1,L],n∈[1,N]

[0152] Among them, W i Let w represent the generated i-th white noise sequence. i (n) represents the nth noise signal in the i-th white noise sequence. L is the number of white noise sequences generated, and N represents the number of noise signals in each white noise sequence, which is the same as the number of signals in the radar signal sequence to be decomposed.

[0153] The L forward noise-adding sequences of the radar signals to be decomposed in step 2 are specifically defined as follows:

[0154]

[0155]

[0156] i∈[1,L],n∈[1,N]

[0157] in, This represents the i-th forward noise-added sequence of the radar signal to be decomposed. This represents the nth signal in the forward noise-adding sequence of the i-th radar signal to be decomposed.

[0158] The L negative noise-adding sequences of the radar signals to be decomposed in step 2 are specifically defined as follows:

[0159]

[0160]

[0161] i∈[1,L],n∈[1,N]

[0162] in, This represents the i-th negative noise-added sequence of the radar signal to be decomposed. This represents the nth signal in the negative noise-added sequence of the i-th radar signal to be decomposed;

[0163] The multi-layered positive intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is defined as follows:

[0164]

[0165] i∈[1,L],n∈[1,N],j∈[1,J]

[0166] Where J is the number of empirical mode decomposition layers. This represents the j-th layer of the positive intrinsic mode signal sequence of the i-th radar signal to be decomposed. This represents the nth positive intrinsic mode signal in the j-th layer of the positive intrinsic mode signal sequence of the i-th radar signal to be decomposed;

[0167] The forward residual signal sequence of each radar signal to be decomposed in step 2 is defined as follows:

[0168]

[0169] i∈[1,L],n∈[1,N]

[0170] in, This represents the positive residual signal sequence of the i-th radar signal to be decomposed. This represents the nth positive residual signal in the sequence of positive residual signals of the i-th radar signal to be decomposed;

[0171] The multi-layer negative intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is defined as follows:

[0172]

[0173] i∈[1,L],j∈[1,J]

[0174] Where J is the number of empirical mode decomposition layers. This represents the j-th layer negative intrinsic mode signal sequence of the i-th radar signal to be decomposed. This represents the nth negative intrinsic mode signal in the j-th layer negative intrinsic mode signal sequence of the i-th radar signal to be decomposed;

[0175] The negative residual signal sequence of each radar signal to be decomposed in step 2 is defined as follows:

[0176]

[0177] i∈[1,L],n∈[1,N]

[0178] in, This represents the negative residual signal sequence of the i-th radar signal to be decomposed. This represents the nth negative residual signal in the negative residual signal sequence of the i-th radar signal to be decomposed;

[0179] The multi-layer intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is as follows:

[0180] C j,i ={c j,i (1), c j,i (2), ..., c j,i (N)}

[0181]

[0182] i∈[1,L],j∈[1,J]

[0183] Among them, C j,i Let c represent the sequence of intrinsic mode signals of the j-th layer of the i-th radar signal to be decomposed. j,i (n) represents the nth intrinsic mode signal in the j-th intrinsic mode signal sequence of the i-th radar signal to be decomposed;

[0184] The residual signal sequence for each radar signal to be decomposed in step 2 is as follows:

[0185] R i ={r i (1), r i (2), ..., r i (N)}

[0186]

[0187] i∈[1,L]

[0188] Among them, R i Let r represent the residual signal sequence of the i-th radar signal to be decomposed. i (n) represents the nth residual signal in the residual signal sequence of the i-th radar signal to be decomposed;

[0189] The multi-layer intrinsic mode signal sequence mentioned in step 2 is defined as follows:

[0190] C j ={c j (1), c j (2), ..., c j (N)}

[0191]

[0192] Among them, C j Let c represent the intrinsic mode signal sequence of the j-th layer. j (n) represents the nth intrinsic mode signal in the j-th layer intrinsic mode signal sequence;

[0193] The residual signal sequence mentioned in step 2 is defined as follows:

[0194] R={r(1), r(2),..., r(N)}

[0195]

[0196] Where R represents the residual signal sequence, and r(n) represents the nth residual signal in the residual signal sequence;

[0197] Step 3: Divide the multi-layer intrinsic mode signal sequence into high-frequency intrinsic mode signal sequences and low-frequency intrinsic mode signal sequences. Perform improved wavelet threshold transform filtering on each high-frequency intrinsic mode signal sequence to obtain the reconstructed high-frequency intrinsic mode signal sequence. Perform Savitzky-Golay smoothing filtering on each low-frequency intrinsic mode signal sequence to obtain the reconstructed low-frequency intrinsic mode signal sequence.

[0198] Step 3 involves dividing the multi-layer intrinsic mode signal sequence into high-frequency intrinsic mode signal sequences and low-frequency intrinsic mode signal sequences for each layer, as detailed below:

[0199] Step 3.1: Construct a reconstructed signal sequence after discarding each layer of intrinsic mode signals and residual sequences, and calculate the cross-correlation coefficient between the reconstructed signal sequence after discarding each layer of intrinsic mode signals and the radar signal sequence to be decomposed;

[0200] The reconstructed signal sequence after discarding the intrinsic mode sequence of each layer is defined as follows:

[0201]

[0202]

[0203] in, This represents the reconstructed signal sequence after discarding the m-layer intrinsic mode sequences. This represents the nth signal in the reconstructed signal sequence after discarding the m-layer intrinsic mode sequences;

[0204] The cross-correlation coefficient between the reconstructed signal sequence after discarding the intrinsic mode sequences of each layer and the radar signal sequence to be decomposed is defined as follows:

[0205]

[0206] Where ρ(m) represents the cross-correlation coefficient between the reconstructed signal after discarding the m-layer intrinsic mode signal sequence and the radar signal sequence to be decomposed, z d (n) represents the nth radar signal to be decomposed in the radar signal sequence to be decomposed, n∈[1,N], and N is the length of each differential absorption lidar measured signal;

[0207] Step 3.2: m∈[1,J], set the initial value of m to 1, the step to 1, and repeat step 3.1 until ρ(m) is less than the threshold, then stop the calculation. Let m = M at this time;

[0208] Step 3.3: Record C Mis the boundary layer sequence of the intrinsic mode signal. If j < M, then C j is the high-frequency intrinsic mode signal sequence of the j-th layer. If M ≤ j ≤ J, then C j is the low-frequency intrinsic mode signal sequence of the j-th layer;

[0209] The improved wavelet threshold transform filtering described in step 3 is as follows:

[0210] Select the db3 wavelet basis, perform wavelet transform on the high-frequency intrinsic mode signal sequence of each layer to obtain the wavelet coefficients after wavelet transform, process the wavelet coefficients using the improved soft threshold equation to obtain the wavelet coefficients after threshold processing, and reconstruct and calculate through the wavelet coefficients after threshold processing and the db3 wavelet basis to obtain the reconstructed high-frequency intrinsic mode signal sequence;

[0211] The wavelet coefficients after the wavelet transform are defined as follows:

[0212] A j ={a j (1), a j (2),..., a j (n),..., a j (K j )}

[0213] j ∈ [1, M]

[0214] where K j represents the number of wavelet coefficients after wavelet transform of the high-frequency intrinsic mode signal sequence of the j-th layer, A j represents the wavelet coefficient sequence after wavelet transform of the high-frequency intrinsic mode signal sequence of the j-th layer, and a j (n) represents the n-th coefficient of the wavelet coefficient sequence after wavelet transform of the high-frequency intrinsic mode signal sequence of the j-th layer;

[0215] The wavelet coefficients obtained after the improved threshold equation processing are defined as follows:

[0216]

[0217] where K j represents the number of wavelet coefficients obtained after wavelet transform and improved threshold equation processing of the high-frequency intrinsic mode signal sequence of the j-th layer, represents the wavelet coefficient sequence obtained after wavelet transform and improved threshold equation processing of the high-frequency intrinsic mode signal sequence of the j-th layer, represents the n-th coefficient of the wavelet coefficient sequence obtained after wavelet transform and improved threshold equation processing of the high-frequency intrinsic mode signal sequence of the j-th layer.

[0218] The improved threshold processing equation is defined as follows:

[0219] When A j When ≤λ,

[0220] When A j When >λ, satisfy

[0221]

[0222] When A j When <λ, satisfy

[0223]

[0224] Where λ is the denoising threshold, and the threshold is selected as follows:

[0225]

[0226] Where σ is the noise standard deviation estimated from the first layer mother wavelet coefficients, and N is the length of each differential absorption lidar measured signal;

[0227] The reconstructed high-frequency intrinsic mode signal sequence described in step 3 is defined as follows:

[0228]

[0229] in, This represents the reconstructed high-frequency intrinsic mode signal sequence after wavelet transform and thresholding of the j-th layer intrinsic mode signal sequence. This represents the nth intrinsic mode signal in the reconstructed high-frequency intrinsic mode signal sequence after wavelet transformation and thresholding of the j-th intrinsic mode signal sequence.

[0230] Step 3.3 describes performing Savitzky-Golay smoothing filtering on the low-frequency intrinsic mode signal sequence to obtain the reconstructed low-frequency intrinsic mode signal sequence;

[0231] The reconstructed low-frequency intrinsic mode signal sequence described in step 3 is defined as follows:

[0232]

[0233] in, This represents the low-frequency intrinsic mode signal sequence after the j-th layer intrinsic mode signal sequence has been smoothed by Savitzky-Golay filtering. This represents the nth intrinsic mode signal in the low-frequency intrinsic mode signal sequence after the j-th layer intrinsic mode signal sequence has been smoothed by Savitzky-Golay filtering;

[0234] Step 4: Using the reconstructed high-frequency intrinsic mode signal sequence and the reconstructed low-frequency intrinsic mode signal sequence, perform residual signal sequence reconstruction calculation to obtain the denoised differential absorption lidar signal sequence, such as... Figure 4 The image shown is a diagram of the denoised echo signal according to an embodiment of the present invention.

[0235] The denoised differential absorption lidar signal sequence described in step 4 is defined as follows:

[0236] P = {p(1), p(2), p(3), ..., p(N)}

[0237]

[0238] Where P represents the denoised differential absorption lidar signal sequence, p(n) represents the nth denoised differential absorption lidar signal in the denoised differential absorption lidar signal sequence, J is the empirical mode decomposition level, and M is the level of the first low-frequency intrinsic mode signal sequence in the intrinsic mode signal sequence. This represents the nth intrinsic mode signal in the reconstructed high-frequency intrinsic mode signal sequence after wavelet transform and thresholding of the j-th layer intrinsic mode signal sequence. Let r(n) represent the nth intrinsic mode signal in the low-frequency intrinsic mode signal sequence after the j-th layer intrinsic mode signal sequence has been smoothed by Savitzky-Golay, and r(n) represent the nth residual signal in the residual signal sequence.

[0239] To demonstrate the denoising effect of the method of this invention on the echo signal of differential absorption lidar, three different denoising methods—wavelet transform, EMD, and EEMD—were applied to the same measured echo signal from a lidar. The denoising effects are as follows: Figure 5 , 6 As shown in Figure 7. Figure 5 The image shows the echo signal after denoising using wavelet transform alone. Because wavelet transform can only select a single wavelet basis for denoising, its global adaptability is poor, resulting in significant noise and noticeable signal spikes and glitches. Figure 6 The image shows the echo signal after denoising using the Empirical Mode Decomposition (EMD) method. Because EMD can result in mode aliasing, many modes are typically retained to avoid losing useful information. While this method improves denoising compared to wavelet transform, some noise remains. For example... Figure 7 The image shows the echo signal after denoising using the complementary set empirical mode decomposition method. The introduction of white noise damages the original signal, resulting in overly smoothed signal and loss of effective signal information. In contrast, the denoising method proposed in this invention removes high-frequency noise while preserving the effective signal information, achieving excellent denoising performance.

[0240] A specific embodiment of the present invention also provides a computer-readable medium.

[0241] The computer-readable medium is a server workstation;

[0242] The server workstation stores the computer program executed by the electronic device. When the computer program runs on the electronic device, it causes the electronic device to perform the steps of the urban road depth image estimation method according to the embodiments of the present invention.

[0243] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0244] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for denoising differential absorption lidar signals, characterized in that, Includes the following steps: Step 1: Perform multi-signal time averaging on the measured signal sequence of the differential absorption lidar to obtain a new differential absorption lidar signal sequence, and then perform moving average processing on the new differential absorption lidar signal sequence to obtain the moving average lidar signal sequence. Step 2: After multiple moving averages, arbitrarily select one sequence from the lidar signal sequences as the radar signal sequence to be decomposed. Randomly generate multiple white noise sequences using the Rand function model. From the radar signal sequence to be decomposed and the multiple white noise sequences, obtain multiple positively and negatively noised sequences of the radar signal to be decomposed. Perform empirical mode decomposition on each positively noised sequence of the radar signal to be decomposed to obtain a multi-layered positive intrinsic mode signal sequence and a positive residual signal sequence of each radar signal to be decomposed. Perform empirical mode decomposition on each negatively noised sequence of the radar signal to be decomposed to obtain a multi-layered negative intrinsic mode signal sequence of each radar signal to be decomposed. The process involves: obtaining the state signal sequence and the negative residual signal sequence of each radar signal to be decomposed; calculating the multi-layered intrinsic mode signal sequence of each radar signal to be decomposed using the multi-layered positive intrinsic mode signal sequence and the multi-layered negative intrinsic mode signal sequence of each radar signal to be decomposed; calculating the residual signal sequence of each radar signal to be decomposed using the positive residual signal sequence and the negative residual signal sequence of each radar signal to be decomposed; calculating the multi-layered intrinsic mode signal sequence using the information from the multi-layered intrinsic mode signal sequences of multiple radar signals to be decomposed; and calculating the residual signal sequence using the residual signal sequence of multiple radar signals to be decomposed. Step 3: Divide the multi-layer intrinsic mode signal sequence into high-frequency intrinsic mode signal sequences and low-frequency intrinsic mode signal sequences. Perform improved wavelet threshold transform filtering on each high-frequency intrinsic mode signal sequence to obtain the reconstructed high-frequency intrinsic mode signal sequence. Perform Savitzky-Golay smoothing filtering on each low-frequency intrinsic mode signal sequence to obtain the reconstructed low-frequency intrinsic mode signal sequence. Step 4: Perform residual signal sequence reconstruction calculation using the reconstructed high-frequency intrinsic mode signal sequence and the reconstructed low-frequency intrinsic mode signal sequence to obtain the denoised differential absorption lidar signal sequence.

2. The differential absorption lidar signal denoising method according to claim 1, characterized in that: Each measured signal sequence of the differential absorption lidar mentioned in step 1 is defined as follows: in, N The length of the measured signal from each differential absorption lidar line. Indicates the first k A sequence of measured signals from a differential absorption lidar. Indicates the first k The first of the measured signal sequences of differential absorption lidar n Measured signals from a differential absorption lidar k= 1, 2, 3… K , n= 1, 2, 3… N , K This represents the number of columns in the new differential absorption lidar signal sequence. Step 1 involves performing multi-signal time averaging to obtain a new differential absorption lidar signal sequence, as detailed below: in, This represents the m-th new differential absorption lidar signal sequence. The number of signal bars averaged over a single time period. This indicates the m-th new differential absorption lidar signal sequence. n Let M be the number of columns in the new differential absorption lidar signal sequence, and N be the length of each measured differential absorption lidar signal. m ∈[1, M ], n ∈[1, N ]; Step 1 involves performing a moving average process on the new differential absorption lidar signal sequence to obtain the moving average lidar signal sequence, as detailed below: in, Indicates the first m The LiDAR signal sequence after moving average, Indicates the first m The first line of the moving averaged lidar signal sequence n After a moving average of several lidar signals, M is the number of columns in the new differential absorption lidar signal sequence, and N is the length of each measured differential absorption lidar signal. m ∈[1, M ], n ∈[1, N ].

3. The differential absorption lidar signal denoising method according to claim 2, characterized in that: Step 2 involves decomposing the radar signal sequence, which is specifically defined as follows: The radar signal sequence to be decomposed is specifically defined as follows: in, This represents the radar signal sequence to be decomposed. Indicates the first element in the radar signal sequence to be decomposed. n A radar signal to be decomposed. n ∈[1, N ], N The length of the measured signal from each differential absorption lidar line; Step 2 describes the random generation using the Rand function model. L A sequence of white noise, specifically defined as follows: in, Indicates the generated first i A white noise sequence, Indicates the first i The first white noise sequence n There are 10 noise signals; L is the number of white noise sequences generated, and N represents the signal length of each white noise sequence, which is the same as the number of radar signal sequences to be decomposed. Step 2 L The radar signal to be decomposed has a forward noise-added sequence, specifically defined as follows: in, This represents the i-th forward noise-added sequence of the radar signal to be decomposed. This represents the nth signal in the forward noise-adding sequence of the i-th radar signal to be decomposed; Step 2 L The negative noise-added sequence of the radar signal to be decomposed is defined as follows: in, This represents the i-th negative noise-added sequence of the radar signal to be decomposed. This represents the nth signal in the negative noise-added sequence of the i-th radar signal to be decomposed.

4. The differential absorption lidar signal denoising method according to claim 3, characterized in that: The multi-layered positive intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is defined as follows: in, J The number of empirical mode decomposition layers. Indicates the first i The first radar signal to be decomposed j Layer positive intrinsic mode signal sequence, Indicates the first i The first radar signal to be decomposed j The first layer of positive intrinsic mode signal sequence n One positive intrinsic mode signal; The forward residual signal sequence of each radar signal to be decomposed in step 2 is defined as follows: in, This represents the positive residual signal sequence of the i-th radar signal to be decomposed. This represents the nth positive residual signal in the sequence of positive residual signals of the i-th radar signal to be decomposed; The multi-layer negative intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is defined as follows: in, J The number of empirical mode decomposition layers. Indicates the first i The first radar signal to be decomposed j Layer negative intrinsic mode signal sequence, Indicates the first i The first radar signal to be decomposed j The first layer of negative intrinsic mode signal sequence n One negative intrinsic mode signal; The negative residual signal sequence of each radar signal to be decomposed in step 2 is defined as follows: in, This represents the negative residual signal sequence of the i-th radar signal to be decomposed. This represents the nth negative residual signal in the negative residual signal sequence of the i-th radar signal to be decomposed.

5. The differential absorption lidar signal denoising method according to claim 4, characterized in that: The multi-layer intrinsic mode signal sequence of each radar signal to be decomposed in step 2 is as follows: in, Indicates the first i The first radar signal to be decomposed j Layer intrinsic mode signal sequence, Indicates the first i The first radar signal to be decomposed j The first layer of intrinsic mode signal sequence n One inherent modal signal; The residual signal sequence for each radar signal to be decomposed in step 2 is as follows: in, This represents the residual signal sequence of the i-th radar signal to be decomposed. This represents the nth residual signal in the residual signal sequence of the i-th radar signal to be decomposed; The multi-layer intrinsic mode signal sequence mentioned in step 2 is defined as follows: in, This represents the intrinsic mode signal sequence of the j-th layer. This represents the nth intrinsic mode signal in the j-th layer intrinsic mode signal sequence; The residual signal sequence mentioned in step 2 is defined as follows: in, Represents the residual signal sequence. This represents the nth residual signal in the residual signal sequence.

6. The differential absorption lidar signal denoising method according to claim 5, characterized in that: Step 3 involves dividing the multi-layer intrinsic mode signal sequence into high-frequency intrinsic mode signal sequences and low-frequency intrinsic mode signal sequences for each layer, as detailed below: Step 3.1: Construct a reconstructed signal sequence after discarding each layer of intrinsic mode signals and residual sequences, and calculate the cross-correlation coefficient between the reconstructed signal sequence after discarding each layer of intrinsic mode signals and the radar signal sequence to be decomposed; The reconstructed signal sequence after discarding the intrinsic mode sequence of each layer is defined as follows: in, This represents the reconstructed signal sequence after discarding the m-layer intrinsic mode sequences. This represents the nth signal in the reconstructed signal sequence after discarding the m-layer intrinsic mode sequences; The cross-correlation coefficient between the reconstructed signal sequence after discarding the intrinsic mode sequences of each layer and the radar signal sequence to be decomposed is defined as follows: in, This represents the cross-correlation coefficient between the reconstructed signal after discarding the m-layer intrinsic mode signal sequence and the radar signal sequence to be decomposed. Indicates the first element in the radar signal sequence to be decomposed. n A radar signal to be decomposed. n ∈[1, N ], N The length of the measured signal from each differential absorption lidar line; Step 3.2: Set the initial value of m to 1, the step size to 1, and repeat step 3.1 until... If the value is less than the threshold, stop the calculation, and denote m=M at this point. Step 3.3: Record For the intrinsic mode signal boundary layer sequence, if ,but Let j be the high-frequency intrinsic mode signal sequence of the j-th layer. ,but It is the low-frequency intrinsic mode signal sequence of the j-th layer.

7. The differential absorption lidar signal denoising method according to claim 6, characterized in that: The improved wavelet threshold transform filtering described in step 3 includes the following specific steps: The db3 wavelet basis is selected, and wavelet transform is performed on the high-frequency intrinsic mode signal sequence of each layer to obtain the wavelet coefficients after wavelet transform. The wavelet coefficients are processed by an improved soft thresholding equation to obtain the thresholded wavelet coefficients. The reconstructed high-frequency intrinsic mode signal sequence is obtained by reconstructing the wavelet coefficients and the db3 wavelet basis. The wavelet coefficients after wavelet transform are defined as follows: j∈[1,M] in, Indicates the first j The number of wavelet coefficients after wavelet transform of the high-frequency intrinsic mode signal sequence. Indicates the first j Wavelet coefficient sequence after wavelet transform of layer high-frequency intrinsic mode signal sequence Indicates the first j The nth coefficient of the wavelet coefficient sequence after wavelet transform of the high-frequency intrinsic mode signal sequence; The wavelet coefficients obtained after processing with the improved threshold equation are defined as follows: in, Indicates the first j The number of wavelet coefficients obtained after processing the high-frequency intrinsic mode signal sequence of the layer through wavelet transform and improved threshold equation. Indicates the first j The wavelet coefficient sequence of the high-frequency intrinsic mode signal sequence after wavelet transform and improved threshold equation processing. Indicates the first j The nth coefficient of the wavelet coefficient sequence after the high-frequency intrinsic mode signal sequence of the layer is processed by wavelet transform and improved threshold equation; The improved threshold processing equation is defined as follows: when hour, ; when hour, satisfy when hour, satisfy ; in, The noise reduction threshold is selected as follows: in, The standard deviation of the noise is estimated from the first-layer mother wavelet coefficients. N The length of the measured signal from each differential absorption lidar line; The reconstructed high-frequency intrinsic mode signal sequence described in step 3 is defined as follows: in, This represents the reconstructed high-frequency intrinsic mode signal sequence after wavelet transform and thresholding of the j-th layer intrinsic mode signal sequence. This represents the nth intrinsic mode signal in the reconstructed high-frequency intrinsic mode signal sequence after wavelet transform and thresholding of the j-th intrinsic mode signal sequence; Step 3.3 describes performing Savitzky-Golay smoothing filtering on the low-frequency intrinsic mode signal sequence to obtain the reconstructed low-frequency intrinsic mode signal sequence; The reconstructed low-frequency intrinsic mode signal sequence described in step 3 is defined as follows: in, Indicates the first j The low-frequency intrinsic mode signal sequence after the layer intrinsic mode signal sequence is smoothed by Savitzky-Golay filtering. Indicates the first j The nth intrinsic mode signal in the low-frequency intrinsic mode signal sequence after the layer intrinsic mode signal sequence has been smoothed by Savitzky-Golay filtering.

8. The differential absorption lidar signal denoising method according to claim 7, characterized in that: The denoised differential absorption lidar signal sequence described in step 4 is defined as follows: Where P represents the denoised differential absorption lidar signal sequence. This represents the nth denoised differential absorption lidar signal in the denoised differential absorption lidar signal sequence. J Let M be the number of empirical mode decomposition levels, and M be the number of levels in the intrinsic mode signal sequence where the first low-frequency intrinsic mode signal sequence is located. This represents the nth intrinsic mode signal in the reconstructed high-frequency intrinsic mode signal sequence after wavelet transform and thresholding of the j-th layer intrinsic mode signal sequence. Indicates the first j The nth intrinsic mode signal in the low-frequency intrinsic mode signal sequence after the layer intrinsic mode signal sequence has been smoothed by Savitzky-Golay filtering. This represents the nth residual signal in the residual signal sequence.

9. A computer-readable medium, characterized in that, It stores a computer program executed by an electronic device, which, when run on the electronic device, causes the electronic device to perform the steps of the method as described in any one of claims 1-8.

Images