Semi-airborne transient electromagnetic de-noising method based on sparrow optimization algorithm optimized Kalman filter
By optimizing the Kalman filter parameters using the sparrow search algorithm, the problem of severe noise interference in semi-aerospace transient electromagnetic signals was solved, thereby improving signal quality and preserving features, adapting to complex noise environments, and enhancing the accuracy of signal processing.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XINJIANG UNIVERSITY
- Filing Date
- 2026-03-12
- Publication Date
- 2026-06-12
AI Technical Summary
In existing technologies for semi-aerospace transient electromagnetic signals, the late-stage signals are weak and severely affected by complex noise interference, resulting in poor data quality and interpretation accuracy. The fixed Kalman filter parameters lead to insufficient adaptability and difficulty in effectively denoising.
The Kalman filter is optimized using the sparrow search algorithm. A dynamic noise covariance matrix is constructed, and the key intensity parameters of the Kalman filter are globally adaptively optimized using the sparrow search algorithm to optimize the parameter combination of the Kalman filter to adapt to different noise environments.
It significantly improves the signal-to-noise ratio, effectively suppresses various types of noise, preserves the signal attenuation characteristics, and improves signal quality and subsequent inversion accuracy.
Smart Images
Figure CN122196340A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geophysical exploration and signal processing technology, and in particular to a Kalman filter-based method for denoising semi-airborne transient electromagnetic signals optimized by the Sparrow Search Algorithm (SSA). Background Technology
[0002] Semi-airborne transient electromagnetic method (SEM) is a highly efficient geophysical exploration technique widely used in deep resource exploration and hydrogeological surveys. However, the late-stage signals acquired by this method are weak and easily overwhelmed by complex and diverse environmental noise, severely affecting data quality and the accuracy of interpretation.
[0003] Currently, various methods exist for denoising transient electromagnetic signals, such as empirical mode decomposition, wavelet transform, and singular value decomposition. However, these traditional methods often suffer from incomplete denoising and limited signal feature preservation capabilities in complex noise environments. Kalman filtering, as an optimal estimation theory, is suitable for processing linear or linearized systems with approximately exponential decay characteristics, such as transient electromagnetic signals. However, its filtering performance is highly dependent on the accurate setting of the statistical characteristics of process noise and observation noise (i.e., the noise covariance matrix). In actual exploration, the noise environment is complex and variable, and using fixed noise covariance matrix parameters is difficult to achieve the best filtering effect, and may even lead to filtering failure or signal distortion.
[0004] Chinese patent application CN117056677A discloses a transient electromagnetic signal denoising method based on the improved variational mode decomposition (VMD) using the sparrow optimization algorithm. The method involves two steps: first, globally optimizing the penalty factor α and the number of modes K in the VMD using the sparrow optimization algorithm to obtain the optimal parameters [K, α]; second, using the optimal parameter combination obtained after optimization to perform variational mode decomposition on the acquired transient electromagnetic signal, thus achieving the denoising process of the original signal. However, in complex noisy environments, VMD may not be able to completely separate noise modes from useful signal modes. Even with a reduced envelope entropy, some non-stationary, broadband noise may still remain in the reconstructed signal, especially in the late weak signal segment, limiting its ability to preserve signal characteristics and affecting the accuracy of subsequent inversion.
[0005] In existing technologies, although some studies have attempted to apply Kalman filtering to electromagnetic data denoising, they usually fail to perform global and adaptive optimization of the core intensity parameters in the noise covariance matrix. When faced with complex noise with time-varying intensity and characteristics in semi-airborne transient electromagnetic data, its adaptability and robustness are still insufficient. Summary of the Invention
[0006] The purpose of this invention is to address the technical problems of weak late-stage semi-airborne transient electromagnetic signals, severe interference from complex noise, and poor performance of existing denoising methods due to poor adaptability and fixed parameters. This invention provides a semi-airborne transient electromagnetic denoising method based on the Sparrow Search Algorithm (SSA) optimized Kalman filter. This method constructs a dynamic noise covariance matrix and introduces the Sparrow Search Algorithm (SSA) to globally adaptively optimize the key intensity parameters of the Kalman filter, thereby achieving effective suppression of different types and intensities of noise. While improving the signal-to-noise ratio, it better preserves the attenuation characteristics of the original signal.
[0007] To achieve the above objectives, the present invention adopts the following technical solution: A semi-airborne transient electromagnetic denoising method based on the sparrow algorithm-optimized Kalman filter includes: 1) Acquire semi-airborne transient electromagnetic measured signal data.
[0008] 2) Preprocess the measured signal data to remove baseline drift interference. Specifically, wavelet multi-resolution analysis can be used, such as using the sym8 wavelet for multi-level decomposition, extracting low-frequency approximate components as baseline estimates and then removing them.
[0009] 3) Establish a Kalman filter model suitable for the characteristics of semi-aerospace transient electromagnetic signals. This model establishes a state-space model based on the linear decay of the signal in the late stage in a double logarithmic coordinate system and constructs a dynamic noise covariance matrix. The system noise covariance matrix Q... k Reflecting the uncertainty in state prediction, its strength is controlled by the parameter β; the observation noise covariance matrix R k It reflects the reliability of the observation, and its strength is related to the signal amplitude and controlled by the parameter σ.
[0010] 4) The Sparrow Search algorithm is used to globally optimize the key parameter combination (β, σ) in the Kalman filter model. The core of this step is to design a reasonable fitness function. Based on the theoretical attenuation characteristics of the late-stage semi-airborne transient electromagnetic signal, this invention constructs a fitness function by using the closeness of the late-stage slope of the denoised signal in a double logarithmic coordinate system to the theoretical target slope as the evaluation criterion. Guided by this fitness function, the SSA algorithm efficiently searches for the optimal solution in the parameter space.
[0011] The optimal parameter combination (β) obtained by the sparrow search algorithm is used to optimize the sparrow search algorithm. opt ,σ opt Substitute the signal into the Kalman filter model and perform filtering on the preprocessed signal to obtain a denoised and clean signal.
[0012] Furthermore, the system noise covariance matrix Q mentioned in step 3 k=β·[Δt³ / 3,Δt² / 2;Δt² / 2,Δt], where Δt is the time interval.
[0013] Furthermore, the observation noise covariance matrix R mentioned in step 3 k =[σ / (10 xk ·ln(10))]², where x k This is the estimated value of the signal amplitude.
[0014] Furthermore, the fitness function mentioned in step 4 is F(X) i )=|k filtered (X i )-k target |, where k target =-5 / 2.
[0015] The beneficial effects of this invention are: the method has strong adaptability, dynamically optimizing the Kalman filter parameters through the sparrow search algorithm, enabling the filter to adapt to different noise environments and effectively overcoming the shortcomings of poor adaptability of fixed parameters; at the same time, the denoising effect is significant, which can significantly improve the signal-to-noise ratio and reduce the root mean square error; in addition, the method has good feature preservation, using the theoretical attenuation slope of the signal as the optimization target, which can effectively suppress Gaussian white noise, atmospheric noise, power frequency noise and their mixed noise, significantly improve the signal-to-noise ratio, and better preserve the original attenuation characteristics of the signal. Attached Figure Description
[0016] Figure 1 This is a schematic diagram of a semi-airborne transient electromagnetic detection system; Figure 2 This is the overall flowchart of the Kalman filter based on the sparrow search algorithm optimization.
[0017] Figure 3 The diagram illustrates the baseline drift correction process for measured data: (a) original signal, (b) estimated baseline drift, and (c) corrected signal.
[0018] Figure 4 This is a comparison chart of attenuation curves after denoising the measured data using different methods.
[0019] Figure 5 The induced electromotive force profile curve before noise reduction of the measured data.
[0020] Figure 6 Measured data: induced electromotive force profile curves before and after noise reduction. Detailed Implementation
[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0022] The structures, proportions, and sizes illustrated in the accompanying drawings are merely for illustrative purposes and to aid those skilled in the art in understanding and reading the invention. They are not intended to limit the scope of the invention and therefore have no substantial technical significance. Any modifications to the structure, changes in proportions, or adjustments to size, provided they do not affect the effectiveness or purpose of the invention, should still fall within the scope of the technical content disclosed herein. Furthermore, the terms "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity and not intended to limit the scope of the invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention's implementation.
[0023] Figure 1 This is a schematic diagram of a ground-to-air temporal electromagnetic detection system. A long conductive wire source laid on the ground in Lichuan City, Hubei Province, emits bipolar square waves, and a receiving coil in the air collects the magnetic field response. A Kalman filter optimized based on the sparrow search algorithm is used to filter the semi-airborne electromagnetic measurement data.
[0024] See Figure 2 Combination Figure 1 As shown, a semi-aeronautical transient electromagnetic denoising method based on the sparrow algorithm to optimize Kalman filtering includes: Step 1: Data Acquisition. Semi-airborne transient electromagnetic field measurement data were acquired near Kanjia Village, Lichuan City. System operating parameters: transmit current 12.8A, long conductor source length 900m, flight altitude 60m, sampling rate 256kHz.
[0025] Step 2: Preprocessing (baseline drift correction). For example... Figure 3 As shown, the measured signal exhibits significant low-frequency baseline drift. A 12-level decomposition of the single-channel signal is performed using the sym8 wavelet basis, and the approximate coefficients of the 12th level are extracted to reconstruct the signal as the baseline drift estimate. Figure 3 b). The original signal ( Figure 3 a) Subtracting this estimate yields the baseline-corrected signal. Figure 3 c).
[0026] Step 3: Establish the Kalman filter model. 1. State equation: , where F k The state transition matrix is set according to the signal attenuation characteristics; W k The system noise has a covariance matrix of Q. k 2. Observation equation: ,wherein,wherein H k =[1,0],v k For observation noise, the covariance matrix is R. k 3. Construct the dynamic covariance matrix: Qk =β·[Δt³ / 3,Δt² / 2;Δt² / 2,Δt], R k =[σ / (10 xk ·ln(10))]²,x k Let be the estimated value of the signal amplitude in the state vector. Here, β and σ are the intensity parameters to be optimized.
[0027] Step 4: Optimize the sparrow search algorithm parameters. The specific process for this step is as follows: 1. Initialize the sparrow search algorithm population: Set the search range of parameter β to [1e-10, 1e-1], and the search range of σ to [1e-10, 1e-1]. Randomly generate N sparrow individuals (N=50) to form a population X={X1,X2,…,X…} N}, each individual's position X i =(x i1 ,x i2 )= (β i ,σ i ) represents a set of KF (Kalman filter) parameter combinations.
[0028] 2. Define the fitness function: Based on the theory of late response of semi-airborne transient electromagnetic systems, in a uniform half-space, the late slope k in a double logarithmic coordinate system is... target =-5 / 2. For each individual X i , using its parameter (β) i ,σ i Perform Kalman filtering (KF) denoising and calculate the linear fitting slope k of the late segment of the denoised signal. filtered (X i The fitness function is then defined as: F(X). i )=∣k filtered (X i The smaller the fitness value, the closer the attenuation characteristics of the denoised signal are to the theoretical value, and the better the parameter combination.
[0029] 3. Iterative Optimization (Position Update): Following the mechanism of the sparrow search algorithm, individual sparrows are divided into discoverers, joiners, and watchers, and their positions are updated according to the following rules (corresponding to the parameters ( β,σ ): a. Discoverer Location Update: Discoverers are responsible for finding food and providing orientation for the population. Their location update formula is: , Where t represents the current iteration number, j = 1, 2, 3, ..., d; iter max X is a constant representing the maximum number of iterations; t i,jLet represent the position information of the i-th sparrow in the j-th dimension; α∈(0,1] is a random number; R2 and ST represent the warning value and the safety value, respectively, R2∈[0,1], ST∈[0.5,1]; Q is a random number that follows a normal distribution; L represents a 1×d matrix, where each element in the matrix is 1; 2) Update the location of new members , Among them, X p t+1 This is currently the optimal position occupied by the discoverer, X. worst This represents the current worst position globally. A represents an l×2 matrix; where each element is randomly assigned a value of 1 or -1, and A + =A T (AA T ) -1 Individuals whose membership is greater than n / 2 are considered to be less fit and will fly to other areas to forage.
[0030] 3) Guardian location update , in, X best It is the current global optimal position, and b, as the step size control parameter, is a random number that follows a standard normal distribution. K ∈[-1,1] is a random number. f i This is the fitness value of individual sparrow i. f g and f w These are the current best and worst fitness values globally, respectively. ε is a very small constant to avoid the denominator being zero. When f i >f g When this occurs, it indicates that the individual is on the edge of the population and vulnerable to predation, and will move towards the optimal position; when f i = f g When the individual is alerted to danger, it will move closer to other sparrows to avoid it. The fitness value of the entire population is recalculated after each iteration.
[0031] 4. Termination and Output: Determine if the maximum number of iterations has been reached. If so, select the individual with the lowest fitness value and set its position. X best =(β opt ,σ opt ) This is the optimal parameter combination obtained by the sparrow search algorithm. Figure 4 The convergence of the optimal fitness value during the optimization process is shown, demonstrating that the algorithm can quickly converge to a stable optimal value.
[0032] Step 5: Kalman filtering for noise reduction. The optimal parameter combination (β) obtained in Step 4 is then applied... opt ,σ opt Substitute the Kalman filter model established in step three. For the single-channel signal processed in step two, execute the Kalman filter's "prediction-update" recursive process, ultimately outputting the denoised signal estimate. .
[0033] Verification by measured data: Figure 4 The results of the measured attenuation curve after denoising using this method are shown. It can be seen that the denoised curve is relatively smooth throughout the entire period, and spikes and fluctuations are effectively suppressed.
[0034] Figure 5 , Figure 6 The induced electromotive force profiles of the entire measurement line before and after noise reduction were compared. Before noise reduction ( Figure 5 The profile curves are messy and have severe intersections; after denoising using the Sparrow Search Algorithm-Kalman Filter (SSA-KF)... Figure 6 The cross-section becomes smooth and regular, conforming to the laws of electromagnetic field propagation.
[0035] In summary, the method of this invention uses the sparrow search algorithm to intelligently and globally optimize the core parameters of the Kalman filter, effectively solving the denoising problem of semi-airborne transient electromagnetic signals, especially late-stage weak signals, and providing a reliable technical means for high-precision geophysical exploration in complex noise environments.
[0036] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.
Claims
1. A semi-aeronautical transient electromagnetic denoising method based on the sparrow algorithm-optimized Kalman filter, characterized in that, include: 1) Acquire semi-airborne transient electromagnetic measured signal data; 2) The measured signal data is preprocessed to remove baseline drift interference; 3) Establish a Kalman filter model suitable for the characteristics of semi-airborne transient electromagnetic signals. The model includes state equations, observation equations, and dynamic noise covariance matrix. The dynamic noise covariance matrix includes system noise covariance matrix and observation noise covariance matrix. 4) Use the sparrow search algorithm to perform global optimization of the parameter combination (β, σ) in the Kalman filter model, where β is the intensity parameter to be optimized in the system noise covariance matrix and σ is the intensity parameter to be optimized in the observation noise covariance matrix. 5) Combine the optimal parameter combination (β) obtained in step 4). opt ,σ opt The signal is applied to the Kalman filter model to filter and denoise the signal after preprocessing in step 2, resulting in a denoised semi-aeronautical transient electromagnetic signal.
2. The semi-aeronautical transient electromagnetic denoising method based on the sparrow algorithm-optimized Kalman filter as described in claim 1, characterized in that, In step 2, the preprocessing specifically involves: using the sym8 wavelet basis to perform multi-level decomposition on the original signal, extracting its low-frequency approximate components as an estimate of the baseline drift, and then subtracting this estimate from the original signal to correct the baseline drift.
3. The semi-aeronautical transient electromagnetic denoising method based on the sparrow algorithm-optimized Kalman filter as described in claim 1, characterized in that, In step 3), the system noise covariance matrix is constructed as follows: Q k =β·M, where M=[Δt³ / 3,Δt² / 2;Δt² / 2,Δt], Δt is the sampling time interval, and β is the intensity parameter to be optimized.
4. The semi-aeronautical transient electromagnetic denoising method based on the sparrow algorithm-optimized Kalman filter as described in claim 1, characterized in that, In step 3), the observation noise covariance matrix is constructed as follows: R k =[σ / (10 xk ·ln(10))]², where x k Let σ be the estimated value of the signal amplitude at time k, and σ be the intensity parameter to be optimized.
5. The semi-aeronautical transient electromagnetic denoising method based on the sparrow algorithm-optimized Kalman filter as described in claim 1, characterized in that, In step 4), the fitness function of the sparrow search algorithm is defined as the absolute error between the slope of the late segment of the denoised signal in a double logarithmic coordinate system and the theoretical slope of the target: F(X) i )=|k filtered (X i )-k target |, where X i Represents the i-th group of parameter combinations to be evaluated (β) i ,σ i ), k filtered (X i ) indicates the use of parameter combination X i The late slope of the signal obtained after Kalman filtering denoising, k target This represents the theoretical target slope value of the late-stage semi-airborne transient electromagnetic signal in a double logarithmic coordinate system.
6. The semi-aeronautical transient electromagnetic denoising method based on the sparrow algorithm-optimized Kalman filter as described in claim 5, characterized in that, Step 4) includes the following specific steps: 4.1) Initialize the population for the sparrow search algorithm by randomly generating several sparrow individuals within the preset parameter (β,σ) search space, with each individual's position corresponding to a set of parameter combinations; 4.2) For each individual in the population, perform Kalman filtering to remove noise and calculate its fitness value based on the fitness function; 4.3) Based on the rules of the sparrow search algorithm, simulate the position update behavior of the discoverer, joiner and watcher, and perform iterative search in the parameter space to guide the population to move to the region with better fitness; 4.4) Determine if the iteration termination condition is met. If so, output the parameter combination corresponding to the current globally optimal individual as the optimal parameter combination (β). opt ,σ opt Otherwise, return to step 4.2) and continue iterating.
7. The semi-aeronautical transient electromagnetic denoising method based on the sparrow algorithm-optimized Kalman filter according to claim 6, characterized in that, In step 4.3), the position update rule of the sparrow search algorithm is as follows: 1) Discoverer location update , Where t represents the current iteration number, j = 1, 2, 3, ..., d; iter max X is a constant representing the maximum number of iterations; t i,j Let represent the position information of the i-th sparrow in the j-th dimension; α∈(0,1] is a random number; R2 and ST represent the warning value and the safety value, respectively, R2∈[0,1], ST∈[0.5,1]; Q is a random number that follows a normal distribution; L represents a 1×d matrix, where each element in the matrix is 1; 2) Update the location of new members , Among them, X p t+1 This is currently the optimal position occupied by the discoverer, X. worst This represents the current worst-case position globally; A represents an l×d matrix; where each element is randomly assigned a value of 1 or -1, and A + =A T (AA T ) -1 ; 3) Guardian location update , in, X best is the current global optimal position, and b is a random number that follows a normal distribution with a mean of 0 and a variance of 1, which is used as the step size control parameter. K ∈[-1,1] is a random number. f i This is the fitness value of individual sparrow i. f g and f w These are the current best and worst fitness values globally, respectively, and ε is the smallest constant.