Method for extracting amplitude and phase of multi-frequency time-varying mixed signal based on rls algorithm

Abstract

The application relates to a multi-frequency time-varying mixed signal amplitude and phase extraction method based on an RLS algorithm. For a ground-to-space frequency domain detection signal with time-varying amplitude and phase, the method inputs a collected signal into a double channel, respectively adopts a sine reference signal and a cosine reference signal, separates frequency components of the signal through an RLS algorithm, and can simultaneously extract time-varying amplitudes and phases of all frequency components. The application can be applied to the field of non-stationary signal processing, can accurately extract time-domain waveforms of amplitudes and phases of frequency signals, and provides data support for model inversion.

Description

Technical Field

[0001] This invention belongs to the field of stable signal processing, specifically a method for extracting the amplitude and phase of multi-frequency time-varying mixed signals based on the RLS algorithm. Background Technology

[0002] Non-stationary signals are random signals whose distribution parameters or distribution laws change over time. Traditional analysis methods include time-domain and frequency-domain analysis. In recent years, time-frequency analysis (TFA) methods such as short-time Fourier transform, wavelet transform (WT), and empirical mode decomposition have been commonly used in the field of non-stationary signal separation and parameter estimation. TFA can map a one-dimensional signal to two dimensions and use time-frequency representation (TFR) to characterize the time-varying characteristics of the signal. For multi-frequency mixed non-stationary signals, the amplitude and phase of each frequency component change over time. Traditional analysis methods such as Fourier transform cannot directly and effectively analyze such non-stationary signals. In engineering applications, the ability to accurately and efficiently denoise and separate the frequency components directly determines the data processing effect.

[0003] CN105717490A discloses a "time-frequency analysis-based method for LFM signal separation and parameter estimation", which is applied to the field of radar signal reconnaissance technology. It provides a time-frequency analysis method based on wavelet transform, which utilizes the energy concentration characteristics of non-stationary signals to achieve the separation of mixed signals. It has good time-frequency concentration for multilinear frequency modulated signals, strong robustness, and is suitable for the separation and estimation of multilinear frequency modulated signals.

[0004] CN109885805A discloses a "method for instantaneous frequency estimation of multi-component non-stationary signals." This method employs the Viterbi algorithm to perform coarse and precise instantaneous frequency estimations of the signal's time-frequency distribution, resulting in a precise instantaneous frequency estimate. This method effectively suppresses jumps in the instantaneous frequency curve, improves the accuracy of instantaneous frequency estimation, and solves the problem that conventional time-frequency analysis methods for pulse signals cannot simultaneously improve time-frequency resolution. However, the quadratic time-frequency analysis method has high redundancy and computational complexity, and it encounters technical problems related to cross-terms when applied to multi-component signals.

[0005] CN108563254B discloses an active control system for multi-frequency time-varying narrowband vibration noise. Through multiple frequency / phase adjustment subsystems and corresponding control signal generation subsystems, it can effectively suppress target noise in the absence of a reference sensor. However, it cannot extract the amplitude and phase of the signal. Summary of the Invention

[0006] For noisy multi-frequency mixed signals where both amplitude and phase vary over time, this invention provides a method for extracting the amplitude and phase of multi-frequency time-varying mixed signals based on the RLS algorithm. This method, implemented using the RLS algorithm, employs multi-frequency sine and cosine reference signals respectively. By separating the frequency components using the RLS algorithm, it can simultaneously extract the time-varying amplitude and phase information of all frequency components. In signal analysis and processing using the ground-space frequency domain electromagnetic method, the changes in resistivity and other parameters of the measured target can be further inverted based on the changes in signal amplitude and phase, enabling the analysis of underground ore bodies and geological structures.

[0007] This invention is implemented as follows:

[0008] A method for extracting amplitude and phase of multi-frequency time-varying mixed signals based on the RLS algorithm is proposed. The multi-frequency time-varying mixed signal is input into an orthogonal dual channel. In each channel, the frequency components are separated using the RLS algorithm to obtain the result matrices of the two channels. The phase and amplitude of the signal are calculated based on the result matrices, and phase dewinding is performed based on the phase to obtain the true phase.

[0009] Furthermore, the multi-frequency time-varying hybrid signal refers to the signal transmitted by the transmitting system at a frequency of f during the detection process of the controllable source electromagnetic method. N f The number of transmission frequencies is given by f, and the electromagnetic signal s collected by the receiving system is given by f, where s(n) is the data from the nth sampling point, for a total of N sampling points. The sampling frequency of the receiving system is f. s .

[0010] Furthermore, before inputting the orthogonal dual channels, the regularization parameter δ and the forgetting factor λ of the RLS algorithm are selected based on the signal-to-noise ratio and other characteristics of the electromagnetic signal s, and the filter order M is determined.

[0011] Furthermore, the signal processing steps for one of the channels include:

[0012] Step a: Initialize the reference signal Represents N f A real space of ×N dimensions.

[0013]

[0014] Initialize filter coefficients Initialize the autocorrelation inverse matrix P1 = δ -1 I, I is M×M×N f The identity matrix; the initialization result matrix Set the iteration step size to μ, and take n = M;

[0015] Step b: Take the (n-M+1)th to the nth column of X1 as the tap reference signal for the nth iteration.

[0016] Step c: Calculate the estimation error vector for the nth iteration: in represents the filter coefficients of the nth iteration, ⊙ is the Hadamard product, which means that the corresponding elements of two matrices are multiplied to obtain a matrix of the same dimension, and ∑(·) means the summation of all elements of the matrix;

[0017] Step d: Calculate the output signal T of the nth iteration. 1_n =Z 1_n ⊙X 1_n , where X 1_n and Z 1_n These represent the nth column of X1 and Z1, respectively;

[0018] Step e: Calculate the error of the result of the nth iteration:

[0019] Step f: Calculate the update direction for the nth iteration: ξ 1_n =e Z1 (n)·X 1_n Update the result matrix: Z 1_n+1 =Z 1_n +μξ 1_n ;

[0020] Step g: Calculate the gain of the nth iteration. Inverse correlation matrix Filter coefficients For i=1,2,…,N f Calculate the gain of the i-th row according to equation (1). and filter coefficients and the inverse correlation matrix on page i

[0021]

[0022] in, The conjugate of ε1(n); T represents the transpose;

[0023] Step h: Let n = n + 1, repeat steps 3b to 3g until n = N - 1.

[0024] Furthermore, the signal processing steps for the other channel include:

[0025] Step i: Initialize the reference signal in

[0026]

[0027] Initialize the filter coefficients ω2 = 0. Initialize the autocorrelation inverse matrix P2 = δ -1 I; Initialize the result matrix Z2 = 0, Set the iteration step size to μ, and take n = M;

[0028] Step j: Take the (n-M+1)th column to the nth column of the reference signal X2 as the -tap reference signal for the nth iteration.

[0029] Step k: Calculate the estimation error vector for the nth iteration: in The filter coefficients represent the nth iteration.

[0030] Step 1: Calculate the output signal Y of the nth iteration. 2_n =Z 2_n ⊙X 2_n , where X 2_n and Z 2_n These represent the nth columns of X2 and Z2, respectively.

[0031] Step m: Calculate the error of the result of the nth iteration:

[0032] Step n: Calculate the update direction for the nth iteration: ξ 2_n =e Z2 (n)·X 2_n Update the result matrix: Z 2_n+1 =Z 2_n +μξ 2_n ;

[0033] Step o: Calculate the gain of the nth iteration. Inverse correlation matrix Filter coefficients For i=1,2,…,N f Calculate the gain of the i-th row according to equation (2). and filter coefficients and the inverse correlation matrix on page i

[0034]

[0035] Step p: Let n = n + 1, repeat steps 3i to 3o, and stop when n = N - 1.

[0036] Furthermore, the result matrices Z1 and Z2 obtained from the two channels are used to calculate the amplitude matrix A of each frequency component signal in the mixed signal as a function of time according to equation (3);

[0037]

[0038] Furthermore, the phase ψ of each frequency component signal in the mixed signal as a function of time is calculated according to the four-quadrant arctangent function of equation (4), where arctan(·) represents the arctangent;

[0039]

[0040] Furthermore, phase unwinding is performed on phase ψ. Phase ψ is traversed from front to back. When the phase difference between adjacent points is greater than or equal to π, the phase of the next point and all subsequent points is reduced by 2π. When the phase difference between adjacent points is less than or equal to -π, the phase of the next point and all subsequent points is increased by 2π to obtain its true phase φ.

[0041] Compared with existing technologies, the advantages of this invention are as follows: The method for extracting multi-frequency mixed signals in this invention solves the shortcomings of traditional spectrum analysis methods in processing controllable source electromagnetic data, which have low resolution and cannot handle non-stationary signals. Compared with time-frequency analysis methods such as short-time Fourier transform and wavelet transform, this method has lower time and space complexity, faster extraction speed, and higher accuracy. The method disclosed in this invention uses dual-channel acquisition of input signals and performs parallel processing on signals of multiple frequencies, which can effectively improve signal processing efficiency. Attached Figure Description

[0042] Figure 1 A flowchart of a method for extracting amplitude and phase of multi-frequency time-varying mixed signals based on the RLS algorithm;

[0043] Figure 2 The time-domain waveform of the electromagnetic signal s provided in the embodiments of the present invention;

[0044] Figure 3 The waveform of the amplitude of the multi-frequency time-varying mixed signal obtained by the method provided in the embodiments of the present invention is shown in the time domain.

[0045] Figure 4 The result is the phase-time domain waveform of the multi-frequency time-varying mixed signal obtained by the method provided in the embodiments of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0047] like Figure 1As shown, a method for extracting the amplitude and phase of multi-frequency time-varying mixed signals based on the Recursive Least Square (RLS) algorithm is presented. For signals where both amplitude and phase change with time, this method inputs the signal into orthogonal dual channels and uses the RLS algorithm to separate its frequency components. This allows for the simultaneous extraction of the amplitude and phase changes of all frequency components over time. The specific working process of this invention is as follows:

[0048] Step 1: The time-domain waveform of the electromagnetic signal s collected by the receiving system during the detection process of the controlled-source electromagnetic method is as follows: Figure 2 As shown, the frequency of the transmitted signal is f = [16Hz, 32Hz, 64Hz, 80Hz, 96Hz, 112Hz, 128Hz, 144Hz, 176Hz, 208Hz, 224Hz, 240Hz, 256Hz, 272Hz, 288Hz, 304Hz, 336Hz, 368Hz, 384Hz, 448Hz, 576Hz, 640Hz, 688Hz, 720Hz, 752Hz, 768Hz, 1280Hz], and the number of frequency components is N. f =27, the sampling frequency of the receiving system is f s =12000Hz, number of sampling points N=2400000;

[0049] Step 2: Based on the signal-to-noise ratio and other characteristics of the electromagnetic signal s, select the regularization parameter δ and the forgetting factor λ of the RLS algorithm to determine the filter order M. In this embodiment, the forgetting factor λ = 0.9995 and the regularization parameter δ = 1 × 10⁻⁶. -5 Let M = 1;

[0050] Step 3: Input the electromagnetic signal s into two orthogonal channels respectively, and extract the signal amplitude and phase iteratively based on the RLS algorithm to obtain orthogonal components of multiple frequencies.

[0051] The specific steps for channel 1 are as follows:

[0052] Step 3a: Initialize the reference signal ( Represents N f (a real space of ×N dimensions), where x1(f,n)=sin(2πfn)∈X1; initialize the filter coefficients ω1=0 Initialize the autocorrelation inverse matrix P1 = δ -1 I, I is M×M×N f The identity matrix; the initialization result matrix Z1 = 0 Set the iteration step size to μ, and take n = M. The algorithm automatically generates a reference signal after the input electromagnetic signal.

[0053] Step 3b: Take the (n-M+1)th to the nth column of X1 as the tap reference signal for the nth iteration.

[0054] Step 3c: Calculate the estimation error vector for the nth iteration: in represents the filter coefficients of the nth iteration, ⊙ is the Hadamard product, which means multiplying corresponding elements of two matrices to obtain a matrix of the same dimension, and ∑(·) represents the summation of all elements of the matrix.

[0055] Step 3d: Calculate the output signal of the nth iteration: Y 1_n =Z 1_n ⊙X 1_n , where X 1_n and Z 1_n These represent the nth column of X1 and Z1, respectively.

[0056] Step 3e: Calculate the error of the result of the nth iteration:

[0057] Step 3f: Calculate the update direction for the nth iteration: ξ 1_n =e Z1 (n)·X 1_n Update the result matrix: Z 1_n+1 =Z 1_n +μξ 1_n .

[0058] Step 3g: Calculate the gain of the nth iteration. Inverse correlation matrix Filter coefficients For i=1,2,…,N f Calculate the gain of the i-th row according to equation (1). and filter coefficients and the inverse correlation matrix on page i

[0059]

[0060] in, It is the conjugate of ε1(n);

[0061] Step 3h: Let n = n+1, repeat steps 3b to 3g until n = N-1;

[0062] Similarly, the specific steps for channel 2 are as follows:

[0063] Step 3i: Initialize the reference signal Where x2(f,n)=cos(2πfn)∈X2; initialize the filter coefficients. Initialize the autocorrelation inverse matrix P2 = δ -1 I; Initialize the result matrix Set the iteration step size to μ, and take n = M.

[0064] Step 3j: Take the (n-M+1)th to the nth column of X2 as the tap reference signal for the nth iteration.

[0065] Step 3k: Calculate the estimation error vector for the nth iteration: in This represents the filter coefficients for the nth iteration.

[0066] Step 31: Calculate the output signal of the nth iteration: Y 2_n =Z 2_n ⊙X 2_n , where X 2_n and Z 2_n point

[0067] Let n represent the nth column of X2 and Z2.

[0068] Step 3m: Calculate the error of the result of the nth iteration:

[0069] Step 3n: Calculate the update direction for the nth iteration: ξ 2_n =e Z2 (n)·X 2_n Update the result matrix: Z 2_n+1 =Z 2_n +μξ 2_n .

[0070] Step 30: Calculate the gain of the nth iteration Inverse correlation matrix Filter coefficients For i=1,2,…,N f Calculate the gain of the i-th row according to equation (2). and filter coefficients and the inverse correlation matrix on page i

[0071]

[0072] Step 3p: Let n = n + 1, repeat steps 3i to 3o until n = N - 1;

[0073] Step 4: Using Z1 and Z2 obtained in Step 3, calculate the amplitude A of each frequency component signal in the mixed signal as a function of time according to Equation (3), such as... Figure 3 As can be seen from the figure, the present invention accurately extracts the changes in amplitude of each frequency component of the input signal s over time.

[0074]

[0075] Step 5: Calculate the phase ψ of each frequency component signal in the mixed signal as a function of time according to the four-quadrant arctangent function of equation (4), such as... Figure 4 a;

[0076]

[0077] Step 6: Perform phase unwinding on phase ψ. Specifically, iterate through phase ψ from front to back. When the phase difference between adjacent points (phase value of the later point minus phase value of the earlier point) is greater than or equal to π, subtract 2π from the phase of the later point and all subsequent points. Similarly, when the phase difference between adjacent points is less than or equal to -π, add 2π to the phase of the later point and all subsequent points to obtain its true phase φ. Figure 4 b.

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for extracting the amplitude and phase of a multi-frequency time-varying mixed signal based on RLS algorithm, characterized in that, The multi-frequency time-varying mixed signal is input into a quadrature dual channel, each frequency component is separated in each channel by using an RLS algorithm to obtain a result matrix of the two channels respectively, the phase and amplitude of the signal are calculated according to the result matrix, and the real phase is obtained by performing phase unwrapping according to the phase; The multi-frequency time-varying mixed signal is a frequency of a signal transmitted by a transmitting system in a detection process of the controllable source electromagnetic method , , is a number of transmitting frequencies, and the electromagnetic signal collected by the receiving system , wherein is data of an i th sampling point, a total number of sampling points is n , and a sampling frequency of the receiving system is f . Before inputting the orthogonal dual channels, based on the electromagnetic signal Based on characteristics such as signal-to-noise ratio, regularization parameters are selected. Forgetting factor of RLS algorithm Determine the filter order ; The step of processing the signal in one of the channels comprises: Step a: Initialization of reference signal , represent dimensional real space, ， Initialize filter coefficients , ); Initialize the autocorrelation inverse matrix , for The identity matrix; the initialization result matrix Set the iteration step size ,Pick ; Step b: Take the first column to the second column as the tap reference signal for the first iteration ; and the second column to the third column as the tap reference signal for the second iteration. Step c: Calculate the estimated error vector for the ith iteration: where represents the filter coefficients for the ith iteration, is the Hadamard product, which means the multiplication of the elements in the corresponding positions of two matrices, resulting in a matrix of the same dimension, denotes the summation of all elements of a matrix; Step d: Calculate the output signal of the n-th iteration: wherein and represent the n-th column of and respectively.​ Step e: Calculate the result error of the second iteration: ; Step f: Calculate the update direction of the second iteration: , update result matrix: ; Step g: Calculate the first Gain of the next iteration Inverse correlation matrix Filter coefficients ,right Calculate the first according to formula (1) row gain and filter coefficients and the Page inverse correlation matrix , : ， wherein is the conjugate of T represents the transpose; Step h: Let , repeat steps 3b to 3g until stop.

2. The method for extracting the amplitude and phase of a multi-frequency time-varying mixed signal based on the RLS algorithm according to claim 1, characterized in that, The step of processing the signal in the other channel comprises: Step i: Initialization of reference signal wherein ， Initializing filter coefficients , ; initializing autocorrelation inverse matrix ; initializing result matrix ; setting iteration step , taking ; Step j: taking the reference signal of the first column to the column as the -tap reference signal for the first iteration , ; Step k: compute the estimated error vector for the nth iteration: where represents the filter coefficients for the nth iteration; Step 1: Calculate the output signal of the first iteration: Step 2: Calculate the output signal of the second iteration: where and represent the nth column of and respectively. Step m: Calculate the result error of the second iteration: ; Step n: Compute the update direction for the nth iteration: , the update result matrix: ; Step o: calculate the gain of the first iteration , the inverse correlation matrix , the filter coefficients , the gain of the first row and the filter coefficients of the first page inverse correlation matrix , according to equation (2) , : ， Step p: Let Step 3i to step 3o are repeated until stop.

3. The method for extracting the amplitude and phase of a multi-frequency time-varying mixed signal based on the RLS algorithm according to claim 1, characterized in that, The resultant matrix of two channels is obtained With The amplitude matrix of each frequency component signal in the mixed signal changing with time is calculated according to formula (3) ; 。 4. The method for extracting the amplitude and phase of a multi-frequency time-varying mixed signal based on the RLS algorithm according to claim 1, characterized in that, The phase of each frequency component signal in the mixed signal varying with time is calculated according to the four-quadrant arctangent function of formula (4) wherein represents arctangent; 。 5. The method for extracting the amplitude and phase of a multi-frequency time-varying mixed signal based on the RLS algorithm according to claim 4, characterized in that, phase phase unwrapping, traversing the phase from front to back when the phase difference between adjacent points is greater than or equal to phase of the latter point and all points thereafter when the phase difference between adjacent points is less than or equal to phase of the latter point and all points thereafter obtaining the true phase .

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