A method for estimating frequency, amplitude and phase of single-frequency sinusoidal signal based on minimum MSE

Abstract

The present invention discloses a method for estimating the frequency, amplitude and phase of a single-frequency sinusoidal signal based on minimum MSE, including taking the frequency estimation results of an M‑Rife algorithm and an HAQSE algorithm as two initial frequency estimation results, fitting the signal to be estimated using the two initial frequency estimation results and a three-parameter or four-parameter sinusoidal fitting algorithm, obtaining two corresponding fitting results, and respectively calculating the MSE between the two fitting results and the signal to be estimated, and selecting the estimation result with the smaller MSE as the starting value of the frequency search. Then, iterate in an interval near the starting value of the frequency search, and find the estimated frequency corresponding to the minimum MSE value in the interval as the frequency estimation result. The present invention can not only accurately estimate the frequency of a single-frequency sinusoidal signal, bring the estimated frequency into a three-parameter or four-parameter sinusoidal fitting algorithm, but also accurately estimate the amplitude and phase of the signal, thereby obtaining all physical quantities of the single-frequency signal.

Description

Technical Field

[0001] The invention relates to the technical field of signal processing, and in particular to a method for estimating the frequency, amplitude and phase of a single-frequency sinusoidal signal based on a minimum MSE. Background Art

[0002] The frequency, amplitude and phase of a single-frequency sinusoidal signal are important physical quantities that characterize a single-frequency sinusoidal signal, among which the frequency is the most important physical quantity of a single-frequency sinusoidal signal.

[0003] In engineering applications, we often need to estimate the frequency of certain signals. Frequency estimation refers to solving the problem of signal frequency estimation in different frequency systems or non-cooperative systems by calculating the signal sampling values, so as to complete the filter design, signal modulation and demodulation and other tasks more targeted. The frequency estimation of sinusoidal signals has important applications in traditional industries such as microwave communications, electronic reconnaissance, sonar and radar signal processing, as well as emerging fields such as speech signal processing and brain wave processing. Therefore, the frequency estimation of sinusoidal signals is an important task.

[0004] From the Fourier transform, we know that any signal can be regarded as the weighted addition of several sinusoidal signals with different frequencies, so the significance of accurate frequency estimation of sinusoidal signals is obvious. Gaussian white noise is the most commonly used noise model when dealing with signal problems. In theoretical analysis and practical engineering applications, it is often necessary to deal with signals under the background of Gaussian white noise, so the frequency estimation of sinusoidal signals under the background of Gaussian white noise is of great research value.

[0005] The prior art generally adopts a frequency estimation algorithm based on FFT, a Rife algorithm, an M-Rife algorithm and a HAQSE (hybrid A&M and q-shift estimator) algorithm.

[0006] The FFT-based frequency estimation algorithm has a "fence effect", which will cause a huge estimation error in the case of non-integer period sampling.

[0007] In the Rife algorithm, when the signal frequency is located in the center area of ​​two adjacent quantized frequency points of Discrete Fourier Transform (DFT), the estimation accuracy of the Rife algorithm is high, and the estimation results at other positions have large deviations.

[0008] When the signal-to-noise ratio of the estimated signal of the M-Rife algorithm is low, the frequency estimation accuracy is poor.

[0009] When the signal-to-noise ratio of the estimated signal of the HAQSE (hybrid A&M and q-shift estimator) algorithm is high, the frequency estimation accuracy is poor.

[0010] In view of the above problems, the present invention provides a method for estimating the frequency, amplitude and phase of a single-frequency sinusoidal signal based on minimum MSE, which can accurately estimate the frequency of the single-frequency sinusoidal signal. Summary of the invention

[0011] The invention provides a single-frequency sinusoidal signal frequency, amplitude and phase estimation method based on minimum MSE, which can accurately estimate the frequency of the single-frequency sinusoidal signal.

[0012] The object of the present invention is to provide a method for estimating the frequency, amplitude and phase of a single-frequency sinusoidal signal based on minimum MSE, the estimation method comprising the following steps:

[0013] Step 1: Perform FFT on the digital signal x[n] to obtain:

[0014]

[0015] Where X[k] is the result of FFT of x[n], A(unknown) is the amplitude of the signal, is the phase of the signal, j is the imaginary unit, f(unknown) is the signal frequency, f s is the sampling rate, N is the length of the signal, and W[k] is the FFT result of the noise in the signal;

[0016] Step 2: Use X[k], M-Rife algorithm and HAQSE algorithm to perform frequency estimation on the signal to be estimated x[n], and the estimated results are f1 and f2 respectively;

[0017] Step 3: Substitute the estimated frequencies f1 and f2 into the three-parameter or four-parameter sine fitting algorithm to obtain the estimated sine signals as follows:

[0018]

[0019] Among them, f1 and f2 are the frequency estimation results obtained in step 2. Amp1 and φ 01 Substitute the three-parameter or four-parameter sine fitting algorithm for f1; Amp2 and φ 02 is the result obtained by substituting three-parameter or four-parameter sine fitting algorithm for f2. s is the sampling rate;

[0020] Step 4: Calculate the MSE of the estimated signals x[n] and x1[n], denoted as MSE1, and calculate the MSE of the estimated signals x[n] and x2[n], denoted as MSE2. If MSE1≤MSE2, the initial estimated frequency is f0=f1, and x0[n]=x1[n]. Otherwise, the initial estimated frequency is f0=f2 and x0[n]=x2[n].

[0021] Step 5: When x0[n] obtained in the fourth step is a signal without noise, and the signal to be estimated x[n] is a signal containing noise, then the noise is noise=x[n]-x0[n], and the signal-to-noise ratio of the signal to be estimated x[n] is calculated, denoted as snr;

[0022] Step 6: Use iterative algorithm to estimate signal frequency.

[0023] Furthermore, the specific calculation steps of the iterative algorithm in step six are as follows:

[0024] Step 1: According to the signal-to-noise ratio snr estimated in step 5, determine the iteration interval step size BW: if snr≤0, then the iteration interval step size BW=512Hz; if snr>0, then the iteration interval step size BW=32Hz;

[0025] Step 2, large interval iteration: Iterate at equal intervals in the frequency interval [f0-BW, f0+BW], with a total of 5 frequency points, namely f0-BW, f0-BW / 2, f0, f0+BW / 2, f0+BW. Using these 5 frequency points, according to the algorithms of steps 3 and 4, 5 MSEs are obtained respectively. The two smallest MSEs are selected and recorded as MSE01 and MSE02 respectively, and the corresponding frequency points are recorded as f 01 and f 02 ;

[0026] Step 3: The first round of small-cell iteration: at frequency f 01 and f 02 Iterate at equal intervals, for a total of 5 frequency points. According to the algorithms in step 3 and step 4, 5 MSEs are obtained respectively. The two smallest MSEs are selected and recorded as MSE11 and MSE12 respectively. The corresponding frequency points are recorded as f 11 and f 12 ;

[0027] Step 4: Repeat the process in step 3 to further reduce the interval and perform the second, third and fourth rounds of small interval iterations. The frequency corresponding to the minimum MSE of the fourth round of small interval iteration is the final estimated frequency result f out ; frequency f out The amplitude and phase obtained by substituting the three-parameter or four-parameter sine fitting algorithm are the final amplitude and phase estimation results.

[0028] The present invention has the following advantages: the present invention brings the frequency estimation result into a three-parameter or four-parameter sinusoidal fitting algorithm to obtain an estimated signal, and then obtains the MSE between the estimated signal and the signal to be estimated, and the estimation result corresponding to the minimum MSE is the optimal result, which provides a clear evaluation index for the accuracy of frequency estimation, and can always obtain better estimation results, and can obtain all physical quantities (frequency, amplitude and phase) of a single-frequency sinusoidal signal.

[0029] The iterative algorithm proposed in the present invention only needs to calculate a few fitting values, which greatly reduces the number of iterations and the amount of calculation, and can flexibly increase or decrease the number of iterations and the amount of calculation according to actual needs (such as estimation accuracy), thereby obtaining an ideal estimation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a diagram of the frequency estimation iterative process of the present invention;

[0031] Figure 2 It is a comparison diagram of the frequency estimation results of the present invention. DETAILED DESCRIPTION

[0032] The present invention provides a method for estimating the frequency, amplitude and phase of a single-frequency sinusoidal signal based on minimum MSE. The estimation method comprises the following steps:

[0033] Step 1: Perform FFT on the digital signal x[n] to obtain:

[0034]

[0035] Where X[k] is the result of FFT of x[n], A(unknown) is the amplitude of the signal, is the phase of the signal, j is the imaginary unit, f(unknown) is the signal frequency, f s is the sampling rate, N is the length of the signal, and W[k] is the FFT result of the noise in the signal;

[0036] Step 2: Use X[k], M-Rife algorithm and HAQSE algorithm to perform frequency estimation on the signal to be estimated x[n], and the estimated results are f1 and f2 respectively;

[0037] Step 3: Substitute the estimated frequencies f1 and f2 into the three-parameter or four-parameter sine fitting algorithm to obtain the estimated sine signals as follows:

[0038]

[0039] Among them, f1 and f2 are the frequency estimation results obtained in step 2, Amp1 and φ 01 Substitute the three-parameter or four-parameter sine fitting algorithm for f1, Amp2 and φ02 is the result obtained by substituting f2 into the three-parameter or four-parameter sine fitting algorithm, f s is the sampling rate;

[0040] Step 4: Calculate the MSE of the estimated signals x[n] and x1[n], denoted as MSE1, and calculate the MSE of the estimated signals x[n] and x2[n], denoted as MSE2. If MSE1≤MSE2, the initial estimated frequency is f0=f1, and x0[n]=x1[n]. Otherwise, the initial estimated frequency is f0=f2 and x0[n]=x2[n].

[0041] Step 5: When x0[n] obtained in the fourth step is a signal without noise, and the signal to be estimated x[n] is a signal containing noise, then the noise is noise=x[n]-x0[n], and the signal-to-noise ratio of the signal to be estimated x[n] is calculated, denoted as snr;

[0042] Step 6: Use iterative algorithm to estimate signal frequency.

[0043] Furthermore, the specific calculation steps of the iterative algorithm in step six are as follows:

[0044] Step 1: According to the signal-to-noise ratio snr estimated in step 5, determine the iteration interval step size BW: if snr≤0, then the iteration interval step size BW=512Hz; if snr>0, then the iteration interval step size BW=32Hz;

[0045] Step 2, large interval iteration: Iterate at equal intervals in the frequency interval [f0-BW, f0+BW], with a total of 5 frequency points, namely f0-BW, f0-BW / 2, f0, f0+BW / 2, f0+BW. Using these 5 frequency points, according to the algorithms of steps 3 and 4, 5 MSEs are obtained respectively. The two smallest MSEs are selected and recorded as MSE01 and MSE02 respectively, and the corresponding frequency points are recorded as f 01 and f 02 ;

[0046] Step 3: The first round of small-cell iteration: at frequency f 01 and f 02 Iterate at equal intervals, for a total of 5 frequency points. According to the algorithms in step 3 and step 4, 5 MSEs are obtained respectively. The two smallest MSEs are selected and recorded as MSE11 and MSE12 respectively. The corresponding frequency points are recorded as f 11 and f 12 ;

[0047] Step 4: Repeat the process in step 3 to further reduce the interval and perform the second, third and fourth rounds of small interval iterations. The frequency corresponding to the minimum MSE of the fourth round of small interval iteration is the final estimated frequency result f out ; frequency fout The amplitude and phase obtained by substituting the three-parameter or four-parameter sine fitting algorithm are the final amplitude and phase estimation results.

[0048] In this embodiment, Figure 2 As shown in FIG. 1 , under the same conditions, the estimation result within the signal-to-noise ratio (-10 to 100) dB is closer to the Cramer-Rao Lower Bound (CRLB) than other algorithms.

[0049] In this embodiment, not only can the frequency of the single-frequency sinusoidal signal be accurately estimated, and the estimated frequency can be brought into a three-parameter or four-parameter sinusoidal fitting algorithm, but the amplitude and phase of the signal can also be accurately estimated, thereby obtaining all physical quantities of the single-frequency signal.

[0050] Although the specific implementation of the present invention is described in detail in conjunction with the drawings, it should not be understood as limiting the scope of protection of this patent. Within the scope described in the claims, various modifications and variations that can be made by those skilled in the art without creative work still fall within the scope of protection of this patent.

Claims

1. A method for estimating frequency, amplitude and phase of a single-frequency sinusoidal signal based on minimum MSE, characterized by: The estimation method comprises the following steps: Step 1: Perform FFT on the digital signal x[n] to obtain: ; Where X[k] is the result of FFT of x[n], A is the amplitude of the signal, φ0 is the phase of the signal, j is the imaginary unit, f is the signal frequency, f s is the sampling rate; N is the length of the signal, W[k] is the FFT result of the noise in the signal; k is the index value of X[k]; Step 2: Use X[k], M-Rife algorithm and HAQSE algorithm to perform frequency estimation on the signal to be estimated x[n], and the estimation results are f1 and f2 respectively; Step 3: Substitute the estimated frequencies f1 and f2 into the three-parameter or four-parameter sine fitting algorithm to obtain the estimated sine signals as follows: ; ; Among them, f1 and f2 are the frequency estimation results obtained in step 2, Amp1 and φ 01 Substitute f1 into the result obtained by the three-parameter or four-parameter sine fitting algorithm, Amp2 and φ 02 Substitute f2 into the result of the three-parameter or four-parameter sine fitting algorithm, f s is the sampling rate; Step 4: Calculate the MSE of the estimated signals x[n] and x1[n], denoted as MSE1, and calculate the MSE of the estimated signals x[n] and x2[n], denoted as MSE2. If MSE1≤MSE2, the initial estimated frequency is f0=f1, and x0[n]=x1[n]. Otherwise, the initial estimated frequency is f0=f2 and x0[n]=x2[n]. Step 5: When x0[n] obtained in step 4 is a signal without noise, and the signal to be estimated x[n] is a signal containing noise, then the noise is noise = x[n]- x0[n], and the signal-to-noise ratio of the signal to be estimated x[n] is calculated, denoted as snr; Step 6: Use an iterative algorithm to estimate the signal frequency, and then substitute the final estimated signal frequency into the amplitude and phase obtained by the three-parameter or four-parameter sine fitting algorithm, which are the final amplitude and phase estimation results.

2. The method for estimating frequency, amplitude and phase of a single-frequency sinusoidal signal based on minimum MSE as claimed in claim 1, characterized in that: The specific calculation steps of the iterative algorithm in step 6 are as follows: Step 61: According to the signal-to-noise ratio snr estimated in step 5, determine the iteration interval step size BW: if snr≤0, then the iteration interval step size BW=512 Hz; if snr>0, then the iteration interval step size BW=32 Hz; Step 62, large interval iteration: Iterate at equal intervals in the frequency interval [f0-BW, f0+BW], for a total of 5 frequency points, namely f0-BW, f0-BW / 2, f0, f0+BW / 2, f0+BW. Using these 5 frequency points, according to the algorithms of steps 3 and 4, 5 MSEs are obtained respectively. The two smallest MSEs are selected and recorded as MSE01 and MSE02 respectively, and the corresponding frequency points are recorded as f 01 and f 02 ; Step 63, the first round of inter-cell iteration: at frequency point f 01 and f 02 Iterate at equal intervals between the two frequencies, for a total of 5 frequency points. According to the algorithms in step 3 and step 4, 5 MSEs are obtained respectively. The two smallest MSEs are selected and recorded as MSE11 and MSE12 respectively. The corresponding frequency points are recorded as f 11 and f 12 ; Step 64, repeat the process of step 63, further reduce the interval, and perform the second, third and fourth rounds of small interval iterations. The frequency corresponding to the minimum MSE of the fourth round of small interval iteration is the final estimated signal frequency; the amplitude and phase obtained by substituting the final estimated signal frequency into the three-parameter or four-parameter sine fitting algorithm are the final amplitude and phase estimation results.

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