High-precision vibration displacement extraction method based on FMCW radar

Abstract

The invention provides a high-precision vibration displacement extraction method based on an FMCW radar, and the method comprises the steps: obtaining a beat signal, and carrying out the data preprocessing of the beat signal; data optimization is carried out on the pre-processed beat signal to obtain an optimal beat signal, and the data optimization comprises the steps that an objective function is constructed based on a maximum likelihood estimation method, a Nelder-Mead optimization algorithm is applied to the objective function, a beat frequency estimation value obtained based on a zero-filling FFT method is used as an initial guess value of the Nelder-Mead optimization algorithm, and the optimal beat signal is obtained. The optimal beat frequency is determined through iterative positioning; based on the optimal beat frequency, a maximum likelihood estimation method is utilized to obtain a phase time sequence of beat signals under different signal-to-noise ratio conditions, and then a vibration displacement time sequence is obtained. The method is high in measurement accuracy and can be used for performance evaluation and optimization design of a radar system.

Description

Technical Field

[0001] The present application belongs to the technical field of radar signal processing, and in particular, relates to a high-precision vibration displacement extraction method based on FMCW radar. Background Art

[0002] FMCW radar has the advantages of non-contact, high precision and high efficiency, and has been used in vibration analysis, structural monitoring, health detection and object tracking. It is expected to promote the realization of the Internet of Things, covering smart cities, smart homes, industrial automation and other fields. The non-contact displacement measurement provided by FMCW radar technology can greatly make up for the shortcomings of traditional methods, such as cumbersome sensor installation, susceptibility to environmental noise, and interference with the object being measured.

[0003] Traditional non-contact displacement measurement technologies include laser triangulation, structured light, and visual measurement. Among them, the laser triangulation method projects a laser beam onto the surface of the object to be measured and uses the position change of the light spot to calculate the displacement. This method has a fast response speed and is suitable for objects of various materials and shapes; the structured light method projects a grating or stripe light onto the surface of the object and measures the displacement by analyzing the changes in the stripes. This method can achieve high-precision measurement and has good anti-interference performance; visual measurement analyzes the position change of the object to be measured through digital image processing. This method is suitable for objects with complex shapes and dynamic changes. However, the above traditional methods have certain limitations in practical applications, such as complex operation, limited measurement range and accuracy, etc.

[0004] As an emerging non-contact measurement method, FMCW radar has shown great potential in vibration displacement measurement with its unique advantages. FMCW radar extracts the vibration information of the target by emitting continuously modulated microwave signals and analyzing the received echo signals. Compared with traditional non-contact measurement methods, FMCW radar has stronger anti-interference ability, wider measurement range and higher accuracy, so it is very suitable for measurement in complex environments and monitoring of dynamic processes.

[0005] In recent years, vibration displacement extraction technology based on FMCW has attracted extensive attention. Anghel et al. improved the resolution and detection capability of FMCW radar systems by adopting outlier transceivers and advanced nonlinear correction algorithms. Xiong et al. proposed an approximate MLE method to extract the phase history of the beat signal over multiple scanning cycles. Park et al. studied a signal processing algorithm for extracting human cardiopulmonary vibration information, which combines DC offset compensation and arc tangent demodulation. Wang et al. proposed a gesture detection method to estimate distance and Doppler parameters by performing FFT on the raw gesture data. Tian et al. introduced a vibration similarity index for rapid positioning of vibrating objects, thereby reducing the time required for vibration parameter estimation. Xiong et al. proposed a scanning microwave vibrometer method that uses phase-encoded synthetic beam scanning and linear FMCW technology for full-field and long-range vibration measurement. Wang et al. used an edge-driven phase demodulator to process the rectified square wave intermediate signal. It is believed that this method can eliminate detection zeros and maintain constant gain without four-phase demodulation. Liu et al. studied a cumulative imaging and decoupled tracking method to accurately measure the full-field displacement of nearby targets. Lv et al. studied a time-domain phase demodulation technique to improve the accuracy and efficiency of non-contact displacement detection by reconstructing motion patterns. It must be mentioned that existing studies have not considered beat frequency optimization and its impact on vibration information extraction under different SNR conditions.

[0006] In summary, existing vibration displacement extraction methods have certain limitations and limited measurement accuracy. Summary of the invention

[0007] In view of this, the present application aims to propose a high-precision vibration displacement extraction method based on FMCW radar to solve the limitations of existing vibration displacement extraction methods and the problems of limited measurement accuracy.

[0008] To achieve the above purpose, the technical solution of this application is implemented as follows:

[0009] The present application provides a high-precision vibration displacement extraction method based on FMCW radar, comprising:

[0010] Acquire a beat signal, and perform data preprocessing on the beat signal;

[0011] Performing data optimization on the preprocessed beat signal to obtain an optimal beat signal, wherein the data optimization includes: constructing an objective function based on a maximum likelihood estimation method, applying a Nelder-Mead optimization algorithm to the objective function, and using a beat frequency estimation value obtained based on a zero-filled FFT algorithm as an initial guess value of the Nelder-Mead optimization algorithm to iteratively locate and determine the optimal beat frequency;

[0012] Based on the optimal beat frequency, the maximum likelihood estimation method is used to obtain the phase time series of the beat signal under different signal-to-noise ratio conditions, and then the vibration displacement time series is obtained.

[0013] Furthermore, the beat signal of the i-th scanning cycle is obtained, and its formula is expressed as:

[0014]

[0015] Among them, f b represents the beat frequency, ε(t) represents Gaussian white noise, θ0 represents the initial phase, and T represents the pulse duration;

[0016] The tail of the beat signal within a scanning cycle is zero-filled, and the beat signal after zero-filling is fast Fourier transformed to obtain the beat frequency estimation value, and the estimation value formula is expressed as:

[0017]

[0018] Among them, f s represents the sampling frequency, N represents the signal length after zero padding, and the beat signal after zero padding is recorded as S B (iT+t1), fft[·] represents fast Fourier transform, abs{·} represents taking the absolute value, and max(·) represents searching for the maximum value.

[0019] Furthermore, the objective function is expressed as:

[0020]

[0021] in, represents the beat frequency to be estimated, S Bi represents the beat signal with Gaussian white noise, A represents the amplitude, represents the phase to be estimated.

[0022] Furthermore, the beat frequency estimation value obtained based on the zero-filled FFT method is used as the initial guess value of the Nelder-Mead optimization algorithm to iteratively locate the optimal beat frequency, which is expressed as follows:

[0023]

[0024] Among them, min(·) means searching for the minimum value; represents the initial beat frequency of the iteration; represents the initial beat frequency after estimation using zero-padded FFT.

[0025] Furthermore, the phase time series formula is:

[0026]

[0027] Where arg[·] represents the extracted phase angle, M represents the number of discrete points in the frequency sweep period, and S B (iT+nT s ) represents the discrete value of the beat signal in the i-th frequency sweep cycle, T s Indicates the sampling interval.

[0028] Furthermore, the displacement time series is calculated by the phase time series formula, and its formula is expressed as:

[0029]

[0030] Among them, Δx represents the displacement change, λ c represents the carrier wavelength, Indicates the phase change.

[0031] Compared with the prior art, the high-precision vibration displacement extraction method based on FMCW radar described in this application has the following beneficial effects:

[0032] The present application describes a high-precision vibration displacement extraction method based on FMCW radar, which mainly solves the important problem of the operational limitations and limited measurement accuracy of existing vibration displacement measurement methods, and focuses on the influence of the optimal beat frequency under different SNRs using different sampling frequencies on subsequent vibration displacement extraction; the method is easy to operate and has high measurement accuracy, and is used for performance evaluation and optimization design of radar systems. Experimental results show that the method proposed in this embodiment can be used for high-precision measurement of target vibration displacement. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0034] Figure 1 This is a flow chart of a high-precision vibration displacement extraction method based on FMCW radar described in an embodiment of the present application;

[0035] Figure 2 This is an error comparison diagram of the phase time series of the beat signal and the actual phase time series obtained by combining the optimal beat frequency with the MLE method in the embodiment of the present application;

[0036] Figure 3 For the embodiment of this application Figure 2Based on this, different sampling frequencies are used at different SNRs to obtain a comparison chart of the root mean square error between the beat signal phase time series and the actual phase time series. DETAILED DESCRIPTION

[0037] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0038] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should be the usual meanings understood by people with ordinary skills in the field to which the present application belongs. The "first", "second" and similar words used in the embodiments of the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Including" or "comprising" and similar words mean that the elements or objects appearing in front of the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0039] Explanation of professional terms:

[0040] Nelder-Mead: Also known as the downhill simplex method, it is an algorithm for finding the local minimum of a multivariate function. Its advantage is that it does not require the function to be differentiable and can converge to the local minimum quickly. The algorithm requires an initial point in the function's independent variable space and starts from this point to find the local minimum.

[0041] MLE: Maximum Likelihood Estimation method.

[0042] FFT: Fast Fourier Transform.

[0043] SNR: signal-to-noise ratio.

[0044] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0045] See also Figure 1 As shown, this embodiment provides a high-precision vibration displacement extraction method based on FMCW radar, which specifically includes the following steps:

[0046] Step S101, obtaining a beat signal, and performing data preprocessing on the beat signal;

[0047] Specifically, in this embodiment, numerical simulation is used to verify the robustness of the proposed vibration displacement extraction method. Table 1 lists the simulation parameters used. Considering the point scatterer, the historical phase change is the superposition of two sinusoidal signals. Therefore, the beat signal of the i-th scanning cycle can be given by the following formula:

[0048]

[0049] Among them, f b represents the beat frequency. The beat frequency f in this embodiment b Take 2562, ε(t) is Gaussian white noise.

[0050] In this embodiment, the preprocessing of the acquired beat signal includes but is not limited to analog-to-digital conversion, signal filtering and other operations, which will not be described in detail here.

[0051] Step S102, performing data optimization on the preprocessed beat signal to obtain an optimal beat signal, wherein the data optimization includes: constructing an objective function based on a maximum likelihood estimation method, applying a Nelder-Mead optimization algorithm to the objective function, and using a beat frequency estimation value obtained based on a zero-filled FFT algorithm as an initial guess value of the Nelder-Mead optimization algorithm to iteratively locate and determine the optimal beat frequency.

[0052] Specifically, in this embodiment, first, the objective function is derived using MLE. Subsequently, the optimal beat frequency is located by applying the Nelder-Mead algorithm to the objective function, where the estimated beat frequency based on the zero-filled FFT technique is used as an initial guess for iteration. Once the iteration is completed, the optimal beat frequency estimate is found.

[0053] First, perform zero-filled FFT on the tail of the beat signal within a scanning cycle to make its length twice that of the original signal. In this way, the beat frequency estimate is obtained as:

[0054]

[0055] Among them, f s is the sampling frequency; N is the signal length after zero padding; the beat signal after zero padding is recorded as S B (iT+t1); fft[·] means FFT; abs{·} means taking the absolute value; max(·) means searching for the maximum value.

[0056] Since the relevant scanning period is arbitrary, i can be set to 0 without loss of generality. Zero padding the signal before FFT can improve the resolution of the spectrum and make the peaks on the spectrum clearer. It should be noted that the zero-padding FFT method does not add any information to the signal, but only improves the visual resolution of the spectrum. Therefore, this algorithm can quickly estimate the beat frequency, but the accuracy is limited.

[0057] For the convenience of expression, the beat signal with Gaussian white noise is simplified to S Bi From the beat signal formula, we can see that within a given time, the beat signal follows a Gaussian distribution, and its probability density function (PDF) is

[0058]

[0059] Among them, the mean is zero and the variance is σ 2 , μ is the expected value. According to the beat frequency estimation formula, the likelihood function can be obtained:

[0060]

[0061] in, is the beat frequency to be estimated, A is the amplitude, and A is usually set to 1 without loss of generality. Represents the phase to be estimated. Using the likelihood function, the objective function can be obtained as:

[0062]

[0063] because is a constant term and can therefore be ignored when searching for the maximum value. In addition, by taking The opposite value of can be used to transform the search for the maximum value into the search for the minimum value, simplifying the objective function to:

[0064]

[0065] In order to find the minimum value of the objective function, the Nelder-Mead optimization algorithm is used. The above beat frequency estimation based on zero-filled FFT can be used as the initial guess value (i.e., the initial point) of the Nelder-Mead algorithm.

[0066]

[0067] Among them, min(·) means searching for the minimum value; represents the initial beat frequency of the iteration; represents the beat frequency estimated using zero-padded FFT.

[0068] Step S103: Based on the optimal beat frequency, the phase time series of the beat signal under different signal-to-noise ratio conditions is obtained by using the maximum likelihood estimation method, and then the vibration displacement time series is obtained.

[0069] Specifically, in this embodiment, the optimal beat frequency is substituted into the following formula to obtain the phase time series.

[0070]

[0071] Where arg[·] represents the extracted phase angle; M is the number of discrete points in the frequency sweep period; S B (iT+nT s ) is the discrete value of the beat signal in the i-th frequency sweep cycle, T is the pulse duration, T s is the sampling interval.

[0072] Substitute the phase time series into the following formula to obtain the displacement time series.

[0073]

[0074] Among them, Δx represents the displacement change, λ c represents the carrier wavelength, Indicates the phase change.

[0075] The method described in this embodiment mainly solves the important problem of the operational limitations and limited measurement accuracy of the existing vibration displacement measurement methods, and focuses on the influence of the optimal beat frequency under different SNRs using different sampling frequencies on the subsequent vibration displacement extraction. The method is easy to operate and has high measurement accuracy. It is used for performance evaluation and optimization design of radar systems. Experimental results show that the method proposed in this embodiment can be used for high-precision measurement of target vibration displacement.

[0076] When the simulation test is performed based on the above method, the set simulation parameters are shown in Tables 1 and 2. Table 3 is a comparison chart of the beat frequency estimation results obtained based on this method and the estimation results obtained by the existing solution.

[0077] Table 1 is as follows:

[0078] parameter Numeric <![CDATA[Beat frequency (f b )]]> 2562Hz <![CDATA[Sampling frequency (f s )]]> 60kHz Signal-to-Noise Ratio (SNR) 20dB <![CDATA[Initial phase (θ0)]]> 8 / π

[0079] Table 2 is as follows:

[0080]

[0081]

[0082] Table 3 shows the comparison of the beat frequency estimation results.

[0083] algorithm Beat frequency estimated average value (Hz) Estimation error (Hz) <![CDATA[Estimated variance (Hz 2 )]]> This method 2562.0087 0.0087 0.1055 Traditional FFT 2547 15 /

[0084] Table 3 shows the estimation results obtained based on the method described in this embodiment and the simulation parameters shown in Table 1. From the table, it can be seen that the estimation errors and variances of the traditional FFT and the proposed method.

[0085] Figure 2 The phase time series results obtained by FMCW radar based on the simulation parameters shown in Table 1 are given. It can be seen from the figure that the estimated phase time series is basically consistent with the actual value, and the difference between the two is negligible, indicating the accuracy of phase extraction and providing a simple and high-precision vibration displacement measurement method.

[0086] Figure 3 The phase time series results obtained under different SNRs using different sampling frequencies of the FMCW radar are given based on the simulation parameters shown in Table 2. As can be seen from the figure, as the sampling frequency and SNR continue to increase, the root mean square error value of the phase continues to decrease, indicating an increase in measurement accuracy.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

[0088] The embodiments of the present application are intended to cover all such substitutions, modifications and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present application should be included in the scope of protection of the present application.

Claims

1. A high-precision vibration displacement extraction method based on FMCW radar, characterized in that: include: Acquire a beat signal, and perform data preprocessing on the beat signal; Performing data optimization on the preprocessed beat signal to obtain an optimal beat signal, wherein the data optimization includes: constructing an objective function based on a maximum likelihood estimation method, applying a Nelder-Mead optimization algorithm to the objective function, and using a beat frequency estimation value obtained based on a zero-filled FFT algorithm as an initial guess value of the Nelder-Mead optimization algorithm to iteratively locate and determine the optimal beat frequency; Based on the optimal beat frequency, the maximum likelihood estimation method is used to obtain the phase time series of the beat signal under different signal-to-noise ratio conditions, and then the vibration displacement time series is obtained.

2. The method according to claim 1, characterized in that The beat signal of the i-th scanning cycle is obtained, and its formula is expressed as: Among them, f b represents the beat frequency, ε(t) represents Gaussian white noise, θ0 represents the initial phase, and T represents the pulse duration; The tail of the beat signal within a scanning cycle is zero-filled, and the beat signal after zero-filling is fast Fourier transformed to obtain the beat frequency estimation value, and the estimation value formula is expressed as: Among them, f s represents the sampling frequency, N represents the signal length after zero padding, and the beat signal after zero padding is recorded as S B (iT+t1), fft[·] represents fast Fourier transform, abs{·} represents taking the absolute value, and max(·) represents searching for the maximum value.

3. The method according to claim 2, characterized in that The objective function is expressed as: in, represents the beat frequency to be estimated, S Bi represents the beat signal with Gaussian white noise, A represents the amplitude, represents the phase to be estimated.

4. The method according to claim 3, characterized in that The beat frequency estimate obtained based on the zero-filled FFT method is used as the initial guess value of the Nelder-Mead optimization algorithm to iteratively locate the optimal beat frequency. The formula is expressed as: Among them, min(·) means searching for the minimum value; represents the initial beat frequency of the iteration; represents the initial beat frequency after estimation using zero-padded FFT.

5. The method according to claim 4, characterized in that The phase time series formula is: Where arg[·] represents the extracted phase angle, M represents the number of discrete points in the frequency sweep period, and S B (iT+nT s ) represents the discrete value of the beat signal in the i-th frequency sweep cycle, T s Indicates the sampling interval.

6. The method according to claim 5, characterized in that The displacement time series is calculated by the phase time series formula, and its formula is expressed as: Among them, Δx represents the displacement change, λ c represents the carrier wavelength, Indicates the phase change.

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