Continuous wave radar speed measurement method based on single-channel mixing and second derivative signal thereof

Abstract

The invention belongs to the technical field of continuous wave radar speed measurement, and discloses a continuous wave radar speed measurement method based on single-channel mixing and a second derivative signal thereof, which comprises the following steps of: S1, acquiring a discrete single-channel mixing signal; s2, acquiring a low-order discrete single-channel frequency mixing signal; s3, acquiring a second derivative signal; step S4, constructing a Toeplitz square matrix; s5, constructing a generalized characteristic equation; and S6, solving the generalized eigenvalue. According to the continuous wave radar speed measurement method based on the single-channel mixing and the second derivative signal of the single-channel mixing, on the basis of an existing single-channel single-frequency continuous wave radar, accurate solution of the target speed is achieved by solving a generalized characteristic equation of the mixing signal, and the accurate speed of a moving target is obtained; compared with a traditional method, the method effectively solves the problem that the speed measurement precision is limited by the sampling frequency and the frequency resolution.

Description

Technical Field

[0001] The invention relates to the technical field of continuous wave radar speed measurement, and in particular to a continuous wave radar speed measurement method based on single-channel frequency mixing and its second-order derivative signal. Background Art

[0002] In the field of traffic speed measurement, continuous wave radar has the advantages of simple equipment, light weight, high speed measurement accuracy and no close-range blind spots, and has been widely used in the speed measurement of vehicle targets. With the development of digital signal processing technology, continuous wave radar mainly uses the digital phase comparison method based on FFT transformation to measure speed, and its speed measurement accuracy is related to spectrum estimation, that is, frequency resolution.

[0003] Spectrum estimation is usually used in radar signal processing. Discrete Fourier transform (DFT), as a basic method in classical spectrum estimation theory, was originally used to calculate the mixing frequency of radar to extract the target distance. Subsequently, the development of fast Fourier transform (FFT) significantly enhanced the application of DFT in frequency domain analysis. However, when there is a fixed sampling interval and a finite length, spectrum leakage and fence effect seriously affect the frequency estimation accuracy of FFT, resulting in ranging errors. To solve these problems, many studies have focused on interpolation techniques, that is, reducing spectrum leakage and fence effect through window functions and interpolation. Despite their popularity, interpolation methods have low accuracy when coherent signals exist in the spectrum.

[0004] At present, frequency estimation methods are mainly divided into time domain and frequency domain methods. Time domain methods include maximum likelihood (ML) algorithm, autoregressive (AR) spectrum estimation method, multiple signal classification (MUSIC) algorithm and signal parameter estimation with rotation invariance technique (ESPRIT) algorithm. Each of the above methods has its own advantages and disadvantages. For example, the ML method has high computational complexity; the AR spectrum estimation method is easily affected by noise and outliers; the MUSIC algorithm has limitations when processing coherent signal sources and has high computational complexity; the ESPRIT algorithm has limitations in small sample size applications, etc.

[0005] Relatively speaking, the frequency domain method is more suitable for real-time signal processing because of its small computational complexity and high efficiency. In essence, it uses FFT transform and frequency refinement technology for accurate frequency estimation. Frequency domain methods mainly include amplitude ratio method, neighbor spectrum refinement method, autocorrelation method and spectrum line fitting method. Although the above methods are simple to calculate, the estimation accuracy is low and they are easily affected by the target distance. Unlike FFT-based techniques, matrix-based singular value decomposition (SVD) and singular spectrum decomposition (SSD) aim to represent the signal as a linear combination of basic variable modes without redundant harmonic components. Although these techniques do not provide spectrum estimation, they act as powerful denoising filters that can separate autocorrelation features from random features. In addition, wavelet transform (WT) and Hilbert-Huang transform (HHT) are often used to extract signal features, but they cannot accurately calculate the frequency of multi-frequency signals.

[0006] In order to achieve accurate calculation of the frequency of the mixing signal, the present invention proposes a continuous wave radar accurate speed measurement method based on a single-channel mixing signal and its second-order derivative signal based on basic theoretical calculations, which can achieve accurate solution of the target speed. Summary of the invention

[0007] The purpose of the present invention is to provide a continuous wave radar speed measurement method based on single-channel mixing and its second-order derivative signal. On the basis of the existing single-channel single-frequency continuous wave radar, the generalized characteristic equation of the mixing signal is solved to achieve accurate solution of the target speed and obtain the accurate speed of the moving target. Compared with the traditional method, the problem that the speed measurement accuracy is limited by the sampling frequency and frequency resolution is effectively solved.

[0008] To achieve the above object, the present invention provides a continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal, comprising the following steps:

[0009] Step S1, obtaining a discrete single-channel mixing signal;

[0010] Step S2, obtaining a low-order discrete single-channel mixing signal;

[0011] Step S3, obtaining a second-order derivative signal;

[0012] Step S4, construct a Toeplitz matrix;

[0013] Step S5, constructing a generalized characteristic equation;

[0014] Step S6: solving the generalized eigenvalue.

[0015] Preferably, in step S1, a discrete single-channel mixing signal is obtained, and the specific process is as follows:

[0016] Step S11: The single-frequency continuous wave radar transmits a signal with a frequency of f0, a period of T, and an initial phase of Amplitude is A T The microwave signal is as follows:

[0017]

[0018] Step S12, the velocity is v r The moving target is reflected and received, and the received signal is as follows:

[0019]

[0020] Where k is the received signal amplitude attenuation coefficient; τ = 2v r t / c is the echo delay caused by the moving target, is the phase of the received signal;

[0021] Step S13: Mix the transmitted signal and the received signal and perform low-pass filtering to obtain a mixed signal, as shown below:

[0022]

[0023] Among them, f d =2v r f0 / c is the Doppler frequency caused by the moving target; is the phase difference between the transmitted signal and the received signal;

[0024] Step S14: digitally sample the mixed signal at a sampling frequency of F. s , the number of sampling points is N, and the discrete mixing signal is obtained as follows:

[0025]

[0026] Preferably, in step S2, a low-order discrete single-channel mixing signal is obtained, and the specific process is as follows:

[0027] Step S21, performing N-point FFT transformation on the discrete mixing signal in step S1 to obtain the frequency spectrum information of the moving target;

[0028] Step S22: Select the spectrum peak point f max , and its left frequency f left =f max -df is used as the reference frequency to construct a reference signal as follows:

[0029]

[0030] Where, df = 1 / T is the frequency sampling interval;

[0031] Step S23, performing left frequency shift processing on the discrete single-channel mixing signal to obtain a low-order discrete single-channel mixing signal, as shown below:

[0032]

[0033] in,

[0034] Preferably, in step S3, the low-order discrete single-channel mixing signal in step S2 is subjected to a second-order derivative to obtain a second-order derivative signal, as shown below:

[0035]

[0036] Preferably, in step S4, according to the low-order discrete single-channel mixing signal and its second-order derivative signal in step S2 and step S3, a corresponding Toeplitz matrix is ​​constructed as shown below:

[0037]

[0038] Among them, the mth row and lth column of the square matrix H can be expressed as:

[0039]

[0040] phalanx The mth row and lth column of can be expressed as:

[0041]

[0042] Preferably, in step S5, the Toeplitz matrix H constructed in step S4 and Using the relationship between the low-order discrete single-channel mixing signal and its second-order derivative signal, the generalized characteristic equation is constructed as follows:

[0043]

[0044] Preferably, in step S6, the generalized characteristic equation of step S5 is solved to obtain a generalized eigenvalue matrix λ, and its maximum eigenvalue is selected, as shown below:

[0045]

[0046] Preferably, in step S7, the speed of the moving target is accurately converted according to the maximum eigenvalue solved in step S6, and the speed of the moving target is as follows:

[0047]

[0048] Therefore, the present invention adopts the above-mentioned continuous wave radar speed measurement method based on single-channel mixing and its second-order derivative signal. On the basis of the existing single-channel single-frequency continuous wave radar, the generalized characteristic equation of the mixing signal is solved to achieve accurate solution of the target speed and obtain the precise speed of the moving target. Compared with the traditional method, it effectively solves the problem that the speed measurement accuracy is limited by the sampling frequency and frequency resolution.

[0049] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The present invention is a flow chart of a continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal. DETAILED DESCRIPTION

[0051] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0052] like Figure 1 As shown, the continuous wave radar speed measurement method based on single-channel mixing and its second-order derivative signal of the present invention includes the following steps:

[0053] Step S1, obtaining a discrete single-channel mixing signal;

[0054] Step S2, obtaining a low-order discrete single-channel mixing signal;

[0055] Step S3, obtaining a second-order derivative signal;

[0056] Step S4, construct a Toeplitz matrix;

[0057] Step S5, constructing a generalized characteristic equation;

[0058] Step S6: solving the generalized eigenvalue.

[0059] Example

[0060] Step S1, obtaining a discrete single-channel mixing signal.

[0061] Step S11: The single-frequency continuous wave radar transmits a signal with a frequency of f0, a period of T, and an initial phase of Amplitude is A T The microwave signal is as follows:

[0062]

[0063] Step S12, the velocity is v r The moving target is reflected and received, and the received signal is as follows:

[0064]

[0065] Where k is the received signal amplitude attenuation coefficient; τ = 2v r t / c is the echo delay caused by the moving target, is the phase of the received signal;

[0066] Step S13: Mix the transmitted signal and the received signal and perform low-pass filtering to obtain a mixed signal, as shown below:

[0067]

[0068] Among them, f d =2v r f0 / c is the Doppler frequency caused by the moving target; is the phase difference between the transmitted signal and the received signal.

[0069] Step S14: digitally sample the mixed signal at a sampling frequency of F. s , the number of sampling points is N, and the discrete mixing signal is obtained as follows:

[0070]

[0071] Step S2: Obtain a low-order discrete single-channel mixing signal.

[0072] Step S21, performing N-point FFT transformation on the discrete mixing signal in step S1 to obtain the frequency spectrum information of the moving target.

[0073] Step S22: Select the spectrum peak point f max , and its left frequency f left =f max -df is used as the reference frequency to construct a reference signal as follows:

[0074]

[0075] Wherein, df=1 / T is the frequency sampling interval.

[0076] Step S23, performing left frequency shift processing on the discrete single-channel mixing signal to obtain a low-order discrete single-channel mixing signal, as shown below:

[0077]

[0078] in,

[0079] Step S3: Obtain a second-order derivative signal.

[0080] The low-order discrete single-channel mixing signal in step S2 is subjected to a second-order derivative to obtain a second-order derivative signal, as shown below:

[0081]

[0082] Step S4: construct a Toeplitz matrix.

[0083] According to the low-order discrete single-channel mixing signal and its second-order derivative signal in step S2 and step S3, the corresponding Toeplitz matrix is ​​constructed as shown below:

[0084]

[0085] Among them, the mth row and lth column of the square matrix H can be expressed as:

[0086]

[0087] phalanx The mth row and lth column of can be expressed as:

[0088]

[0089] Step S5: construct a generalized characteristic equation.

[0090] According to the Toeplitz matrix H constructed in step S4 and Using the relationship between the low-order discrete single-channel mixing signal and its second-order derivative signal, the generalized characteristic equation is constructed as follows:

[0091]

[0092] Step S6: solving the generalized eigenvalue.

[0093] The generalized characteristic equation of step S5 is solved to obtain the generalized eigenvalue matrix λ, and its maximum eigenvalue is selected as shown below:

[0094]

[0095] Step S7: moving target speed conversion.

[0096] According to the maximum eigenvalue solved in step S6, the speed of the moving target is accurately converted, and the speed of the moving target is as follows:

[0097]

[0098] Therefore, the present invention adopts the above-mentioned continuous wave radar speed measurement method based on single-channel mixing and its second-order derivative signal. On the basis of the existing single-channel single-frequency continuous wave radar, the generalized characteristic equation of the mixing signal is solved to achieve accurate solution of the target speed and obtain the precise speed of the moving target. Compared with the traditional method, it effectively solves the problem that the speed measurement accuracy is limited by the sampling frequency and frequency resolution.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal, characterized in that: The following steps are involved: Step S1, obtaining a discrete single-channel mixing signal; Step S2, obtaining a low-order discrete single-channel mixing signal; Step S3, obtaining a second-order derivative signal; Step S4, construct a Toeplitz matrix; Step S5, constructing a generalized characteristic equation; Step S6: solving the generalized eigenvalue.

2. The continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal according to claim 1 is characterized in that: In step S1, a discrete single-channel mixing signal is obtained, and the specific process is as follows: Step S11: The single-frequency continuous wave radar transmits a signal with a frequency of f0, a period of T, and an initial phase of Amplitude is A T The microwave signal is as follows: Step S12, the velocity is v r The moving target is reflected and received, and the received signal is as follows: Where k is the received signal amplitude attenuation coefficient; τ = 2v r t / c is the echo delay caused by the moving target, is the phase of the received signal; Step S13: Mix the transmitted signal and the received signal and perform low-pass filtering to obtain a mixed signal, as shown below: Among them, f d =2v r f0 / c is the Doppler frequency caused by the moving target; is the phase difference between the transmitted signal and the received signal; Step S14: digitally sample the mixed signal at a sampling frequency of F. s , the number of sampling points is N, and the discrete mixing signal is obtained as follows:

3. The continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal according to claim 2 is characterized in that: In step S2, a low-order discrete single-channel mixing signal is obtained, and the specific process is as follows: Step S21, performing N-point FFT transformation on the discrete mixing signal in step S1 to obtain the frequency spectrum information of the moving target; Step S22: Select the spectrum peak point f max , and its left frequency f left =f max -df is used as the reference frequency to construct a reference signal as follows: Where, df = 1 / T is the frequency sampling interval; Step S23, performing left frequency shift processing on the discrete single-channel mixing signal to obtain a low-order discrete single-channel mixing signal, as shown below: in, 4. The continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal according to claim 3 is characterized in that: In step S3, the low-order discrete single-channel mixing signal in step S2 is subjected to a second-order derivative to obtain a second-order derivative signal, as shown below:

5. The continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal according to claim 4 is characterized in that: In step S4, according to the low-order discrete single-channel mixing signal and its second-order derivative signal in step S2 and step S3, a corresponding Toeplitz matrix is ​​constructed as shown below: Among them, the mth row and lth column of the square matrix H can be expressed as: phalanx The mth row and lth column of can be expressed as:

6. The continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal according to claim 5 is characterized in that: In step S5, the Toeplitz matrix H constructed in step S4 and Using the relationship between the low-order discrete single-channel mixing signal and its second-order derivative signal, the generalized characteristic equation is constructed as follows:

7. The continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal according to claim 6 is characterized in that: In step S6, the generalized characteristic equation of step S5 is solved to obtain the generalized eigenvalue matrix λ, and its maximum eigenvalue is selected, as shown below:

8. The continuous wave radar speed measurement method based on single channel mixing and its second-order derivative signal according to claim 7 is characterized in that: In step S7, the speed of the moving target is accurately converted according to the maximum eigenvalue solved in step S6. The speed of the moving target is as follows:

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