FMCW radar high-precision ranging method based on improved dichotomy interpolation

Abstract

The invention discloses an FMCW high-precision distance measurement method based on an improved dichotomy, and aims to solve the problems that the traditional FFT frequency estimation precision is not high and the calculation amount of a narrow-band frequency spectrum refining technology is large. The method is a frequency analysis method based on the combination of FFT and improved dichotomy interpolation refinement. The method comprises the following steps: performing initial frequency estimation by using FFT (Fast Fourier Transform) to obtain an initial amplitude spectrum of a signal, performing iterative interpolation refinement between an initial maximum amplitude and an initial secondary amplitude by using an improved dichotomy, and continuously iteratively reducing a frequency estimation interval to obtain a final frequency estimation result. The actual distance between the radar and the object can be accurately calculated according to the final frequency estimation result and the radar parameters. According to the method, FFT and improved dichotomy interpolation refinement are combined, the precision of frequency estimation and distance measurement is improved, and compared with a traditional refinement method, the calculated amount is smaller, and the real-time performance of radar system distance measurement is improved.

Description

Technical Field

[0001] The invention relates to the technical field of radar signal processing, and in particular to a high-precision distance measurement method for an FMCW radar based on improved binary interpolation. Background Art

[0002] As an important sensing technology in recent years, FMCW radar has developed rapidly and has been widely used in the fields of autonomous driving, industrial ranging, medical diagnosis, etc. Its advantages over traditional pulse radars are insensitivity to changes in temperature, pressure and chemical properties, strong stability and high anti-interference ability. Therefore, in industrial ranging applications, FMCW radar is gradually replacing traditional pulse radars. In the FMCW ranging system, the radar transmission signal is generally a sweep signal modulated by a sawtooth wave or a triangle wave. After the transmitted signal reaches the target object, the reflected signal is received by the radar. Because there is a time delay between the received reflected signal and the transmitted signal. When the two signals are at the same time point, there is a frequency difference between the two signals. The beat signal output after mixing contains frequency information. The target distance can be obtained based on the solved frequency information.

[0003] The frequency of the beat signal is generally obtained through fast Fourier transform (FFT), but this method is limited by the frequency resolution, which seriously affects the accuracy of the beat signal frequency estimation and the accuracy of radar ranging. In order to solve the accuracy problem, a narrowband spectrum refinement technology was subsequently proposed. Only part of the spectrum needs to be refined and interpolated. This method improves the accuracy of frequency estimation and ranging, but it will further increase the amount of calculation and affect the real-time performance of the FMCW radar ranging system. Summary of the invention

[0004] In order to solve the problem of low FFT frequency estimation accuracy and large calculation amount of narrowband spectrum refinement technology, the present invention proposes a high-precision FMCW radar ranging method with improved binary interpolation, which combines FFT and narrowband spectrum refinement technology, first obtains the spectrum of the signal according to FFT, and then uses the improved binary interpolation method to interpolate the spectrum. This method combines the advantages of small FFT calculation amount and high precision of narrowband spectrum refinement technology, improves the accuracy of frequency estimation and ranging accuracy, and enhances the real-time performance of the system.

[0005] The technical solution adopted by the present invention is:

[0006] The FMCW radar high-precision ranging method with improved binary interpolation includes the following steps:

[0007] Step 1: The FMCW radar transmits a linearly transformed carrier signal to the target object and receives an echo signal reflected by the target; Step 2: The carrier signal transmitted by the FMCW radar in step 1 is mixed with the received echo signal to obtain a beat signal x(t);

[0008] Step 3: Use high-speed AD to sample the continuous beat signal x(t) in step 2 to obtain a discrete beat signal x(n);

[0009] Step 4: Perform a fast Fourier transform (FFT) on the discrete beat signal x(n) in step 3 to obtain an amplitude spectrum |X(k)| of the beat signal;

[0010] Step 5: According to the amplitude spectrum |X(k)| of the beat signal in step 4, obtain the initial maximum amplitude |X(k m )| and the initial sub-amplitude|X(k s )|, and the corresponding frequency point k m and k s The final frequency estimation result range is within k m and k s between.

[0011] Step 6: According to the final frequency estimation result range obtained in step 5, use the improved dichotomy method to perform interpolation iteration within the range and convert k m and k s The segments are divided according to the golden ratio of 0.382:0.618, and at the golden section point k ui Interpolate at the golden section point and compare the amplitude |X(k ui )| and the initial maximum amplitude|X(k m )|;

[0012] Step 7: According to the comparison result in step 6, continue to interpolate at the golden section point to obtain the amplitude |X(k ui )|, and keep repeating the operation of step 6 to gradually approach the final frequency estimation result;

[0013] Step 8: When the amplitude at the golden section point |X(k ui )| and the initial maximum amplitude|X(k m )| are equal, the midpoint of the golden section point and the frequency point corresponding to the initial maximum amplitude is the final frequency result f c ;

[0014] Step 9: According to the final frequency result f c , the FMCW radar ranging formula is as follows:

[0015]

[0016] Where: c is the speed of light, T is the modulation signal sweep time, B is the modulation signal sweep bandwidth, and f0 is the frequency of the beat signal. In step 2, the beat signal x(t) is expressed in the time domain as follows:

[0017]

[0018] Where a is the amplitude of the signal; is the initial phase of the signal; w(t) is the noise signal and has no definite expression; f0 represents the true frequency of the signal.

[0019] In step 3, the discrete beat signal x(n) is:

[0020]

[0021] Where: f s is the sampling rate of high-speed AD; N is the number of sampling points; n is the sequence index; w(n) is the discrete noise signal; a represents the amplitude of the signal; The expression representing the discrete signal can also be written as When n takes different values, different.

[0022] In step 4, the fast Fourier transform (FFT) formula is as follows:

[0023]

[0024] Where: k is the index of the frequency value, k e is the frequency index where the amplitude is maximum, is the initial phase of the signal, a is the amplitude of the signal;

[0025] The Fourier transform amplitude is as follows:

[0026]

[0027] Among them: || represents the modulus value.

[0028] In step 5, the initial maximum amplitude and the initial sub-amplitude According to the Fourier transform amplitude formula in step 4, the final frequency estimation result is located at k m and k s between.

[0029] In step 6, the initial maximum amplitude |X(k m )| and the initial sub-amplitude|X(k s )|The corresponding frequency points are k m and ks The gold ratio is 0.382:0.618.

[0030] At the golden point k ui =k m +0.382(k m -k s ) is interpolated, such as Figure 3 As shown, the details are as follows: k m -k s =1, in k ui =k m Interpolate at +0.382 to get the amplitude The interpolation point obtained is (k ui ,|X(k ui )), the maximum and second maximum values ​​become |X(k m )| and |X(k ui )|, the corresponding index is k m and k ui . At this time, the index of the real frequency is located at k m and k ui The interpolation interval is continuously reduced by iterative interpolation through this method until the maximum amplitude and the second maximum amplitude are equal.

[0031] The amplitude at the golden section point is In step 8, the final frequency result f c =f s / N×(k ui +k m ) / 2,f s is the sampling rate of high-speed AD, and N is the number of sampling points.

[0032] The present invention provides a high-precision FMCW radar ranging method based on improved binary interpolation, and the technical effects are as follows:

[0033] 1) The FMCW radar high-precision ranging method provided by the method of the present invention is based on the idea of ​​spectrum refinement. Interpolation and refinement are performed on the spectrum after Fourier transform to obtain a refined spectrum. By searching the refined spectrum, the final frequency f can be found more accurately. c , improving the accuracy of frequency estimation and radar ranging.

[0034] 2) The FMCW radar high-precision ranging method provided by the method of the present invention uses an improved binary search method for interpolation, and there is no need to refine the interpolation of the entire interval. The method has a small amount of calculation and meets the real-time requirements. In addition, it has been verified by experiments that the method can improve the anti-interference ability.

[0035] 3) This method combines FFT and improved binary interpolation refinement to improve the accuracy of frequency estimation and ranging. Compared with traditional refinement methods, the present invention has smaller calculation amount and improves the real-time performance of radar system ranging. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0037] Figure 1 This is a flow chart of the FMCW radar ranging provided by the present invention.

[0038] Figure 2 It is a comparison chart of the FMCW radar high-range measurement algorithm of FFT+parabola fitting, CZT refinement algorithm and the improved dichotomy interpolation algorithm of the present invention.

[0039] Figure 3 Spectrum plot for the golden point interpolation. DETAILED DESCRIPTION

[0040] The FMCW radar high-precision ranging method based on improved binary interpolation combines FFT and improved binary interpolation to improve the accuracy and real-time performance of frequency estimation. This method performs Fourier transform on the collected discrete beat signal to obtain its amplitude |X(k)|. At the initial maximum amplitude |X(k m )| and the initial sub-amplitude|X(k s )|, and after multiple iterations, the search frequency interval is continuously narrowed until the final frequency estimation result f is found. c According to the final frequency estimation result f c And FMCW radar parameters, get the distance d between the radar and the object. This method does not need to refine the spectrum of the entire interval, greatly reduces the amount of calculation, improves the real-time performance of the radar ranging system, and further improves the accuracy of frequency estimation and radar ranging.

[0041] The FMCW radar high-precision ranging method based on improved binary interpolation includes the following steps:

[0042] Step S1: pre-process the beat signal. The detailed steps are as follows:

[0043] Step S1.1: After the FMCW radar transmits a signal that contacts the target object, the reflected signal is received by the FMCW radar, and the transmit signal is mixed with the received signal to obtain a beat signal. a is the amplitude of the signal, is the initial phase of the signal, w(t) is the noise signal with no definite expression.

[0044] Step S1.2: After the continuous time domain beat signal is collected, a discrete beat signal is obtained. f s is the sampling frequency of high-speed AD acquisition, N is the number of sampling points, n is the sequence index, and w(n) is the discrete noise signal.

[0045] Step S1.3: Perform Fourier transform on the discrete beat signal x(n) to obtain the amplitude k is the index of the frequency value, k m is the frequency index where the amplitude is maximum, and || represents the modulus value.

[0046] Step S1.4: Find the maximum spectral line |X(k m )| and the initial second largest spectral line|X(k s )|, and the corresponding frequency point k m and k s .

[0047] Step S2: At the maximum spectral line |X(k m )| and the initial second largest spectral line|X(k s )|, the improved bisection interpolation refinement step includes:

[0048] Step S2.1: Set the initial maximum amplitude |X(k m )| and the initial sub-amplitude|X(k s )|The corresponding frequency points are k m and k s The segments are divided into sections according to the ratio of 0.382:0.618.

[0049] Step S2.2: According to the segmentation points in step S2.1, such as k m <k s , at segment point k ui =k m +0.382 is interpolated. m >k s , at segment point k ui =k m Interpolation is performed at -0.382.

[0050] Step S2.3: Compare the amplitudes of the segment points |X(k ui )| and the initial maximum amplitude|X(k m )|, if |X(k ui )|>|X(k m )|, then another k m =k ui , k s =k m , if |X(k ui )|<|X(k m )|, then another km Keep unchanged, k s =k ui , and continue the loop iteration from S1.4.

[0051] Step S2.4: According to the iteration in step S2.3, when the initial maximum amplitude |X(k m )| and the amplitude at the segmentation point|X(k ui )| are equal, the maximum amplitude k e and the frequency value k at the segment ui The midpoint k c =(k ui +k e ) is the final result, and the final frequency estimation result f c =f s / N×k c .

[0052] Step S3: Use the final frequency estimation result f obtained in step S2.4 c , the FMCW radar ranging formula is as follows:

[0053]

[0054] c is the speed of light, T is the modulation signal sweep time, B is the modulation signal sweep bandwidth, f c is the final frequency estimation result of the beat signal.

[0055] In order to verify the performance of the improved binary interpolation FMCW radar high-precision ranging method proposed in the present invention, FFT+parabola fitting and CZT refinement algorithms are used to compare with the algorithm of the present invention. The simulation parameters are set as follows: sampling rate f s The frequency of the sine signal to be processed is 5kHz, the number of sampling points N is 1024, the frequency of the sine signal to be processed is 5kHz, and the CZT refinement multiple M is 64. The signal-to-noise ratio range is set to -5 to 25dB, and it is increased by 1dB step, and 500 simulation experiments are performed at each signal-to-noise ratio. The Cramer-Rao boundary (CRLB) and the root mean square error (RMSE) are used as standards to verify the advantages of the present invention: The Cramer-Rao boundary formula is as follows:

[0056]

[0057] Where f s is the sampling frequency of high-speed AD acquisition, and SNR is the signal-to-noise ratio.

[0058] The root mean square error formula is as follows:

[0059]

[0060] Where f cis the final frequency estimation result of the beat signal, f i is the real frequency of the beat signal, K=500 is the number of simulations. Figure 2 As shown in the figure, the root mean square error (RMSE) of frequency estimation of three algorithms is compared under different signal-to-noise ratios. When the signal-to-noise ratio is high, the RMSE of the present invention is closest to CRLB, followed by CZT algorithm, and FFT+parabola fitting has the worst effect. When the signal-to-noise ratio is low, it can be seen that the RMSE of the algorithm of the present invention is the smallest. Experimental verification shows that the method of the present invention improves the accuracy and anti-interference ability of frequency estimation while reducing the amount of calculation.

Claims

1. Improve the high-precision ranging method of FMCW radar using binary interpolation, Features The following steps are involved: Step 1: The FMCW radar transmits a linearly transformed carrier signal to the target object and receives the echo signal reflected by the target; Step 2: Mix the carrier signal transmitted by the FMCW radar in step 1 with the received echo signal to obtain a beat signal x(t); Step 3: Sampling the continuous beat signal x(t) in step 2 to obtain a discrete beat signal x(n); Step 4: Perform a fast Fourier transform on the discrete beat signal x(n) in step 3 to obtain the amplitude spectrum |X(k)| of the beat signal; Step 5: According to the amplitude spectrum |X(k)| of the beat signal in step 4, obtain the initial maximum amplitude |X(k m )| and the initial sub-amplitude|X(k s )|, and the corresponding frequency point k m and k s The final frequency estimation result range is within k m and k s between; Step 6: According to the final frequency estimation result range obtained in step 5, use the improved dichotomy method to perform interpolation iteration within the range and convert k m and k s The segments are divided according to the golden ratio, and at the golden section point k ui Interpolate at the golden section point and compare the amplitude |X(k ui )| and the initial maximum amplitude|X(k m )|; Step 7: According to the comparison result in step 6, continue to interpolate at the golden section point to obtain the amplitude |X(k ui )|, and keep repeating the operation of step 6, gradually approaching the final frequency estimation result; Step 8: When the amplitude at the golden section point |X(k ui )| and the initial maximum amplitude|X(k m )| are equal, the midpoint of the golden section point and the frequency point corresponding to the initial maximum amplitude is the final frequency result f c ; Step 9: According to the final frequency result f c , the FMCW radar ranging formula is as follows: Where: c is the speed of light, T is the modulation signal sweep time, B is the modulation signal sweep bandwidth, f 0 is the frequency of the beat signal.

2. The FMCW radar high-precision ranging method according to claim 1 with improved binary interpolation, Features: In step 2, the beat signal x(t) is expressed in the time domain as follows: Where a is the amplitude of the signal; is the initial phase of the signal; w(t) is the noise signal; f 0 Represents the true frequency of the signal.

3. The FMCW radar high-precision ranging method according to claim 1 with improved binary interpolation, Features: In step 3, the discrete beat signal x(n) is: Where: f s is the sampling rate of high-speed AD; N is the number of sampling points; n is the sequence index; w(n) is the discrete noise signal; a represents the amplitude of the signal; An expression representing a discrete signal.

4. The FMCW radar high-precision ranging method according to claim 1, Features: In step 4, the fast Fourier transform formula is as follows: Where: k is the index of the frequency value, k e is the frequency index where the amplitude is maximum, is the initial phase of the signal, a is the amplitude of the signal; The Fourier transform amplitude is as follows: Among them: || represents the modulus value.

5. The FMCW radar high-precision ranging method according to claim 1, Features: In step 5, the initial maximum amplitude and the initial sub-amplitude According to the Fourier transform amplitude formula in step 4, the final frequency estimation result is located at k m and k s between.

6. The FMCW radar high-precision ranging method according to claim 1 with improved binary interpolation, Features: In step 6, the initial maximum amplitude |X(k m )| and the initial sub-amplitude|X(k s )|The corresponding frequency points are divided between km and ks according to the golden ratio of 0.382:0.

618. The amplitude at the golden section point is 7. The FMCW radar high-precision ranging method according to claim 6, Features: At the golden point k ui =k m +0.382(k m -k s ) are interpolated as follows: k m -k s =1, in k ui =k m Interpolate at +0.382 to get the amplitude The interpolation point obtained is (k ui ,|X(k ui )), the maximum and second maximum values ​​become |X(k m )| and |X(k ui )|, the corresponding index is k m and k ui ; At this time, the index of the real frequency is located at k m and k ui The interpolation interval is continuously reduced by iterative interpolation through this method until the maximum amplitude and the second maximum amplitude are equal.

8. The FMCW radar high-precision ranging method according to claim 1, Features: In step 8, the final frequency result f c =f s / N×(k ui +k m ) / 2,f s is the sampling rate of high-speed AD, and N is the number of sampling points.

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