Non-linear error correction method, system, equipment and medium for FMCW radar

Abstract

The invention relates to the technical field of frequency-modulated continuous wave radars, and discloses a nonlinear error correction method, system and device for an FMCW radar and a medium, and the method comprises the steps: obtaining a difference frequency signal containing a nonlinear error, and extracting a first time frequency signal; performing phase fitting on the first time frequency signal to obtain a first time frequency signal error coefficient, and performing error coefficient conversion on the first time frequency signal error coefficient to obtain a difference frequency signal error coefficient; constructing a matching signal according to the difference frequency signal error coefficient, and performing demodulation and low-pass filtering on the difference frequency signal according to the matching signal to obtain a residual signal; judging a signal type, and calculating a residual signal error coefficient by adopting a corresponding optimization algorithm; and combining the difference frequency signal error coefficient and the residual signal error coefficient to obtain a phase error correction factor, and performing nonlinear correction on the resampled difference frequency signal according to the phase error correction factor. The estimation precision of the nonlinear error coefficient can be improved, and the overall performance of a radar system is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of frequency modulated continuous wave radar, and in particular to a nonlinear error correction method, system, equipment and medium for FMCW radar. Background Art

[0002] With the rapid development of radar technology, broadband linear frequency modulated continuous wave (FMCW) radar has been widely used in the field of high-resolution imaging. The FMCW imaging system using demultiplexing can obtain intermediate frequency signals at a lower sampling rate, thereby reducing the complexity and cost of the system. However, nonlinear errors are inevitable in actual systems, such as modulator nonlinearity, temperature drift, and device aging. These errors have a negative impact on imaging quality and reduce the accuracy of target detection and recognition.

[0003] Traditional nonlinear correction methods are mainly divided into hardware correction and software correction. Hardware correction methods reduce nonlinear errors by dynamically adjusting the real-time output signal in the hardware circuit. Common technologies include pre-distortion compensation, delayed phase detection, and delayed phase lock. Although these methods can output highly linear linear frequency modulation signals in real time, they are extremely sensitive to environmental interference, resulting in unstable correction results. In addition, these methods have a long debugging cycle, high equipment cost, and can only compensate for nonlinear errors at the transmitter, but cannot solve the nonlinear problems at the receiver.

[0004] The software correction method compensates for nonlinear errors by digitally processing the received signal, which has the advantages of high flexibility and low cost. However, existing nonlinear error compensation methods usually require the reference difference frequency signal to have a high signal-to-noise ratio (SNR), and it is difficult to effectively extract nonlinear errors when multiple reference targets are close to each other. These limitations significantly reduce the applicability and reliability of the compensation method in actual engineering applications. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a nonlinear error correction method, system, device and medium for FMCW radar, which can extract nonlinear error coefficients from a reference signal containing multiple closely spaced noise targets, and improve the estimation accuracy of the nonlinear error coefficients through matching demodulation, so as to achieve effective correction of nonlinear errors, thereby improving the imaging quality of the FMCW radar system.

[0006] In a first aspect, the present invention provides a nonlinear error correction method for an FMCW radar, the method comprising:

[0007] A difference frequency signal including a nonlinear error is obtained according to an echo signal of the FMCW radar, a first time-frequency signal is extracted from the difference frequency signal using a variational nonlinear chirp mode decomposition technique, and a first conversion relationship between an error coefficient of the difference frequency signal and an error coefficient of the first time-frequency signal is obtained according to the difference frequency signal and the first time-frequency signal;

[0008] Performing phase fitting on the first time-frequency signal to obtain a first time-frequency signal error coefficient, and performing error coefficient conversion on the first time-frequency signal error coefficient according to the first conversion relationship to obtain a difference frequency signal error coefficient, wherein the phase fitting includes high-order polynomial phase fitting and periodic multi-sine phase fitting;

[0009] constructing a matching signal corresponding to the difference frequency signal according to the difference frequency signal error coefficient, and performing signal demodulation and low-pass filtering on the difference frequency signal according to the matching signal to obtain a residual signal;

[0010] Determine the signal type of the echo signal, and calculate the residual signal error coefficient of the residual signal using a corresponding optimization algorithm according to the signal type, wherein the signal type includes a single-target signal and a multi-target signal;

[0011] The difference frequency signal error coefficient and the residual signal error coefficient are combined to obtain a phase error correction factor, the difference frequency signal is resampled in the time domain, and the resampled difference frequency signal is nonlinearly corrected according to the phase error correction factor to obtain the corrected difference frequency signal.

[0012] Furthermore, the step of performing phase fitting on the first time-frequency signal to obtain the first time-frequency signal error coefficient includes:

[0013] Using the least squares method to perform high-order polynomial fitting on the first time-frequency signal to obtain high-order polynomial error coefficients;

[0014] Acquire a periodic multi-sine phase error of the first time-frequency signal, construct an autocorrelation matrix and perform frequency search on the periodic multi-sine phase error to obtain a frequency estimation value;

[0015] Constructing a phase matching function according to the frequency estimation value, and calculating a periodic multi-sine phase error coefficient according to the phase matching function and the periodic multi-sine phase error;

[0016] The high-order polynomial error coefficient and the periodic multi-sine phase error coefficient are used as the first time-frequency signal error coefficient.

[0017] Furthermore, the step of acquiring the periodic multi-sine phase error of the first time-frequency signal, constructing an autocorrelation matrix and performing frequency search on the periodic multi-sine phase error, and obtaining a frequency estimation value comprises:

[0018] According to the high-order polynomial error coefficient, a high-order polynomial phase error is obtained, and the high-order polynomial phase error is subtracted from the first time-frequency signal to obtain a periodic multi-sine phase error;

[0019] An autocorrelation matrix of the periodic multi-sinusoidal phase error is constructed, spectrum decomposition is performed on the autocorrelation matrix, and frequency search of peak points of the spectrum function is performed according to the orthogonality of the feature space to obtain a frequency estimation value.

[0020] Further, the step of calculating the residual signal error coefficient of the residual signal by using a corresponding optimization algorithm according to the signal type includes:

[0021] In response to the signal type being a single target signal, performing phase unwrapping on the residual signal to obtain a residual signal phase, and performing phase fitting on the residual signal phase to obtain a residual signal error coefficient;

[0022] In response to the signal type multi-target signal, a variational nonlinear chirp mode decomposition technique is used to extract a second time-frequency signal of the residual signal, and a second conversion relationship between an error coefficient of the residual signal and an error coefficient of the second time-frequency signal is obtained according to the residual signal and the second time-frequency signal;

[0023] Phase fitting is performed on the second time-frequency signal to obtain a second time-frequency signal error coefficient, and error coefficient conversion is performed on the second time-frequency signal error coefficient according to the second conversion relationship to obtain a residual signal error coefficient.

[0024] Furthermore, the step of resampling the difference frequency signal in the time domain and performing nonlinear correction on the resampled difference frequency signal according to the phase error correction factor to obtain the corrected difference frequency signal includes:

[0025] Resampling the difference frequency signal in the time domain to obtain a resampled difference frequency signal;

[0026] According to the resampled difference frequency signal, a difference frequency signal phase model is constructed, and nonlinear correction is performed on the difference frequency signal phase model to obtain a corrected difference frequency signal model;

[0027] The corrected difference frequency signal model is calculated according to the phase error correction factor to obtain the corrected difference frequency signal.

[0028] Furthermore, the difference frequency signal is expressed by the following formula:

[0029]

[0030] In the formula, S beat (t) represents the difference frequency signal containing nonlinear error at time t, exp represents the natural exponential function, j represents the imaginary unit, K represents the order of the high-order polynomial phase error, and a k represents the coefficient of the high-order polynomial phase error in the difference frequency signal, M represents the order of the periodic multi-sinusoidal phase error, b m 、f em and θ m represent the amplitude, frequency and initial phase of the periodic multi-sinusoidal phase error in the difference frequency signal respectively;

[0031] The first time-frequency signal is expressed by the following formula:

[0032]

[0033] In the formula, Q represents the number of nonlinear frequency modulation signals in the echo signal, The coefficient of the k-th order of the high-order polynomial phase error of the q-th nonlinear frequency modulation signal in the first time-frequency signal, and They respectively represent the m-th order amplitude, frequency and initial phase of the periodic multi-sine phase error of the q-th nonlinear frequency modulation signal in the first time-frequency signal.

[0034] Furthermore, the corrected difference frequency signal model is expressed by the following formula:

[0035]

[0036] a0=f0τ z

[0037] a1=K r τ z

[0038] Where nT s represents the time after resampling, η(nT s ) represents the new time variable, Z represents the target quantity, a0 represents the constant term, a1 represents the linear term, τ z represents the delay of the zth target, f0 represents the carrier frequency, K r Indicates the frequency modulation.

[0039] In a second aspect, the present invention provides a nonlinear error correction system for an FMCW radar, the system comprising:

[0040] A time-frequency analysis module, configured to obtain a difference frequency signal containing a nonlinear error according to an echo signal of the FMCW radar, extract a first time-frequency signal from the difference frequency signal using a variational nonlinear chirp mode decomposition technique, and obtain a first conversion relationship between an error coefficient of the difference frequency signal and an error coefficient of the first time-frequency signal according to the difference frequency signal and the first time-frequency signal;

[0041] an error coefficient estimation module, configured to perform phase fitting on the first time-frequency signal to obtain a first time-frequency signal error coefficient, and perform error coefficient conversion on the first time-frequency signal error coefficient according to the first conversion relationship to obtain a difference frequency signal error coefficient, wherein the phase fitting includes high-order polynomial phase fitting and periodic multi-sine phase fitting;

[0042] an error coefficient optimization module, configured to construct a matching signal corresponding to the difference frequency signal according to the difference frequency signal error coefficient, and perform signal demodulation and low-pass filtering on the difference frequency signal according to the matching signal to obtain a residual signal;

[0043] Determine the signal type of the echo signal, and calculate the residual signal error coefficient of the residual signal using a corresponding optimization algorithm according to the signal type, wherein the signal type includes a single-target signal and a multi-target signal;

[0044] The nonlinear error correction module is used to combine the difference frequency signal error coefficient and the residual signal error coefficient to obtain a phase error correction factor, resample the difference frequency signal in the time domain, and perform nonlinear correction on the resampled difference frequency signal according to the phase error correction factor to obtain a corrected difference frequency signal.

[0045] In a third aspect, an embodiment of the present invention further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0046] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the above method when executed by a processor.

[0047] The present invention provides a nonlinear error correction method, system, device and medium for FMCW radar. The present invention establishes a complete and accurate error model for the nonlinear error in the difference frequency signal, covering high-order polynomial phase error and periodic multi-sinusoidal phase error, and through a correction method based on variational nonlinear chirp mode decomposition, it can effectively extract the time-frequency information of the reference echo from the echoes of multiple targets. At the same time, in view of the problem that the existing nonlinear estimation method has insufficient anti-noise performance in a low signal-to-noise ratio environment, the present invention combines the least squares method, high-resolution spectrum estimation and phase matching technology, and can accurately estimate the nonlinear phase error in the FMCW radar system, and by adopting a matching demodulation method, it can further improve the estimation accuracy of the nonlinear error coefficient, thereby significantly improving the overall performance of the radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 1 is a flow chart of a nonlinear error correction method for an FMCW radar according to an embodiment of the present invention;

[0049] Figure 2 1 is another flow chart of a nonlinear error correction method for an FMCW radar in an embodiment of the present invention;

[0050] Figure 3 is a schematic diagram of simulation results of error correction in a comparative experiment in an embodiment of the present invention;

[0051] Figure 4 Schematic diagram of time-frequency curve extraction results of a comparative experiment in an embodiment of the present invention;

[0052] Figure 5 Schematic diagram of Monte Carlo experiment results of comparative experiments in an embodiment of the present invention;

[0053] Figure 6 is a schematic diagram of the single-angle reflector correction experimental results of the comparative experiment in the embodiment of the present invention;

[0054] Figure 7 is a schematic diagram of the double-corner reflector correction experimental results of the comparative experiment in the embodiment of the present invention;

[0055] Figure 8 is a schematic diagram of the experimental results of multi-angle reflector imaging correction in a comparative experiment in an embodiment of the present invention;

[0056] Fig. 9 is a schematic structural diagram of a nonlinear error correction system of an FMCW radar in an embodiment of the present invention;

[0057] Fig.10 It is a diagram of the internal structure of a computer device in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] See also Figure 1 The first embodiment of the present invention provides a nonlinear error correction method for an FMCW radar, which includes steps S10 to S50:

[0060] Step S10, obtaining a difference frequency signal containing a nonlinear error according to an echo signal of the FMCW radar, extracting a first time-frequency signal from the difference frequency signal using a variational nonlinear chirp mode decomposition technique, and obtaining a first conversion relationship between an error coefficient of the difference frequency signal and an error coefficient of the first time-frequency signal according to the difference frequency signal and the first time-frequency signal;

[0061] Step S20, performing phase fitting on the first time-frequency signal to obtain a first time-frequency signal error coefficient, performing error coefficient conversion on the first time-frequency signal error coefficient according to the first conversion relationship to obtain a difference frequency signal error coefficient, wherein the phase fitting includes high-order polynomial phase fitting and periodic multi-sine phase fitting;

[0062] Step S30, constructing a matching signal corresponding to the difference frequency signal according to the difference frequency signal error coefficient, and performing signal demodulation and low-pass filtering on the difference frequency signal according to the matching signal to obtain a residual signal;

[0063] Step S40, determining the signal type of the echo signal, and calculating the residual signal error coefficient of the residual signal using a corresponding optimization algorithm according to the signal type, wherein the signal type includes a single target signal and a multi-target signal;

[0064] Step S50, combining the difference frequency signal error coefficient and the residual signal error coefficient to obtain a phase error correction factor, resampling the difference frequency signal in the time domain, and performing nonlinear correction on the resampled difference frequency signal according to the phase error correction factor to obtain the corrected difference frequency signal.

[0065] At present, the nonlinear correction of FMCW radar is generally divided into two methods: hardware and signal processing. The hardware method mainly reduces the nonlinear error by improving the hardware circuit, and the object of correction is the transmitted signal; while the software method refers to the nonlinear estimation and correction of the echo signal collected by the radar, and the object of correction is the difference frequency echo signal after demodulation. The limitations of these two types of methods are that, first, the existing methods have high requirements on the signal-to-noise ratio of the reference target, which limits their effectiveness in practical engineering applications. Secondly, in actual scenarios, the acquired reference signal may contain multiple targets in the frequency domain that are very close to each other and have similar amplitudes. Filtering with a narrowband filter may lead to the loss of distortion information, affecting the integrity of the correction. Finally, the research on periodic phase error is still insufficient, and there is a lack of methods for accurately estimating periodic errors. In order to solve these problems, the present invention proposes a software correction method based on variational nonlinear chirp mode decomposition (VNCMD). The method provided by the present invention can not only extract nonlinear error coefficients from a reference signal containing multiple closely spaced noise targets, but also show excellent performance in terms of noise robustness. Please refer to Figure 2 , the method provided by the present invention is described in detail below.

[0066] In the wideband linear frequency modulated continuous wave radar (FMCW-SAR) system, there are inevitably devices with nonlinear characteristics such as mixers, power amplifiers, digital frequency synthesizers and AD / DA. When these devices are used in a large bandwidth environment, they will introduce nonlinear errors that cannot be ignored. Therefore, the frequency modulated signal transmitted in the actual FMCW-SAR system is no longer an ideal linear signal.

[0067] The ideal linear FMCW linear frequency modulated continuous wave RF signal model is expressed as:

[0068]

[0069] In the formula, S t (t) represents the transmitted signal at time t, exp represents the natural exponential function, j represents the imaginary unit, f0 represents the carrier frequency, K r Indicates the frequency modulation.

[0070] The corresponding received signal is the frequency modulated signal after the time delay τ of the transmitted signal:

[0071]

[0072] In the formula, S r (t) represents the received signal at time t, and τ represents the delay.

[0073] After dechirping the received and transmitted signals, we can get the ideal difference frequency signal:

[0074]

[0075] Among them, S r * (t) represents the conjugate signal of the received signal, K r τt represents the target difference frequency, is the residual time-frequency phase term RVP. In near-field imaging, the time delay is very small, so the RVP term will be ignored in subsequent processing.

[0076] After the amplitude phase error is introduced, the difference frequency signal containing nonlinear phase error can be expressed as:

[0077]

[0078] Where ε(t) represents the nonlinear phase error, and the nonlinear phase error is modeled as:

[0079]

[0080] In this embodiment, the nonlinear phase error function ε(t) is modeled as the sum of a polynomial phase error and a periodic multi-sinusoidal phase error, where: is the phase error of the high-order polynomial, that is, the high-order polynomial remaining after the constant term a0 and the first-order term a1 in the high-order polynomial are extracted, K is the order of the phase error of the high-order polynomial, a k is the coefficient of the high-order polynomial phase error; is the periodic multi-sinusoidal phase error, M is the order of the periodic multi-sinusoidal phase error, b m 、f em and θ m are respectively the amplitude, frequency and initial phase of the periodic multi-sine phase error, that is, the coefficient of the periodic multi-sine phase error.

[0081] In fact, the difference frequency signal containing nonlinear error can be considered as a nonlinear frequency modulation signal, which can be expressed as:

[0082]

[0083] In the formula, A(t) represents the instantaneous amplitude, f(t) represents the instantaneous frequency, and φ represents the initial phase. In actual echo signals, there are often multiple nonlinear frequency modulation signals. Therefore, the echo signal can be expressed as:

[0084]

[0085] Where Q represents the number of nonlinear frequency modulation signals. In the calibration process, echoes with a known number of targets are usually selected for nonlinear extraction, that is, Q is known, and n(t) represents Gaussian white noise.

[0086] First, use the demodulation operator to demodulate the broadband signal of the echo into a narrowband signal:

[0087]

[0088] In the formula, f d (t) and f c are the demodulated frequency and the carrier frequency, Φ - (t) represents the demodulation operator.

[0089] The narrowband signal is then converted to a baseband signal by mixing:

[0090]

[0091] By adjusting f d (t), so that the sum of the signal bandwidths after demodulation and mixing of each mode is minimized, thereby estimating the instantaneous frequency of each mode. Therefore, the echo signal can be rewritten as:

[0092]

[0093] Among them, u q (t) and v q (t) is the demodulated signal.

[0094] The idea of ​​variational nonlinear chirp mode decomposition (VNCMD) is to estimate the signal components by minimizing the bandwidth of the demodulated signal, that is:

[0095]

[0096] Among them, ε is the threshold, which is determined by the intensity of Gaussian white noise.

[0097] Since formula (4) and formula (6) are essentially equivalent, formula (4) is decomposed by VNCMD and optimized by ADMM (alternating direction method of multipliers) algorithm to obtain the time-frequency signal in the difference frequency signal:

[0098]

[0099] Wherein, the superscript q represents the qth nonlinear frequency modulation signal, and the parameters a, b, f and θ with the superscript q are consistent with the parameters in the above formula (4), and will not be repeated here.

[0100] After further simplifying the above formula, we can get:

[0101]

[0102] In the formula, Q represents the number of nonlinear frequency modulation signals in the echo signal, The coefficient of the k-th order of the high-order polynomial phase error of the q-th nonlinear frequency modulation signal in the first time-frequency signal, and They respectively represent the m-th order amplitude, frequency and initial phase of the periodic multi-sine phase error of the q-th nonlinear frequency modulation signal in the first time-frequency signal. It should be noted that the frequency and initial phase here are consistent with the frequency and initial phase of the q-th signal in formula (12), that is, formula (4).

[0103] Comparing the corresponding parameters in formula (12) and formula (13), the conversion relationship obtained is essentially the conversion relationship between the error coefficient in the difference frequency signal and the error coefficient in the time-frequency signal:

[0104]

[0105] The above steps are essentially to extract the time-frequency signal from the difference frequency signal through VNCMD, and then the error coefficient of the time-frequency signal can be obtained through phase fitting. The specific steps include:

[0106] Using the least squares method to perform high-order polynomial fitting on the first time-frequency signal to obtain high-order polynomial error coefficients;

[0107] Acquire a periodic multi-sine phase error of the first time-frequency signal, construct an autocorrelation matrix and perform frequency search on the periodic multi-sine phase error to obtain a frequency estimation value;

[0108] Constructing a phase matching function according to the frequency estimation value, and calculating a periodic multi-sine phase error coefficient according to the phase matching function and the periodic multi-sine phase error;

[0109] The high-order polynomial error coefficient and the periodic multi-sine phase error coefficient are used as the first time-frequency signal error coefficient.

[0110] In this embodiment, phase fitting includes high-order polynomial phase fitting and periodic multi-sine phase fitting, wherein the high-order polynomial phase fitting is used to estimate the error coefficient of the high-order polynomial phase error signal. Specifically, the least square method LSM is used to perform high-order polynomial fitting on the time-frequency signal represented by formula (13), and the coefficient of the high-order polynomial phase error can be obtained.

[0111]

[0112] in,

[0113]

[0114] A is the Vandermonde matrix consisting of N sampling times, and K represents the order of the high-order polynomial.

[0115] Periodic multi-sine phase fitting is used to estimate the coefficients of periodic multi-sine phase errors. First, the frequency of the signal is estimated, and then the error coefficient is calculated based on the estimated parameters. The steps of parameter estimation are as follows:

[0116] According to the high-order polynomial error coefficient, a high-order polynomial phase error is obtained, and the high-order polynomial phase error is subtracted from the first time-frequency signal to obtain a periodic multi-sine phase error;

[0117] An autocorrelation matrix of the periodic multi-sinusoidal phase error is constructed, spectrum decomposition is performed on the autocorrelation matrix, and frequency search of peak points of the spectrum function is performed according to the orthogonality of the feature space to obtain a frequency estimation value.

[0118] In this embodiment, it is assumed that is the estimated high-order polynomial phase error, and the periodic multi-sinusoidal phase error φ(t) can be regarded as the time-frequency signal F of the difference frequency signal f (t) minus the high-order polynomial phase error The residual signal after:

[0119]

[0120] Therefore, the periodic multi-sinusoidal phase error φ(t) can be expressed as:

[0121]

[0122] Where r(n) represents Gaussian white noise.

[0123] After determining the order M of the periodic multi-sinusoidal phase error, the autocorrelation matrix is ​​constructed using φ(t)

[0124]

[0125] Where E is the mathematical expectation.

[0126] The frequency estimation of the signal can be obtained by performing spectral decomposition of the autocorrelation matrix using the eigenvalue decomposition method, also known as the spectral decomposition method, and searching the frequency of the peak point of the spectral function based on the orthogonality of the characteristic subspace and the signal subspace.

[0127] The frequency estimate is then used to construct the phase matching function:

[0128]

[0129] In the formula, t represents time, ω mRepresents the frequency estimate of the mth order, M represents the order, and here θ m It represents the initial phase estimate of the mth order, which can be estimated in subsequent processing.

[0130] The phase matching function is then multiplied by the periodic multi-sine phase error:

[0131]

[0132] In the formula, ω m and are the frequency estimation value and actual frequency value of the mth order respectively, and are the initial phase estimate and actual value of the mth order in the qth signal respectively.

[0133] According to the above formula, when When the DC component is

[0134] When the DC component takes the maximum value, the phase parameter of the frequency component can be obtained. At the same time, half of the DC component is the amplitude parameter of the frequency component That is, through the above steps, the coefficient of the periodic multi-sine phase error corresponding to the mth order can be obtained: and Iterative processing is performed according to the above steps until the parameter values ​​of the M cosine components are estimated, that is, the coefficients of the periodic multi-sine phase errors of all orders are obtained.

[0135] After obtaining the high-order polynomial error coefficient and the periodic multi-sinusoidal phase error coefficient of the time-frequency signal through phase fitting, the nonlinear error coefficient of the difference frequency signal can be obtained according to the conversion relationship of formulas (14) and (15).

[0136] In fact, the correction method provided by the present invention can be divided into three steps: nonlinear error estimation, coefficient optimization and nonlinear correction. The above step is nonlinear error estimation. After estimating the nonlinear error coefficient of the difference frequency signal, the next step of nonlinear error coefficient optimization can be carried out.

[0137] In this embodiment, firstly, a matching signal of the beat frequency signal is constructed according to the estimated nonlinear error coefficient of the beat frequency signal:

[0138]

[0139] Then, the matching signal is used to demodulate the original difference frequency signal, that is, formula (4). If the estimated coefficients are accurate enough, the useful information of the signal will be concentrated near 0 Hz, while the noise will be evenly distributed in the entire bandwidth. At the same time, a robust local weighted quadratic regression smoothing method is selected to perform low-pass filtering on the demodulated signal, thereby obtaining the filtered demodulated signal, that is, the residual signal:

[0140]

[0141] In the formula, represents the conjugate signal of the matching signal, rloess represents local weighted quadratic regression smoothing, smooth represents the sliding filter function, represents the residual signal.

[0142] In this embodiment, the nonlinear error coefficient optimization is divided into two categories. If the difference frequency signal is a single-target signal, the difference frequency signal is phase unwrapped to extract the residual. If the difference frequency signal is a multi-target signal, VNCMD is used to extract the residual in the time-frequency curve. Specifically, first determine whether the signal type of the echo signal is a single-target signal or a multi-target signal. For a single-target signal, different optimization algorithms are used for different types of signals to optimize the coefficients. The steps include:

[0143] In response to the signal type being a single target signal, performing phase unwrapping on the residual signal to obtain a residual signal phase, and performing phase fitting on the residual signal phase to obtain a residual signal error coefficient;

[0144] In response to the signal type multi-target signal, a variational nonlinear chirp mode decomposition technique is used to extract a second time-frequency signal of the residual signal, and a second conversion relationship between an error coefficient of the residual signal and an error coefficient of the second time-frequency signal is obtained according to the residual signal and the second time-frequency signal;

[0145] Phase fitting is performed on the second time-frequency signal to obtain a second time-frequency signal error coefficient, and error coefficient conversion is performed on the second time-frequency signal error coefficient according to the second conversion relationship to obtain a residual signal error coefficient.

[0146] In this embodiment, for a single target signal, the residual signal can be directly subjected to phase unwrapping processing to obtain the residual signal phase:

[0147]

[0148] Where phase represents the phase unwrapping function.

[0149] Then, the extracted residual signal phase is phase-fitted according to the above-mentioned phase fitting method, that is, according to the method of high-order polynomial phase fitting and periodic multi-sine phase fitting of the time-frequency signal in the above steps, the residual signal phase is phase-fitted, so as to obtain the high-order polynomial error coefficient and periodic multi-sine phase error coefficient of the residual signal, that is, the residual error coefficient. The specific steps can refer to the above embodiment, and the time-frequency signal therein can be replaced with the residual signal phase, which will not be repeated here. It should be noted that, since the residual signal at this time is the estimated difference of a single target, VNCMD time-frequency analysis is not required to extract its time-frequency curve, and therefore, there is no need to convert the error coefficient, and it can be used directly in subsequent steps.

[0150] For multi-target signals, the residual signal needs to be converted into a time-frequency signal through VNCMD decomposition, and then the same steps as the phase fitting and error coefficient conversion in the above embodiment are used to estimate the residual error coefficient of each target, that is, the residual signal and the corresponding second time-frequency signal are analyzed to determine the second conversion relationship between the error coefficients of the two, and the error coefficient of the second time-frequency signal is determined by performing high-order polynomial phase fitting and periodic multi-sine phase fitting on the second time-frequency signal, and then converted into the residual error coefficient of the residual signal through the second conversion relationship. It should be noted that since the residual error coefficients of multiple targets are obtained, each error coefficient is theoretically consistent, but only one set of error coefficients is required for correction, so the error coefficient of the strongest point target is selected or selected according to actual needs.

[0151] After the residual error coefficient is obtained through the above steps, it is combined with the nonlinear phase error coefficient of the difference frequency signal estimated previously, that is, the difference frequency signal error coefficient, to obtain the phase error correction factor. Preferably, the coefficient combination can be performed by adding the error coefficients accordingly. Through this embodiment, the high-order polynomial phase error coefficient a in the difference frequency signal can be obtained. k and periodic multi-sine error coefficient b m ,f em ,θ m .

[0152] After the above coefficient estimation and optimization, the third step is to use the time domain resampling algorithm to perform the final nonlinear correction. The specific steps include:

[0153] Resampling the difference frequency signal in the time domain to obtain a resampled difference frequency signal;

[0154] According to the resampled difference frequency signal, a difference frequency signal phase model is constructed, and nonlinear correction is performed on the difference frequency signal phase model to obtain a corrected difference frequency signal model;

[0155] The corrected difference frequency signal model is calculated according to the phase error correction factor to obtain the corrected difference frequency signal.

[0156] In this embodiment, the difference frequency signal obtained by time domain resampling of the difference frequency signal of formula (4) can be expressed as:

[0157]

[0158] Where Z represents the number of target echo signals, nT s Indicates the time after resampling.

[0159] The phase model re-established based on the above difference frequency signal can be expressed as:

[0160]

[0161] The purpose of nonlinear correction is to extract the target distance term τ z K r nT s , eliminating the higher-order polynomial phase error terms of order 2 and above and the periodic multi-sinusoidal phase error terms, so the corrected difference frequency signal model can be expressed as:

[0162]

[0163] Where a0 = f0τ z , a1=K r τ z .

[0164] According to the above formula, the high-order polynomial phase error coefficient a in the difference frequency signal obtained by the above estimation is k and periodic multi-sine error coefficient b m ,f em ,θ m , we can get η(nT s ). That is, by substituting the estimated error coefficient into the corrected difference frequency signal model, the nonlinear error correction of the radar signal can be completed. The phase of the corrected difference frequency signal only contains the constant term a0, the linear term a1 and the new time variable η(nT s ), high-order polynomials above the second order and periodic multi-sinusoidal phase errors are eliminated. The resampling process is to convert the traditional time variable nT s Converted to time variable η(nT s ), that is, the phase of the difference frequency signal is about the new variable η(nT s ), so the nonlinear errors of all objectives are eliminated simultaneously.

[0165] The correction effect of the correction method provided by the present invention is verified by comparative experiments. In this experiment, the comparative algorithms used include a method based on the least squares method (LSM), a method based on a higher-order ambiguity function (HAF), a method based on the recursive least squares method (RLS), and a method based on the multi-synchronous squeezing transform (MSST). The parameters of the broadband FMCW radar simulation system used in the experiment are shown in Table 1 below:

[0166] Table 1 Wideband FMCW radar system parameters

[0167] System Parameters Numeric unit Center frequency 9-9.5 GHz bandwidth 0.5 GHz Scan cycle 0.08 ms Frequency adjustment 6.25x109 Hz / s

[0168] In order to verify the effectiveness of the correction algorithm provided by the present invention, the algorithm is used to correct the signal containing nonlinear phase error, and the error correction result obtained is as follows: Figure 3 As shown, Figure 3 (a) is the multi-target signal correction result, Figure 3 The signal in (b) is the single target signal correction result, such as Figure 3 As shown in the figure, the peak sidelobe ratio (PSLR) at 15 meters and 20 meters is reduced to -13.05dB and -13.10dB respectively, which is very close to the PSLR of the ideal model. At the same time, the main lobe can be focused to the ideal state. This experiment proves the effectiveness of the algorithm.

[0169] In order to verify the ability of this algorithm to extract nonlinear errors from multiple adjacent targets, two targets located at 15 meters and 18 meters were set in this experiment. Figure 4 (a) shows the multi-target difference frequency signal. Due to the nonlinear effect, it can be observed that the energy diffusion in the distance direction becomes more serious. Therefore, in this case, the narrowband filter is not enough to effectively decompose the signal. In this experiment, the time-frequency curve is extracted by VNCMD and MSST. The extracted time-frequency curve is shown in Figure 4 As shown in (b), it can be seen that when the signal-to-noise ratio (SNR) is 0, the time-frequency curve extracted by MSST is quite different from the ideal situation, while VNCMD still maintains a certain degree of accuracy.

[0170] In order to further verify the correction performance of the correction method provided by the present invention, in this experiment, a Monte Carlo experiment is performed to verify the performance of the above four methods and the method proposed by the present invention in the estimation of high-order PPS parameters. 500 random averages are performed at each signal-to-noise ratio (SNR). The results are as follows: Figure 5 As shown, Figure 5 (a) is the estimation result of the first-order term (distance direction), Figure 5(b) is the estimation result of the fifth-order term, CRLB represents the Cramer-Rao lower bound, Proposed represents the algorithm provided by the present invention, MSE represents the mean square error, SNR represents the signal-to-noise ratio, Figure 5 It can be seen that the LSM, HAF and RLS methods can only achieve accurate estimation when the SNR threshold exceeds 10. Although the MSST method can reach the SNR threshold when the SNR is 0, its estimation performance is obviously inferior to the algorithm proposed in the present invention. When the SNR is 0, only the algorithm proposed in the present invention can achieve accurate estimation. This experiment further proves that the correction algorithm provided by the present invention has extremely high accuracy.

[0171] In order to further verify the effectiveness of the correction method provided by the present invention, the algorithm is used to correct the measured data of the radar system. First, a single-angle reflector correction experiment is carried out, and the algorithm is used to perform nonlinear phase correction on the target at 3.9 meters. In order to show the respective effects of high-order polynomial error correction and periodic multi-sine error correction, these two corrections are performed separately here, but in actual application they are applied simultaneously. The correction results are shown in Figure 2. Figure 6 As shown in the figure, the original nonlinear signal has many high side lobes. Through high-order polynomial error correction and periodic multi-sine error correction, the side lobes in the far field are significantly reduced, the main lobe position is shifted, and the side lobes in the near field are also greatly suppressed. PSLR is reduced from -15dB to -41dB. The corner reflector experiment shows that the algorithm proposed in the present invention can effectively improve the peak sidelobe ratio PSLR and range resolution of the range profile.

[0172] Then the double-angle reflector correction experiment is carried out, such as Figure 7 (a) shows the original one-dimensional range profile of the dual-corner reflector, where the nonlinear effects of the system lead to higher side lobes. Figure 7 (b) shows the time-frequency curves extracted by MSST and VNCMD. Due to the high signal-to-noise ratio of the data in the laboratory environment, both methods can extract the time-frequency profiles more accurately. However, due to the different solution methods of the two methods, there are some differences in the extracted time-frequency curves. Figure 7 (c) shows the correction results based on VNCMD. Figure 7 (d) shows the comparison results of the two correction methods. It can be observed that the algorithm proposed in the present invention performs better in terms of correction performance.

[0173] Finally, a multi-angle reflector imaging correction experiment was conducted, and the normalized two-dimensional SAR imaging results are shown in Figure 8 (a) Figure 8 (b) and Figure 8 (c), where Figure 8 (a) is the original image before correction. Figure 8(b) is the imaging based on MSST correction. Figure 8 (c) is the imaging based on the correction method proposed by the present invention. Figure 8 As shown in (a), the five point targets are defocused in the distance direction, resulting in multiple false targets with a certain regularity. Therefore, it can be considered that the FMCW radar system has systematic errors. Figure 8 (a), this experiment applied a nonlinear correction method based on MSST and the correction method proposed in this invention. Figure 8 As shown in (b), the error correction based on the MSST correction method suppresses the defocusing phenomenon of the five targets in the distance direction, but some false targets still exist. Figure 8 As shown in (c), the method proposed by the present invention mostly eliminates the false targets caused by defocusing in the range direction, and the azimuth and range resolution of the target are improved. The above comparative experiments prove that the method proposed by the present invention has a significant correction effect in correcting the nonlinear error in the FMCW radar system.

[0174] The present embodiment provides a nonlinear error correction method for an FMCW radar. The present invention establishes an FMCW radar difference frequency signal model containing nonlinear errors and uses variational nonlinear chirp mode decomposition to perform time-frequency analysis. The time-frequency information of reference echoes can be effectively extracted from the echoes of multiple targets. The nonlinear phase error in the FMCW radar system is accurately estimated through phase matching technology. The estimation accuracy of the nonlinear error coefficient is further improved by using a matching demodulation method. The present invention can effectively correct the nonlinear error of the radar difference frequency signal, thereby significantly improving the overall performance of the radar system.

[0175] See also Fig. 9 Based on the same inventive concept, a nonlinear error correction system for an FMCW radar is proposed in a second embodiment of the present invention, comprising:

[0176] The time-frequency analysis module 10 is used to obtain a difference frequency signal containing a nonlinear error according to the echo signal of the FMCW radar, extract a first time-frequency signal from the difference frequency signal by using a variational nonlinear chirp mode decomposition technique, and obtain a first conversion relationship between an error coefficient of the difference frequency signal and an error coefficient of the first time-frequency signal according to the difference frequency signal and the first time-frequency signal;

[0177] an error coefficient estimation module 20, configured to perform phase fitting on the first time-frequency signal to obtain a first time-frequency signal error coefficient, and perform error coefficient conversion on the first time-frequency signal error coefficient according to the first conversion relationship to obtain a difference frequency signal error coefficient, wherein the phase fitting includes high-order polynomial phase fitting and periodic multi-sine phase fitting;

[0178] The error coefficient optimization module 30 is used to construct a matching signal corresponding to the difference frequency signal according to the difference frequency signal error coefficient, and perform signal demodulation and low-pass filtering on the difference frequency signal according to the matching signal to obtain a residual signal;

[0179] Determine the signal type of the echo signal, and calculate the residual signal error coefficient of the residual signal using a corresponding optimization algorithm according to the signal type, wherein the signal type includes a single-target signal and a multi-target signal;

[0180] The nonlinear error correction module 40 is used to combine the difference frequency signal error coefficient and the residual signal error coefficient to obtain a phase error correction factor, resample the difference frequency signal in the time domain, and perform nonlinear correction on the resampled difference frequency signal according to the phase error correction factor to obtain a corrected difference frequency signal.

[0181] The technical features and technical effects of the nonlinear error correction system of the FMCW radar proposed in the embodiment of the present invention are the same as those of the method proposed in the embodiment of the present invention, and are not described in detail here. Each module in the nonlinear error correction system of the FMCW radar can be implemented in whole or in part by software, hardware, and a combination thereof. Each of the above modules can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute the operations corresponding to each of the above modules.

[0182] In addition, an embodiment of the present invention further provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0183] See also Fig.10 , an internal structure diagram of a computer device in one embodiment, the computer device can specifically be a terminal or a server. The computer device includes a processor, a memory, a network interface, a display and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a nonlinear error correction method for FMCW radar is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0184] It can be understood by those skilled in the art that Fig.10 The structure shown in the figure is only a block diagram of a part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. The specific computing device may include more or fewer components than shown in the figure, or combine certain components, or have the same component arrangement.

[0185] In addition, an embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented.

[0186] In summary, an embodiment of the present invention proposes a nonlinear error correction method, system, device and medium for an FMCW radar. The method obtains a difference frequency signal containing a nonlinear error according to an echo signal of the FMCW radar, extracts a first time-frequency signal from the difference frequency signal using a variational nonlinear chirp mode decomposition technique, and obtains a first conversion relationship between an error coefficient of the difference frequency signal and an error coefficient of the first time-frequency signal according to the difference frequency signal and the first time-frequency signal; performs phase fitting on the first time-frequency signal to obtain a first time-frequency signal error coefficient, performs error coefficient conversion on the first time-frequency signal error coefficient according to the first conversion relationship to obtain a difference frequency signal error coefficient, and the phase fitting includes a high-order polynomial phase fitting. Combining and periodic multi-sine phase fitting; constructing a matching signal corresponding to the difference frequency signal according to the difference frequency signal error coefficient, and performing signal demodulation and low-pass filtering on the difference frequency signal according to the matching signal to obtain a residual signal; judging the signal type of the echo signal, and according to the signal type, using a corresponding optimization algorithm to calculate the residual signal error coefficient of the residual signal, wherein the signal type includes a single-target signal and a multi-target signal; combining the difference frequency signal error coefficient and the residual signal error coefficient to obtain a phase error correction factor, resampling the difference frequency signal in time domain, and performing nonlinear correction on the resampled difference frequency signal according to the phase error correction factor to obtain a corrected difference frequency signal. The present invention establishes an FMCW radar beat frequency signal model containing nonlinear errors and uses variational nonlinear chirp mode decomposition to perform time-frequency analysis, thereby effectively extracting time-frequency information of reference echoes from echoes of multiple targets. The nonlinear phase error in the FMCW radar system is accurately estimated through phase matching technology, and the estimation accuracy of the nonlinear error coefficient is further improved by using a matching demodulation method. The present invention can effectively correct the nonlinear error of the radar beat frequency signal and significantly improve the overall performance of the radar system.

[0187] Each embodiment in this specification is described in a progressive manner, and the same or similar parts of each embodiment can be directly referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. It should be noted that the technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above-mentioned embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0188] The above-mentioned embodiments only express several preferred implementation modes of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in the technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be regarded as the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be based on the protection scope of the claims.

Claims

1. A nonlinear error correction method for FMCW radar, characterized in that: include: A difference frequency signal including a nonlinear error is obtained according to an echo signal of the FMCW radar, a first time-frequency signal is extracted from the difference frequency signal using a variational nonlinear chirp mode decomposition technique, and a first conversion relationship between an error coefficient of the difference frequency signal and an error coefficient of the first time-frequency signal is obtained according to the difference frequency signal and the first time-frequency signal; Performing phase fitting on the first time-frequency signal to obtain a first time-frequency signal error coefficient, and performing error coefficient conversion on the first time-frequency signal error coefficient according to the first conversion relationship to obtain a difference frequency signal error coefficient, wherein the phase fitting includes high-order polynomial phase fitting and periodic multi-sine phase fitting; constructing a matching signal corresponding to the difference frequency signal according to the difference frequency signal error coefficient, and performing signal demodulation and low-pass filtering on the difference frequency signal according to the matching signal to obtain a residual signal; Determine the signal type of the echo signal, and calculate the residual signal error coefficient of the residual signal using a corresponding optimization algorithm according to the signal type, wherein the signal type includes a single-target signal and a multi-target signal; The difference frequency signal error coefficient and the residual signal error coefficient are combined to obtain a phase error correction factor, the difference frequency signal is resampled in the time domain, and the resampled difference frequency signal is nonlinearly corrected according to the phase error correction factor to obtain the corrected difference frequency signal.

2. The nonlinear error correction method of FMCW radar according to claim 1, characterized in that: The step of performing phase fitting on the first time-frequency signal to obtain the first time-frequency signal error coefficient comprises: Using the least squares method to perform high-order polynomial fitting on the first time-frequency signal to obtain high-order polynomial error coefficients; Acquire a periodic multi-sine phase error of the first time-frequency signal, construct an autocorrelation matrix and perform frequency search on the periodic multi-sine phase error to obtain a frequency estimation value; Constructing a phase matching function according to the frequency estimation value, and calculating a periodic multi-sine phase error coefficient according to the phase matching function and the periodic multi-sine phase error; The high-order polynomial error coefficient and the periodic multi-sine phase error coefficient are used as the first time-frequency signal error coefficient.

3. The nonlinear error correction method of FMCW radar according to claim 2, characterized in that: The step of acquiring the periodic multi-sine phase error of the first time-frequency signal, constructing an autocorrelation matrix and performing frequency search on the periodic multi-sine phase error, and obtaining a frequency estimation value comprises: According to the high-order polynomial error coefficient, a high-order polynomial phase error is obtained, and the high-order polynomial phase error is subtracted from the first time-frequency signal to obtain a periodic multi-sine phase error; An autocorrelation matrix of the periodic multi-sinusoidal phase error is constructed, spectrum decomposition is performed on the autocorrelation matrix, and frequency search of peak points of the spectrum function is performed according to the orthogonality of the feature space to obtain a frequency estimation value.

4. The nonlinear error correction method of FMCW radar according to claim 2, characterized in that: The step of calculating the residual signal error coefficient of the residual signal by using a corresponding optimization algorithm according to the signal type comprises: In response to the signal type being a single target signal, performing phase unwrapping on the residual signal to obtain a residual signal phase, and performing phase fitting on the residual signal phase to obtain a residual signal error coefficient; In response to the signal type multi-target signal, a variational nonlinear chirp mode decomposition technique is used to extract a second time-frequency signal of the residual signal, and a second conversion relationship between an error coefficient of the residual signal and an error coefficient of the second time-frequency signal is obtained according to the residual signal and the second time-frequency signal; Phase fitting is performed on the second time-frequency signal to obtain a second time-frequency signal error coefficient, and error coefficient conversion is performed on the second time-frequency signal error coefficient according to the second conversion relationship to obtain a residual signal error coefficient.

5. The nonlinear error correction method of FMCW radar according to claim 1, characterized in that: The step of resampling the difference frequency signal in the time domain and performing nonlinear correction on the resampled difference frequency signal according to the phase error correction factor to obtain the corrected difference frequency signal comprises: Resampling the difference frequency signal in the time domain to obtain a resampled difference frequency signal; According to the resampled difference frequency signal, a difference frequency signal phase model is constructed, and nonlinear correction is performed on the difference frequency signal phase model to obtain a corrected difference frequency signal model; The corrected difference frequency signal model is calculated according to the phase error correction factor to obtain the corrected difference frequency signal.

6. The nonlinear error correction method of FMCW radar according to claim 5, characterized in that: The difference frequency signal is expressed by the following formula: In the formula, S beat (t) represents the difference frequency signal containing nonlinear error at time t, exp represents the natural exponential function, j represents the imaginary unit, K represents the order of the high-order polynomial phase error, and a k represents the coefficient of the high-order polynomial phase error in the difference frequency signal, M represents the order of the periodic multi-sinusoidal phase error, b m 、f em and θ m represent the amplitude, frequency and initial phase of the periodic multi-sinusoidal phase error in the difference frequency signal respectively; The first time-frequency signal is expressed by the following formula: In the formula, Q represents the number of nonlinear frequency modulation signals in the echo signal, The coefficient of the k-th order of the high-order polynomial phase error of the q-th nonlinear frequency modulation signal in the first time-frequency signal, and They respectively represent the m-th order amplitude, frequency and initial phase of the periodic multi-sine phase error of the q-th nonlinear frequency modulation signal in the first time-frequency signal.

7. The nonlinear error correction method of FMCW radar according to claim 6, characterized in that: The corrected difference frequency signal model is expressed by the following formula: a0=f0τ z a1=K r τ z Where nT s Represents the time after resampling, η(nT s ) represents the new time variable, Z represents the target quantity, a0 represents the constant term, a1 represents the linear term, τ z represents the delay of the zth target, f0 represents the carrier frequency, K r Indicates the frequency modulation.

8. A nonlinear error correction system for FMCW radar, characterized in that: include: A time-frequency analysis module, configured to obtain a difference frequency signal containing a nonlinear error according to an echo signal of the FMCW radar, extract a first time-frequency signal from the difference frequency signal using a variational nonlinear chirp mode decomposition technique, and obtain a first conversion relationship between an error coefficient of the difference frequency signal and an error coefficient of the first time-frequency signal according to the difference frequency signal and the first time-frequency signal; an error coefficient estimation module, configured to perform phase fitting on the first time-frequency signal to obtain a first time-frequency signal error coefficient, and perform error coefficient conversion on the first time-frequency signal error coefficient according to the first conversion relationship to obtain a difference frequency signal error coefficient, wherein the phase fitting includes high-order polynomial phase fitting and periodic multi-sine phase fitting; an error coefficient optimization module, configured to construct a matching signal corresponding to the difference frequency signal according to the difference frequency signal error coefficient, and perform signal demodulation and low-pass filtering on the difference frequency signal according to the matching signal to obtain a residual signal; Determine the signal type of the echo signal, and calculate the residual signal error coefficient of the residual signal using a corresponding optimization algorithm according to the signal type, wherein the signal type includes a single-target signal and a multi-target signal; The nonlinear error correction module is used to combine the difference frequency signal error coefficient and the residual signal error coefficient to obtain a phase error correction factor, resample the difference frequency signal in the time domain, and perform nonlinear correction on the resampled difference frequency signal according to the phase error correction factor to obtain a corrected difference frequency signal.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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