Nonlinear amplitude and phase error correction method and device suitable for broadband FMCW radar imaging

Abstract

The present application provides a nonlinear amplitude and phase error correction method and device suitable for broadband FMCW radar imaging. The method includes: establishing a frequency modulated continuous wave radar difference frequency signal model containing nonlinear errors; correcting the amplitude error using an envelope normalization correction method; estimating the high-order polynomial phase error using a method combining a phase unwrapping recursive least squares method with an O'Shea optimization strategy to obtain high-order polynomial phase parameters; estimating the periodic multi-sine phase error using a method combining a MUSIC algorithm with a trust region algorithm to obtain periodic multi-sine phase parameters; based on the estimation results of the high-order polynomial phase parameters and the periodic multi-sine phase parameters, using a time domain resampling method to perform phase error correction. The device includes a non-volatile memory storing executable code and a processor for implementing the above method. The technical solution of the present application can solve the problem of insufficient noise resistance that is common in existing methods.

Description

Technical Field

[0001] The present invention relates to the field of radar imaging technology, and in particular to a nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging. Background Art

[0002] Compared with traditional pulse radar, frequency modulated continuous wave (FMCW) radar has the advantages of low peak transmission power, simple structure, high resolution, low power consumption and low sampling rate requirements. Therefore, it is not only widely used in near-field imaging, but also in the fields of self-driving cars, motion detection, target positioning and vital signs detection. However, as various application scenarios have higher requirements for imaging accuracy, the instantaneous bandwidth of radar is also getting larger. The increasing instantaneous bandwidth brings great pressure to the acquisition system. Faced with bandwidths of tens or hundreds of GHz, it is difficult for modern acquisition systems to directly complete the analog-to-digital conversion of signals. Even if the acquisition is barely achieved, the sampling bit number is very low, and the dynamic range and sampling accuracy cannot meet the requirements. Therefore, under the premise of transmitting the commonly used linear frequency modulation (LFM) signal, analog dechirp has become one of the few receiver solutions. Using a broadband mixer, analog dechirp can convert the LFM echo signal with a very large instantaneous bandwidth into a difference frequency signal with a very small bandwidth while maintaining the useful information of the echo. After that, the analog-to-digital conversion of the signal can be completed by using an AD chip with a sampling rate of tens of megahertz, which can significantly reduce the system power consumption, volume and cost. In current and future ultra-large bandwidth radar systems, where direct acquisition is difficult to apply, Dechirp technology will be widely used as an effective solution.

[0003] Although Dechirp technology can solve the problem of receiving and collecting ultra-wide bandwidth signals, it must also meet prerequisites. Dechirp requires that the transmitted signal must be a strict linear frequency modulation signal in order to obtain a one-dimensional range compression image with good focusing performance. Otherwise, the target one-dimensional range image will be defocused, and in severe cases, it may even fail to form an image. Figure 1 As shown in the figure, the nonlinearity of the linear modulation rate will cause the Dechirp-based pulse compression results to have problems such as main lobe broadening, side lobe enlargement, and peak decrease. In addition, these defocusing effects also have spatial deformation. As the target distance increases, the degree of defocusing will gradually increase.

[0004] Nonlinear correction technology can compensate for the nonlinear phase in the Dechirp difference frequency echo signal caused by the imperfect transmission signal, thereby improving the range compression quality and further improving the radar resolution and image contrast. Nonlinear correction is particularly necessary for millimeter wave / terahertz band imaging radar due to its large bandwidth and poor linearity. It can be said that nonlinear correction has become an unavoidable core key technology for ultra-wideband imaging radar systems receiving Dechirp.

[0005] 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 transmission signal; while the software method specifically refers to the nonlinear estimation and correction of the echo signal collected by the radar, and the object of correction is the post-dechirp difference frequency echo signal.

[0006] The hardware method mainly performs early real-time processing from the perspective of signal generation, and minimizes the nonlinearity of frequency modulation while ensuring a certain hardware complexity. The main methods used in hardware circuit design at home and abroad are: pre-distortion voltage compensation method, delayed phase detection method and delayed phase locking method, as well as various pre-distortion methods, such as VCO modulation voltage distortion method and DDS digital distortion method.

[0007] Although the hardware method can output a frequency modulated signal with high linearity in real time, it is easily affected by environmental interference, resulting in unstable correction effect, and it also has the disadvantages of long debugging cycle and high equipment cost. In contrast, signal processing has attracted more attention from researchers due to its strong versatility and flexibility. At present, the methods proposed in the literature related to the nonlinear correction of FMCW-SAR systems are mainly based on nonlinear phase error calibration. Nonlinear software estimation and correction is a non-real-time method, which mainly uses digital signal processing to estimate and correct the nonlinear factors in the sampled difference frequency signal. Domestic and foreign researchers have proposed many methods. Most of these methods are aimed at the estimation and correction of the nonlinearity of the transmission link.

[0008] Nonlinear Estimation Methods

[0009] In 2002, Chen Weidong and others used the zero-crossing moment (zero-crossing position) of the de-skewing signal to obtain the sampling information of the instantaneous phase of the signal. After removing the trend term, the periodogram method was used to estimate the nonlinear residual frequency difference. Since this method only uses the phase of the signal, the extracted phase is greatly affected by noise and can only work under high signal-to-noise ratio.

[0010] Zheng Wei et al. used the instantaneous frequency of the signal to obtain the frequency modulation curve and proposed a weighted phase difference estimator reconstruction method to estimate the instantaneous frequency of the direct sampling signal. The method is derived based on high signal-to-noise ratio and approximation, and its accuracy and versatility need to be improved.

[0011] In 2015, Xiao Wei et al. used the unique advantages of fractional Fourier transform (FrFT) in analyzing linear frequency modulation signals, combined with the idea of ​​improving the signal-to-noise ratio by sliding overlapping segments, and proposed a VCO nonlinearity detection method based on sliding FrFT instantaneous frequency estimation. First, the output signal of the VCO is segmented by sliding overlapping to improve its noise resistance; second, the frequency of the intermediate time point of the segmented signal is detected by sliding FrFT; then, the instantaneous frequency estimation accuracy is improved by cubic spline interpolation of the frequency estimation value of the intermediate time point of the segmented signal; finally, the nonlinearity of the VCO is detected based on the estimated instantaneous frequency. This method has good noise resistance and can detect the nonlinearity of the VCO more accurately, but does not involve correction methods.

[0012] The above methods all have a prerequisite, that is, the transmitted signal must be directly collected and digitized first. However, when the bandwidth of the transmitted signal is extremely large, direct collection is not advisable. Therefore, some scholars have turned to studying the nonlinear estimation and correction method based on the difference frequency signal after Dechirp.

[0013] The residual video phase method was proposed by Adriano Meta and others from Delft University of Technology in the Netherlands. The original intention was to solve the nonlinear problem of airborne frequency-modulated continuous wave imaging radar and obtain a well-focused SAR image. This method embeds a delay line in the RF front end of the system, so that the nonlinear phase in the difference frequency signal is estimated as the product of the derivative of the transmission nonlinearity and the time delay. The nonlinear error is a typical space-varying error, and its phase error is related to the delay. The estimation of the transmission nonlinearity is achieved by performing phase integration. The advantage of this method is that the estimation process uses a non-parametric method and there is no need to establish a mathematical model of the nonlinear phase. The disadvantage is that only the phase information of the delay line echo is used, and the anti-interference and noise performance is poor; in addition, the echo signal phase needs to be unwrapped, which introduces more uncertain factors.

[0014] Andrei Anghel and others from Romania proposed a method for estimating a higher-order ambiguity function (HAF). This method starts with the difference frequency signal, models the nonlinear terms in it as a polynomial phase signal, and then uses the higher-order ambiguity function method to estimate the polynomial coefficients for strong scattering points. This estimation process belongs to the parameter estimation method and has good noise resistance. The disadvantage is that the higher-order ambiguity function estimation method has the problem of error transmission, and the nonlinear estimation accuracy is limited by the order of the polynomial.

[0015] RJCMiddleton et al. proposed to use the phase gradient autofocus (PGA) method to estimate the nonlinear phase in the difference frequency signal. The PGA algorithm requires very strong scattering points in the scene. Because it only uses the phase for estimation, the anti-noise performance is poor, and the actual use effect is not satisfactory.

[0016] R. Zheng, C. Wang et al. used the transform domain method, Multiple Synchronous Squeezed Transform (MSST), to estimate the time-frequency relationship of fast-changing frequency signals. However, when the signal-to-noise ratio (SNR) of the nonlinear beat signal is low (such as 0 dB), the time-frequency curve extraction is not always successful due to the influence of severe noise.

[0017] Nonlinear Correction Methods

[0018] The current nonlinear correction methods mainly include frequency scaling method, interpolation resampling method, matched Fourier transform method and frequency domain correction method.

[0019] The frequency scaling method is widely used in SAR imaging. Adriano Meta and others from Delft University of Technology in the Netherlands borrowed this method and used the residual video phase in the frequency modulated continuous wave to achieve range dimension de-skew, compensating the space-variant nonlinearity to non-space-variant. After estimating the nonlinearity of the transmitted signal, only the space-variant receiving nonlinearity remains. The frequency scaling is used to align the echo spectrum, and finally all distance units are phase compensated to obtain a well-focused range image. This nonlinear correction method is combined with the nonparametric estimation method, and it does not need to know the specific signal form of the nonlinearity, that is, it can correct complex nonlinear modulation. However, this algorithm uses many approximations in the derivation process, and is only applicable to situations where the product of the distance nonlinearity is small. When the target distance is far or the nonlinearity is severe, resulting in severe defocusing of the distance compression, the method will fail.

[0020] In order to achieve large nonlinear correction, RJC Middleton et al. proposed the idea of ​​time domain bending, which is essentially the same as the interpolation resampling adopted by Andrei Anghel et al. of Bucharest Polytechnic University in Romania, that is, non-uniform sampling of the time axis in the presence of nonlinearity to achieve nonlinear correction of all distance units. This nonlinear correction method has strong engineering applicability and can correct a large degree of nonlinear modulation (generally up to several percent); however, in combination with parameterized estimation, it is necessary to know the specific analytical expression of the nonlinearity. If the polynomial order is small or the periodic phase is not considered in the estimation, there will be residual nonlinearity after correction, which restricts the performance to a certain extent. In addition, the calculation of the signal resampling time point is achieved by solving equations. Even if the periodic phase in the nonlinearity is estimated, it is difficult to quickly solve the complex transcendental equation.

[0021] Wang Shengli and others proposed a new transform, the matched Fourier transform, and later Li Gongquan, Lai Tao and others used this method to realize radar periodic nonlinear phase correction. The matched Fourier transform is a generalized Fourier transform for nonlinear modulated signals. This method adjusts the transform basis according to the signal form and can simultaneously achieve the resolution of multiple targets in the matched Fourier domain.

[0022] Hong Rujia and others from Xiamen University collected artificial single scattering point model echoes and extracted the distortion function from them. This distortion function was transformed into the frequency domain through processing and distortion correction was performed in the frequency domain.

[0023] In summary, the current nonlinear correction of broadband linear frequency modulation continuous wave radar is mainly focused on software methods. However, there are some common problems. On the one hand, most studies only correct the polynomial phase error and ignore the periodic phase error, resulting in false targets in the imaging results; on the other hand, the existing methods generally have the problem of insufficient noise resistance. Summary of the invention

[0024] The present application aims to provide a nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging, which solves the problem of insufficient noise resistance of nonlinear estimation and can complete amplitude error correction to further improve the imaging quality of broadband linear frequency modulation continuous wave radar.

[0025] According to one aspect of the present application, a method for nonlinear amplitude and phase error correction applicable to broadband FMCW radar imaging is provided, which is used for nonlinear amplitude and phase error correction of frequency modulated continuous wave radar, comprising:

[0026] Establishing a frequency modulated continuous wave radar difference frequency signal model containing nonlinear errors, wherein the nonlinear errors include amplitude errors and phase errors, and the phase errors include high-order polynomial phase errors and periodic multi-sinusoidal phase errors;

[0027] The amplitude error is corrected by using an envelope normalization correction method;

[0028] The phase error of the high-order polynomial is estimated by combining the phase unwrapping recursive least square method with the O'Shea optimization strategy to obtain the phase parameters of the high-order polynomial.

[0029] The periodic multi-sine phase error is estimated by using a method combining a MUSIC algorithm and a trust region algorithm to obtain a periodic multi-sine phase parameter;

[0030] Based on the high-order polynomial phase parameter and the periodic multi-sine phase parameter estimation results, the phase error correction is performed using a time domain resampling method.

[0031] According to some embodiments, the method further comprises: estimating the high-order polynomial phase parameter by using a phase unwrapping recursive least squares method to obtain a rough estimate, and then using an O'Shea optimization estimation strategy to improve the accuracy of the high-order polynomial phase parameter rough estimate.

[0032] According to some embodiments, the O'Shea optimization estimation strategy includes: demodulating the original signal using the rough estimate of the high-order polynomial phase parameter; low-pass filtering the demodulated signal using a sliding average filter to improve the signal-to-noise ratio of the demodulated signal; performing phase unwrapping on the filtered demodulated signal and performing parameter estimation using the least squares method to obtain the difference between the true value and the rough estimate of the high-order polynomial phase parameter; based on the difference between the true value and the rough estimate of the high-order polynomial phase parameter, combined with the rough estimate of the high-order polynomial phase parameter, obtaining the final precise estimate of the high-order polynomial phase parameter.

[0033] According to some embodiments, the method further comprises: using a MUSIC algorithm in combination with phase matching to obtain a rough estimate of a periodic multi-sine phase parameter, and then using a trust region algorithm to optimize the rough estimate of the periodic multi-sine phase parameter.

[0034] According to some embodiments, the method of combining the MUSIC algorithm with phase matching to obtain a rough estimate of a periodic multi-sine phase parameter includes: obtaining a frequency estimate of a periodic multi-sine phase error function using the MUSIC algorithm; constructing a phase matching function using the frequency estimate; multiplying the phase matching function with the periodic multi-sine phase error function to construct an ergodic function; and obtaining a periodic multi-sine phase parameter rough estimate in the interval The phase parameter is traversed, and the phase parameter value when the DC component of the traversal function takes the maximum value is used as the phase parameter of the frequency component, and half of the DC component of the traversal function is used as the amplitude parameter of the frequency component.

[0035] According to some embodiments, the FMCW radar difference frequency signal model including nonlinear errors

[0036] for

[0037] in, is the amplitude error, is the phase error, is the carrier frequency, is the residual video phase term, τ is the target echo signal delay, To adjust the frequency, t is the time variable of the difference frequency signal.

[0038] According to some embodiments, the phase error The model is:

[0039]

[0040] in, is the high-order polynomial phase error, is the polynomial order, are the polynomial coefficients, is the periodic multi-sinusoidal phase error, is the order of the periodic multi-sinusoidal phase error, , , are the amplitude, frequency and initial phase of the periodic multi-sinusoidal phase error respectively.

[0041] According to some embodiments, the method of correcting the amplitude error using the envelope normalization correction method includes: de-skewing the echo signal to obtain a difference frequency signal, performing modulo processing on the difference frequency signal to obtain an amplitude correction factor; applying the amplitude correction factor to the difference frequency signal, and normalizing the difference frequency signal by removing the correction factor.

[0042] According to another aspect of the present application, a nonlinear amplitude and phase error correction device suitable for broadband FMCW radar imaging is also provided, the device comprising a non-volatile memory and one or more processors, the non-volatile memory storing executable code, and the processor executing the executable code to implement the method as described above.

[0043] According to another aspect of the present application, a computer-readable storage medium is further provided, wherein the computer-readable storage medium includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the method as described above.

[0044] According to the embodiments of the present application, the method proposed in the present application combining the phase unwrapping-recursive least squares method with the O'Shea optimization for high-order polynomial phase parameter estimation has a lower signal-to-noise ratio threshold than the existing method, and under the condition that the signal-to-noise ratio exceeds the signal-to-noise ratio threshold, the mean-square error (MSE) is closer to the Cramer-Rao low bound (CRLB); the method proposed in the present application combining the MUSIC algorithm with the trust region algorithm for periodic multi-sine phase parameter estimation has a lower signal-to-noise ratio threshold than the existing method. Therefore, the present application can greatly improve the accuracy of nonlinear correction under low signal-to-noise ratio conditions.

[0045] It should be understood that the foregoing general description and the following detailed description are exemplary only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 The figure shows the comparison between linear frequency modulation signal and nonlinear frequency modulation signal, (a) is the receiving and transmitting frequency modulation signal, (b) is the intermediate frequency signal, and (c) is the spectrum of the intermediate frequency signal.

[0048] Figure 2 A flow chart of a nonlinear amplitude and phase error correction method suitable for wideband FMCW radar imaging according to an example embodiment is shown.

[0049] Figure 3 A schematic diagram of a nonlinear amplitude and phase error correction method suitable for wideband FMCW radar imaging according to an example embodiment is shown.

[0050] Figure 4 The following is a Monte Carlo simulation experiment result diagram of a nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging according to an example embodiment, wherein (a) is the Monte Carlo simulation experiment result of a high-order polynomial phase parameter estimation algorithm, and (b) is the Monte Carlo simulation experiment result of a periodic multi-sine phase parameter estimation. In the figure, the horizontal axis is the signal-to-noise ratio in dB; the vertical axis is the mean square error (MSE) in dB. In the figure legend, Proposed represents the method proposed in this application, RLS represents the recursive least squares method, HAF represents the high-order fuzzy function method, DFT-OP represents the discrete Fourier transform + optimization algorithm (this optimization algorithm can be a conventional optimization algorithm such as the Newton method or the quasi-Newton method), and CRLB represents the Cramer-Rao lower bound, which is the lower bound of the theoretically estimated variance.

[0051] Figure 5 The figure shows the simulation results of the correction experiment under different SNR conditions, where (a) is the simulation result of the correction experiment under SNR=5 dB, and (b) is the simulation result of the correction experiment under SNR=10 dB. In the legend of the figure, RLS represents the recursive least squares method, RLS+O'Shea represents the optimization of RLS using the O'Shea optimization strategy, Linear signal represents the ideal linear signal, and Nonlinear signal represents the nonlinear signal.

[0052] Figure 6The following is a comparison of simulation results of a nonlinear amplitude and phase error correction method for broadband FMCW radar imaging under different SNR conditions with existing least squares method (LSM), high-order ambiguity function method (HAF), multiple synchronous compression transform method (MSST) and other methods in high-order polynomial phase error correction, wherein (a) is a comparison of the correction results of the LSM method and the method proposed in the present application when the signal-to-noise ratio is 15, (b) is a comparison of the correction results of the LSM method and the method proposed in the present application when the signal-to-noise ratio is 5, (c) is a comparison of the correction results of the MSST method and the method proposed in the present application when the signal-to-noise ratio is 15, (d) is a comparison of the correction results of the MSST method and the method proposed in the present application when the signal-to-noise ratio is 5, (e) is a comparison of the correction results of the HAF method and the method proposed in the present application when the signal-to-noise ratio is 15; (f) is a comparison of the correction results of the HAF method and the method proposed in the present application when the signal-to-noise ratio is 5. In the legend of the figure, Linear signal represents an ideal linear signal, Nonlinearsignal represents a nonlinear signal, LSM represents the least squares method, MSST represents the multiple synchronous compression transform method, HAF represents the high-order fuzzy function method, and Proposed represents the method proposed in this application.

[0053] Figure 7 Figures showing simulation experimental data of a nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging according to an example embodiment, wherein (a) is a diagram showing the amplitude error interference and correction effect, (b) is a diagram showing the target correction effect at 10 meters, (c) is a diagram showing the simulation effect of introducing a periodic multi-sine wave phase error when correcting a point target at 10 meters, and (d) is a diagram showing the target correction effect at 17 meters and 17.5 meters.

[0054] Figure 8 A physical picture of a W-band FMCW radar is shown.

[0055] Fig. 9 A diagram showing measured data correction results of a nonlinear amplitude and phase error correction method suitable for wideband FMCW radar imaging according to an example embodiment is shown.

[0056] Fig.10 The following diagrams show the imaging correction results of a nonlinear amplitude-phase error correction method suitable for broadband FMCW radar imaging in a multi-angle anti-complex scene according to an example embodiment, wherein (a) is the imaging image before the nonlinear amplitude-phase correction, and (b) is the imaging image after the nonlinear amplitude-phase correction.

[0057] Fig.11 A block diagram of a nonlinear amplitude and phase error correction device according to an exemplary embodiment of the present application is shown. DETAILED DESCRIPTION

[0058] The embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. It should be clear that the described embodiments are only 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] Those skilled in the art should know that the following specific embodiments or specific implementations are a series of optimized settings listed by the present invention to further explain the specific content of the invention, and these settings can be combined or used in association with each other, unless the present invention clearly states that some or a specific embodiment or implementation cannot be associated or used together with other embodiments or implementations. At the same time, the following specific embodiments or implementations are only used as the most optimized settings, and are not to be understood as limiting the scope of protection of the present invention.

[0060] Nonlinear error signal model construction

[0061] Wideband linear frequency modulation continuous wave radar systems inevitably contain components with nonlinear characteristics such as mixers, power amplifiers, digital frequency synthesizers and AD / DA. When these components are used in a large bandwidth environment, they will introduce nonlinear errors that cannot be ignored. Therefore, the frequency modulation signal transmitted in the actual FMCW-SAR system is no longer an ideal linear signal.

[0062] The ideal broadband linear frequency modulated continuous wave RF signal model is expressed as:

[0063] (1)

[0064] in, is the carrier frequency, is the frequency modulation frequency, and A is the signal amplitude. The received signal is the frequency modulation signal after the time delay τ of the transmitted signal, which is expressed as:

[0065] (2)

[0066] Among them, τ is the target delay, , is the distance between the radar and the target, and c is the speed of light.

[0067] After dechirping the received signal and the transmitted signal, the ideal difference frequency signal can be obtained, that is,

[0068] (3)

[0069] in," " is the conjugate operation, represents the target beat frequency, is the residual video phase (RVP). In near-field imaging, the time delay is very small, so the RVP term can be ignored in subsequent processing. The amplitude phase error is introduced, so the difference frequency signal containing the amplitude phase error can be expressed as:

[0070] (4)

[0071] in, represents the amplitude error, Indicates the phase error.

[0072] The nonlinear phase error is modeled as:

[0073] (5)

[0074] in, is the high-order polynomial phase (PPS) error, is the polynomial order, are the polynomial coefficients, is the periodic multi-sine phase (PMSPS) error, is the order of the periodic multi-sinusoidal phase error, , , They are the amplitude, frequency, and initial phase of the periodic multi-sine phase error. The high-order polynomial phase error mainly affects the main lobe width, the near-side lobe peak, and the main lobe position. The periodic multi-sine phase error will produce paired side lobes at both ends of the main lobe, resulting in complex paired echoes at both ends of the main lobe, but will not affect the main lobe width and position.

[0075] Figure 2 A flow chart of a nonlinear amplitude and phase error correction method suitable for wideband FMCW radar imaging is shown.

[0076] Figure 3 A schematic diagram of a nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging is shown.

[0077] See also Figure 2 and Figure 3 Based on the figure, the implementation method of the present application scheme "A nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging" is explained.

[0078] In S201, a frequency modulated continuous wave radar difference frequency signal model including nonlinear errors is established.

[0079] According to some embodiments, referring to the discussion above, the method of establishing a frequency modulated continuous wave radar difference frequency signal model containing nonlinear errors is: taking an ideal linear frequency modulated continuous wave RF signal model as a transmitting signal, adding a time delay as an ideal linear frequency modulated continuous wave radar echo signal, i.e., a receiving signal; performing de-skewing processing, i.e., Dechirp, on the receiving signal and the transmitting signal to obtain an ideal difference frequency signal; adding an amplitude phase error to the ideal difference frequency signal to obtain a difference frequency signal model containing an amplitude phase error. Among them, the phase error model is the sum of a high-order polynomial phase error and a periodic multi-sinusoidal phase error.

[0080] In S202, echo signals of targets such as corner reflectors and delay lines are collected. In a FMCW-SAR system with a Dechirp structure, the echo signal is a demodulated difference frequency signal.

[0081] In S203, a modulo process is performed on the amplitude of the difference frequency signal, and the modulo process is used as an amplitude error correction factor.

[0082] In S204, the phase of the difference frequency signal is unwrapped, and a high-order polynomial phase error coefficient and a periodic multi-sine phase error coefficient are estimated and used as a phase error correction factor.

[0083] According to some embodiments, a high-order polynomial phase error estimation algorithm combining the recursive least squares method with the O'shea optimization strategy is used, which can effectively solve the problem of insufficient noise resistance of the phase unwrapping recursive least squares method with a slight increase in the amount of calculation.

[0084] The high-order polynomial phase error model of formula (5) is modified and the expression is as follows:

[0085] (6)

[0086] In the formula, is a phase error signal containing only high-order polynomials, where k and are the polynomial order and polynomial coefficient respectively. The first-order polynomial represents the distance term in the phase of the difference frequency signal. The phase error is represented by a higher-order polynomial of more than 2 times. is Gaussian white noise.

[0087] The paper "A polynomial phase parameter estimation-phase unwrapping algorithm" (BJ Slocumb and J. Kitchenin Proc. IEEE Int. Conf. Acoust. Speech, Signal Process. (ICASSP), Adelaide, Australia, Apr. 1994, vol. 4, pp.129–132) proposed a recursive least squares method for phase unwrapping.

[0088] In this embodiment, the steps of using the phase unwrapping recursive least squares method to estimate the high-order polynomial phase error are as follows:

[0089] Step 1: Phase unwrapping of the signal to obtain the difference frequency signal phase , N is the total number of difference frequency signal samples.

[0090] Step 2: Use the least square method, i.e., formula (7), to make an initial estimate of the first U unwrapped phase signals to obtain the initial estimate of the polynomial coefficients: .

[0091] (7)

[0092] in, is the Vandermonde matrix formed by the first U sample times, K is the polynomial order, is the first U unwrapped phase signal, , the superscript T represents the matrix transpose, and the superscript -1 represents the matrix inverse.

[0093] (8)

[0094] Step 3: Use the initial estimate Update Phase:

[0095] (9)

[0096] Step 4: Update the phase Perform phase unwrapping:

[0097] (10)

[0098] Angle represents the phase function. is the L+1th term of the difference frequency echo signal, is the phase signal obtained by unwrapping.

[0099] Step 5, use recursive least squares method to update the high-order polynomial coefficients:

[0100] (11)

[0101] in

[0102] (12)

[0103] is the updated phase coefficient.

[0104] Iterate steps 3 to 5 until you get The iteration is completed and a rough estimate of the phase coefficient of the high-order polynomial is obtained.

[0105] After obtaining the rough estimates of the phase coefficients of the high-order polynomial, the O'Shea optimization strategy is used to improve the accuracy of parameter estimation.

[0106] The paper "On refining polynomial phase signal parameter estimates" (P. O'Shea, IEEE Trans. Aerosp. Electron., vol. 46, no. 3, pp. 978–987, 2010) proposed the O'Shea optimization strategy.

[0107] According to some embodiments, the steps of using the O'Shea optimization strategy to improve the accuracy of parameter estimation are:

[0108] Step 6: Get the rough estimated coefficients After that, the coefficient is used to demodulate the original signal. If the accuracy of the rough estimation coefficient is high enough, the useful information of the demodulated signal will be concentrated near 0 Hz, while the noise will be evenly distributed over the entire bandwidth:

[0109] (13)

[0110] is the original signal containing high-order polynomial phase error, is the signal after demodulation.

[0111] Step 7: Use a sliding average filter to filter the demodulated signal By performing low-pass filtering, the signal-to-noise ratio of the demodulated signal will be improved.

[0112] (14)

[0113] in It represents the signal obtained after the demodulated signal is subjected to sliding filtering. , represents the number of samples of the sliding filter, N is the number of samples of the difference frequency signal, Should be compared N Small, and must be an odd number.

[0114] Step 8: After filtering, Perform phase unwrapping and use the least squares method to estimate the parameters to obtain the difference between the true value and the rough estimate , as shown below:

[0115] (15)

[0116] Among them, angle represents the phase function, unwrap represents phase unwrapping, k is the polynomial order.

[0117] Step 9: Estimated value based on the above formula , combined with the rough estimate , and obtain the final high-order polynomial phase parameter estimate :

[0118] (16)

[0119] Through the above steps 6 to 9, the optimization of the rough estimation value of the high-order polynomial phase parameter is completed.

[0120] In actual scenarios, after the above-mentioned polynomial phase error correction, the side lobes of the range compression image can generally be suppressed to a large extent. However, the existence of periodic multi-sinusoidal phase errors will produce paired echoes near the target, seriously affecting the detection of weak targets close to the main target.

[0121] According to some embodiments, a MUSIC algorithm is combined with phase matching to obtain a rough estimate of a periodic multi-sine phase parameter, and then a trust region algorithm is used to optimize the rough estimate of the periodic multi-sine phase parameter.

[0122] The periodic multi-sinusoidal phase error can be regarded as the residual phase after the original phase is corrected by a high-order polynomial phase error:

[0123] (17)

[0124] is the original phase unwrapped data of the difference frequency signal, is the estimated high-order polynomial phase error. Since phase unpacking is not required here, the periodic multi-sine phase error estimation can be transformed into multi-component sinusoidal signal parameter estimation. Therefore, the periodic multi-sine phase error in formula (5) can be simplified as:

[0125] (18)

[0126] in, is the amplitude coefficient of the periodic phase error, is the frequency coefficient, is the phase coefficient, subscript m Indicates the serial number of the periodic multi-sinusoidal phase error signal, t is the time variable, the constant term , this item does not affect the subsequent sinusoidal parameter estimation. The parameter estimation of real sinusoidal signals with noise is generally based on frequency estimation to estimate other parameters, and the MUSIC algorithm is used to estimate the frequency of multi-component sinusoidal signals.

[0127] The basic idea of ​​the MUSIC algorithm is to perform eigenvalue decomposition on the signal autocorrelation matrix to obtain the signal subspace corresponding to the signal component and the noise subspace orthogonal to the signal component. Then the orthogonality of the signal subspace and the noise subspace is used to estimate the signal parameters. The steps of the MUSIC algorithm to estimate the frequency of a multi-component sinusoidal signal are as follows:

[0128] Determine the order M of the multi-component sinusoidal signal model;

[0129] Constructing the Autocorrelation Matrix Using Phase Signal Data

[0130] (19)

[0131] in, is the mathematical expectation. Perform eigenvalue decomposition and calculate the eigenvalues Sorting by size, signal subspace The noise subspace consists of the first 2M eigenvectors. It consists of the last H–2M eigenvectors, where H is the number of eigenvalues. is the noise variance.

[0132] (20)

[0133] According to the orthogonality of the characteristic subspace and the noise subspace, the spectral function Perform a frequency search for P peak points to obtain an estimated frequency value .

[0134] (twenty one)

[0135] in

[0136] (twenty two)

[0137] After obtaining the frequency estimated by the MUSIC algorithm, the frequency parameter is used to construct the phase matching function:

[0138] (twenty three)

[0139] The phase matching function is combined with the periodic multi-sinusoidal phase error signal Multiply to get the traversal function :

[0140] (twenty four)

[0141] when , then the DC component is ,exist right When the DC component reaches its maximum value, the phase parameter of the frequency component is obtained, and half of the DC component is the amplitude parameter of the frequency component.

[0142] At this point, a rough estimate of the periodic multi-sinusoidal phase parameters can be obtained.

[0143] The steps for optimizing the rough estimate of periodic multi-sinusoidal phase parameters using the trust region algorithm are as follows:

[0144] Establish a periodic multi-sinusoidal phase parameter optimization objective function model:

[0145] (25)

[0146] in are the coefficients to be optimized, Represents the original periodic sinusoidal phase signal, and the nonlinear least squares objective function can be expressed as:

[0147] (26)

[0148] function The extreme point The objective function When solving nonlinear least squares problems, the trust region algorithm is used to At the point Taylor expansion to quadratic terms:

[0149] (27)

[0150] In the formula, and They are exist The gradient vector and Hesse matrix at ; yes The main idea of ​​the trust region algorithm is to In the neighborhood of The minimum approximation of , and order As The new approximation of the minimum solution is obtained by iterating the above process. When the estimated error satisfies the iteration termination error, the algorithm terminates.

[0151] In S205, echo data of the actual scene is collected.

[0152] In S206, an amplitude normalization process is performed using the amplitude error correction factor to correct the amplitude error; and a phase error correction factor is used to correct the phase error through time resampling.

[0153] According to some embodiments, an amplitude normalization process is performed using an amplitude error correction factor to correct the amplitude error, and the specific steps are as follows:

[0154] The difference frequency signal is modulo processed, that is, its amplitude information is obtained, while the phase information is ignored, and the amplitude correction factor is obtained.

[0155] Envelope normalization processing: Apply the amplitude correction factor to the difference frequency signal, and normalize the frequency domain difference frequency signal by removing the correction factor.

[0156] The paper "Shortrange wideband FMCW radar for millimetric displacement measurements" (A. Anghel, G. Vasile, R. Cacoveanu, C. Ioana, and S. Ciochina, IEEE Trans. Geosci. Remote Sens., vol. 52, no. 9, pp. 5633–5642, Sep. 2014) proposed a time domain resampling method.

[0157] According to some embodiments, the steps of correcting the phase error using the time domain resampling method using the phase error correction factor are as follows:

[0158] As shown in formula (4), the sampled difference frequency signal can be expressed as:

[0159] (28)

[0160] in, is the sampling time interval.

[0161] Rebuild the phase model:

[0162] (29)

[0163] The purpose of nonlinear correction is to extract the target distance term , eliminating the higher-order terms above the second order and the periodic multi-sinusoidal phase error terms, so the corrected difference frequency signal model is as follows:

[0164] (30)

[0165] The resampling process is to convert the traditional time variable Convert to time variable , that is, the phase of the difference frequency signal is about the new variable The target distance term becomes Therefore, all nonlinear errors of the target are eliminated simultaneously.

[0166] In S207, imaging processing is performed on the echo data after the amplitude error and phase error correction.

[0167] Figure 4 The following is a diagram showing the results of a Monte Carlo simulation experiment of a nonlinear amplitude-phase error correction method suitable for wideband FMCW radar imaging according to an example embodiment, wherein (a) is the Monte Carlo simulation experiment result of a high-order polynomial phase parameter estimation algorithm, and (b) is the Monte Carlo simulation experiment result of a periodic multi-sinusoidal phase parameter estimation algorithm.

[0168] In order to prove the superiority of the method of the present application, a Monte Carlo simulation experiment was conducted to verify the estimation performance of the method of the present application under different signal-to-noise ratios. First, 500 Monte Carlo experiments were conducted on one of the high-order polynomial phase parameters. The results are shown in Figure 2. Figure 4 As shown in (a). The method proposed in this application (labeled as proposed in the legend) is compared with the unoptimized phase unwrapping recursive least squares method (labeled as RLS in the legend) and the traditional HAF method (labeled as HAF in the legend). The experimental results show that the method proposed in this application has a lower signal-to-noise ratio threshold than the other two types of methods, and when the signal-to-noise ratio exceeds the signal-to-noise ratio threshold, the mean-square error (MSE) is closer to the Cramer-Rao low bound (CRLB) (labeled as CRLB in the legend).

[0169] Figure 4(b) shows the results of periodic multi-sinusoidal phase parameter estimation under different SNRs. The experimental results show that the parameter estimation method based on the MUSIC algorithm and the trust region algorithm proposed in this application (marked as proposed in the legend) has a lower SNR threshold than the method based on DFT and trust region algorithm optimization (marked as DFT-OP in the legend). This is because the MUSIC algorithm has a higher frequency resolution than the conventional DFT algorithm, which provides a more accurate initial value for the subsequent optimization algorithm, thereby improving the accuracy of the calculation.

[0170] Figure 5 The figure shows the correction experiment simulation result under different SNR conditions, where (a) is the correction experiment simulation result under SNR=5 dB, and (b) is the correction experiment simulation result under SNR=10 dB.

[0171] Figure 5 It shows the necessity of introducing O'Shea algorithm for high-order polynomial phase parameter estimation under low SNR conditions, such as Figure 5 As shown in (b), when SNR = 10, the correction results are almost the same with or without O'Shea's optimization; but when SNR = 5, the correction fails without O'Shea. This shows that the traditional RLS method encounters difficulties in a low signal-to-noise ratio environment, and the algorithm introduced by the O'Shea optimization proposed in this application has high robustness, which verifies the necessity of introducing O'Shea optimization.

[0172] Figure 6 The following is a comparison of simulation results of a nonlinear amplitude and phase error correction method for broadband FMCW radar imaging under different SNR conditions, with existing least squares method (LSM), high-order ambiguity function method (HAF), multiple synchronous compression transform method (MSST) and other methods in performing high-order polynomial phase error correction, wherein (a) is a comparison of the correction results of the LSM method and the method proposed in the present application when the signal-to-noise ratio is 15, (b) is a comparison of the correction results of the LSM method and the method proposed in the present application when the signal-to-noise ratio is 5, (c) is a comparison of the correction results of the MSST method and the method proposed in the present application when the signal-to-noise ratio is 15, (d) is a comparison of the correction results of the MSST method and the method proposed in the present application when the signal-to-noise ratio is 5, (e) is a comparison of the correction results of the HAF method and the method proposed in the present application when the signal-to-noise ratio is 15; (f) is a comparison of the correction results of the HAF method and the method proposed in the present application when the signal-to-noise ratio is 5.

[0173] Figure 6In the figure, the one-dimensional distance profile of the uncorrected nonlinear difference frequency signal is marked as Nonlinearsignal in the legend, the one-dimensional distance profile of the linear difference frequency signal is marked as linear signal in the legend, the one-dimensional distance profile after the nonlinear difference frequency signal is corrected by the least squares method (LSM) is marked as LSM in the legend, the one-dimensional distance profile after the nonlinear difference frequency signal is corrected by the MSST method is marked as MSST in the legend, the one-dimensional distance profile after the nonlinear difference frequency signal is corrected by the HAF method is marked as HAF in the legend, and the one-dimensional distance profile after the nonlinear difference frequency signal is corrected by the method of the present application is marked as Proposed in the legend.

[0174] like Figure 6 As shown in the figure, when the signal-to-noise ratio is 5 and the signal-to-noise ratio is 10, the high-order polynomial nonlinear phase error correction is performed, and the method proposed in this application, the HAF method, the MSST method, and the traditional least square method (LSM) are used to estimate the high-order polynomial phase error. In order to achieve nonlinear correction, time resampling is used for unified processing. After correction, Figure 6 (a)–(f) show the one-dimensional range profile of the difference frequency signal. Figure 6 (a), (c) and (e) compare the correction results of the method proposed in this application with those of the other three methods when the signal-to-noise ratio is 15. Figure 6 (b), (d) and (f) compare the correction results of the method proposed in this application with those of the other three methods when the signal-to-noise ratio is 5. The results show that at a higher signal-to-noise ratio, the correction results of the other three methods are similar to those of the method proposed in this application. However, at a lower signal-to-noise ratio, the other three methods all show correction failures to varying degrees, while the method proposed in this application is still effective, and its correction results are close to the ideal state. Therefore, the method proposed in this application shows superiority in nonlinear correction.

[0175] In order to prove the practicability and feasibility of the method of this application, a simulation experiment was carried out.

[0176] Table 1 Wideband FMCW radar system parameters

[0177]

[0178] Figure 7 A simulation experimental data diagram of a nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging is shown.

[0179] like Figure 7As shown in (a), after the LFM signal is processed by amplitude distortion, a pair of side lobes will appear. The distance between the side lobes and the target main lobe is about 0.5 meters, which is equivalent to a main lobe frequency offset of 10kHz. For amplitude error correction, the envelope normalization correction method is adopted, that is, the echo of the corner reflector or delay line is de-slanted, and the difference frequency signal envelope is extracted as the correction factor. The correction factor is used to perform amplitude correction on other targets in the same scene. The simulation correction effect is shown in Figure 7 (a) shown.

[0180] The system simulation parameters are set according to the parameters listed in Table 1. The simulation targets are set to 10 meters, 17 meters, and 17.5 meters respectively. The range imaging effects before and after correction are shown in Figure 1. Figure 7 (b)(d) As shown. Figure 7 The polynomial phase error shown increases the target side lobes, disperses the main lobe, and reduces the range resolution. As the distance increases, the phase error will cause the resolution to deteriorate further. After estimating and correcting the phase error using the method proposed in this application, as shown in Figure 7 As shown in (b), after the target at 10 meters is corrected, the result is comparable to the ideal model. Figure 7 As shown in (d), the peak sidelobe ratio (PSLR) at 17 meters and 17.5 meters is reduced to -13.05dB and -13.10 dB respectively, which is very close to the PSLR of the ideal model. At the same time, the main lobe can also be focused to the ideal state.

[0181] To verify the periodic multi-sinusoidal phase error correction algorithm, simulations are performed using the same system parameters in Table 1 and a third-order sinusoidal periodic phase error is introduced. To highlight the impact of the periodic error, a Hamming window is added to the main lobe. Figure 7 As shown in (c), the periodic phase error can lead to paired side lobes near the main lobe. The simulation results show that the periodic phase error has no effect on the resolution, but will produce serious paired side lobes, resulting in a decrease in the peak sidelobe ratio. However, after correction, the side lobes can be close to the side lobes of the ideal model.

[0182] Figure 8 A physical picture of a W-band FMCW radar is shown.

[0183] Fig. 9 A diagram showing measured data correction results of a nonlinear amplitude and phase error correction method suitable for wideband FMCW radar imaging according to an example embodiment is shown.

[0184] Fig.10 A diagram showing imaging correction results of a nonlinear amplitude and phase error correction method suitable for wideband FMCW radar imaging in a multi-angle anti-complex scene according to an example embodiment is shown.

[0185] In order to verify the effectiveness of the amplitude and phase error correction method proposed in this application, an imaging experiment was carried out using a W-band FMCW radar system. Figure 8 As shown. The system first uses a corner reflector or a delay line to collect the nonlinear error of the system, and then uses the proposed amplitude and phase error correction algorithm to correct it. Therefore, the correction technology proposed in this application can be widely used without the need for additional auxiliary correction devices.

[0186] The amplitude and phase correction factors are extracted using the angle echo data, and then the system nonlinear error correction is achieved through time domain resampling, such as Fig. 9 As shown in the figure, the intercepted distance profile of the measured echo data at about 3 meters is subjected to amplitude correction, polynomial phase correction and periodic multi-sine phase correction in sequence. It can be seen from the figure that the side lobes of the original image (red dotted line) are very high, and after amplitude correction (green solid line), the side lobes are slightly reduced. After high-order polynomial phase error correction (blue dotted line), the main lobe moves, and the side lobes at the near end are well suppressed. Finally, through periodic multi-sine phase error correction, the side lobes at farther distances are also well suppressed. Fig.10 These are some correction effect diagrams for complex scenes. For the nonlinear error correction of multiple corner reflectors in the same scene, the nonlinear error coefficient extracted from a single corner reflector is used for correction. Fig.10 (a) shows the imaging result before correction, where each corner reflector has a different degree of defocusing at a distance, resulting in many false targets in front of and behind the target, and the scattering characteristics of each corner reflector show similar regularity. Fig.10 (b) shows the corrected imaging result, where each corner reflector is focused at a distance, false targets are eliminated, and the distance resolution is significantly improved. The multi-corner reflector experiment shows that the method proposed in this application can effectively correct the nonlinear errors of multiple targets in the same scene.

[0187] It can be seen from the above measured data results that the method proposed in this application can effectively improve the detection and imaging effects of the target and has good engineering applicability.

[0188] Fig.11 A block diagram of a nonlinear amplitude and phase error correction device according to an exemplary embodiment of the present application is shown.

[0189] like Fig.11 As shown, a nonlinear amplitude and phase error correction device suitable for broadband FMCW radar imaging is provided, including a non-volatile memory and one or more processors, wherein the non-volatile memory stores executable code, and when the processor executes the executable code, it is used to implement the multimodal contrast learning method based on optimal transmission theory in the above embodiment.

[0190] The embodiment of a nonlinear amplitude and phase error correction device suitable for broadband FMCW radar imaging provided in the present application can be applied to any device with data processing capabilities, and the device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented through software, or through hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capabilities in which it is located reading the corresponding computer program instructions in the non-volatile memory into the internal memory for execution. From a hardware perspective, if Fig.11 As shown in FIG. 1 , a hardware structure diagram of a nonlinear amplitude and phase error correction device for broadband FMCW radar imaging according to the present invention is provided for any device with data processing capability, except Fig.11 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in which the apparatus in the embodiments is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0191] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0192] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of the present invention. Ordinary technicians in this field can understand and implement it without paying creative work.

[0193] A specific embodiment of the present application further provides a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, a nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging in the above embodiment is implemented.

[0194] The computer-readable storage medium may be an internal storage unit of any device with data processing capability described in any of the aforementioned embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be an external storage device of any device with data processing capability, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capability. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capability, and may also be used to temporarily store data that has been output or is to be output.

[0195] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A nonlinear amplitude and phase error correction method suitable for broadband FMCW radar imaging, used for nonlinear amplitude and phase error correction of frequency modulated continuous wave radar, characterized in that: include: Establishing a frequency modulated continuous wave radar difference frequency signal model containing nonlinear errors, wherein the nonlinear errors include amplitude errors and phase errors, and the phase errors include high-order polynomial phase errors and periodic multi-sinusoidal phase errors; The amplitude error is corrected by using an envelope normalization correction method; The phase error of the high-order polynomial is estimated by combining the phase unwrapping recursive least square method with the O'Shea optimization strategy to obtain the phase parameters of the high-order polynomial. The periodic multi-sine phase error is estimated by using a method combining a MUSIC algorithm and a trust region algorithm to obtain a periodic multi-sine phase parameter; Based on the high-order polynomial phase parameter and the periodic multi-sine phase parameter estimation results, a time domain resampling method is used to perform the phase error correction; The method of combining the phase unwrapping recursive least squares method with the O'Shea optimization strategy to estimate the phase error of the high-order polynomial is achieved through the following process: using the phase unwrapping recursive least squares method to estimate the phase parameters of the high-order polynomial to obtain a rough estimate, and then using the O'Shea optimization strategy to improve the accuracy of the rough estimate of the phase parameters of the high-order polynomial; The O'Shea optimization strategy includes: Demodulating the original signal using the coarse estimated value of the high-order polynomial phase parameter; The demodulated signal is low-pass filtered using a sliding average filter to improve the signal-to-noise ratio of the demodulated signal; Performing phase unwrapping on the filtered demodulated signal and performing parameter estimation using a least square method to obtain a difference between a true value and a coarse estimated value of the phase parameter of the high-order polynomial; Based on the difference between the true value and the rough estimate of the high-order polynomial phase parameter, combined with the rough estimate of the high-order polynomial phase parameter, a final precise estimate of the high-order polynomial phase parameter is obtained.

2. The method according to claim 1, characterized in that The method of estimating the periodic multi-sine phase error by combining the MUSIC algorithm with the trust region algorithm is achieved through the following process: the MUSIC algorithm is combined with phase matching to obtain a rough estimate of the periodic multi-sine phase parameter, and then the trust region algorithm is used to optimize the rough estimate of the periodic multi-sine phase parameter.

3. The method according to claim 2, characterized in that The method of combining the MUSIC algorithm with phase matching to obtain a rough estimate of periodic multi-sine phase parameters includes: The MUSIC algorithm is used to obtain the frequency estimate of the periodic multi-sinusoidal phase error function; constructing a phase matching function using the frequency estimate; Multiplying the phase matching function with the periodic multi-sine phase error function to construct an ergodic function; In the interval The phase parameter is traversed, and the phase parameter value when the DC component of the ergodic function takes the maximum value is used as the phase parameter of the frequency estimation value, and half of the DC component of the ergodic function is used as the amplitude parameter of the frequency estimation value.

4. The method according to claim 1, characterized in that: The frequency modulated continuous wave radar difference frequency signal model containing nonlinear errors for in, is the amplitude error, is the phase error, is the carrier frequency, is the residual video phase term, τ is the target echo signal delay, To adjust the frequency, t is the time variable of the difference frequency signal.

5. The method according to claim 4, characterized in that Said The model is in, is the high-order polynomial phase error, is the polynomial order, are the polynomial coefficients, is the periodic multi-sinusoidal phase error, is the order of the periodic multi-sinusoidal phase error, , , are the amplitude, frequency and initial phase of the periodic multi-sinusoidal phase error respectively.

6. The method according to claim 1, characterized in that The use of the envelope normalization correction method to correct the amplitude error is achieved by: De-skewing the echo signal to obtain a difference frequency signal; Performing modulo processing on the difference frequency signal to obtain an amplitude correction factor; The amplitude correction factor is applied to the difference frequency signal, and the difference frequency signal is normalized by removing the correction factor.

7. A nonlinear amplitude and phase error correction device suitable for wideband FMCW radar imaging, comprising a nonvolatile memory and one or more processors, wherein the nonvolatile memory stores executable code, and when the processor executes the executable code, it is used to implement the nonlinear amplitude and phase error correction method suitable for wideband FMCW radar imaging according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the nonlinear amplitude and phase error correction method applicable to wideband FMCW radar imaging according to any one of claims 1 to 6.

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