Frequency modulation step radar motion compensation method under low signal-to-noise ratio condition

Abstract

The application discloses a frequency modulation step-by-step radar motion compensation method under a low signal-to-noise ratio condition, and specific steps include: processing a received echo to obtain a one-dimensional range image spectrum of each sub-pulse, and intercepting an overlapping spectrum of adjacent sub-pulses; performing inverse Fourier transform on the overlapping spectrum to obtain a corresponding time domain signal; calculating an initial phase difference at a main peak position of the time domain signal; accumulating to construct a phase compensation factor; and performing phase correction on a sub-pulse frequency domain signal by using the phase compensation factor. The application directly utilizes the overlapping spectrum of adjacent sub-pulses to complete initial phase estimation introduced by target translation, extracts a phase difference at a main peak position of echo energy concentration, effectively suppresses interference of noise and non-main scattering points, makes the phase estimation process more robust, has low calculation complexity, and improves adaptability under a complex motion scene.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and further relates to a motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio (SNR) conditions in high-resolution one-dimensional range imaging technology. This invention can be used to compensate for the initial phase difference introduced by target translation between sub-pulses when performing frequency-domain bandwidth synthesis of frequency-modulated stepping signals under low SNR conditions, thereby improving the range image quality. Background Technology

[0002] High range resolution is one of the key technical specifications of imaging radar systems. Achieving high range resolution typically requires transmitting radar signals with a large time span and wide bandwidth. However, due to limitations in transmission and reception hardware, directly implementing a large-bandwidth linear frequency modulated (LFM) signal presents certain challenges. LFM stepped signals, as an equivalent broadband signal, consist of multi-carrier stepped LFM sub-pulse signals. Each LFM sub-pulse has a relatively narrow instantaneous bandwidth. By performing frequency domain bandwidth synthesis processing on the sub-pulse echo signals, a range resolution comparable to that of a large-time-span broadband LFM signal can be obtained, thus demonstrating significant application value in imaging radar systems. When using LFM stepped signals for bandwidth synthesis, target translation introduces an additional initial phase difference between adjacent sub-pulses. If this initial phase difference cannot be effectively compensated, the frequency domain bandwidth synthesis result will become decoherent, affecting the range image quality. Therefore, compensating for the initial phase introduced by target translation is a prerequisite for achieving frequency domain bandwidth synthesis of LFM stepped signals.

[0003] Beijing Institute of Technology proposed a high-speed target synthetic broadband imaging method based on echo model inversion in its patent application, "A High-Speed ​​Target Synthetic Broadband Imaging Method Based on Echo Model Inversion" (Patent Application No.: CN202211659671.X, Publication No.: CN116299445A). The specific steps of this method are as follows: First, a high-speed target echo model based on the radar's transmitted frequency-modulated step signal is established, which needs to consider the influence of intra-pulse Doppler modulation. Then, high-precision velocity information is obtained by performing phase estimation acceleration processing on pulses with the same frequency point in different frame echoes. Finally, synthetic broadband imaging processing is performed. Based on compensation for intra-pulse Doppler modulation and inter-pulse range migration, pulse compression processing is performed using a reference signal containing modulation factors. Then, spectral truncation and stitching processing is performed, and phase jumps at the stitching points are compensated to reconstruct a wide spectrum with linear phase, obtaining high-quality synthetic broadband imaging results. However, the drawback of this method is that it requires the establishment of a target echo model that includes intra-pulse Doppler modulation and inter-pulse distance migration, and relies on target motion parameter estimation to complete motion compensation. When the echo signal-to-noise ratio is low, the model matching error and parameter estimation error increase, which in turn affects the phase compensation accuracy.

[0004] Xi'an University of Electronic Science and Technology proposed a high-speed target velocity estimation method based on a coarse-fine combined search using minimum entropy in its patent application, "High-Speed ​​Target Velocity Estimation Method Based on Coarse-Fine Combined Search Using Minimum Entropy" (Patent Application No.: CN202511480578.6, Publication No.: CN121410692A). The specific steps of this method are as follows: First, the characteristics of the frequency-modulated step signal are used to perform bandwidth synthesis processing on the linear frequency-modulated step echo to obtain a broadband echo signal. Then, a coarse velocity search is performed under multiple candidate velocities. A phase compensation function is constructed to perform phase compensation and coherent accumulation on the sub-pulses. The optimal coarse velocity is determined based on the waveform entropy value of the range image. Based on this, intra-pulse Doppler coupling compensation and range compression processing are completed, and a fine grid search is performed in the coarse velocity neighborhood. Finally, the optimal fine velocity is obtained based on the minimum entropy criterion, realizing the velocity estimation of high-speed targets and high-resolution synthetic broadband imaging. However, the drawback of this method is that it adopts a coarse-fine two-level velocity search framework based on the minimum entropy criterion, which requires explicit estimation of the target's velocity. When the noise is large, the velocity search decision is easily affected by noise, leading to an increase in estimation error and thus affecting the quality of the range image. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technologies by proposing a motion compensation method for frequency-modulated step radar under low signal-to-noise ratio conditions. This method solves the problem that existing technologies typically rely on target echo models or explicit estimation of target motion parameters to construct phase compensation functions. Under low signal-to-noise ratio conditions, the model matching error and parameter estimation error increase, leading to a decrease in phase compensation accuracy.

[0006] To achieve the above objectives, the technical approach of this invention is as follows: Based on the step interval between the carrier frequencies of adjacent sub-pulses in a frequency-modulated step signal, this invention extracts the overlapping spectral portions in the one-dimensional range image spectrum of adjacent sub-pulses and uses this overlapping spectrum to estimate the initial phase introduced by target translational motion. This solves the problem that existing technologies, which achieve motion compensation by establishing echo models or explicitly estimating motion parameters, are prone to model mismatch and target motion parameter estimation deviations in low signal-to-noise ratio environments. This invention converts the overlapping spectrum to the time domain and determines the initial phase difference between adjacent sub-pulses by analyzing the phase information at the main peak position of the converted time-domain signal. Since the main peak position in the time domain corresponds to the main energy concentration area of ​​the target echo, calculating the phase difference at this position can effectively improve the stability of phase estimation and solve the problem that existing technologies are susceptible to noise interference in phase difference estimation under low signal-to-noise ratio conditions, leading to a decrease in phase compensation stability and imaging quality.

[0007] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0008] Step 1: Process the received frequency-modulated step radar echo signal to obtain the one-dimensional range image spectrum corresponding to each sub-pulse;

[0009] Step 2: Generate the overlapping spectrum between adjacent sub-pulses, and convert the two overlapping spectrum segments to the same frequency range using a frequency mapping method;

[0010] Step 3: Perform inverse Fourier transform on the overlapping spectrum data extracted from adjacent sub-pulses to obtain the corresponding time-domain signals, determine the main peak position of each time-domain signal, and calculate the initial phase difference between each sub-pulse;

[0011] Step 4: Accumulate the initial phase difference between adjacent sub-pulses, construct a phase compensation factor, and perform phase correction on the frequency domain signal of the sub-pulses;

[0012] Step 5: The frequency domain signals of each sub-pulse are spliced ​​together according to the carrier frequency order to construct a continuous wide spectrum, and the wide spectrum is subjected to inverse Fourier transform to obtain a high-resolution range image.

[0013] Furthermore, the processing of the received frequency-modulated step radar echo signal refers to multiplying the echo signal of a set of received linear frequency-modulated step frequency signals with the local oscillator signal, and converting the sub-pulse echo signal of the echo signal into the following baseband video signal:

[0014] ;

[0015] in, Indicates the first At the [time]th moment The baseband video signal after frequency modulation processing of the sub-pulse echo signal. , Indicates a fast time. Indicates the first The transmission time of each sub-pulse , , This represents the total number of sub-pulses in a set of linear frequency modulated step signals. This indicates the repetition period of the sub-pulse. Indicates the scattering intensity at the scattering point. Represents a linear frequency modulated subpulse In the transmission delay The time delay form under the action, , Represents the gate function. Indicates the pulse width. Represented by natural constant Index-based operations. Represents the imaginary unit. Represents pi (π). Indicates the frequency modulation slope. , Indicates the bandwidth of the sub-pulse signal. Indicates the launch number The distance between the radar and the target scattering point when a sub-pulse signal is received. , Indicates the initial distance of the scattering point. Indicates the radial velocity of the target. Represents the speed of light. Indicates the first The carrier frequency of each sub-pulse , Indicates the starting carrier frequency. This indicates the carrier frequency step interval.

[0016] Furthermore, the one-dimensional range profile spectrum corresponding to each sub-pulse is as follows:

[0017] ;

[0018] in, Indicates the first The one-dimensional range image spectrum corresponding to each sub-pulse Indicates the baseband frequency variable. , Indicates the amplitude symbol. Indicates the first The linear phase term introduced by the radial motion of the target in each sub-pulse. , Indicates the first The initial phase term is introduced by the carrier frequency jump of the sub-pulse and the target's motion velocity. .

[0019] Furthermore, the step of generating overlapping spectral data between adjacent sub-pulses is as follows:

[0020] The first step is to use the envelope alignment method to compensate the one-dimensional range image spectrum corresponding to each sub-pulse, and the compensated spectrum signal of each sub-pulse is as follows:

[0021] ;

[0022] in, Indicates the first The spectrum signal of the one-dimensional range image spectrum corresponding to each sub-pulse after envelope alignment compensation;

[0023] The second step is to extract the envelope alignment compensation data according to the following formula. The latter half of the spectrum of the one-dimensional range image of each sub-pulse and the first The first half of the one-dimensional range image spectrum of each sub-pulse is obtained.

[0024] ;

[0025] ;

[0026] in, Indicates the compensation after the first The latter half of the one-dimensional range image spectrum of each sub-pulse. Indicates the first The frequency variable of the second half of the spectrum of the one-dimensional range image of each sub-pulse. , Indicates the first The initial phase introduced by the carrier frequency jump of the sub-pulse and the target's motion velocity. , Indicates the compensation after the first The first half of the one-dimensional range image spectrum of each sub-pulse No. The frequency variable of the first half of the spectrum of the one-dimensional range image of each sub-pulse .

[0027] Furthermore, the steps for converting two overlapping spectrum segments to the same frequency range using the frequency mapping method are as follows:

[0028] Will Substitute into the first The first half of the spectrum of the one-dimensional range image of the sub-pulse In the middle, we get:

[0029] ;

[0030] in, Indicates the frequency mapping and the first The latter half of the one-dimensional range image spectrum of each sub-pulse The first in the same frequency range The first half of the spectrum of the one-dimensional range image of the sub-pulse.

[0031] Furthermore, the time-domain signal corresponding to the overlapping spectrum of the adjacent sub-pulses is as follows:

[0032] ;

[0033] ;

[0034] in, Indicates the first At the [time]th moment The time-domain signal corresponding to the overlapping spectrum of the sub-pulses Represents the Sink function, Indicates the first At the [time]th moment The time-domain signal corresponding to the overlapping spectrum of the sub-pulses.

[0035] Furthermore, determining the main peak position of each time-domain signal means that the time-domain signals corresponding to the overlapping spectra of adjacent sub-pulses have the same envelope shape and are all within... At the point where the maximum amplitude is obtained, The location was determined to be the main peak position of the signal.

[0036] Furthermore, the step of calculating the initial phase difference between each sub-pulse is as follows:

[0037] The first step is to extract the phase of the complex signal at the main peak position of the time-domain signal corresponding to the overlapping spectrum of two adjacent sub-pulses. The phase of the complex signal at the main peak position of the time-domain signal corresponding to the overlapping spectrum of adjacent sub-pulses is as follows:

[0038] ;

[0039] ;

[0040] in, Indicates the first The phase of the complex signal at the main peak position of the time-domain signal corresponding to the overlapping spectrum of each sub-pulse. Indicates the first The phase of the complex signal at the main peak position of the time-domain signal corresponding to the overlapping spectrum of the sub-pulses.

[0041] The second step is to perform a differential operation on the phase of the complex signal at the main peak of adjacent sub-pulses to obtain the initial phase difference between each sub-pulse as follows:

[0042] ;

[0043] in, Indicates the first Subpulse and The initial phase difference between the sub-pulses.

[0044] Furthermore, the step of accumulating the initial phase difference between adjacent sub-pulses to construct the phase compensation factor is as follows:

[0045] The first step is to successively accumulate the initial phase difference between adjacent sub-pulses to obtain the phase compensation amount for each sub-pulse:

[0046] ;

[0047] in, Indicates the first Phase compensation amount of each sub-pulse. , The summation symbol is used to represent the summation symbol. Indicates the first Sub-pulse and the first The initial phase difference between the sub-pulses;

[0048] The second step is to construct the phase compensation factor for each sub-pulse based on the phase compensation amount of each sub-pulse, as follows:

[0049] ;

[0050] in, Indicates the first Phase compensation factor for each sub-pulse.

[0051] Furthermore, the corrected spectral signals of each sub-pulse are as follows:

[0052] ;

[0053] in, Indicates the first The spectrum signal after sub-pulse correction.

[0054] Compared with the prior art, the present invention has the following advantages:

[0055] First, because the present invention directly estimates the initial phase difference between sub-pulses by using the phase relationship at the main peak of the time domain corresponding to the overlapping spectrum of adjacent sub-pulses, it overcomes the problem of decreased phase compensation accuracy caused by model mismatch and parameter estimation errors when the signal-to-noise ratio is low in the prior art. This allows the present invention to not rely on the construction of the target echo model, nor to perform explicit estimation of motion parameters. Instead, it directly uses the overlapping spectrum of adjacent sub-pulses to complete the initial phase estimation of the target translational motion, reducing the dependence on the target motion model and improving the adaptability of the frequency-modulated stepping radar motion compensation method in complex motion scenarios.

[0056] Second, this invention transforms the overlapping spectrum of adjacent sub-pulses to the time domain and extracts the phase difference at the main peak position of the echo energy concentration. Since the main peak position corresponds to the main energy region of the target echo, its equivalent signal-to-noise ratio is high. Calculating the phase difference at this position can effectively reduce the interference of noise on phase estimation. Using the phase information at the main peak in the time domain corresponding to the overlapping spectrum for phase difference estimation overcomes the shortcomings of existing technologies where model matching errors and parameter estimation errors increase under low signal-to-noise ratio conditions. This invention effectively suppresses the interference of noise and non-main scattering points, making the phase estimation process more robust. Furthermore, this method only involves inverse Fourier transform and difference operations, with a clear algorithm structure, low computational complexity, and ease of engineering implementation. Attached Figure Description

[0057] Figure 1 This is a flowchart of the present invention;

[0058] Figure 2 These are comparison images of high-resolution range images of stationary and moving targets obtained under different processing methods in simulation experiment 1 of this invention;

[0059] Figure 3 This is a comparison image of high-resolution distance images obtained by the method of this invention and existing technologies under different signal-to-noise ratio conditions in simulation experiment 2 of this invention. Detailed Implementation

[0060] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0061] Reference Figure 1 The implementation steps of the embodiments of the present invention will be described in further detail below.

[0062] Step 1: Process the received frequency-modulated step radar echo signal to obtain the one-dimensional range image spectrum corresponding to each sub-pulse.

[0063] Step 1.1: Transmit a set of linear frequency modulated step frequency signals, and perform frequency mixing processing on the echo signals of each sub-pulse to obtain the corresponding baseband video signal.

[0064] Assume the step frequency signal is from Composed of linear frequency modulated subpulses, the first... The transmitted signal of each sub-pulse can be represented as:

[0065] ;

[0066] in, For chirp sub-pulses, For gate functions, Indicates the frequency modulation slope. The bandwidth of the sub-pulse signal. The pulse width. For the first The carrier frequency of each sub-pulse This is the carrier frequency step interval. To save time, Indicates the first The transmission time of each sub-pulse This is the pulse repetition period.

[0067] Under the 'stop-go' motion hypothesis, when the first... When a sub-pulse signal is received, the distance between the radar and the target scattering point can be expressed as:

[0068] ;

[0069] in, Indicates the initial distance of the scattering point. This represents the radial velocity of the target. Assuming the target is an isolated scattering point, then the... The expression for the video signal obtained after the echo signals of the sub-pulses are mixed is as follows:

[0070] ;

[0071] in, At the speed of light, The intensity of the scattering point.

[0072] Step 1.2: Perform matched filtering on the baseband video signal to achieve pulse compression and obtain the one-dimensional range image spectrum corresponding to each sub-pulse.

[0073] Let the matched filter be ,in , Indicates complex conjugation. The Fourier transform operator, used for pulse compression of the sub-pulse video signal, has the following expression in the frequency domain for its matched filter output:

[0074] ;

[0075] in, For amplitude, , , This indicates the baseband frequency.

[0076] The range resolution of the sub-pulse one-dimensional range image is determined by the baseband frequency. The bandwidth of the support domain is determined by the frequency modulated step signal bandwidth synthesis. The core objective of this synthesis is to stitch together the spectral data of multiple sub-pulses in the frequency domain to form a larger spectral support domain, thereby achieving one-dimensional range imaging with high range resolution.

[0077] Further analysis of the two main phase terms of the one-dimensional range image spectrum of the sub-pulse and .

[0078] The linear phase term representing the radial motion of the target results in a one-dimensional range profile of the sub-pulse.

[0079] Time shifts occur because the number of sub-pulses within a single pulse group is limited, and the overall observation duration generally does not exceed [a certain value]. Therefore, the influence of this phase term is relatively easy to correct. In practical processing, the traditional envelope alignment method can be used to align the one-dimensional range images of each sub-pulse within the pulse group.

[0080] The initial phase term is introduced by the sub-pulse carrier frequency jump and the target's motion velocity, and the compensation accuracy of this term is... Clearly, achieving [the desired effect] relies on the estimation of target motion parameters. Precise correction is difficult to achieve in practical engineering. Especially under low signal-to-noise ratio conditions, traditional self-focusing methods are difficult to be effective because the carrier frequencies of each sub-pulse within the pulse group are distributed in a jump manner.

[0081] In embodiments of the present invention, the starting carrier frequency of the linear frequency modulated stepped frequency signal transmitted by the radar... Frequency step size Transmitted signal bandwidth sampling frequency Pulse repetition period The pulse width is Number of pulses ,by Taking a scattering point as an example, the radial velocity Initial scattering distance They are respectively , , , , The synthesized distance resolution .

[0082] Step 2: Extract the overlapping spectrum of adjacent sub-pulses.

[0083] Step 2.1: Based on the step interval between the carrier frequencies of adjacent sub-pulses of the frequency-modulated step signal, perform bandwidth selection on the one-dimensional range image spectrum of adjacent sub-pulses in the frequency domain, and extract the overlapping spectral portions.

[0084] Based on the step interval between the carrier frequencies of adjacent sub-pulses of the frequency-modulated step signal, bandwidth selection is performed on the one-dimensional range image spectrum of adjacent sub-pulses in the frequency domain, and the overlapping spectral portions are extracted.

[0085] First, the signal is compensated using the envelope alignment method. The compensated signal can be expressed as:

[0086] ;

[0087] In the radar system used in the embodiments of the present invention, the subpulse bandwidth and carrier frequency step The relationship between them is satisfied Sampling rate .

[0088] Based on this, the first segment is extracted respectively. The latter half of the spectrum of each sub-pulse and the first The first half of the spectrum of each sub-pulse is used to form the overlapping spectrum between adjacent sub-pulses. The expression for the overlapping spectrum of adjacent sub-pulses after truncation is:

[0089] ; ;

[0090] in, , , and The first The and the first Overlapping spectral data of adjacent sub-pulses, with an effective bandwidth of for each overlapping spectrum segment. Because the radar system used in the embodiments of the present invention ,so .

[0091] Step 2.2: The two overlapping spectrum segments are converted to the same frequency range by frequency mapping to facilitate subsequent phase relationship analysis and coherent processing.

[0092] To facilitate subsequent coherent processing, the overlapping spectra of two adjacent sub-pulses need to be mapped to the same frequency domain, thereby establishing a correspondence between their local frequency variables. The embodiment of this invention selects the first... The frequency domain of the nth sub-pulse is used as a common reference, and the nth sub-pulse is used as the common reference. The overlapping spectrum of each sub-pulse is projected onto the reference frequency domain.

[0093] set up For the first The local frequency variables of each sub-pulse, the frequency range defined by their overlapping portion is: .set up For the first The local frequency variables of each sub-pulse, the frequency range defined by their overlapping portion is: By substitution of variables, ,when At that time, variables Just cover the range Substitute the above variables into the relation Substitute the first Sub-pulse overlap spectrum From the expression, we can obtain:

[0094] .

[0095] Step 3: Perform inverse Fourier transform on the overlapping spectrum of adjacent sub-pulses to obtain the corresponding time-domain signal; calculate the initial phase difference between adjacent sub-pulses based on the phase information at the main peak position of each time-domain signal.

[0096] Step 3.1: Perform inverse Fourier transform on the overlapping spectra of adjacent sub-pulses to obtain the corresponding time-domain signals, and determine the main peak position of each time-domain signal.

[0097] The obtained first With the The overlapping spectral data of the adjacent sub-pulses are denoted as follows: , .

[0098] Performing an inverse Fourier transform on the above frequency domain signal can restore it to the time domain, yielding the corresponding time domain echo signals, respectively. , .

[0099] right Performing the inverse Fourier transform yields:

[0100] ;

[0101] Similarly, for Performing the inverse Fourier transform yields:

[0102] ;

[0103] in, It is the inverse Fourier transform operator.

[0104] The results above show that the time-domain echo signals corresponding to the overlapping spectra of adjacent sub-pulses have the same envelope shape, and both time-domain signals are in... The maximum amplitude value is obtained at the location where the main peak position is consistent, and the radial distance information of the target is corresponding to the position of the main peak.

[0105] Step 3.2: Extract the phase value at the main peak position of each time domain signal, and obtain the initial phase difference between adjacent sub-pulses by performing differential operation on the phases of adjacent main peaks.

[0106] Based on the time-domain echo signals obtained in step 3.1 for each sub-pulse, for the first... The and the first Extract the main peak position of each of the adjacent sub-pulses. The phase of the complex signal at point is denoted as: , ,in, This represents the angle operation of complex signals.

[0107] Based on the analytical form of the time-domain echo signal in step 3.1, we can obtain:

[0108] ;

[0109] Similarly, the first The phase of the main peak of each sub-pulse can be written as:

[0110] ;

[0111] By subtracting the phases of adjacent main peaks, we can obtain the first... With the Initial phase difference between sub-pulses:

[0112] ;

[0113] Substituting into the phase expression above and simplifying, we get:

[0114] .

[0115] Step 4: Accumulate the initial phase difference of the adjacent sub-pulses, construct a phase compensation factor, and perform phase correction on the frequency domain signal of the sub-pulses to achieve coherent alignment of the sub-pulse spectrum.

[0116] In step 3.2, the initial phase difference between adjacent sub-pulses within the pulse group was obtained by extracting the complex phase at the main peak of adjacent sub-pulses. Suppose the pulse group contains If there are several sub-pulses, then we can obtain... The initial phase difference between adjacent sub-pulses is denoted as: .

[0117] Step 4.1, phase difference accumulation and construction of phase compensation factor.

[0118] The first sub-pulse is used as the reference sub-pulse, and its phase compensation is set to zero. For the second sub-pulse... The cumulative phase compensation of each sub-pulse is obtained by accumulating the phase differences between adjacent sub-pulses:

[0119] ;

[0120] Based on this, construct the first... The phase compensation factor corresponding to each sub-pulse is:

[0121] ;

[0122] Step 4.2, phase correction of the sub-pulse frequency domain signal.

[0123] Let the 1st envelope be aligned The spectrum of the one-dimensional range image of each sub-pulse is as follows: The phase compensation factor Applying phase correction to the corresponding sub-pulse frequency domain signal, the corrected spectral signal is obtained as follows:

[0124] ;

[0125] The phase correction operation described above can effectively compensate for the initial phase difference between different sub-pulses of the target, so that the frequency domain signals of each sub-pulse are kept in phase, and the sub-pulse spectrum is coherently aligned, laying the foundation for subsequent broadband spectrum stitching and high-resolution range image generation.

[0126] Step 5: Sub-pulse spectrum stitching and high-resolution range image generation.

[0127] After completing the phase correction of the sub-pulse frequency domain signal in step 4, the frequency domain signals of each sub-pulse are spliced ​​together in order of low to high corresponding carrier frequencies to construct a continuous wide spectrum. Then, an inverse Fourier transform is performed on the wide spectrum to obtain a high-resolution range image.

[0128] Specifically, to reduce the impact of sub-pulse spectral edges on spectrum splicing, only the middle portion of the frequency domain signal of each sub-pulse is selected as the effective spectrum for splicing. This operation is mathematically equivalent to multiplying the spectrum of each sub-pulse by a bandpass rectangular window function. Let the first... The frequency domain signal after phase correction of each subpulse is Then the effective spectrum of its participation in splicing is represented as:

[0129] ;

[0130] Will The effective spectra of the sub-pulses are concatenated sequentially according to their carrier frequencies. The resulting total spectrum can be expressed as:

[0131] ;

[0132] in, As a frequency domain selector, its function is to limit the first... The effective spectrum of each sub-pulse only appears at the corresponding frequency band position in the synthesized spectrum.

[0133] The total bandwidth of the synthesized spectrum is For the synthesized wide spectrum Performing an inverse Fourier transform yields a high-resolution range image with a range resolution of [missing value]. .

[0134] The effects of the present invention will be further explained below with reference to simulation experiments.

[0135] 1. Conditions for simulation experiments.

[0136] The hardware platform for the simulation experiment of this invention is: an AMD Ryzen 5 3550H processor with Radeon Vega Mobile Gfx, with a clock speed of [missing information]. Memory is .

[0137] The software platform for the simulation experiment of this invention is: Windows 11 operating system and Matlab R2020b.

[0138] The simulation data for this invention are: the starting carrier frequency of the linear frequency modulated step-frequency signal transmitted by the radar. Frequency step size Transmitted signal bandwidth sampling frequency Pulse repetition period The pulse width is Number of pulses ,by Taking a scattering point as an example, the radial velocity Initial scattering distance They are respectively , , , , The synthesized distance resolution .

[0139] 2. Simulation content and result analysis:

[0140] There are two simulation experiments for this invention.

[0141] Simulation Experiment 1: Under the above simulation conditions, the signal-to-noise ratio is set to... This paper compares and analyzes one-dimensional range images of stationary and moving targets obtained under different processing methods. Specifically, it presents one-dimensional range images obtained by directly performing frequency domain bandwidth synthesis on stationary targets, one-dimensional range images obtained by directly performing frequency domain bandwidth synthesis on moving targets without motion compensation, and one-dimensional range images obtained by performing phase correction on moving targets using the motion compensation method proposed in this invention before frequency domain bandwidth synthesis. The results are as follows: Figure 2 As shown.

[0142] Figure 2 The horizontal axis in the figure represents distance, in units of 1. The vertical axis represents the normalized amplitude value, in units of 1. . Figure 2The dotted lines in the figure represent the one-dimensional range envelope curve after frequency domain synthesis of a stationary target, the solid lines represent the range envelope curve obtained by direct frequency domain synthesis of a moving target without motion compensation, and the dashed lines represent the range envelope curve obtained by frequency domain synthesis of a moving target after phase correction by the motion compensation method of this invention.

[0143] Depend on Figure 2 It can be seen that, without motion compensation, the one-dimensional range envelope of the moving target exhibits significant widening and mismatch compared to that of the stationary target. However, after applying the motion compensation method proposed in this invention, the one-dimensional range envelope of the moving target essentially coincides with that of the stationary target, indicating that the initial phase introduced by the sub-pulse is effectively compensated for the target's translational motion.

[0144] Simulation Experiment 2: Under the above simulation conditions, 500 Monte Carlo simulation experiments were further conducted. The motion compensation method proposed in this invention and a prior art were used to perform motion compensation on the moving target under different signal-to-noise ratio conditions. After completing frequency domain bandwidth synthesis, the quality of the obtained high-resolution range image was compared and analyzed. The simulation results are as follows: Figure 3 As shown.

[0145] The existing technology used in Simulation Experiment 2 is the motion compensation method based on bandwidth phase coherence processing proposed by Gao Zhaozhao in his doctoral dissertation "Research on New Technologies for High-Resolution ISAR Imaging" in April 2009.

[0146] Figure 3 The horizontal axis in the figure represents distance, in units of 1. The vertical axis represents the normalization amplitude, in units of... .in, Figure 3 (a) and Figure 3 (b) The corresponding signal-to-noise ratio is The situation. Figure 3 (a) is a high-resolution range image obtained after motion compensation using existing techniques. Figure 3 (b) is a high-resolution range image obtained after phase correction using the motion compensation method proposed in this invention; Figure 3 (c) and Figure 3 (d) The corresponding signal-to-noise ratio is In this situation, Figure 3 (c) A high-resolution range image obtained after motion compensation using existing techniques. Figure 3 (d) is a high-resolution range image obtained after phase correction using the motion compensation method proposed in this invention.

[0147] Depend on Figure 3 (a) and Figure 3 (b) It can be seen that when the signal-to-noise ratio is When the motion compensation method of the present invention is used to perform phase correction on the moving target, the high-resolution range image quality obtained by frequency domain bandwidth synthesis is good, and the difference between the two is not obvious.

[0148] Depend on Figure 3 (c) and Figure 3 (d) It can be seen that when the signal-to-noise ratio is When the motion compensation method proposed in this invention is used to perform phase correction on the moving target and frequency domain bandwidth synthesis, the high-resolution range image quality obtained is significantly better than that obtained by using existing technologies.

[0149] Simulation Experiment 2 shows that under low signal-to-noise ratio conditions, existing technologies are greatly affected by noise and are prone to large phase compensation errors, which leads to a decrease in the quality of the one-dimensional range image after frequency domain bandwidth synthesis. In contrast, the motion compensation method proposed in this invention has good noise suppression capabilities and can achieve effective motion compensation for moving targets under low signal-to-noise ratio conditions, thereby obtaining a high-quality high-resolution range image.

Claims

1. A motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions, characterized in that, The specific steps of this compensation method include the following: Step 1: Process the received frequency-modulated step radar echo signal to obtain the one-dimensional range image spectrum corresponding to each sub-pulse; Step 2: Generate the overlapping spectrum between adjacent sub-pulses, and convert the two overlapping spectrum segments to the same frequency range using a frequency mapping method; Step 3: Perform inverse Fourier transform on the overlapping spectrum data extracted from adjacent sub-pulses to obtain the corresponding time-domain signals, determine the main peak position of each time-domain signal, and calculate the initial phase difference between each sub-pulse; Step 4: Accumulate the initial phase difference between adjacent sub-pulses, construct a phase compensation factor, and perform phase correction on the frequency domain signal of the sub-pulses; Step 5: The frequency domain signals of each sub-pulse are spliced ​​together according to the carrier frequency order to construct a continuous wide spectrum, and the wide spectrum is subjected to inverse Fourier transform to obtain a high-resolution range image.

2. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 1, characterized in that, The processing of the received frequency-modulated step radar echo signal in step 1 refers to multiplying the echo signal of a set of received linear frequency-modulated step frequency signals with the local oscillator signal, and converting the sub-pulse echo signal of the echo signal into the following baseband video signal: ； in, Indicates the first At the [time]th moment The baseband video signal after frequency modulation processing of the sub-pulse echo signal. , Indicates a fast time. Indicates the first The transmission time of each sub-pulse , , This represents the total number of sub-pulses in a set of linear frequency modulated step signals. This indicates the repetition period of the sub-pulse. Indicates the scattering intensity at the scattering point. Represents a linear frequency modulated subpulse In the transmission delay The time delay form under the action, , Represents the gate function. Indicates the pulse width. Represented by natural constant Index-based operations. Represents the imaginary unit. Represents pi (π). Indicates the frequency modulation slope. , Indicates the bandwidth of the sub-pulse signal. Indicates the launch number The distance between the radar and the target scattering point when a sub-pulse signal is received. , Indicates the initial distance of the scattering point. Indicates the radial velocity of the target. Represents the speed of light. Indicates the first The carrier frequency of each sub-pulse , Indicates the starting carrier frequency. This indicates the carrier frequency step interval.

3. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 2, characterized in that, The one-dimensional range profile spectrum corresponding to each sub-pulse mentioned in step 1 is as follows: ； in, Indicates the first The one-dimensional range image spectrum corresponding to each sub-pulse Indicates the baseband frequency variable. , Indicates the amplitude symbol. Indicates the first The linear phase term introduced by the radial motion of the target in each sub-pulse. , Indicates the first The initial phase term is introduced by the carrier frequency jump of the sub-pulse and the target's motion velocity. .

4. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 3, characterized in that, The steps for generating overlapping spectral data between adjacent sub-pulses in step 2 are as follows: The first step is to use the envelope alignment method to compensate the one-dimensional range image spectrum corresponding to each sub-pulse, and the compensated spectrum signal of each sub-pulse is as follows: ； in, Indicates the first The spectrum signal of the one-dimensional range image spectrum corresponding to each sub-pulse after envelope alignment compensation; The second step is to extract the envelope alignment compensation data according to the following formula. The latter half of the spectrum of the one-dimensional range image of each sub-pulse and the first The first half of the one-dimensional range image spectrum of each sub-pulse is obtained. ； ； in, Indicates the compensation after the first The latter half of the one-dimensional range image spectrum of each sub-pulse. Indicates the first The frequency variable of the second half of the spectrum of the one-dimensional range image of each sub-pulse , Indicates the first The initial phase introduced by the carrier frequency jump of the sub-pulse and the target's motion velocity. , Indicates the compensation after the first The first half of the spectrum of the one-dimensional range image of the sub-pulse No. The frequency variable of the first half of the spectrum of the one-dimensional range image of each sub-pulse .

5. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 4, characterized in that, The steps described in step 2 for converting two overlapping spectrum segments to the same frequency range using frequency mapping are as follows: Will Substitute into the first The first half of the spectrum of the one-dimensional range image of the sub-pulse In the middle, we get: ； in, Indicates the frequency mapping and the first -1 sub-pulse one-dimensional range image spectrum of the latter half The first in the same frequency range The first half of the spectrum of the one-dimensional range image of the sub-pulse.

6. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 5, characterized in that, The time-domain signal corresponding to the overlapping spectrum of adjacent sub-pulses in step 3 is as follows: ； ； in, Indicates the first At the [time]th moment The time-domain signal corresponding to the overlapping spectrum of -1 sub-pulses Represents the Sink function, Indicates the first At the [time]th moment -1 The time-domain signal corresponding to the overlapping spectrum of sub-pulses.

7. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 6, characterized in that, The determination of the main peak position of each time-domain signal in step 3 means that the time-domain signals corresponding to the overlapping spectra of adjacent sub-pulses have the same envelope shape and are all within the range of... At the point where the maximum amplitude is obtained, The location was determined to be the main peak position of the signal.

8. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 7, characterized in that, The steps for calculating the initial phase difference between each sub-pulse in step 3 are as follows: The first step is to extract the phase of the complex signal at the main peak position of the time-domain signal corresponding to the overlapping spectrum of two adjacent sub-pulses. The phase of the complex signal at the main peak position of the time-domain signal corresponding to the overlapping spectrum of adjacent sub-pulses is as follows: ； ； in, Indicates the first -1 The phase of the complex signal at the main peak position of the time-domain signal corresponding to the overlapping spectrum of the sub-pulses Indicates the first The phase of the complex signal at the main peak position of the time-domain signal corresponding to the overlapping spectrum of each sub-pulse; The second step is to perform a differential operation on the phase of the complex signal at the main peak of adjacent sub-pulses to obtain the initial phase difference between each sub-pulse as follows: ； in, Indicates the first -1 sub-pulse and The initial phase difference between the sub-pulses.

9. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 8, characterized in that, The steps in step 4 for accumulating the initial phase difference between adjacent sub-pulses and constructing the phase compensation factor are as follows: The first step is to successively accumulate the initial phase difference between adjacent sub-pulses to obtain the phase compensation amount for each sub-pulse: ； in, Indicates the first Phase compensation amount of each sub-pulse. , The summation symbol is used to represent the summation symbol. Indicates the first Sub-pulse and the first The initial phase difference between the sub-pulses; The second step is to construct the phase compensation factor for each sub-pulse based on the phase compensation amount of each sub-pulse, as follows: ； in, Indicates the first Phase compensation factor for each sub-pulse.

10. The motion compensation method for frequency-modulated stepping radar under low signal-to-noise ratio conditions according to claim 1, characterized in that, The corrected spectral signals of each sub-pulse described in step 4 are as follows: ； in, Indicates the first The spectrum signal after sub-pulse correction.

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