Parameter inversion method, device and electronic equipment

Abstract

The embodiment of the application provides a parameter inversion method, device and electronic equipment, wherein the parameter inversion method comprises: performing interference suppression on a received incomplete SAR signal to obtain a non-interference signal matrix; wherein the non-interference signal matrix comprises a plurality of non-interference pulse signals with time sequence continuity, and the incomplete SAR signal represents that the SAR signal is incomplete; sequentially performing data processing on each non-interference pulse signal to obtain pulse parameters of each non-interference pulse signal; the pulse parameters at least comprise a stationary phase center position, a termination point, a pulse bandwidth, a pulse signal frequency modulation rate and a peak position; based on the pulse parameters of each non-interference pulse signal, signal parameters of the incomplete SAR signal are inverted to obtain transmission parameters of the incomplete SAR signal; the signal parameters at least comprise a pulse width, a bandwidth, a frequency modulation rate, a pulse repetition interval and a pulse repetition frequency.

Description

Technical Field

[0001] This application relates to the field of radar technology, and includes, but is not limited to, a parameter inversion method, apparatus, and electronic device. Background Technology

[0002] Spaceborne Synthetic Aperture Radar (SAR) is an active microwave remote sensing system that achieves high-resolution imaging by emitting electromagnetic waves and receiving echo signals from ground targets. Spaceborne SAR offers all-weather, all-day observation capabilities and is widely used in resource exploration and disaster monitoring. In SAR countermeasures, signal acquisition and parameter inversion are crucial, especially under conditions of low signal-to-noise ratio and signal incompleteness, where accurately extracting key parameters of the SAR signal becomes a significant technical challenge.

[0003] In related technologies, parameter inversion methods for Linear Frequency Modulation (LFM) SAR signals mainly include traditional mathematical transformation methods, cyclostationary processing methods, time-frequency analysis methods, and deep learning-based methods. Among these, methods such as maximum likelihood estimation rely on multidimensional search, resulting in high computational complexity; while time-frequency analysis methods can effectively handle non-stationary signals, they are sensitive to noise and subject to cross-term interference; and although deep learning-based methods improve robustness and efficiency, they still struggle to accurately compensate for pulse width and invert complete parameters when pulse signals are partially missing.

[0004] Existing technologies lack effective data recovery mechanisms when processing incomplete SAR signals, especially when the first half of the pulse is missing. This leads to significant parameter estimation errors, affecting the formulation and implementation of subsequent interference strategies. Therefore, there is an urgent need for a technical solution that can effectively suppress interference, restore signal integrity, and improve parameter inversion accuracy. Summary of the Invention

[0005] To address the problems existing in the related technologies, embodiments of this application provide a parameter inversion method, apparatus, and electronic device.

[0006] Firstly, this application provides a parameter inversion method, which includes:

[0007] Interference suppression is performed on the received incomplete SAR signal to obtain an interference-free signal matrix; wherein, the interference-free signal matrix includes multiple interference-free pulse signals with temporal continuity, and the incomplete SAR signal represents the presence of missing SAR signals;

[0008] Each interference-free pulse signal is processed sequentially to obtain the pulse parameters of each interference-free pulse signal; the pulse parameters include at least the stationary phase center position, termination point, pulse bandwidth, pulse signal modulation frequency, and peak position;

[0009] Based on the pulse parameters of each interference-free pulse signal, the signal parameters of the incomplete SAR signal are inverted to obtain the transmission parameters of the incomplete SAR signal; the signal parameters include at least pulse width, bandwidth, modulation frequency, pulse repetition interval, and pulse repetition frequency.

[0010] In some embodiments, the step of suppressing interference in the received incomplete SAR signal to obtain an interference-free signal matrix includes: performing a Fast Fourier Transform on each pulse echo signal in the incomplete SAR signal to obtain the spectral amplitude of each pulse echo signal; performing strong point-frequency interference suppression on the spectral amplitude of each pulse echo signal to obtain a plurality of first suppression signals; the number of the first suppression signals is less than or equal to the number of pulse echo signals in the incomplete SAR signal; constructing a spectral amplitude threshold for each first suppression signal based on the spectral amplitude of each first suppression signal and a first preset adjustment factor; and filtering the corresponding first suppression signals based on the spectral amplitude threshold of each first suppression signal to obtain the interference-free signal matrix.

[0011] In some embodiments, the step of suppressing strong point-frequency interference on the spectral amplitude of each pulse echo signal to obtain multiple first suppression signals includes: performing multiple energy integration operations on each pulse echo signal based on the spectral amplitude of each pulse echo signal to obtain multiple maximum energies of each pulse echo signal; determining an energy ratio based on the multiple maximum energies of each pulse echo signal and the total spectral energy; identifying pulse echo signals in the incomplete SAR signal whose energy ratio is less than a preset ratio threshold as the first suppression signals, thus obtaining the multiple first suppression signals; wherein, the energy integration operation includes: sorting the energy to obtain the frequency point corresponding to the highest spectral energy point and the symmetrical bandwidth of the frequency point; integrating the spectral energy within the symmetrical bandwidth to obtain a single maximum energy of each pulse echo signal; and setting the spectral energy in the symmetrical bandwidth to zero before the next energy integration operation.

[0012] In some embodiments, the step of filtering the corresponding first suppressed signals based on the spectral amplitude threshold of each first suppressed signal to obtain the interference-free signal matrix includes: determining the frequency points in each first suppressed signal whose spectral amplitude is greater than the spectral amplitude threshold as a first frequency point set; determining the spectral bandwidth of each first suppressed signal based on the first frequency point set and the frequency resolution; the frequency resolution is determined based on the sampling frequency of the incomplete SAR signal and the number of sampling points of the pulse echo signal; determining the first suppressed signals whose spectral bandwidth is greater than a preset spectral bandwidth threshold as second suppressed signals to obtain a plurality of second suppressed signals; determining the plurality of second suppressed signals with temporal continuity between the first consecutive adjacent signals as a plurality of interference-free signals based on the pulse time of the plurality of second suppressed signals; and constructing the interference-free signal matrix based on the plurality of interference-free signals.

[0013] In some embodiments, the step of sequentially processing each interference-free pulse signal to obtain pulse parameters for each interference-free pulse signal includes: performing a Hilbert transform on each interference-free pulse signal to obtain an analytic signal; determining the instantaneous phase of each interference-free pulse signal based on the analytic signal; unwrapping the instantaneous phase to obtain a first unwrapped phase; differentiating the first unwrapped phase to obtain the first and second derivatives of the first unwrapped phase; determining the position where the second derivative first exceeds a first preset threshold as the termination point of each interference-free pulse signal; the first preset threshold is based on the second derivative. The second preset adjustment factor is determined; the position corresponding to the minimum value of the first derivative before the termination point is determined as the stationary phase center position; correspondingly, the transmission parameters of the incomplete SAR signal are inverted based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal, including: determining the pulse width of each interference-free pulse signal based on the sampling frequency of the incomplete SAR signal, the stationary phase center position of each interference-free pulse signal and the termination point; averaging the pulse width of each interference-free pulse signal to obtain the pulse width of the incomplete SAR signal.

[0014] In some embodiments, the step of sequentially processing each interference-free pulse signal to obtain the pulse parameters of each interference-free pulse signal includes: performing a fast Fourier transform on each interference-free pulse signal to obtain the frequency domain amplitude spectrum of each interference-free pulse signal; based on the frequency domain amplitude spectrum, determining the frequency points in each interference-free pulse signal with energy greater than a second preset threshold as a second set of frequency points; and determining the pulse bandwidth of each interference-free pulse signal based on the second set of frequency points and the frequency resolution. Correspondingly, the step of inverting the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal includes: compensating the pulse bandwidth of each interference-free pulse signal based on the stationary phase center position and the termination point of each interference-free pulse signal to obtain the compensated bandwidth of each interference-free pulse signal; and averaging the compensated bandwidth of each interference-free pulse signal to obtain the bandwidth of the incomplete SAR signal.

[0015] In some embodiments, the step of sequentially processing each interference-free pulse signal to obtain the pulse parameters of each interference-free pulse signal includes: performing phase expansion on each interference-free pulse signal to obtain a second unwrapped phase; performing first-order differentiation on the second unwrapped phase to obtain the instantaneous frequency at each sampling time point in each interference-free pulse signal; performing linear fitting on the instantaneous frequency at each sampling time point based on multiple preset sliding windows to obtain the fitted modulation frequency; performing global residual detection on the fitted modulation frequency to remove outliers and obtain the pulse signal modulation frequency of each interference-free pulse signal; correspondingly, the step of inverting the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal includes: averaging the pulse signal modulation frequency of each interference-free pulse signal to obtain the modulation frequency of the incomplete SAR signal.

[0016] In some embodiments, the step of sequentially processing each interference-free pulse signal to obtain the pulse parameters of each interference-free pulse signal includes: determining the first interference-free pulse signal in the interference-free signal matrix as a reference pulse signal; performing pulse compression on each interference-free pulse signal after the first interference-free pulse signal based on a matched filter of the reference pulse signal to obtain a matched-filtered echo signal; extracting the main peak position of each echo signal to obtain the main peak position; symmetrically adjusting the main peak position to obtain the peak position of each interference-free pulse signal; correspondingly, the step of processing the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal... The transmission parameters of the incomplete SAR signal are obtained by performing an inversion, including: determining the delay time of the peak position of each interference-free pulse signal based on the sampling frequency of the incomplete SAR signal and the peak position of each interference-free pulse signal; obtaining the actual arrival time of the main peak of each interference-free pulse signal based on the delay time and the frame header trigger time of each interference-free pulse signal; determining the time interval between adjacent signals in the interference-free signal matrix based on the actual arrival time of the main peak of each interference-free pulse signal; determining the average time interval of the interference-free signal matrix based on the time interval; and calculating the pulse repetition interval and the pulse repetition frequency based on the average time interval.

[0017] Secondly, embodiments of this application provide a parameter inversion device, comprising: an interference suppression module for suppressing interference in a received incomplete SAR signal to obtain an interference-free signal matrix; wherein the interference-free signal matrix includes multiple interference-free pulse signals with temporal continuity, and the incomplete SAR signal represents the presence of missing data in the SAR signal; a data processing module for sequentially processing each interference-free pulse signal to obtain pulse parameters of each interference-free pulse signal; the pulse parameters include at least the stationary phase center position, termination point, pulse bandwidth, pulse signal modulation frequency, and peak position; and an inversion module for inverting the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal; the signal parameters include at least the pulse width, bandwidth, modulation frequency, pulse repetition interval, and pulse repetition frequency.

[0018] Thirdly, embodiments of this application provide an electronic device, including: a memory for storing executable instructions; and a processor for executing the executable instructions stored in the memory to implement the steps in the parameter inversion method described above.

[0019] Fourthly, embodiments of this application provide a computer-readable storage medium storing executable instructions, which, when executed by a processor, implement the steps in the parameter inversion method described above.

[0020] Fifthly, embodiments of this application provide a computer program product, including a computer program or instructions, which, when executed by a processor, implement the steps in the parameter inversion method described above.

[0021] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application;

[0023] Figure 2 This is an optional flowchart illustrating the parameter inversion method provided in this application embodiment. Figure 1 ;

[0024] Figure 3 This is a flowchart illustrating the low signal-to-noise ratio incomplete SAR signal parameter inversion method proposed in this application embodiment;

[0025] Figure 4 This is a schematic diagram of the pulse real part amplitude provided in an embodiment of this application;

[0026] Figure 5 This is a schematic diagram of the SAR range-direction frequency domain amplitude boundary obtained by bandwidth inversion according to an embodiment of this application;

[0027] Figure 6 This is a schematic diagram of the frequency modulation based on local fitting of a sliding window provided in an embodiment of this application;

[0028] Figure 7 This is a schematic diagram of the pulse compression result when the inversion pulse repetition frequency is provided in the embodiments of this application. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. The described embodiments should not be regarded as limitations on this application. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0030] In the following description, references to "some embodiments" refer to a subset of all possible embodiments. However, it is understood that "some embodiments" may be the same or different subsets of all possible embodiments and may be combined with each other without conflict. Unless otherwise defined, all technical and scientific terms used in the embodiments of this application have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of this application pertain. The terminology used in the embodiments of this application is for the purpose of describing the embodiments of this application only and is not intended to limit the application.

[0031] Currently, with the widespread application of spaceborne SAR in military and civilian fields, countering spaceborne SAR has become increasingly important. How to interfere with SAR reconnaissance, weaken its effectiveness in peacetime, disrupt SAR guidance and strike chains, and effectively protect important equipment and key targets from surveillance is an extremely urgent practical need. As a crucial prerequisite for interfering with SAR reconnaissance, SAR signal reception and parameter inversion have become important research topics in the field of SAR jamming. In the process of receiving SAR signals, to meet the requirements of high sampling rate and large bandwidth SAR signal interception, the receiver adopts a triggered signal reception mechanism. This mechanism leads to the phenomenon of missing SAR signals. Under low signal-to-noise ratio conditions, facing this incomplete signal situation, especially the missing first half of the pulse, specific methods must be used to compensate for the pulse width, thereby accurately inverting the parameters of the SAR signal.

[0032] Related technologies address the parameter inversion problem of linear frequency modulated (LFM) signals transmitted by SAR, proposing numerous analysis and processing methods, including traditional parameter inversion methods, cyclostationary processing methods, time-frequency analysis methods, and deep learning-based parameter inversion methods. These methods can achieve various parameter estimations of SAR signals, including carrier frequency, modulation slope, and pulse width. The methods in these technologies achieve parameter estimation through multidimensional search or mathematical transformations; for example, maximum likelihood estimation is theoretically optimal, while LFM de-modulation techniques improve computational efficiency through dimensionality reduction. Cyclostationary processing methods utilize the periodic statistical properties of signals to extract parameters without prior knowledge. Time-frequency analysis methods process non-stationary signals through joint time-frequency analysis; for example, the Wigner-Ville distribution (WVD) exhibits excellent time-frequency clustering in LFM signals. Deep learning methods, driven by data, significantly improve computational efficiency and robustness through techniques such as complex-valued convolutional neural networks (CNNs) and attention mechanisms.

[0033] Despite the numerous processing methods proposed in related technologies, these methods exhibit limitations under low signal-to-noise ratio (SNR) conditions: maximum likelihood estimation suffers from high computational complexity due to multidimensional search; delinear frequency modulation (DMFM) exhibits poor noise resistance and insufficient accuracy; and the discrete Chirp-Fourier transform (DFT) relies on strict constraints and is prone to failure when the signal is distorted. While cyclostationary processing methods perform well in multi-time-code signals, their accuracy in estimating symbol rate and bandwidth significantly decreases under low SNR. In time-frequency analysis methods, the Short-Time Fourier Transform (STFT) is limited by its fixed time window resolution, while the WVD generates cross-term interference in multi-component signals due to its bilinear characteristics; even with improved smoothed pseudo-WVD, the reduced SNR still leads to blurred time-frequency maps. For incomplete SAR signals, existing methods often rely on prior information or ideal assumptions; for example, the discrete Chirp-Fourier transform requires strict initial frequency and frequency modulation slope constraints, and its parameter estimation performance deteriorates sharply when key signal features are missing. While deep learning methods excel in computational efficiency and noise resistance, their training data diversity and signal type coverage are limited, and they struggle to handle signal structure abrupt changes or non-ideal sampling scenarios.

[0034] To address the problems existing in related technologies, this application provides a parameter inversion method for incomplete SAR signals under low signal-to-noise ratio (SNR) conditions. This method solves the problem that related technologies struggle to accurately invert key parameters of SAR signals in complex electromagnetic environments with high interference, signal gaps, and low SNR. By combining key techniques such as interference suppression, phase unwrapping and derivative analysis, spectral gradient compensation, and sliding window fitting, a complete step-by-step multidimensional estimation plus missing value compensation and correction parameter inversion process is constructed, achieving high-precision inversion of transmission parameters such as pulse width, bandwidth, modulation frequency, pulse repetition interval, and pulse repetition frequency.

[0035] Figure 1 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Figure 1 The illustrated electronic device includes at least one processor 110, a memory 150, at least one network interface 120, and a user interface 130. The various components of the electronic device are coupled together via a bus system 140. It is understood that the bus system 140 is used to implement communication between these components. In addition to a data bus, the bus system 140 also includes a power bus, a control bus, and a status signal bus. However, for clarity, ... Figure 1 The general labeled all buses as Bus System 140.

[0036] The processor 110 can be an integrated circuit chip with signal processing capabilities, such as a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0037] User interface 130 includes one or more output devices 131 that enable the presentation of media content, and one or more input devices 132.

[0038] Memory 150 may be removable, non-removable, or a combination thereof. Exemplary hardware devices include solid-state memory, hard disk drives, optical disk drives, etc. Memory 150 may optionally include one or more storage devices physically located remote from processor 110. Memory 150 may include volatile memory or non-volatile memory, or both. Non-volatile memory may be read-only memory (ROM), and volatile memory may be random access memory (RAM). The memory 150 described in this application embodiment is intended to include any suitable type of memory. In some embodiments, memory 150 is capable of storing data to support various operations, examples of which include programs, modules, and data structures, or subsets or supersets thereof, as exemplified below.

[0039] Operating system 151 includes system programs for handling various basic system services and performing hardware-related tasks, such as the framework layer, core library layer, driver layer, etc., for implementing various basic business functions and handling hardware-based tasks;

[0040] The network communication module 152 is used to reach other computing devices via one or more (wired or wireless) network interfaces 120, such as Bluetooth, WiFi, and Universal Serial Bus.

[0041] The input processing module 153 is used to detect one or more user inputs or interactions from one or more input devices 132, and to translate the detected inputs or interactions.

[0042] In some embodiments, the apparatus provided in this application may be implemented in software. Figure 1A parameter inversion device 154 stored in memory 150 is shown. This device 154 can be software in the form of programs and plug-ins in an electronic device, and includes the following software modules: an interference suppression module 1541, a data processing module 1542, and an inversion module 1543. These modules are logically linked and can therefore be arbitrarily combined or further separated according to their implemented functions. The functions of each module will be described below.

[0043] In other embodiments, the apparatus provided in this application can also be implemented in hardware. As an example, the parameter inversion apparatus provided in this application can be a processor in the form of a hardware decoding processor, which is programmed to execute the parameter inversion method provided in this application. For example, the processor in the form of a hardware decoding processor can be one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components.

[0044] The parameter inversion method disclosed in this application is executed by an electronic device, which may be a SAR signal receiving device or a server; this application does not limit the scope of the device.

[0045] The technical solution of this application will now be described in detail with reference to the accompanying drawings.

[0046] Figure 2 This is an optional flowchart illustrating the parameter inversion method provided in this application embodiment. Figure 1 ,like Figure 2 As shown, the parameter inversion method provided in this application embodiment can be implemented through steps S201 to S203:

[0047] Step S201: Perform interference suppression on the received incomplete SAR signal to obtain an interference-free signal matrix; wherein, the interference-free signal matrix includes multiple interference-free pulse signals with temporal continuity, and the incomplete SAR signal represents the absence of SAR signal.

[0048] In this embodiment of the application, an incomplete SAR signal may refer to a received signal in which some pulse signals are lost or interfered with due to low signal-to-noise ratio and signal interception mechanism.

[0049] Before performing parameter inversion, the incomplete SAR signal must be preprocessed and interference suppressed. Fast sliding window filtering can be used to smooth the noise in the original signal, combined with a triple-peak notch filtering algorithm to identify and remove sudden point-frequency interference. The processing using fast sliding window filtering and the triple-peak notch filtering algorithm effectively improves signal quality, providing a reliable data foundation for subsequent signal parameter inversion.

[0050] The final interference-free signal matrix can be a two-dimensional complex matrix composed of multiple time-series continuous interference-free pulse signals, with each row representing one interference-free pulse signal and each column representing equally spaced sampling points of the interference-free pulse signal in the distance direction.

[0051] Step S202: Perform data processing on each interference-free pulse signal in sequence to obtain the pulse parameters of each interference-free pulse signal; the pulse parameters include at least the stationary phase center position, termination point, pulse bandwidth, pulse signal modulation frequency, and peak position.

[0052] In some embodiments, for each interference-free pulse signal, key parameters of each interference-free pulse signal can be extracted separately. Among these, the stationary phase center position can represent the position where the instantaneous phase change in the signal is most stable, and the stationary phase center position usually appears in the central region of the signal backbone; the termination point can represent the position where the signal ends, and the termination point is used to determine the length boundary of the signal; the pulse bandwidth can refer to the width of the energy distribution of the signal in the frequency domain, and the pulse bandwidth reflects the modulation characteristics of the signal; the pulse signal modulation frequency can represent the rate of change of the signal frequency with time, and the pulse signal modulation frequency is one of the key characteristics of linear frequency modulated signals; the peak position can be the sampling point index corresponding to the maximum amplitude of the signal in the time domain, and the peak position is used to help determine the start and end times of the signal.

[0053] In some embodiments, the stationary phase center position can be determined by calculating the first derivative of the unwrapped instantaneous phase and finding the minimum point. The stationary phase center position reflects the most stable phase position in the signal and is often used for signal symmetry analysis and compensation estimation. The termination point can be determined by a combination of second derivative detection and dynamic thresholding, representing the end position of the signal on the time axis. The pulse bandwidth can be determined by a combination of spectral amplitude gradient analysis and dynamic thresholding algorithms, reflecting the signal's distribution range in the frequency dimension. The pulse signal frequency modulation can be obtained by sliding window fitting and global residual optimization of the instantaneous frequency, used to describe the frequency change trend of the signal. The peak position can be determined by finding the maximum response point in the compression result of the matched filter output, which helps to further confirm the temporal characteristics of the signal.

[0054] The embodiments of this application can construct a complete characteristic description of each pulse through pulse parameters, providing an accurate basis for subsequent transmission parameter inversion.

[0055] Step S203: Based on the pulse parameters of each interference-free pulse signal, the signal parameters of the incomplete SAR signal are inverted to obtain the transmission parameters of the incomplete SAR signal; the signal parameters include at least pulse width, bandwidth, modulation frequency, pulse repetition interval and pulse repetition frequency.

[0056] In this embodiment, the pulse width can be estimated by the distance between the stationary phase center and the termination point, and compensated using the symmetry of the signal and the information of the latter half, thereby obtaining a more accurate pulse width estimate; the bandwidth can be calculated by a combination of spectral amplitude gradient analysis and dynamic threshold algorithm, taking into account the influence of missing parts of the signal for correction; the modulation frequency can be estimated by a combination of sliding window local fitting and global linear fitting, which has high noise resistance; the pulse repetition interval can be calculated by differential calculation of the time series of the pulse compression main peak, and further calibrated by combining the frame header trigger time; the pulse repetition frequency can be calculated by the reciprocal of the pulse repetition interval, which is used to describe the average frequency of the transmitted pulse per unit time.

[0057] In some embodiments, by performing statistical analysis and mean calculation on the pulse parameters of each pulse, the transmission parameters of the entire incomplete SAR signal can be obtained, thereby achieving high-precision parameter inversion. This not only improves the accuracy of the inversion but also enhances the robustness of incomplete SAR signals under low signal-to-noise ratio conditions.

[0058] This application embodiment removes strong point-frequency and broadband interference from incomplete SAR signals through interference suppression, filtering out interference-free pulse signals with temporal continuity to form an interference-free signal matrix. Then, key pulse parameters, such as the stationary phase center position, termination point, pulse bandwidth, and modulation frequency, are extracted for each interference-free pulse signal, and the complete signal transmission parameters are further inverted based on these parameters. In this way, on the one hand, by removing strong point-frequency and broadband interference from incomplete SAR signals through interference suppression, interference signals in complex environments can be effectively eliminated, improving signal quality; on the other hand, through the second-half compensation mechanism, parameters such as pulse width and bandwidth can be accurately inverted under incomplete signal conditions, avoiding estimation bias caused by signal missingness, thereby significantly improving the accuracy and stability of parameter inversion under low signal-to-noise ratio conditions.

[0059] In this embodiment of the application, step S201 can be implemented by steps S2011 to S2014:

[0060] Step S2011: Perform a Fast Fourier Transform on each pulse echo signal in the incomplete SAR signal to obtain the spectral amplitude of each pulse echo signal.

[0061] In some embodiments, an incomplete SAR signal can be represented as a two-dimensional complex matrix. In the matrix, each row represents a radar pulse echo, and the columns represent the equally spaced sampling points of the pulse in the range direction. The incomplete SAR signal can be represented as shown in formula (1):

[0062] (1);

[0063] Where M is the total number of pulses, and N is the number of sampling points per pulse. For the i-th pulse, the first... Complex signal values ​​at each sampling point.

[0064] To extract the frequency domain features of the signal, we can process each line of the signal, i.e., each pulse echo signal. Applying a Fast Fourier Transform yields the corresponding frequency domain representation. As shown in formula (2):

[0065] (2);

[0066] in, Indicates the first The complex spectrum of the line signal in the frequency domain, This is a Fast Fourier Transform operation. It allows for the calculation of the spectral amplitude of each pulse echo signal. As shown in formula (3):

[0067] (3);

[0068] Among them, spectral amplitude Indicates the first Each pulse at various frequency points The energy intensity at each frequency The amount of energy on the surface can be used to identify subsequent interference based on this amplitude distribution.

[0069] Step S2012: Perform strong point frequency interference suppression on the spectral amplitude of each pulse echo signal to obtain multiple first suppression signals; the number of the first suppression signals is less than or equal to the number of pulse echo signals in the incomplete SAR signal.

[0070] In some embodiments, step S2012 can be implemented by steps S1 to S3:

[0071] Step S1: Based on the spectral amplitude of each pulse echo signal, perform multiple energy integration operations on each pulse echo signal to obtain multiple maximum energies of each pulse echo signal.

[0072] To achieve point-frequency interference detection, this application embodiment can employ the triple maximum energy ratio method to remove strong point-frequency interference. The triple maximum energy ratio can be achieved through multiple energy integration operations. In some embodiments, the energy integration operation in step S1 can be implemented through steps S11 to S13:

[0073] Step S11: Perform energy sorting to obtain the frequency point corresponding to the highest spectral energy and the symmetrical bandwidth of the frequency point.

[0074] First, we can analyze the spectrum. Perform energy sorting to find the frequency point corresponding to the highest point. That is, the frequency point where the energy is strongest.

[0075] Then, the integral bandwidth radius is calculated based on formula (4). :

[0076] (4);

[0077] in, For notch bandwidth, The number of sampling points for the receiver. This refers to the receiver's sampling frequency. Here, the SAR signal contains not only the SAR signal itself but also interference signals. The bandwidth of the interference signal is much smaller than the bandwidth of the SAR signal. The notch bandwidth is the width of the "suppression band" used to suppress interference in the frequency domain. It can be set empirically, and accumulating three times can remove most of the strong point-frequency interference.

[0078] After calculating the integral bandwidth radius After that, the symmetrical bandwidth at the frequency point can be obtained. , ].

[0079] Step S12: Integrate the spectral energy within the symmetrical bandwidth to obtain the maximum energy of each pulse echo signal.

[0080] The first maximum energy can be defined by integrating the spectral energy within the symmetrical bandwidth at the frequency point. As shown in formula (5):

[0081] (5);

[0082] in, For the first The maximum amplitude of the line spectrum corresponds to the frequency.

[0083] Step S13: Before the next energy integration operation, set the spectral energy in the symmetric bandwidth to zero.

[0084] Before the next energy integration operation, the symmetry bandwidth [ , Set the spectral energy in the spectrum to zero, find the frequency point corresponding to the highest point in the spectrum energy after it is set to zero, and repeat steps S11 to S13 multiple times, for example three times, to obtain the three maximum energies.

[0085] Step S2: Determine the energy ratio based on the multiple maximum energies and total spectral energy of each pulse echo signal.

[0086] The three maximum total energy is obtained based on the three maximum energies of each pulse echo signal. As shown in formula (6):

[0087] (6);

[0088] In some embodiments, to determine the proportion of interference, the maximum total energy can be calculated three times. Energy ratio relative to total spectral energy As shown in formula (7):

[0089] (7);

[0090] Step S3: Identify the pulse echo signals in the incomplete SAR signals whose energy ratio is less than a preset ratio threshold as the first suppression signals, and obtain the plurality of first suppression signals.

[0091] Here, the preset ratio threshold can be set based on experience, such as 0.2. When the energy ratio R exceeds 0.2, it can be determined that the current pulse echo signal has strong point frequency interference. Pulse echo signals with strong point frequency interference will be discarded and will not be used for inversion.

[0092] When the energy ratio R does not exceed 0.2, broadband interference identification based on the dynamic threshold method is performed.

[0093] Step S2013: Based on the spectral amplitude of each first suppression signal and the first preset adjustment factor, construct the spectral amplitude threshold of each first suppression signal.

[0094] Broadband interference identification based on the dynamic threshold method can first calculate the baseline average energy of the spectrum. As shown in formula (8):

[0095] (8);

[0096] This application's embodiments introduce a first preset adjustment factor. and The threshold values ​​for constructing the spectral amplitude are shown in formulas (9) and (10), respectively:

[0097] (9);

[0098] (10);

[0099] in, This represents the standard deviation of the spectral amplitude. The spectral amplitude threshold. It can be shown in formula (11):

[0100] (11);

[0101] Step S2014: Based on the spectral amplitude threshold of each first suppression signal, the corresponding first suppression signal is filtered to obtain the interference-free signal matrix.

[0102] Based on the spectral amplitude threshold of each first suppression signal, all frequency points whose amplitude exceeds the threshold can be selected, and then the bandwidth of each first suppression signal can be calculated.

[0103] In some embodiments, step S2014 can be implemented by steps S21 to S25:

[0104] Step S21: Determine the frequency points in each first suppression signal whose spectral amplitude is greater than the spectral amplitude threshold as the first frequency point set.

[0105] In some embodiments, in each first suppression signal, a set can be formed by selecting all frequency points whose amplitude exceeds the spectral amplitude threshold. As shown in formula (12):

[0106] (12);

[0107] Step S22: Based on the first set of frequency points and the frequency resolution, determine the spectral bandwidth of each first suppressed signal; the frequency resolution is determined based on the sampling frequency of the incomplete SAR signal and the number of sampling points of the pulse echo signal.

[0108] In some embodiments, frequency resolution is defined as Resolution = Fs / N, i.e., the unit frequency step size. Spectral bandwidth. As shown in formula (13):

[0109] (13);

[0110] If the bandwidth is greater than 70MHz, the first suppression signal is determined to be a normal signal; if it is less than 70MHz, the first suppression signal is considered to be destroyed by broadband interference and is discarded.

[0111] Step S23: The first suppression signal with a spectral bandwidth greater than a preset spectral bandwidth threshold is determined as the second suppression signal, and multiple second suppression signals are obtained.

[0112] Here, the preset spectrum bandwidth threshold can be set empirically. The first suppression signal with a spectrum bandwidth greater than the preset spectrum bandwidth threshold is determined as the second suppression signal, resulting in multiple second suppression signals. Here, the number of second suppression signals is less than or equal to the number of first suppression signals.

[0113] Step S24: Based on the pulse time of the plurality of second suppression signals, the plurality of second suppression signals that have temporal continuity between the first consecutive adjacent signals are determined as a plurality of interference-free signals.

[0114] Here, after filtering out all the second suppression signals that meet the spectral criteria, in order to ensure the timing continuity of the pulses, it is necessary to index the row numbers of the multiple second suppression signals. By performing a successive difference operation, multiple second suppression signals with temporal continuity between consecutive adjacent signals are determined. Here, the successive difference operation can be shown as in formula (14):

[0115] (14);

[0116] when When this condition is met, it indicates that the current second suppression signal has temporal continuity with its adjacent second suppression signal.

[0117] Here, the first C consecutive normal second suppression signals can be extracted from multiple second suppression signals and used as multiple interference-free signals.

[0118] Step S25: Construct the interference-free signal matrix based on the plurality of interference-free signals.

[0119] After identifying multiple interference-free signals, an interference-free signal matrix can be obtained. As shown in formula (15):

[0120] (15);

[0121] The interference-free signal matrix serves as the direct input for subsequent pulse width, bandwidth, and frequency modulation inversion steps. Through the spectral energy assessment, triple peak detection, and dynamic threshold bandwidth identification methods of this application, strong point-frequency interference and complex broadband interference in SAR signals can be effectively addressed, achieving high-precision preliminary screening of SAR signals under low signal-to-noise ratio conditions.

[0122] This application embodiment obtains the spectral amplitude by performing a Fast Fourier Transform on each pulse echo signal, and then uses the triple maximum energy integration method to identify and remove strong point-frequency interference, which can effectively preserve the main characteristics of the signal and reduce the impact of interference on subsequent parameter estimation. In addition, by introducing a first preset adjustment factor to construct a dynamic threshold, it can adapt to interference signals of different intensities, achieve more accurate signal screening, and thus provide a high-quality data foundation for subsequent parameter inversion.

[0123] In some embodiments, since the incomplete SAR signal may have a missing first half during reception, the direct measurement of the pulse width is uncertain. This application proposes a method for compensation estimation based on the complete information of the second half, effectively improving the pulse width inversion accuracy in low signal-to-noise ratio environments. Here, the pulse parameters can be the stationary phase center position and the termination point. Step S202 can be implemented through steps S2021 to S2026:

[0124] Step S2021: Perform Hilbert transform on each interference-free pulse signal to obtain the analytical signal.

[0125] In some embodiments, for each interference-free pulse signal, its corresponding pulse width can be derived based on the temporal structure relationship between the phase center and the termination point.

[0126] Here, any interference-free pulse signal can be represented by formula (16):

[0127] (16);

[0128] in, This represents a noise-free pulse signal with a length of [length missing]. The corresponding distance sampling points (these N points are arranged along the distance direction).

[0129] To extract the instantaneous phase characteristics of an interference-free pulse signal, the real-valued form of the signal needs to be constructed into a complex analytic signal. The construction method involves taking the signal and its Hilbert transform to form a complex number, as shown in formula (17):

[0130] (17);

[0131] in, To analyze the signal, The imaginary unit, For the timeline, Indicates the signal The result obtained by applying the Hilbert transform.

[0132] Step S2022: Based on the analyzed signal, determine the instantaneous phase of each interference-free pulse signal.

[0133] In some embodiments, the Hilbert transform essentially projects the real signal onto the imaginary axis, forming a complex envelope, which is beneficial for subsequent phase extraction. The instantaneous phase can be calculated from the analytic signal. As shown in formula (18):

[0134] (18);

[0135] After calculating the instantaneous phase, the phase jumps between -π and π, creating a discontinuity that affects subsequent frequency and pulse width analysis. Therefore, unwrapping the phase is an essential operation. The purpose is to unfold the originally periodically jumping phase into a continuous curve, so that the phase change can accurately reflect the true characteristics of the signal.

[0136] Step S2023: Unwrap the instantaneous phase to obtain the first unwrapped phase.

[0137] In some embodiments, the first untangling phase after untangling As shown in formula (19):

[0138] (19);

[0139] in, For continuous phase, This represents the number of transitions accumulated during the unwrapping process. The first unwrapped phase can fully reflect the structural characteristics of the frequency-modulated signal and lays the foundation for subsequent first-order derivative and signal boundary determination.

[0140] Step S2024: Differentiate the first unwrapped phase to obtain the first and second derivatives of the first unwrapped phase.

[0141] To identify the center and end positions of the stationary phase of the signal, the first derivative of the first unwrapped phase is calculated, and the first derivative of the first unwrapped phase is shown in formula (20):

[0142] (20);

[0143] The first derivative can reflect the rate of change of phase on the time axis, i.e. the frequency trend, which is usually stable in the main part of the signal, but fluctuates violently in the noise region.

[0144] Since high-frequency noise in actual data can easily cause the derivative to be unstable, the embodiments of this application can use a sliding window to smooth the first derivative of the first unwrapped phase, as shown in formula (21):

[0145] (twenty one);

[0146] in, The window length is smoothed. The smoothed derivative curve makes it easier to identify stable signal segments and boundaries.

[0147] To further characterize the location of abrupt changes in the signal structure, the second derivative of the first unwrapped phase can be calculated. As shown in formula (22):

[0148] (twenty two);

[0149] The second derivative reflects the acceleration of frequency change; it is generally small within the main signal region, but usually increases sharply in the noise region.

[0150] Step S2025: The position where the second derivative first exceeds a first preset threshold is determined as the termination point of each interference-free pulse signal; the first preset threshold is determined based on the second derivative and a second preset adjustment factor.

[0151] To accurately identify the signal termination point, a dynamic threshold criterion based on energy averaging can be constructed. Firstly, a baseline value can be calculated based on the second derivative. As shown in formula (23):

[0152] (twenty three);

[0153] Then, two adjustment coefficients are defined, namely the second preset adjustment factor. and As shown in formulas (24) and (25):

[0154] (twenty four);

[0155] (25);

[0156] The first preset threshold can be obtained based on the benchmark value and the second preset adjustment factor. As shown in formula (26):

[0157] (26);

[0158] Here, the position where the second derivative first exceeds the first preset threshold can be recorded as the end position of the signal, i.e., the termination point. .

[0159] Step S2026: Determine the position corresponding to the minimum value of the first derivative before the termination point as the position of the stationary phase center.

[0160] Here, at that endpoint Within the previous range, find the position corresponding to the minimum value of the first derivative as the stationary phase center position of the signal. .

[0161] Correspondingly, step S203 can be achieved through steps S2031 and S2032:

[0162] Step S2031: Based on the sampling frequency of the incomplete SAR signal, the stationary phase center position of each interference-free pulse signal, and the termination point, determine the pulse width of each interference-free pulse signal.

[0163] In this embodiment, based on the symmetry characteristic, the pulse width of each interference-free pulse signal is as shown in formula (27):

[0164] (27);

[0165] in, This represents the final estimated pulse width. The sampling frequency (Hz) and These are the termination point and the center of symmetry obtained by the second derivative method and the derivative minimum method, respectively.

[0166] Step S2032: Average the pulse width of each interference-free pulse signal to obtain the pulse width of the incomplete SAR signal.

[0167] To enhance robustness, the above steps are sequentially performed on each interference-free pulse signal in the interference-free signal matrix. After obtaining the pulse width, the mean is statistically analyzed to obtain the average pulse width estimate of the SAR signal for the current time period. The parameter inversion method provided in this application does not require a complete signal structure and makes full use of the latter half of the signal information for compensation inversion, significantly improving the accuracy of pulse width estimation under incomplete conditions.

[0168] This application's embodiments construct an analytical signal and extract the instantaneous phase using Hilbert transform, followed by phase unwrapping and derivative calculation, which accurately identifies the signal's termination point and the location of the stationary phase center. By utilizing the latter half of the signal's information, high-precision pulse width estimation is achieved under incomplete signal conditions, solving the measurement error problem caused by signal loss in related technologies.

[0169] In some embodiments, the signal bandwidth can be accurately retrieved by calculating the SAR signal spectral amplitude, selecting the bandwidth boundary based on a dynamic threshold algorithm, and compensating for the missing bandwidth proportion. This application embodiment can analyze the spectral characteristics of incomplete SAR signals, accurately retrieve the signal bandwidth, and compensate for missing portions by combining spectral amplitude with a dynamic threshold. Similar to pulse width estimation, it is also based on pulse-by-pulse analysis and average statistics, thereby improving the bandwidth estimation accuracy under low signal-to-noise ratio conditions.

[0170] Therefore, step S202 can also be achieved through steps S31 to S33:

[0171] Step S31: Perform a fast Fourier transform on each of the interference-free pulse signals to obtain the frequency domain amplitude spectrum of each interference-free pulse signal.

[0172] Here, any interference-free pulse signal can be represented as Applying a Fast Fourier Transform to the signal yields the frequency domain amplitude spectrum of the interference-free pulse signal. As shown in formula (28):

[0173] (28);

[0174] here, Indicates the signal at frequency The range of the upper part, This represents the Fast Fourier Transform.

[0175] Step S32: Based on the frequency domain amplitude spectrum, determine the frequency points in each interference-free pulse signal whose energy is greater than the second preset threshold as the second frequency point set.

[0176] In some embodiments, a reference energy can be calculated for the spectral amplitude of each interference-free pulse signal. As shown in formula (29):

[0177] (29);

[0178] And introduce dynamic adjustment factors and As shown in formulas (30) and (31):

[0179] (30);

[0180] (31);

[0181] Based on benchmark energy The dynamic adjustment factor can be used to construct a second preset threshold. As shown in formula (32):

[0182] (32);

[0183] In some embodiments, a set of frequency points with energy values ​​greater than a second preset threshold can be extracted, i.e., the second frequency point set. As shown in formula (33):

[0184] (33);

[0185] Step S33: Based on the second set of frequency points and frequency resolution, determine the pulse bandwidth of each interference-free pulse signal.

[0186] In the embodiments of this application, the pulse bandwidth As shown in formula (34):

[0187] (34);

[0188] in, Frequency resolution (Hz) The sampling frequency (Hz) This indicates the number of frequency points that meet the conditions.

[0189] Correspondingly, step S203 can also be achieved through steps S2033 and S2034:

[0190] Step S2033: Based on the stationary phase center position and the termination point of each interference-free pulse signal, the pulse bandwidth of each interference-free pulse signal is compensated to obtain the compensated bandwidth of each interference-free pulse signal.

[0191] In some embodiments, since the absence of the first half of the signal may lead to an underestimation of the actual bandwidth in the spectral analysis, the embodiments of this application can compensate for the pulse bandwidth of each interference-free pulse signal to obtain the compensated bandwidth of each interference-free pulse signal. As shown in formula (35):

[0192] (35);

[0193] in, and These are the termination point and the stationary phase center position, respectively.

[0194] Step S2034: Average the compensation bandwidth of each interference-free pulse signal to obtain the bandwidth of the incomplete SAR signal.

[0195] The bandwidth compensation in this embodiment considers signal symmetry and the actual lost portion, making the estimated value closer to the true bandwidth of the complete pulse. The average bandwidth inversion result of the incomplete SAR signal segment can be obtained by calculating the compensation bandwidth for each interference-free pulse signal in the interference-free signal matrix and taking the average. This method, combining dynamic thresholding, spectral analysis, and pulse width information, can still effectively achieve accurate bandwidth estimation under broadband interference conditions even with low signal-to-noise ratios.

[0196] This application's embodiments, through frequency domain amplitude spectrum analysis combined with a dynamic threshold algorithm, can accurately identify the bandwidth boundaries of a signal and perform bandwidth compensation based on the stationary phase center and termination point. This method considers the signal symmetry and the influence of the actual lost portion, making the bandwidth estimation closer to the true value and overcoming the underestimation problem of related methods under incomplete signal conditions.

[0197] In some embodiments, after bandwidth inversion, to further obtain the frequency modulation (FM) parameters of low signal-to-noise ratio (SNR) incomplete SAR signals, this application proposes a FM inversion method based on sliding window local linear fitting. Considering that methods in related technologies are difficult to accurately estimate instantaneous frequency changes in low SNR environments, the estimation accuracy and robustness of the FM can be effectively improved through first-order derivative analysis and global residual optimization within the sliding window. Here, the instantaneous frequency can be obtained by performing phase expansion and first-order derivative calculation on the SAR signal. Then, global linear fitting is performed based on the optimal window fitting model to obtain the final FM estimate.

[0198] Therefore, step S202 can also be achieved through steps S41 to S44:

[0199] Step S41: Perform phase unwrapping on each interference-free pulse signal to obtain the second unwrapped phase.

[0200] Any interference-free pulse signal can be represented as Build a timeline As shown in formula (36):

[0201] (36);

[0202] in, Sampling frequency, This represents the number of sampling points along the distance. By constructing a time axis, the sampling points in the interference-free pulse signal can be effectively correlated with the actual time, laying the foundation for subsequent frequency modulation calculations.

[0203] To obtain the instantaneous frequency of each interference-free pulse signal, the signal first needs to be phase-expanded. Since there are phase jumps in SAR signals, directly calculating the phase leads to phase unwrapping problems. The Hilbert transform can be used to obtain the phase information, and phase expansion can be performed, as shown in formula (37):

[0204] (37);

[0205] in, Indicates the untangling phase. It is a phase unwrapping operation that calculates the phase of a complex signal.

[0206] Step S42: Take the first derivative of the second unwrapped phase to obtain the instantaneous frequency of each sampling time point in each interference-free pulse signal.

[0207] In some embodiments, the instantaneous frequency at each sampling time point in each interference-free pulse signal, i.e. the first derivative of the phase, is as shown in formula (38):

[0208] (38);

[0209] in, The sampling time interval (seconds). This is the instantaneous frequency, measured in Hz.

[0210] Step S43: Based on multiple preset sliding windows, perform linear fitting on the instantaneous frequency at each sampling time point to obtain the fitted frequency modulation.

[0211] Since the instantaneous frequency curve may contain a large number of local disturbances under low signal-to-noise ratio conditions, a sliding window local linear fitting is required to enhance robustness. Let the window length be as shown in formula (39):

[0212] (39);

[0213] The sliding step size is shown in formula (40):

[0214] (40);

[0215] in This indicates rounding down, and the total number of windows is shown in formula (41):

[0216] (41);

[0217] Within each sliding window, a linear model is fitted to the instantaneous frequency, as shown in Equation (42):

[0218] (42);

[0219] in, This represents the fitted slope (local tuning frequency) within the window. The intercept is used. Calculate the fitting residual for each sliding window. As shown in formula (43):

[0220] (43);

[0221] The window with the smallest residual can be selected as the optimal window, and the in-window fitting slope within that window can be set. As a preliminary frequency modulation estimate, i.e., the fitted frequency modulation value .

[0222] Step S44: Perform global residual detection on the fitted frequency modulation to remove outliers and obtain the pulse signal modulation frequency of each interference-free pulse signal.

[0223] To further verify the accuracy of the estimation, global residual detection and outlier removal can be employed. A global expression is constructed based on the best window fitting model. As shown in formula (44):

[0224] (44);

[0225] in, Find the optimal window fit intercept. Calculate the global residual. As shown in formula (45):

[0226] (45);

[0227] To remove outliers, first calculate the standard deviation of the residuals. As shown in formula (46):

[0228] (46);

[0229] in, This represents the global residual mean. Three standard deviations are set as the outlier threshold. As shown in formula (47):

[0230] (47);

[0231] It can filter out all that meet the requirements. The normal point index set.

[0232] Finally, a global least squares linear fit is performed on the data in the normal point index set to obtain the final frequency modulation estimate, that is, the pulse signal modulation frequency of each interference-free pulse signal, as shown in formula (48):

[0233] (48);

[0234] in, and These are the average values ​​of time and instantaneous frequency, respectively.

[0235] Correspondingly, step S203 can also be achieved through step S2035:

[0236] Step S2035: Average the pulse signal modulation frequency of each interference-free pulse signal to obtain the modulation frequency of the incomplete SAR signal.

[0237] The embodiments of this application can perform the above steps on all interference-free pulse signals in the interference-free signal matrix one by one, and take the average of the pulse signal modulation frequency as the final modulation frequency inversion result of the SAR data segment. This method takes into account both local fitting and global optimization, which greatly enhances the reliability of modulation frequency estimation under low signal-to-noise ratio and incomplete conditions.

[0238] This application's embodiments effectively extract the frequency modulation (FM) parameters of a signal by combining sliding window local fitting with global residual optimization, avoiding estimation bias caused by noise interference in low signal-to-noise ratio (SNR) environments. This not only improves the robustness of FM estimation but also enhances its applicability under incomplete signal conditions.

[0239] In some embodiments, the peak position of each pulse can be extracted using the pulse compression result as a time feature; the peak positions of adjacent pulses can be differentiated to obtain the pulse time interval; and the pulse repetition interval and pulse repetition frequency can be calculated by combining the frame header time derivative. Here, the peak position of each pulse can be extracted based on the pulse compression result, and the pulse repetition interval (PRI) and pulse repetition frequency (PRF) can be calculated by combining the frame header trigger time.

[0240] Therefore, step S202 can also be achieved through steps S51 to S54:

[0241] Step S51: Determine the first interference-free pulse signal in the interference-free signal matrix as the reference pulse signal.

[0242] Here, the first interference-free pulse signal can be... The reference pulse signal is set. Its matched filter expression in the frequency domain is shown in equation (49):

[0243] (49);

[0244] in, Represents the Fast Fourier Transform. This indicates the complex conjugate operation.

[0245] Step S52: Based on the matched filter of the reference pulse signal, pulse compression is performed on each interference-free pulse signal after the first interference-free pulse signal to obtain the echo signal after matched filtering.

[0246] A matched filter based on a reference pulse signal performs pulse compression on each interference-free pulse signal after the first interference-free pulse signal to obtain the matched-filtered echo signal. As shown in formula (50):

[0247] (50);

[0248] in, The echo signal after matched filtering contains a distinct main peak.

[0249] Step S53: Extract the main peak position of each echo signal to obtain the main peak position.

[0250] In some embodiments, the position of the main peak is extracted. As shown in formula (51):

[0251] (51);

[0252] Step S54: The position of the main peak is symmetrically adjusted to obtain the peak position of each interference-free pulse signal.

[0253] In some embodiments, to correct the peak position shift caused by the periodicity of FFT, the position of the main peak can be symmetrically adjusted, as shown in formula (52):

[0254] (52);

[0255] in, This represents the number of sampling points along the distance.

[0256] Correspondingly, step S203 can also be achieved through steps S61 to S65:

[0257] Step S61: Based on the sampling frequency of the incomplete SAR signal and the peak position of each interference-free pulse signal, determine the delay time of the peak position of each interference-free pulse signal.

[0258] Here, the delay time of the peak position of each interference-free pulse signal As shown in formula (53):

[0259] (53);

[0260] in, The range sampling frequency is (Hz).

[0261] Step S62: Based on the delay time and the frame header trigger time of each interference-free pulse signal, obtain the actual arrival time of the main peak of each interference-free pulse signal.

[0262] Here, the frame header trigger time of each interference-free pulse signal can be combined. The actual arrival time of the main peak of each interference-free pulse signal is obtained. As shown in formula (54):

[0263] (54);

[0264] Step S63: Based on the actual arrival time of the main peak of each interference-free pulse signal, determine the time interval between adjacent signals in the interference-free signal matrix.

[0265] Based on the actual arrival time of the main peak of each interference-free pulse signal in the interference-free signal matrix, the time interval between adjacent signals in the interference-free signal matrix can be determined. As shown in formula (55):

[0266] (55);

[0267] Step S64: Determine the average time interval of the interference-free signal matrix based on the time interval.

[0268] To eliminate abnormal frame intervals, the average of all time intervals can be calculated. As shown in formula (56):

[0269] (56);

[0270] Step S65: Calculate the pulse repetition interval and the pulse repetition frequency based on the average time interval.

[0271] In some embodiments, the normal interval index set can be defined as shown in formula (57):

[0272] (57);

[0273] Finally, the average PRI is estimated based on the normal interval as shown in formula (58):

[0274] (58);

[0275] The pulse repetition frequency (PRF) is calculated as shown in formula (59):

[0276] (59);

[0277] in, This represents the average frequency of the emitted pulses per unit time, expressed in Hz.

[0278] This application embodiment, through the combined analysis of compressed main peak sequence and frame header time, can effectively extract the time parameters of SAR signals under complex noise conditions, effectively overcoming the peak blurring and inter-frame jitter problems in low signal-to-noise ratio environments, and providing an important basis for system calibration and subsequent high-precision processing.

[0279] The following will describe an exemplary application of the embodiments of this application in a real-world application scenario.

[0280] Figure 3 This is a flowchart illustrating the low signal-to-noise ratio incomplete SAR signal parameter inversion method proposed in this application. Figure 3 As shown, steps S301 to S305 are included:

[0281] Step S301: SAR signal detection and interference suppression.

[0282] In some embodiments, the detected SAR signal is subjected to fast sliding window filtering, and burst interference in the SAR signal is removed based on triple peak notch filtering.

[0283] Preprocessing and interference suppression of the received SAR signal is a crucial initial step in the entire low signal-to-noise ratio incomplete SAR signal parameter inversion process. First, a fast sliding window filtering method is used for preliminary noise smoothing. Then, burst point frequency interference is identified and removed based on the triple peak notch method, laying the foundation for the subsequent inversion of key parameters such as pulse width, bandwidth, and frequency modulation.

[0284] The original received signal can be represented as a two-dimensional complex matrix. (i.e., interference-free signal matrix), where each row in the matrix represents a radar pulse echo, and the columns represent the equally spaced sampling points of the pulse in the range direction. The signal is defined as shown in formula (60):

[0285] (60);

[0286] Where M is the total number of pulses, and N is the number of sampling points per pulse. For the i-th pulse, the first... Complex signal values ​​at each sampling point.

[0287] To extract the frequency domain features of a signal, each line of the signal can be processed. Applying a Fast Fourier Transform yields the corresponding frequency domain representation. As shown in formula (61):

[0288] (61);

[0289] in, Indicates the first The complex spectrum of the line signal in the frequency domain, This is a Fast Fourier Transform operation. It allows for the calculation of the spectral amplitude. (i.e., spectral amplitude), as shown in formula (62):

[0290] (62);

[0291] Among them, spectral amplitude Indicates the first Each pulse at various frequency points The energy intensity at each frequency The amount of energy on the surface determines the subsequent interference identification, which is based on this amplitude distribution.

[0292] To achieve point-frequency interference detection, this application employs the triple maximum energy ratio method. First, the spectrum... Perform energy sorting to find the center frequency of the highest point. (i.e., the frequency point corresponding to the highest point of spectral energy), and integrate the spectral energy within its symmetrical bandwidth to define the first maximum energy. As shown in formula (63):

[0293] (63);

[0294] in, For the first The maximum amplitude of the line spectrum corresponds to the frequency. Let be the integral bandwidth radius, which is calculated as shown in formula (64):

[0295] (64);

[0296] in, For notch bandwidth, The number of sampling points. The sampling frequency. The current frequency band (i.e., [...]) , After setting the energy of the symmetric bandwidth to zero, repeat the above operation three times, successively calculating the local peak energy and accumulating them to obtain the maximum total energy of the three operations. As shown in formula (65):

[0297] (65);

[0298] To determine the proportion of interference, the maximum total energy was calculated three times. The proportion of relative total spectral energy (i.e., energy ratio), as shown in formula (66):

[0299] (66);

[0300] Here, when the proportion If the threshold value is exceeded (e.g., 0.2), it can be determined that the current pulse has strong point frequency interference. Pulses with strong point frequency interference are discarded and will not be used for inversion.

[0301] For those who do not meet the criterion (i.e., proportion) If the threshold value is not exceeded, pulses without strong point-frequency interference (i.e., the first suppressed signal) proceed to the next stage of broadband interference identification based on the dynamic threshold method. In this part, the baseline average energy of the spectrum must first be calculated. As shown in formula (67):

[0302] (67);

[0303] This application introduces two adjustment factors in its embodiments. and The dynamic thresholds are used to construct the thresholds, as shown in formulas (68) and (69) respectively:

[0304] (68);

[0305] (69);

[0306] in, This represents the standard deviation of the spectral amplitude. The dynamic threshold is defined based on this. (i.e., the spectral amplitude threshold) is shown in formula (70):

[0307] (70);

[0308] Based on this threshold, select all amplitudes that exceed the dynamic threshold. Frequency points constitute a set (i.e., the first set of frequency points), as shown in formula (71):

[0309] (71);

[0310] Calculate the spectrum bandwidth As shown in formula (72):

[0311] (72);

[0312] Wherein, frequency resolution is defined as This refers to the unit frequency step size. If the final bandwidth... If the signal is below the threshold, it is considered a normal signal (i.e., the second suppression signal); if it is below the threshold, the current pulse is considered to be destroyed by broadband interference and is discarded.

[0313] After filtering out all pulses that meet the spectral criteria, it is necessary to index the row numbers of the valid pulses to ensure their temporal continuity. Perform successive differences as shown in formula (73):

[0314] (73);

[0315] when When established, it indicates that the current pulse has temporal continuity with its adjacent pulses. Finally, the continuous and normal preceding pulses are extracted. The pulses form a new interference-free signal matrix As shown in formula (74):

[0316] (74);

[0317] This matrix serves as the direct input for subsequent pulse width, bandwidth, and frequency modulation inversion steps. Through spectral energy assessment, triple peak detection, and dynamic threshold bandwidth identification in this step, the embodiments of this application can effectively address strong point-frequency interference and complex broadband interference, achieving high-precision preliminary screening of SAR signals under low signal-to-noise ratio conditions.

[0318] Step S302: Pulse width inversion based on SAR signal compensation.

[0319] The embodiments of this application can compensate for the SAR signal by calculating the stationary phase center and end position of the signal, thereby deriving an accurate signal pulse width.

[0320] After completing interference suppression and signal filtering in step S301, this step derives the corresponding pulse width for each normal SAR pulse based on the temporal structure relationship between the phase center and the termination point.

[0321] Since incomplete SAR signals may have a missing first half during reception, direct measurement of pulse width is uncertain. This application proposes a method for compensation estimation based on the complete second half of the signal, effectively improving pulse width inversion accuracy in low signal-to-noise ratio environments.

[0322] First, the interference-free SAR signal matrix obtained in step S301 In the middle, select the first The line pulse signal is used as a representative sample, as shown in formula (75):

[0323] (75);

[0324] in, This represents a single pulse signal (i.e., an analytic signal) with a length of [missing information]. The corresponding distance sampling points (these N points are arranged along the distance direction).

[0325] To extract the instantaneous phase features of a signal, the real-valued form of the signal needs to be constructed into a complex analytic signal. The construction method involves taking the signal and its Hilbert transform to form a complex number, as shown in formula (76):

[0326] (76);

[0327] in, To analyze the signal, The imaginary unit, For the timeline, Indicates the signal The result obtained by applying the Hilbert transform.

[0328] The Hilbert transform essentially projects a real signal onto the imaginary axis, forming a complex envelope, which is beneficial for subsequent phase extraction. Instantaneous phase can be calculated from an analytic signal. As shown in formula (77):

[0329] (77);

[0330] After calculating the instantaneous phase, since the phase will... arrive The abrupt changes between phase transitions create discontinuities, affecting subsequent frequency and pulse width analysis. Therefore, unwrapping the phase is an essential operation. The purpose is to unfold the originally periodically changing phase into a continuous curve, allowing the phase changes to accurately reflect the true characteristics of the signal. (Unwrapped phase) (i.e., the first untangling phase), as shown in formula (78):

[0331] (78);

[0332] in, For continuous phase, This represents the number of transitions accumulated during the unwrapping process. The unwrapped phase can fully reflect the structural characteristics of the frequency-modulated signal and lay the foundation for subsequent first-order derivative and signal boundary determination.

[0333] Next, in order to identify the stationary phase center and the end position of the signal, the first derivative of the unwrapped phase is calculated. The first derivative of the unwrapped phase is shown in formula (79):

[0334] (79);

[0335] The first derivative can reflect the rate of change of phase on the time axis, i.e. the frequency trend, which is usually stable in the main part of the signal, but fluctuates violently in the noise region.

[0336] Since high-frequency noise in actual data can easily lead to unstable derivatives, this application uses a sliding window to smooth the first derivative of the unwrapped phase, as shown in formula (80):

[0337] (80);

[0338] in, The window length is smoothed. The smoothed derivative curve makes it easier to identify stable signal segments and boundaries.

[0339] To further characterize the locations of abrupt changes in signal structure, the second derivative of the unwrapped phase can be calculated. As shown in formula (81):

[0340] (81);

[0341] The second derivative reflects the acceleration of frequency change; it is generally small within the main signal region, but usually increases sharply in the noise region.

[0342] To accurately identify the signal termination point, a dynamic threshold criterion based on energy averaging can be constructed. First, a baseline value is calculated. As shown in formula (82):

[0343] (82);

[0344] Then define two adjustment coefficients. and (i.e., the second preset adjustment factor), as shown in formulas (83) and (84):

[0345] (83);

[0346] (84);

[0347] Based on this, the dynamic noise determination threshold is obtained. (i.e., the first preset threshold), as shown in formula (85):

[0348] (85);

[0349] Here, the position where the second derivative first exceeds the threshold can be recorded as the end position of the signal. (i.e., the termination point).

[0350] Next, at the end position Within the previous range, find the position corresponding to the minimum value of the first derivative as the stationary phase center of the signal. (i.e., the location of the stationary phase center).

[0351] Finally, based on this symmetry property, the pulse width estimation in this embodiment is derived as shown in formula (86):

[0352] (86);

[0353] in, This represents the final estimated pulse width (i.e., pulse width). The sampling frequency (Hz) and These are the termination point and the center of symmetry obtained by the second derivative method and the derivative minimum method, respectively.

[0354] To enhance robustness, The above steps are executed sequentially for each pulse to obtain the pulse width. After averaging, the average pulse width estimate of the SAR signal for the current time period is obtained. This method does not require a complete signal structure and makes full use of the information in the latter half of the signal for compensation and inversion, which significantly improves the accuracy of pulse width estimation under incomplete conditions.

[0355] Step S303: Bandwidth inversion based on spectral amplitude gradient analysis.

[0356] The embodiments of this application can accurately invert the signal bandwidth by calculating the SAR signal spectral amplitude, selecting the bandwidth boundary based on the dynamic threshold algorithm, and compensating for the missing bandwidth ratio.

[0357] After completing the pulse width compensation inversion in step S302, this step further analyzes the spectral characteristics of the incomplete SAR signal. By combining spectral amplitude with dynamic thresholding, the signal bandwidth is accurately inverted and the missing parts are compensated and corrected. Similar to pulse width estimation, this method is also based on pulse-by-pulse analysis and average statistics, thereby improving the bandwidth estimation accuracy under low signal-to-noise ratio conditions.

[0358] First, from the interference-free signal matrix extracted in step S301 In the middle, select representative samples (e.g., the first...) Using the pulse signal as the object of analysis, As shown in formula (87):

[0359] (87);

[0360] in, Indicates a line of length The range-direction pulse signal is used for bandwidth analysis. Applying a Fast Fourier Transform to this signal yields the... Frequency domain amplitude spectrum of a traveling pulse signal (i.e., frequency domain amplitude spectrum), as shown in formula (88):

[0361] (88);

[0362] here, Indicates the signal at frequency The range of the upper part, This represents the Fast Fourier Transform. Subsequently, the reference energy for calculating the spectral amplitude is determined. As shown in formula (89):

[0363] (89);

[0364] And introduce dynamic adjustment factors and As shown in formulas (90) and (91):

[0365] (90);

[0366] (91);

[0367] Comprehensive construction of dynamic threshold As shown in formula (92):

[0368] (92);

[0369] Based on this threshold, extract the set of all frequency points whose energy values ​​exceed the threshold. (The second set of frequency points), as shown in formula (93):

[0370] (93);

[0371] And based on this, the initial bandwidth is calculated. (i.e., pulse bandwidth), as shown in formula (94):

[0372] (94);

[0373] in, Frequency resolution (Hz) The sampling frequency (Hz) This indicates the number of frequency points that meet the conditions.

[0374] Since the absence of the first half of the signal may lead to an underestimation of the actual bandwidth in the spectrum analysis, this embodiment of the application introduces a compensation factor to adjust the bandwidth based on the pulse width compensation result in step 102. (i.e., compensated bandwidth), as shown in formula (95):

[0375] (95);

[0376] in, and These are the signal end position and the stationary phase center position determined in pulse width inversion step 102, respectively.

[0377] The bandwidth compensation in this embodiment takes into account signal symmetry and the actual lost portion, making the estimated value closer to the true bandwidth of the complete pulse. Finally, through... The bandwidth of each pulse is calculated individually, and the average value is statistically analyzed to obtain the average bandwidth inversion result of the incomplete SAR signal segment. This method combines dynamic thresholding, spectral analysis, and pulse width information to effectively achieve accurate bandwidth estimation under broadband interference conditions even with low signal-to-noise ratios.

[0378] Step S304: Frequency modulation inversion based on local fitting of the first-order phase derivative using a sliding window.

[0379] The instantaneous frequency is obtained by performing phase expansion and first derivative calculation on the SAR signal. Then, a global linear fit is performed based on the optimal window fitting model to obtain the final frequency modulation estimate.

[0380] After completing the bandwidth inversion in step S303, this step proposes a frequency modulation inversion method based on local linear fitting within a sliding window to further obtain the frequency modulation parameters of the low signal-to-noise ratio incomplete SAR signal. Considering that methods in related technologies are difficult to accurately estimate instantaneous frequency changes in low signal-to-noise ratio environments, this embodiment effectively improves the estimation accuracy and robustness of the frequency modulation through first-order derivative analysis within the sliding window and global residual optimization.

[0381] Specifically, firstly, the interference-free signal matrix selected in step 101... In the middle, select representative pulses (such as the first pulse). Line signals as the object of analysis As shown in formula (96):

[0382] (96);

[0383] in It is a single pulse signal with a length of Building a timeline As shown in formula (97):

[0384] (97);

[0385] in, Sampling frequency, This represents the number of sampling points along the distance. By constructing a time axis, the sampling points can be effectively correlated with real time, laying the foundation for subsequent frequency modulation calculations.

[0386] To obtain the instantaneous frequency of the signal, phase unwrapping is first required. Since SAR signals exhibit phase jumps, directly calculating the phase leads to phase unwrapping problems. The Hilbert transform can be used to obtain phase information, followed by phase unwrapping, as shown in formula (98):

[0387] (98);

[0388] in, This indicates the untangling phase (i.e., the second untangling phase). It is a phase unwrapping operation that calculates the phase of a complex signal.

[0389] Next, the instantaneous frequency is calculated. That is, the first derivative of the phase, as shown in formula (99):

[0390] (99);

[0391] in, The sampling time interval (seconds). This is the instantaneous frequency, measured in Hz.

[0392] Since the instantaneous frequency curve may contain a large number of local disturbances under low signal-to-noise ratio conditions, a sliding window local linear fitting is required to enhance robustness. Let the window length be as shown in formula (100):

[0393] (100);

[0394] The sliding step size is shown in formula (101):

[0395] (101);

[0396] in This indicates rounding down, and the total number of windows is shown in formula (102):

[0397] (102);

[0398] Within each sliding window, a linear model is fitted to the instantaneous frequency to obtain the linear frequency (i.e., the fitted frequency tuning), as shown in formula (103):

[0399] (103);

[0400] in, This represents the fitted slope (local tuning frequency) within the window. The intercept is used. Calculate the fitting residual for each sliding window. As shown in formula (104):

[0401] (104);

[0402] Select the window with the smallest residual as the optimal window, and then set the in-window fitting slope within that window. As a preliminary frequency modulation estimate .

[0403] To further verify the accuracy of the estimation, global residual detection and outlier removal were employed. A global expression was constructed based on the best window fitting model. As shown in formula (105):

[0404] (105);

[0405] in, Find the optimal window fit intercept. Calculate the global residual. As shown in formula (106):

[0406] (106);

[0407] To remove outliers, first calculate the standard deviation of the residuals. As shown in formula (107):

[0408] (107);

[0409] in, This represents the global residual mean. Three standard deviations are set as the outlier threshold. As shown in formula (108):

[0410] (108);

[0411] Filter out all that meet the requirements The normal point index set.

[0412] Finally, a global least squares linear fit is performed on the normal data to obtain the final frequency modulation estimate (i.e., the pulse signal frequency modulation), as shown in formula (109):

[0413] (109);

[0414] in, and These are the average values ​​of time and instantaneous frequency, respectively.

[0415] one by one The above steps are performed on all pulse signals, and the average of the frequency modulation estimates is taken as the final frequency modulation inversion result of that segment of SAR data. This method takes into account both local fitting and global optimization, greatly enhancing the reliability of frequency modulation estimation under low signal-to-noise ratio and incomplete conditions.

[0416] Step S305: Inversion of pulse repetition frequency based on pulse compression results.

[0417] The embodiments of this application can extract the peak position of each pulse using the pulse compression result as a time feature; perform differential calculation on the peak positions of adjacent pulses to obtain the pulse time interval; and combine the time derivative of the frame header to comprehensively calculate the pulse repetition interval and pulse repetition frequency.

[0418] After completing the frequency modulation inversion in step S304, in order to further obtain the time parameters of the SAR system, this step extracts the peak position of each pulse based on the pulse compression result, and calculates the pulse repetition interval (PRI) and pulse repetition frequency (Pulse PRF) in combination with the frame header trigger time.

[0419] This method effectively overcomes the peak blurring and inter-frame jitter problems in low signal-to-noise ratio environments by analyzing the timing of the compressed main peak.

[0420] Specifically, firstly, the interference-free continuous pulse segment obtained in step 101... In the process, each line of signal is extracted as an input frame, denoted as... ,in Indicates the first The pulse index of the row, in total A pulse.

[0421] Assume the first frame signal For the reference pulse (i.e., the reference pulse signal), the expression of its matched filter in the frequency domain is shown in equation (110):

[0422] (110);

[0423] in, Represents the Fast Fourier Transform. This represents the complex conjugate operation. For each subsequent pulse... Pulse compression is performed to obtain the echo signal after matched filtering. As shown in formula (111):

[0424] (111);

[0425] in, The echo signal after matched filtering contains a distinct main peak. The location of the main peak needs to be extracted. As shown in formula (112):

[0426] (112);

[0427] To correct the peak position shift caused by the periodicity of FFT, the main peak position is symmetrically adjusted to obtain the adjusted position (i.e., the peak position), as shown in formula (113):

[0428] (113);

[0429] in, This represents the number of sampling points along the distance. Main Peak Index Corresponding physical delay time (i.e., the delay time at the peak position) is shown in formula (114):

[0430] (114);

[0431] in, The range sampling frequency is (Hz).

[0432] Combined with the frame header trigger time of each frame The actual arrival time of the main echo peak is obtained. As shown in formula (115):

[0433] (115);

[0434] Based on this sequence, the time interval between adjacent pulses is calculated. (That is, the time interval between adjacent signals) is shown in formula (116):

[0435] (116);

[0436] To remove abnormal frame intervals, the average value of all time intervals is calculated. (i.e., the average time interval) is shown in formula (117):

[0437] (117);

[0438] The set of normal interval indices is defined as shown in formula (118):

[0439] (118);

[0440] Finally, the average PRI (pulse repetition interval) is estimated based on the normal interval as shown in formula (119):

[0441] (119);

[0442] The pulse repetition frequency (PRF) is calculated as shown in formula (120):

[0443] (120);

[0444] in, This represents the average frequency of the emitted pulses per unit time, expressed in Hz.

[0445] This application embodiment, through the combined analysis of compressed main peak sequence and frame header time, can effectively extract the time parameters of SAR signals under complex noise conditions, providing an important basis for system calibration and subsequent high-precision processing.

[0446] Based on the aforementioned method, this application provides a specific embodiment.

[0447] Example 1

[0448] The example describes a receiver intercepting X-band spaceborne SAR data. During data reception, the electromagnetic environment was complex, and the leading edge of the received pulse was missing. SAR signal detection and interference suppression were performed on the received data. Figure 4 This is a schematic diagram of the real part amplitude of a pulse provided in an embodiment of this application, where the real part amplitude of the pulse is as follows: Figure 4 As shown in the figure, there is a significant loss at the leading edge of the SAR signal pulse at position 401. Figure 5 This is a schematic diagram of the SAR range-direction frequency domain amplitude boundary obtained by bandwidth inversion according to an embodiment of this application, as shown below. Figure 5 As shown, the frequency domain amplitude of the SAR range direction can be obtained based on the frequency domain amplitude spectrum 501. Figure 6 This is a schematic diagram of frequency modulation based on local fitting of sliding window provided in an embodiment of this application, and the frequency modulation is shown in 601. Figure 7 This is a schematic diagram of the pulse compression result when the inversion pulse repetition frequency is provided in the embodiment of this application. The pulse compression result is shown in 701.

[0449] The inversion results obtained by the inversion methods in related technologies and the parameter inversion method provided in the embodiments of this application are shown in Table 1. It can be seen that the inversion results obtained by the parameter inversion method provided in the embodiments of this application have a deviation of less than 1% from the actual SAR transmission parameters, which is better than the inversion accuracy of related technologies, further verifying the effectiveness of the method proposed in the embodiments of this application.

[0450] Table 1

[0451]

[0452] The parameter inversion method for incomplete SAR signals provided in this application proposes a step-by-step multidimensional estimation and missing value compensation framework, encompassing five major steps: signal detection and interference suppression, pulse width inversion, bandwidth inversion, frequency modulation estimation, and PRF extraction. A spectrum detection model combining triple-peak notch filtering and dynamic threshold determination achieves efficient interference removal in complex environments. A pulse width and bandwidth inversion strategy based on phase unwrapping, derivative analysis, and second-half compensation addresses the parameter estimation bias caused by incomplete SAR signals. A frequency modulation inversion algorithm combining sliding window local fitting and global residual optimization significantly improves estimation accuracy under low SNR conditions. A comprehensive analysis method based on pulse compression main peak and frame header time alignment accurately recovers the PRF. Ultimately, high-precision, full-process, and scalable inversion of key SAR system parameters is achieved under low SNR incomplete received signals.

[0453] This application's embodiments effectively overcome the parameter estimation bias and instability issues of related technologies' parameter inversion algorithms when the signal-to-noise ratio is low or the signal is partially missing, through innovative steps such as multi-stage dynamic threshold judgment, sliding window fitting, phase derivative analysis, and compensation correction. It not only possesses good adaptability and robustness but also has high engineering practical value and promising prospects for widespread application, providing important technical support for SAR system performance optimization and data processing in complex electromagnetic environments.

[0454] It should be noted that the description of the apparatus in this application embodiment is similar to the description of the method embodiment described above, and has similar beneficial effects as the method embodiment; therefore, it will not be repeated. For technical details not disclosed in this apparatus embodiment, please refer to the description of the method embodiment of this application for understanding.

[0455] This application provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements some or all of the steps in the above-described method. The computer-readable storage medium can be transient or non-transient.

[0456] This application provides a computer program including computer-readable code. When the computer-readable code is run in a computer device, the processor in the computer device performs some or all of the steps in the above-described method.

[0457] This application provides a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program. When the computer program is read and executed by a computer, it implements some or all of the steps in the above-described method. This computer program product can be implemented specifically through hardware, software, or a combination thereof. In some embodiments, the computer program product is specifically embodied as a computer storage medium; in other embodiments, the computer program product is specifically embodied as a software product, such as a software development kit (SDK), etc.

[0458] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of this application, the sequence numbers of the above steps / processes do not imply a sequential order of execution; the execution order of each step / process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. The sequence numbers of the above embodiments of this application are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0459] This application uses terms such as "upper," "lower," "top," "bottom," "front," "back," "inner," and "outer" to indicate orientation or positional relationships. This is only for the convenience of describing this application and is not intended to indicate or imply that the device referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation on the scope of protection of this application.

[0460] In the description of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this application depending on the specific circumstances. It should be noted that, in this application, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. In the several embodiments provided in this application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined, integrated into another system, or some features may be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed may be through some interfaces. The indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0461] The units described above as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units; some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, the functional units in the embodiments of this application may all be integrated into one processing unit, or each unit may be a separate unit, or two or more units may be integrated into one unit; the integrated unit may be implemented in hardware or in a combination of hardware and software functional units.

[0462] The above are merely embodiments of this application and are not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, and improvements made within the spirit and scope of this application are included within the scope of protection of this application.

Claims

1. A parameter inversion method, characterized in that, The parameter inversion method includes: Interference suppression is performed on the received incomplete SAR signal to obtain an interference-free signal matrix; wherein, the interference-free signal matrix includes multiple interference-free pulse signals with temporal continuity, and the incomplete SAR signal represents the presence of missing SAR signals; Each interference-free pulse signal is processed sequentially to obtain the pulse parameters of each interference-free pulse signal; the pulse parameters include at least the stationary phase center position, termination point, pulse bandwidth, pulse signal modulation frequency, and peak position; Based on the pulse parameters of each interference-free pulse signal, the signal parameters of the incomplete SAR signal are inverted to obtain the transmission parameters of the incomplete SAR signal; the signal parameters include at least pulse width, bandwidth, modulation frequency, pulse repetition interval, and pulse repetition frequency. The step of sequentially processing each interference-free pulse signal to obtain the pulse parameters of each interference-free pulse signal includes at least the following: Perform a fast Fourier transform on each of the interference-free pulse signals to obtain the frequency domain amplitude spectrum of each of the interference-free pulse signals; Based on the frequency domain amplitude spectrum, the frequency points in each interference-free pulse signal with energy greater than the second preset threshold are determined as the second frequency point set; Based on the second set of frequency points and the frequency resolution, the pulse bandwidth of each interference-free pulse signal is determined; Correspondingly, the step of inverting the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal includes at least: Based on the stationary phase center position and the termination point of each interference-free pulse signal, the pulse bandwidth of each interference-free pulse signal is compensated to obtain the compensated bandwidth of each interference-free pulse signal. The bandwidth of the incomplete SAR signal is obtained by averaging the compensated bandwidth of each interference-free pulse signal.

2. The parameter inversion method according to claim 1, characterized in that, The process of suppressing interference in the received incomplete SAR signal to obtain an interference-free signal matrix includes: Perform a Fast Fourier Transform on each pulse echo signal in the incomplete SAR signal to obtain the spectral amplitude of each pulse echo signal. Strong point-frequency interference suppression is performed on the spectral amplitude of each pulse echo signal to obtain multiple first suppression signals; the number of first suppression signals is less than or equal to the number of pulse echo signals in the incomplete SAR signal; Based on the spectral amplitude of each first suppression signal and the first preset adjustment factor, a spectral amplitude threshold for each first suppression signal is constructed. The first suppressed signals are filtered based on the spectral amplitude threshold of each first suppressed signal to obtain the interference-free signal matrix.

3. The parameter inversion method according to claim 2, characterized in that, The strong point-frequency interference suppression is performed on the spectral amplitude of each pulse echo signal to obtain multiple first suppression signals, including: Based on the spectral amplitude of each pulse echo signal, multiple energy integration operations are performed on each pulse echo signal to obtain multiple maximum energies of each pulse echo signal. The energy ratio is determined based on the multiple maximum energies and total spectral energy of each pulse echo signal; The pulse echo signal with an energy ratio less than a preset ratio threshold in the incomplete SAR signal is determined as the first suppression signal, and the plurality of first suppression signals are obtained. The energy integration operation includes: Energy sorting is performed to obtain the frequency point corresponding to the highest spectral energy and the symmetrical bandwidth of the frequency point; Integrating the spectral energy within the symmetrical bandwidth yields the maximum energy of each pulse echo signal. Before the next energy integration operation, the spectral energy in the symmetric bandwidth is set to zero.

4. The parameter inversion method according to claim 2, characterized in that, The step of filtering the corresponding first suppressed signals based on the spectral amplitude threshold of each first suppressed signal to obtain the interference-free signal matrix includes: The frequency points in each of the first suppression signals whose spectral amplitude is greater than the spectral amplitude threshold are determined as the first frequency point set; Based on the first set of frequency points and the frequency resolution, the spectral bandwidth of each first suppressed signal is determined; the frequency resolution is determined based on the sampling frequency of the incomplete SAR signal and the number of sampling points of the pulse echo signal. The first suppression signal whose spectral bandwidth is greater than a preset spectral bandwidth threshold is determined as the second suppression signal, thus obtaining multiple second suppression signals; Based on the pulse time of the plurality of second suppression signals, the plurality of second suppression signals that have temporal continuity between the first consecutive adjacent signals are determined as a plurality of interference-free signals; Based on the multiple interference-free signals, the interference-free signal matrix is ​​constructed.

5. The parameter inversion method according to any one of claims 1 to 4, characterized in that, The step of sequentially processing each interference-free pulse signal to obtain the pulse parameters of each interference-free pulse signal includes: Perform a Hilbert transform on each interference-free pulse signal to obtain the analytic signal; Based on the analyzed signal, the instantaneous phase of each interference-free pulse signal is determined; The instantaneous phase is unwrapped to obtain the first unwrapped phase; Differentiating the first unwrapped phase yields the first and second derivatives of the first unwrapped phase; The position where the second derivative first exceeds a first preset threshold is determined as the termination point of each interference-free pulse signal; the first preset threshold is determined based on the second derivative and a second preset adjustment factor. The position corresponding to the minimum value of the first derivative before the termination point is determined as the position of the stationary phase center. Correspondingly, the step of inverting the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal includes: Based on the sampling frequency of the incomplete SAR signal, the stationary phase center position of each interference-free pulse signal, and the termination point, the pulse width of each interference-free pulse signal is determined. The pulse width of the incomplete SAR signal is obtained by averaging the pulse width of each interference-free pulse signal.

6. The parameter inversion method according to any one of claims 1 to 4, characterized in that, The step of sequentially processing each interference-free pulse signal to obtain the pulse parameters of each interference-free pulse signal includes: The second unwrapped phase is obtained by performing phase unwinding on each interference-free pulse signal; By taking the first derivative of the second unwrapped phase, the instantaneous frequency at each sampling time point in each of the interference-free pulse signals is obtained; Based on multiple preset sliding windows, the instantaneous frequency at each sampling time point is linearly fitted to obtain the fitted frequency modulation. Global residual detection is performed on the fitted frequency modulation to remove outliers, thereby obtaining the pulse signal modulation frequency of each interference-free pulse signal. Correspondingly, the step of inverting the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal includes: The frequency modulation frequency of the incomplete SAR signal is obtained by averaging the frequency modulation frequency of each interference-free pulse signal.

7. The parameter inversion method according to any one of claims 1 to 4, characterized in that, The step of sequentially processing each interference-free pulse signal to obtain the pulse parameters of each interference-free pulse signal includes: The first interference-free pulse signal in the interference-free signal matrix is ​​determined as the reference pulse signal; Based on the reference pulse signal, the matched filter performs pulse compression on each interference-free pulse signal after the first interference-free pulse signal to obtain the echo signal after matched filtering. The main peak position of each echo signal is extracted to obtain the main peak position; The position of the main peak is symmetrically adjusted to obtain the peak position of each interference-free pulse signal; Correspondingly, the step of inverting the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal includes: Based on the sampling frequency of the incomplete SAR signal and the peak position of each interference-free pulse signal, the delay time of the peak position of each interference-free pulse signal is determined. Based on the delay time and the frame header trigger time of each interference-free pulse signal, the actual arrival time of the main peak of each interference-free pulse signal is obtained. Based on the actual arrival time of the main peak of each interference-free pulse signal, the time interval between adjacent signals in the interference-free signal matrix is ​​determined; Based on the time interval, the average time interval of the interference-free signal matrix is ​​determined; Based on the average time interval, the pulse repetition interval and the pulse repetition frequency are calculated.

8. A parameter inversion device, characterized in that, The parameter inversion device includes: An interference suppression module is used to suppress interference in the received incomplete SAR signal to obtain an interference-free signal matrix; wherein, the interference-free signal matrix includes multiple interference-free pulse signals with temporal continuity, and the incomplete SAR signal represents the presence of missing SAR signals; The data processing module is used to process each interference-free pulse signal sequentially to obtain the pulse parameters of each interference-free pulse signal; the pulse parameters include at least the stationary phase center position, termination point, pulse bandwidth, pulse signal modulation frequency, and peak position. The inversion module is used to invert the signal parameters of the incomplete SAR signal based on the pulse parameters of each interference-free pulse signal to obtain the transmission parameters of the incomplete SAR signal; the signal parameters include at least pulse width, bandwidth, modulation frequency, pulse repetition interval and pulse repetition frequency; The data processing module is further configured to perform a fast Fourier transform on each of the interference-free pulse signals to obtain the frequency domain amplitude spectrum of each interference-free pulse signal; based on the frequency domain amplitude spectrum, determine the frequency points in each interference-free pulse signal whose energy is greater than a second preset threshold as a second set of frequency points; and determine the pulse bandwidth of each interference-free pulse signal based on the second set of frequency points and the frequency resolution. The inversion module is further configured to compensate the pulse bandwidth of each interference-free pulse signal based on the stationary phase center position and the termination point of each interference-free pulse signal, to obtain the compensated bandwidth of each interference-free pulse signal; and to average the compensated bandwidth of each interference-free pulse signal to obtain the bandwidth of the incomplete SAR signal.

9. An electronic device, characterized in that, include: Memory, used to store executable instructions; The processor, when executing executable instructions stored in the memory, implements the steps of the parameter inversion method according to any one of claims 1 to 7.

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