A time-frequency difference parameter estimation method and system based on RANSAC-WLS in a strong interference environment

Abstract

The application discloses a time-frequency difference parameter estimation algorithm based on RANSAC-WLS in a strong interference environment and belongs to the technical field of signal processing and target positioning. Firstly, a narrowband cross ambiguity function and a two-dimensional Fourier transform are used to extract candidate energy points; a RANSAC algorithm is used to construct a straight line model, iteratively screen an inlier point set, and effectively peel off interference outliers; based on the inlier points, a weighted least square method is used to optimize and solve ridge line parameters, and the bias influence of interference on estimation is eliminated; finally, combined with ridge line prior information, one-dimensional fine search is carried out through a wideband cross ambiguity function, and final time difference and scale difference are obtained. The application realizes effective discrimination of target features in a high interference environment, improves the algorithm theory breaking point to about 50%, and significantly enhances the robustness and accuracy of parameter estimation.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the fields of signal processing and target localization technology, and particularly relates to a method and system for estimating time-frequency difference parameters based on RANSAC-WLS under strong interference environments. Background Technology

[0002] In modern electronic warfare, search and rescue, and situational awareness, accurate location and identification of enemy radiation sources are crucial for gaining battlefield initiative. The fundamental task of modern signal processing technology is to extract effective information from complex electromagnetic environments or acoustic backgrounds to accurately characterize target information. In key application areas such as electronic reconnaissance, search and rescue, and electronic warfare, the goal of signal processing technology is to deconstruct the geographic spatial coordinates of the target from intercepted signals. Target location technology can be divided into active and passive location based on whether the observation station actively transmits signals. Active location systems, such as active radar and sonar, offer high positioning accuracy, but are easily exposed in electronic warfare, making them vulnerable to enemy detection and limiting their survivability. Compared to active detection methods, passive location, which relies on passively receiving signals from target radiation sources, offers significant advantages such as strong concealment, high survivability, and long operating range, and has gained widespread attention in national defense, civilian surveillance, and navigation. Passive location technology typically involves two stages: first, parameter estimation, and then solving the location equation to achieve positioning; hence, it is called a two-step method. The basic idea of ​​the two-step positioning method is as follows: First, the receiving station receives signals carrying some parameters related to the target position, such as time of arrival (TOA), angle of arrival (AOA), time difference of arrival (TDOA), and frequency difference of arrival (FDOA). Second, the positioning plane or positioning curve formed by the parameters estimated in the first step is combined with the Earth's surface equations to solve for the target's position.

[0003] The passive bistatic positioning system based on time difference and frequency difference is the most widely used target radiation source positioning system. Because the two receiving stations are at different distances from the target radiation source, the signal emitted by the target radiation source arrives at the two receiving stations at different times, resulting in a time difference between the received signals. This time difference can be used to determine a hyperboloid of revolution. Simultaneously, the two receiving stations typically move at different speeds, resulting in different radial velocities relative to the target radiation source. This causes different Doppler frequency shifts in the signals received by the two receiving stations relative to the emitted signal, leading to different intercepted signal frequencies and a frequency difference. This frequency difference can determine a hyperboloid of revolution. Combined with an ellipsoidal model of the Earth's surface, the intersection of these three surfaces determines two intersection points. After eliminating interference from one ambiguous point, the remaining intersection point is the estimated location of the ground radiation source. The core challenge of the passive positioning system based on time difference and frequency difference lies in effectively handling the nonlinear relationships in the positioning observation equations. To overcome this problem, scholars have proposed various linearization and optimization algorithms to improve computational efficiency and positioning accuracy. In 1976, Foy proposed the Taylor series expansion method. The basic idea of ​​this method is to perform a Taylor expansion on the nonlinear equation at the initial target position, transforming it into a linear equation about the position error, and then iteratively approximating the true solution. It provides a systematic numerical solution approach for nonlinear positioning problems. However, the convergence of this algorithm heavily depends on the accuracy of the initial value. If the initial value deviates significantly, it is prone to iteration divergence or getting trapped in local optima. This shortcoming limits its use in scenarios with scarce prior information. In 1984, Torrieri systematically expounded the statistical theory of passive positioning systems, providing a theoretical foundation and performance analysis framework for various positioning algorithms, including the Taylor series expansion method, but did not fundamentally solve the problem of initial value sensitivity in nonlinear solutions. To get rid of the dependence on iterative initial values, scholars began to seek closed-form solutions. In 1987, Schau and Robinson proposed the spherical intersection method (SX). The basic concept is to construct a series of spherical equations using time difference measurements, with the target position located at the intersection of these spheres. This method provides a direct solution without the need for guessing initial values. In the same year, Smith and Abel proposed spherical interpolation, which constructs a fitted sphere to estimate the target position by minimizing the equation residuals. Both methods avoid iteration and provide computationally efficient analytical solutions; however, they are essentially geometric solvers and do not provide statistically optimal estimates, especially with limited accuracy when measurement noise is high. To obtain a more accurate closed-form solution, Chan and Ho proposed a two-step weighted least squares method in 1994. By introducing the distance between the target and the reference station as an auxiliary variable, the original nonlinear equations are pseudo-linearized.The first step obtains an initial solution by ignoring the constraints between variables, and the second step uses the constraints to correct the estimated value. This method requires no iteration and is independent of initial values, significantly improving the performance of closed-form solutions. In 2004, Ho and Xu successfully extended the TSWLS method to localization problems using TDOA and FDOA, achieving joint closed-form estimation of moving radiation sources and velocities by introducing distance and its rate of change as auxiliary variables. In 2007, Ho et al. studied the localization problem with errors in the receiver station location, improving the original TSWLS algorithm and enhancing its robustness. In 2011, Sun and Ho further extended the applicability of this method to multi-target separation source localization scenarios. However, the TSWLS method also has its inherent defects. In 2012, Ho explicitly pointed out and analyzed the estimation bias problem in subsequent research. His research showed that as measurement noise increases, the error term ignored in the second step of TSWLS leads to significant estimation bias, causing the algorithm's performance to degrade in high signal-to-noise ratio environments.

[0004] In time-frequency difference joint passive localization, the extraction of localization parameters is crucial. The effectiveness of the localization algorithm essentially depends on the accuracy of the physical parameter observations during the parameter extraction process. Time difference and frequency difference characterize the distance difference and relative radial velocity difference between the target radiation source and the receiving station, respectively, and their estimation accuracy directly determines the accuracy of the localization equation and the reliability of the final localization result. This method preprocesses the cross-power spectrum of the two received signals by designing a specific weight function to suppress noise and interference, and then obtains the time delay estimate through inverse Fourier transform. It effectively solves the time delay estimation problem of stationary signals in white noise background. However, its fundamental drawback is that it cannot handle scenarios with Doppler frequency shift, and the time-frequency coupling pairs between signals cause severe dispersion of correlation peaks, resulting in a sharp deterioration in estimation performance. To fundamentally solve the problem of joint estimation of time difference and frequency difference, Stein systematically proposed the mutual ambiguity function (CAF) algorithm in 1981. The CAF algorithm calculates the cross-energy of the signals in the time-delay-Doppler two-dimensional joint domain, and its peak position is the estimation result of the time-frequency difference. In 1993, Stein further proved that under Gaussian white noise conditions, the CAF is the maximum likelihood estimate of the time-frequency difference parameter and has theoretical optimality. However, the core bottleneck of this algorithm lies in its huge two-dimensional search computation, which is difficult to meet the requirements of real-time processing. To overcome the computational bottleneck of CAF, researchers have proposed a variety of optimization search strategies. In the same study in 1981, Stein proposed a multi-level filtering downsampling strategy from coarse to fine. First, a coarse search is performed on a large-scale, low-resolution grid to locate the peak region, and then a fine search is performed in that region to reduce the search range. The principle is to divide the long signal into segments, calculate the short-time CAF for each segment, and then accumulate them in alignment. This solves the distance migration problem caused by target motion under long-time integration and balances the integral gain and signal non-stationarity. However, there are potential risks of accumulated gain loss due to segmentation and error accumulation. In 2011, Zhang and Zhang further proposed a fast algorithm for approximate coherent accumulation, which further reduces the computational burden of this method. In 2018, Kim et al. proposed a resampling-based dynamic resource allocation algorithm. This algorithm dynamically adjusts the sampling rate and computational resources for different regions based on signal bandwidth and potential parameter range, solving the resource waste problem of traditional fixed-grid search and aiming to optimize overall estimation performance within a given computational budget. To address the grid effect in CAF discrete sampling, improving subsampling accuracy has become another key focus. Early researchers proposed using traditional numerical interpolation methods, such as the spline interpolation method proposed by Viola et al. in 2005. The principle is to find subgrid peaks by comparing the discrete CAF values ​​near the given point with a continuous curve or surface. These methods solve the basic accuracy improvement problem and are computationally simple. However, at low signal-to-noise ratios, noise disturbances severely affect the shape of the interpolation function, leading to increased estimation bias and poor robustness.To achieve more robust accuracy, in 2008, Tao et al. proposed the parabolic weighted Z-transform. Its principle is to perform high-resolution analysis in the time domain by weighting and refining the local Z-transform mesh, directly improving parameter resolution at the algorithm level. In 2018, Liu et al. proposed a fitting algorithm based on second-order cone programming (SOCP). By constructing a fitting surface and minimizing the error between it and the discrete CAF value under specific constraints, they solved the problem of traditional interpolation being sensitive to noise, but introduced higher computational complexity. The idea is to decouple TDOA and FDOA estimation through the orthogonality of the signal and noise subspaces, and combine this with Chirp Z-transform to improve frequency resolution, achieving effective parameter separation and high-resolution estimation. To address interference and noise in real-world scenarios, researchers have improved algorithm robustness by focusing on signal characteristics. Utilizing the unique cyclic frequency characteristics of signals, they have demonstrated extremely strong signal selectivity at very low signal-to-interference-plus-noise ratios. By leveraging the suppression properties of higher-order cumulants against Gaussian noise, they have solved the problem of performance degradation of second-order statistics under correlated Gaussian noise environments. For the Linear Frequency Modulated (LFM) signal widely used in radar and sonar, the unique structure of its ambiguity function provides a possibility for dimensionality reduction estimation. Utilizing the characteristic that the LFM signal ambiguity function is a diagonal line passing through the origin, a RAT transformation is performed on the ambiguity function, converting the two-dimensional peak value into a one-dimensional angle search, significantly reducing computational complexity. The principle is that after extracting the ridge line using the least squares (LSE) method, instead of calculating the full-plane RAT, a single-slice RAT transformation is calculated along the ridge line direction. This slice contains complete time delay and Doppler information and suppresses noise. However, its accuracy heavily depends on the accuracy of the first step of frequency modulation estimation. Furthermore, ridge line detection and extraction become difficult in interference environments or multi-component LFM signal scenarios, potentially limiting its applicability. In 2016, Guo et al. proposed a demodulation-based method. Its principle is to demodulate the received signal using a reference frequency-modulated signal, converting the broadband LFM signal into a single-frequency or narrowband signal, thereby simplifying subsequent time delay and frequency difference estimation. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a method based on the RANSAC-WLS algorithm to improve the robustness of dimensionality reduction time-frequency difference parameter estimation under interference environments. It aims to solve the problem that existing dimensionality reduction estimation algorithms based on LFM signals are affected by ridge extraction under interference environments, leading to a decrease in the accuracy of subsequent parameter estimation.

[0006] This invention is implemented as follows: a RANSAC-WLS-based time-frequency difference parameter estimation algorithm under strong interference conditions, the algorithm comprising: S1: Establish a broadband LFM signal reception model:

[0007] in, This represents the complex envelope of the LFM signal received by the first receiving station; and It consists of mutually independent zero-mean Gaussian white noise. The signal can be represented as:

[0008] in, For width is The rectangular window function; The duration of the signal; The initial frequency; For signal The frequency modulation. In the broadband receiver model, due to the large relative radial velocity or bandwidth, the time-domain scaling effect cannot be ignored. In this case, the parameter to be estimated is the time difference. and scale difference .Signal It can be represented as: .

[0009] S2: To utilize the prior characteristics of LFM signals, a narrowband mutual ambiguity function is used to approximate the broadband model to extract the linear ridge, introducing a Doppler frequency shift into the narrowband model. With scale factor Mapping relationship between them:

[0010] in, Let be the center frequency of the signal. Through this mapping relationship, the joint estimation problem of time difference-scale difference under the broadband model can be equivalent to the joint estimation problem of time difference-frequency difference.

[0011] S3: To obtain a linear ridge line on the time-delay-Doppler plane, a narrowband mutual ambiguity function is used to approximate the two received signals:

[0012] The mutual ambiguity function compensates for time delay and Doppler frequency shift in a two-dimensional plane. Its value reaches its maximum when the compensation equals the actual time difference and frequency difference. Furthermore, the narrowband mutual ambiguity function of LFM signals exhibits energy concentration characteristics, showing a ridge in the two-dimensional plane with a peak value and a slope equal to the frequency modulation rate. Therefore, utilizing this ridge distribution characteristic, the original two-dimensional plane search problem can be transformed into a dimensionality-reduced search problem along the ridge.

[0013] S4: To avoid calculating the function values ​​across the entire mutual ambiguity plane, a two-dimensional Fourier transform is used to map the mutual ambiguity function to the frequency domain space, defining the mutual ambiguity function. The two-dimensional Fourier transform is :

[0014] According to the rotational mapping property of Fourier transform, A linear ridge line passing through the origin in a plane, In the plane, the energy concentration line still appears as a straight line passing through the origin; to avoid interference from interfering points in ridge extraction, local peak detection is performed on the frequency domain modulus plane of the narrowband mutually ambiguous function to extract candidate energy points. ,in This represents the normalized amplitude at each point.

[0015] S5: Random sampling point Build a hypothesis model Calculate the set distance from the remaining points in the point set to the model, and set a distance threshold. , distance less than The point is determined as an intra-point set. .

[0016] S6: Pass In the next iteration, the set with the largest number of interior points is selected as the final interior point space. The number of iterations is [number missing]. To ensure probability Number of iterations to obtain a pure subset of samples:

[0017] in, The expected proportion of inliers in the dataset. This is the minimum number of samples.

[0018] S7: Based on the optimal set of local points Extract the corresponding Construct a weight matrix from each interior point. ,in For the first The amplitude values ​​at each interior point; establishing a system of linear equations. ,in:

[0019] in, Indicates the first The observation error vector of each feature point.

[0020] S8: Solving for optimal parameters using weighted least squares method :

[0021] Finally, the slope of the ridge line is obtained. With intercept .

[0022] S9: After obtaining high-precision ridge estimation using the RANSAC-WLS algorithm, the process differs from traditional dimensionality reduction algorithms. Due to the presence of interference points in the environment, RAT transformation cannot be used for energy accumulation along the ridge. Since RAT transformation is a global projection operation, all energy points on the projection path will be accumulated indiscriminately. Even if the projection angle is accurate, RAT transformation causes outliers on the path to participate in the projection, resulting in a shift or broadening of the energy peak and the generation of false peaks. Therefore, based on the segmentation characteristics of target inliers and outliers in the RANSAC-WLS algorithm, the points extracted from the features are directly used for subsequent spatial mapping. This is more robust than re-accumulating all points that may contain interference points using RAT transformation. It not only avoids secondary pollution of peak localization by interference energy but also saves complex calculations such as coordinate rotation.

[0023] Optimal projection angle of ridge line extracted using RANSAC-WLS algorithm and the set of in-place points As a priori guide, the radial characteristic parameters representing the geometric orientation of the ridge line are calculated. The formulas for calculating the projection angle and radial characteristic parameters are as follows: .

[0024] S10: Utilizing the acquired ridge geometric feature parameters, and based on the time-frequency coupling mapping principle, in the time delay... With scale factor Within the constructed space to be estimated, a one-dimensional linear search path equation is established:

[0025] This equation compresses the search range in the two-dimensional parameter space into a deterministic physical trajectory that passes through the energy core.

[0026] S11: Select discrete experimental sampling sequences within the neighborhood of the radial parameter location determined by the feature point cloud. For each Calculate the corresponding scale factor based on the constraints from the previous step. For coordinate pairs Calculate the broadband mutual ambiguity function value: .

[0027] S12: Search for the maximum pointer location on the one-dimensional WBCAF plane to obtain the final time difference estimate. The final estimate of the scale difference is obtained by inverse solving the constraint relationships. : .

[0028] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows: First, the traditional single-slice RAT (SSRAT) algorithm uses the ordinary least squares (OLS) criterion to fit linear relationships to frequency domain feature points during the ridge extraction stage. This criterion aims to minimize the sum of squared residuals of all sample points without identifying the source of the samples. Therefore, when multipath components and coherent interference exist in the electromagnetic environment, outliers will participate in the fitting calculation, leading to a systematic bias in the ridge direction estimation. Simulations show that when the proportion of interference points is only 20%, the ridge angle deviation estimated by OLS can exceed 0.5°, causing the subsequent single-slice projection to deviate from the true signal energy center, ultimately leading to the failure of parameter estimation.

[0029] To address the aforementioned issues, this invention introduces the Random Sample Consensus (RANSAC) algorithm as a pre-screening mechanism for ridge fitting. This algorithm constructs a hypothetical model through iterative random sampling and classifies feature points into "insiders" and "outsiders" based on a distance threshold from the point to the model. Only insiders that pass the consistency test are retained for subsequent weighted least squares (WLS) fitting, fundamentally eliminating outlier contamination. Building upon this, this invention further explores the mapping relationship between ridge geometric features and physical motion parameters, abandoning coordinate rotation and two-dimensional integration operations in traditional RAT transformations, and directly utilizing inside point feature parameters for spatial mapping, reducing computational redundancy. Finally, combined with a one-dimensional refined search using broadband mutual ambiguity functions, it maintains estimation accuracy similar to that in interference-free scenarios even under strong interference environments, achieving real-time and robust time-frequency parameter estimation of broadband LFM signals in complex electromagnetic scenarios.

[0030] Second, as supporting evidence of the inventiveness of the claims of this invention, the technical solution of this invention solves a long-standing but unsolved technical problem: in the field of passive positioning, the estimation of time-frequency difference parameters based on LFM signals has long faced a fundamental contradiction: real-time performance and anti-interference capability are difficult to achieve simultaneously. While traditional two-dimensional search methods (such as the mutual ambiguity function CAF) theoretically possess optimal estimation performance, their computational complexity increases quadratically with the number of sampling points, making it difficult to meet real-time processing requirements. Utilizing the physical property that the energy of the LFM signal ambiguity function converges along a straight line for ridge-based dimensionality reduction has become an inevitable technical route for achieving real-time estimation. However, the success or failure of the ridge-based dimensionality reduction method depends entirely on the accuracy of the first step, "ridge extraction"—once the ridge direction is biased, the subsequent one-dimensional search will deviate from the true energy peak, causing the estimation of time-frequency difference parameters to completely fail. The complexity of the problem lies in the fact that non-target energies such as multipath components and coherent interference, which are prevalent in the actual electromagnetic environment, will form a large number of outliers in the frequency domain feature point cloud. Traditional ridge extraction methods, whether ordinary least squares (OLS), weighted least squares (WLS), or Radon-Ambiguity transform (RAT), cannot effectively distinguish between target points and outliers. The common essence of these methods is that they attempt to directly fit or project integrals onto a dataset containing outliers, only averaging outliers. This means that ridge reduction methods perform exceptionally well in the absence of outliers; their accuracy drops drastically once outliers are introduced. Attached Figure Description

[0031] Figure 1 This is a flowchart of a method for estimating time-frequency difference parameters based on RANSAC-WLS under strong interference conditions, provided by an embodiment of the present invention.

[0032] Figure 2 This is a block diagram of a time-frequency difference parameter estimation system based on RANSAC-WLS under strong interference environment provided by an embodiment of the present invention.

[0033] Figure 3 This is a comparison diagram of OLS ridge estimation in the SSRAT algorithm provided in this embodiment of the invention and RANSAC-WLS ridge estimation proposed in this invention.

[0034] Figure 4 This is a graph showing the variation of ridge estimation error with signal-to-noise ratio in the SSRAT algorithm provided by this invention and the RANSAC-WLS ridge estimation proposed in this invention under interference conditions.

[0035] Figure 5 This is a graph showing the variation of ridge estimation error between OLS ridge estimation and RANSAC-WLS ridge estimation proposed in this invention under different interference ratios in the SSRAT algorithm provided in this embodiment of the invention.

[0036] Figure 6 This is a diagram illustrating the impact of ridgeline estimation error on the estimation performance of time difference and scale difference parameters provided in this embodiment of the invention.

[0037] Figure 7 This is a comparison chart showing the parameter estimation error of the SSRAT algorithm provided in the embodiments of the present invention with and without interference, and the parameter estimation error of the algorithm proposed in the present invention with and without interference, as a function of signal-to-noise ratio. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0039] like Figure 1 As shown, this embodiment of the invention provides a method for estimating time-frequency difference parameters based on RANSAC-WLS under strong interference conditions, including the following steps: S1: Establish a broadband linear frequency modulation signal receiving model. The first receiving station and the second receiving station respectively receive the target signal and superimpose zero-mean Gaussian white noise. The second received signal has time difference parameters and scale difference parameters relative to the first received signal.

[0040] S2: Utilizing the prior structural characteristics of linear frequency modulated signals, the broadband model is converted into a narrowband mutually ambiguous model, and a mapping relationship between the scaling factor and the Doppler frequency shift is established. The Doppler frequency shift is equal to the scaling factor minus 1 multiplied by the signal center frequency.

[0041] S3: Calculate the narrowband mutual ambiguity function for the two received signals, and form a linear ridge with energy accumulation on the two-dimensional parameter plane composed of time delay and Doppler frequency shift.

[0042] S4: Perform a two-dimensional Fourier transform on the mutually ambiguous function to obtain the frequency domain energy distribution, and perform local peak detection in the frequency domain modulus plane to obtain a set of candidate energy points.

[0043] S5: Randomly sample from the candidate energy point set to construct a straight line model, and divide the local point set according to the distance threshold from the point to the model.

[0044] S6: Select the set with the largest number of local points through multiple random sampling iterations, and determine the optimal set of local points.

[0045] S7: Establish a weighted linear model based on the optimal set of local points, with the weights determined by the normalization magnitude of each feature point.

[0046] S8: Solve for the ridge model parameters using the weighted least squares method to obtain the ridge slope and intercept.

[0047] S9: Calculate the ridge projection angle and radial characteristic parameters based on the ridge parameters.

[0048] S10: Establish a linear constraint relationship between time delay and scale factor based on the geometric characteristics of the ridge line, compressing the two-dimensional parameter search space into a one-dimensional search path.

[0049] S11: Calculate the broadband mutual ambiguity function value along the one-dimensional search path.

[0050] S12: Search for the location of the maximum value in the one-dimensional search space to obtain the time difference estimate, and obtain the scale difference estimate based on the constraint relationship.

[0051] The present invention provides a narrowband mutual ambiguity function obtained by compensating for time delay and Doppler frequency shift in a two-dimensional parametric plane. The amplitude of the mutual ambiguity function reaches its maximum when the compensation amount is equal to the actual time difference and frequency difference.

[0052] The present invention provides a candidate energy point set obtained by local peak detection in the frequency domain modulus plane, and each candidate point contains two-dimensional coordinates and normalized amplitude information.

[0053] The iteration number of the random sample consensus algorithm provided in this embodiment of the invention is determined by the following relationship: The number of iterations is equal to 1 minus the logarithm of the probability value divided by 1 minus the logarithm of the minimum number of samples of the local point proportion raised to the power of 1.

[0054] like Figure 2 As shown, this embodiment of the invention provides a RANSAC-WLS-based time-frequency difference parameter estimation system under strong interference conditions, comprising: The signal receiving module is used to receive two linear frequency modulated signals and generate complex envelope received data.

[0055] The mutual fuzziness analysis module is used to calculate the narrowband mutual fuzziness function and generate the time-delayed Doppler two-dimensional energy distribution.

[0056] The frequency domain mapping module is used to perform a two-dimensional Fourier transform on the mutually ambiguous function and generate a frequency domain energy plane.

[0057] The feature extraction module is used to perform local peak detection on the frequency domain energy plane and generate a set of candidate energy points.

[0058] The ridge estimation module is used to estimate ridge model parameters based on the random sample consensus algorithm and the weighted least squares algorithm.

[0059] The path constraint module is used to establish a linear search path for time delay and scale factor based on ridge parameters.

[0060] The parameter solving module is used to calculate the broadband mutual ambiguity function and determine the time difference parameter and scale difference parameter on the one-dimensional search path.

[0061] The ridge estimation module provided in this embodiment of the invention includes a random sampling unit, an inlier discrimination unit, and a weighted least squares solution unit.

[0062] This invention provides a path constraint module for calculating projection angle and radial feature parameters based on ridge slope and intercept, and generating a one-dimensional linear search path.

[0063] This invention provides a method for estimating the time-frequency difference parameter based on the system, which receives two wideband linear frequency modulated signals; Calculate the narrowband mutual ambiguity function and form a time-delayed Doppler two-dimensional plane.

[0064] Candidate energy points are obtained in a two-dimensional plane through frequency domain transformation.

[0065] The random sampling consensus algorithm is used to separate local points from outliers.

[0066] The parameters of the ridge model are estimated using the weighted least squares algorithm.

[0067] A linear constraint path for time delay and scale factor is constructed based on the ridge geometry.

[0068] Calculate the broadband mutual ambiguity function value along the constrained path and determine the time difference parameter and scale difference parameter.

[0069] The embodiments of the present invention provide a one-dimensional search path that is determined by the ridge projection angle, radial characteristic parameters, and frequency modulation.

[0070] This invention provides a method for calculating the amplitude of a broadband mutually fuzzy function by discrete sampling on a one-dimensional search path, and selecting the position of the largest amplitude as the final parameter estimation result.

[0071] This invention provides a RANSAC-WLS-based time-frequency difference parameter estimation algorithm under strong interference conditions. The algorithm includes: S1: Establish a broadband LFM signal reception model:

[0072] in, This represents the complex envelope of the LFM signal received by the first receiving station; and It consists of mutually independent zero-mean Gaussian white noise. The signal can be represented as:

[0073] in, For rectangular window functions, For width is The rectangular window function; The duration of the signal; The initial frequency; For signal The frequency modulation. In the broadband receiver model, due to the large relative radial velocity or bandwidth, the time-domain scaling effect cannot be ignored. In this case, the parameter to be estimated is the time difference. and scale difference .Signal It can be represented as: .

[0074] S2: To utilize the prior characteristics of LFM signals, a narrowband mutual ambiguity function is used to approximate the broadband model to extract the linear ridge, introducing a Doppler frequency shift into the narrowband model. With scale factor Mapping relationship between them:

[0075] in, Let be the center frequency of the signal. Through this mapping relationship, the joint estimation problem of time difference-scale difference under the broadband model can be equivalent to the joint estimation problem of time difference-frequency difference.

[0076] S3: To obtain a linear ridge on the time-delay-Doppler plane, a narrowband mutual ambiguity function is used to approximate the two received signals. The narrowband mutual ambiguity function for the two signals... for:

[0077] The mutual ambiguity function compensates for time delay and Doppler frequency shift in a two-dimensional plane. Its value reaches its maximum when the compensation equals the actual time difference and frequency difference. Furthermore, the narrowband mutual ambiguity function of LFM signals exhibits energy concentration characteristics, showing a ridge in the two-dimensional plane with a peak value and a slope equal to the frequency modulation rate. Therefore, utilizing this ridge distribution characteristic, the original two-dimensional plane search problem can be transformed into a dimensionality-reduced search problem along the ridge.

[0078] S4: To avoid calculating the function values ​​across the entire mutual ambiguity plane, a two-dimensional Fourier transform is used to map the mutual ambiguity function to the frequency domain space, defining the mutual ambiguity function. The two-dimensional Fourier transform is :

[0079] According to the rotational mapping property of Fourier transform, A linear ridge line passing through the origin in a plane, In the plane, the energy concentration line still appears as a straight line passing through the origin; to avoid interference from interfering points in ridge extraction, local peak detection is performed on the frequency domain modulus plane of the narrowband mutually ambiguous function to extract candidate energy points. ,in This represents the normalized amplitude at each point.

[0080] S5: Random sampling point Build a hypothesis model , The slope of the line. For the intercept, calculate the ensemble distance from the remaining points in the point set to the model, and set a distance threshold. , distance less than The point is determined as an intra-point set. .

[0081] S6: Pass In the next iteration, the set with the largest number of interior points is selected as the final interior point space. The number of iterations is [number missing]. To ensure probability Number of iterations to obtain a pure subset of samples:

[0082] in, The expected proportion of inliers in the dataset. To minimize the number of samples, since the model is a straight line, take... .

[0083] S7: Based on the optimal set of local points Extract the corresponding Construct a weight matrix from each interior point. ,in For the first The amplitude values ​​at each interior point; establishing a system of linear equations. ,in:

[0084] in, Indicates the first The observation error vector of each feature point.

[0085] S8: Solving for optimal parameters using weighted least squares method :

[0086] Finally, the slope of the ridge line is obtained. With intercept .

[0087] S9: After obtaining high-precision ridge estimation using the RANSAC-WLS algorithm, the process differs from traditional dimensionality reduction algorithms. Due to the presence of interference points in the environment, RAT transformation cannot be used for energy accumulation along the ridge. Since RAT transformation is a global projection operation, all energy points on the projection path will be accumulated indiscriminately. Even if the projection angle is accurate, RAT transformation causes outliers on the path to participate in the projection, resulting in a shift or broadening of the energy peak and the generation of false peaks. Therefore, based on the segmentation characteristics of target inliers and outliers in the RANSAC-WLS algorithm, the points extracted from the features are directly used for subsequent spatial mapping. This is more robust than re-accumulating all points that may contain interference points using RAT transformation. It not only avoids secondary pollution of peak localization by interference energy but also saves complex calculations such as coordinate rotation.

[0088] Optimal projection angle of ridge line extracted using RANSAC-WLS algorithm and the set of in-place points As a priori guide, the radial characteristic parameters representing the geometric orientation of the ridge line are calculated. Among them, the projection angle With radial characteristic parameters The calculation formula is: .

[0089] S10: Utilizing the acquired ridge geometric feature parameters, and based on the time-frequency coupling mapping principle, in the time delay... With scale factor Within the constructed space to be estimated, a one-dimensional linear search path equation is established:

[0090] This equation compresses the search range in the two-dimensional parameter space into a deterministic physical trajectory that passes through the energy core.

[0091] S11: Select discrete experimental sampling sequences within the neighborhood of the radial parameter location determined by the feature point cloud. For each Calculate the corresponding scale factor based on the constraints from the previous step. For coordinate pairs Calculate the broadband mutual ambiguity function value: .

[0092] S12: Search for the maximum pointer location on the one-dimensional WBCAF plane to obtain the final time difference estimate. The final estimate of the scale difference is obtained by inverse solving the constraint relationships. : .

[0093] Example 1: Parameter Estimation in Basic Signal Scenarios In an environment with minimal or no strong interference, two broadband linear frequency modulated (LFM) signals are received. The first receiving station acquires the complex envelope data of the target signal, while the second receiving station acquires signal data with time delay and scale variations. A narrowband mutual ambiguity function is calculated based on the received data, forming an energy accumulation region in a two-dimensional parameter plane composed of time delay and Doppler frequency shift. A two-dimensional frequency domain transformation is performed on the mutual ambiguity function to obtain a frequency domain energy distribution map. A set of candidate energy points is extracted through local peak detection, and random sampling consistency processing is performed on this set to construct a linear model and filter local points. Subsequently, the ridge parameters are accurately estimated using a weighted least squares method to obtain the ridge slope and intercept. The ridge projection angle and radial characteristic parameters are calculated based on geometric relationships, and a linear search path for time delay and scale factor is constructed. The broadband mutual ambiguity function value is calculated along this path, and finally, the location of the maximum value is determined in the one-dimensional search space, yielding the estimation results of the time difference and scale difference parameters. This implementation verifies the effectiveness of dimensionality reduction search using ridge geometry under conventional signal conditions.

[0094] Example 2: Parameter Estimation in the Presence of Gaussian Noise In environments with strong Gaussian white noise, both received signals are superimposed with noise interference. First, a linear frequency modulated (LFM) signal model is established, and a mapping relationship between the scale factor and Doppler frequency shift is established based on the center frequency. Then, a narrowband mutual ambiguity function is calculated and frequency domain mapping is performed. Local peak detection is conducted in the frequency domain modulus plane to obtain candidate energy points. Since noise generates a large number of outliers, a random sample consensus algorithm is used to fit the model to the candidate points. This algorithm searches for the model with the largest number of inliers through multiple random samplings and uses a probability formula to determine the number of iterations. After obtaining the set of inliers, a weight matrix is ​​constructed based on the amplitude of each feature point, and the ridge parameters are estimated using a weighted least squares method. Experimental results show that even with low signal-to-noise ratios, this method can still stably identify energy ridge structures and obtain accurate time difference and scale difference estimates through one-dimensional search.

[0095] Example 3: Parameter Estimation in Scenarios with Multiple Interference Signals In complex electromagnetic environments, the received signal contains multiple interference signals in addition to the target signal. After obtaining a two-dimensional energy distribution map by calculating the mutual ambiguity function, the interference signals form discrete energy points in the frequency domain plane. The candidate point set obtained through local peak detection includes both target and interference points. The random sample consensus algorithm randomly selects samples from this point set to construct a straight line model and determines the inliers based on a distance threshold. After multiple iterations, an inlier set mainly composed of target points can be obtained. Subsequently, the weighted least squares method is used to accurately fit the ridge line, ensuring that the fitted line is consistent with the target energy distribution. Compared with the traditional projection accumulation method, this method avoids the influence of outliers on energy peaks and improves the accuracy of ridge line localization.

[0096] Example 4: Parameter Estimation in High Dynamic Target Environments When the target has a large radial velocity, the received signal exhibits a significant time-scaling effect. First, a relationship between time delay and scale difference parameters is established based on a broadband linear frequency modulated (LFM) signal model, and a mapping between the scale factor and Doppler frequency shift is established through the center frequency. A two-dimensional energy distribution is obtained using a mutual ambiguity function, and local energy peaks are detected in the frequency domain plane. After identifying energy ridges using a random sample consensus algorithm, stable ridge parameters are obtained through a weighted least squares method. A linear constraint path between time delay and scale factor is constructed based on the ridge geometry, compressing the original two-dimensional search problem into a one-dimensional search problem. A broadband mutual ambiguity function is calculated along this path, and the location of the maximum value is found, thereby obtaining accurate time delay and scale difference estimates. This implementation demonstrates that the method is applicable to high-speed moving target scenarios.

[0097] Example 5: Robust Estimation in Low Signal-to-Noise Ratio Environments Under conditions of low signal power and high noise, the energy distribution in the mutually ambiguous function plane is relatively dispersed. After obtaining the energy plane through frequency domain transformation, local peaks are first screened to construct a candidate energy point set. Then, a random sampling consensus algorithm is used for model identification. Due to the large number of outliers, the random sampling algorithm can gradually filter out a stable set of inliers through multiple iterations. Subsequently, an amplitude-weighted strategy is used to perform weighted least-squares fitting on the inliers, giving higher weights to feature points with stronger energy in model estimation. Finally, stable ridge parameters are obtained, and the final parameter estimation result is determined through a one-dimensional search path. Experimental results show that high estimation accuracy can still be maintained in low signal-to-noise ratio environments.

[0098] Example 6: Application in a Practical Signal Processing System In a practical signal processing system, a receiving module, a mutual ambiguity analysis module, a frequency domain mapping module, a feature extraction module, a ridge estimation module, and a parameter solving module are deployed within the signal processing equipment. The system first receives two linear frequency-modulated signals and calculates the mutual ambiguity function. Subsequently, candidate energy points are extracted in the frequency domain plane, and random sample consistency processing is performed. Ridge model parameters are estimated using a weighted least squares method, and a one-dimensional search path is established based on the ridge geometry. The system calculates the broadband mutual ambiguity function along this path and determines the location of the maximum energy, outputting the time difference parameter and scale difference parameter. Practical applications show that this method can stably identify signal ridge structures even in complex interference environments and effectively improve parameter estimation accuracy, demonstrating significant engineering application value.

[0099] Evidence related to the technical effects obtained by the embodiments of the present invention.

[0100] Simulation 1: To quantitatively evaluate the robustness of the RANSAC-WLS algorithm in parameter estimation under complex interference scenarios, local peak detection and dynamic thresholding are performed on the frequency domain space obtained by the narrowband mutual ambiguity function after two-dimensional Fourier transform. This abstracts the complex two-dimensional continuous distribution into a set of discrete feature point clouds. Simultaneously, to simulate multipath components and coherent interference that may exist in real-world scenarios, controlled outliers are introduced to simulate interference energy point sets that deviate from the main target parameters. The proportion of outliers in the total sample point set is adjusted to control different degrees of extreme electromagnetic environments.

[0101] Figure 3 This paper compares the ridge estimation algorithm based on OLS in the traditional SSRAT algorithm with the RANSAC algorithm presented in this paper in the ridge feature extraction stage under strong interference scenarios. The left subfigure clearly shows the energy distribution in the frequency domain space. In addition to the main ridge sample points in the central region, there are two obvious outlier energy sets whose geometric orientation is inconsistent with the main ridge. The right subfigure shows a comparison of the two algorithms for ridge fitting. The ridge fitted by the OLS algorithm shows a significant slope bias. Since the principle of the OLS algorithm is to minimize the sum of squared residuals of all observation points, the interference point set causes the fitted ridge to deviate from the true ridge direction. The RANSAC algorithm, through an iterative consensus process, successfully identifies and locks the local points and marks the interference energy points as outliers. Finally, the fitted ridge completely coincides with the direction of the main ridge.

[0102] Simulation 2: Using an LFM signal model, the modulation frequency is 40MHz / ms, the carrier frequency is 10MHz, the signal bandwidth is 2MHz, the pulse duration is 50μs, the sampling frequency is 30MHz, the interference ratio is 20%, and the signal-to-noise ratio is from -10dB to 25dB. 500 Monte Carlo experiments are conducted to obtain the RMSE of the slope estimation. In order to clearly show the slope estimation error at a larger modulation frequency, the normalized slope estimation error is used.

[0103] Depend on Figure 4 It can be seen that the OLS ridge estimation algorithm exhibits an almost horizontal distribution across the entire signal-to-noise ratio range. Even when the signal-to-noise ratio is increased to 25 dB, the estimation accuracy remains unchanged, indicating that the estimation accuracy of the OLS algorithm is mainly affected by interference points. The RANSAC-WLS algorithm, on the other hand, shows a significant decreasing trend in RMSE with increasing signal-to-noise ratio. At -10 dB, its estimation accuracy is already about an order of magnitude better than OLS, enabling accurate ridge estimation even under interference conditions.

[0104] Simulation 3: The signal parameters are kept the same as in Simulation 2, and the signal-to-noise ratio is fixed at 10dB. The proportion of interference points in the frequency domain space is changed, and Monte Carlo experiments are performed 500 times at each interference proportion test point, with a step size of 5%, from 0% to 55%.

[0105] Depend on Figure 5 As can be seen, when the interference ratio is less than 50%, the estimation error of the RANSAC-WLS algorithm remains at an extremely low level and exhibits very high stability. When the interference ratio reaches 50%, the estimation error jumps drastically, indicating that the algorithm's breakdown point is 50%. Since interference points account for the majority of the entire sample point set, the algorithm enters the theoretical collapse zone at this point. Although the OLS algorithm performs slightly better than the RANSAC-WLS algorithm in the absence of interference because it can fit all sample points, the estimation error shows a significant upward trend as the interference ratio increases, and the error is much larger than that of the RANSAC-WLS algorithm, indicating weaker anti-interference ability.

[0106] Simulation 4: Using an LFM signal model, carrier frequency 10MHz, signal bandwidth 2MHz, pulse duration... Sampling frequency 30MHz, actual time difference The true scale difference is 1.0004. Assume an amplitude of 0.35 and a time difference... Scale difference Related interference. By changing the angle deviation of the ridgeline estimation. This study investigates the impact of different angular errors on the accuracy of parameter estimation for time difference and scale difference.

[0107] Depend on Figure 6 As shown in the left-middle figure, the RMSE corresponding to time difference and scale difference exhibits an approximately V-shaped symmetrical upward trend as the projection angle deviation increases. This is because the search path of the second-stage broadband mutual ambiguity function is constrained by the angle given by the ridge estimation. If the angle deviates from the true ridge, the one-dimensional search path will no longer pass through the energy peak region of the mutual ambiguity plane, causing the searched maxima to deviate from the target parameters, resulting in a deterioration in parameter estimation accuracy. Figure 6The right figure shows the normalized peak amplitude of the broadband mutual ambiguity function along the search path. As the angle deviation increases, the correlation peak energy drops sharply. When the angle deviation exceeds approximately 0.8°, the peak energy falls below the -3dB threshold. The broadband mutual ambiguity function of the LFM signal has an extremely narrow main lobe and is highly sensitive to angle shifts. When the angle deviation is large, a one-dimensional fine-grained search of the peak path deviating from the ridge cannot capture sufficient coherent gain, leading to parameter estimation failure.

[0108] Simulation 5: The computational complexity of the algorithm is theoretically analyzed and compared with several typical algorithms.

[0109] To ensure the fairness and consistency of the comparison results, uniform parameter configurations and analytical assumptions were set, using the number of complex multiplications as a unified standard to evaluate the complexity of each algorithm. The number of signal sampling points was set to... The search grid for the time domain and scale domain is set as follows: The time sampling length involved in the one-dimensional search in the single-slice RAT algorithm The number of RANSAC iterations corresponding to the algorithm in this paper Number of feature extraction points .

[0110] As shown in Table 1, the algorithm proposed in this invention follows the idea of ​​dimensionality reduction estimation along the ridge, and its computational complexity is significantly reduced compared to the traditional two-dimensional search for the mutual ambiguity function. This paper proposes a dimensionality reduction search method based on the RANSAC algorithm and a single-slice RAT algorithm, both of which use two-dimensional Fourier transform to obtain the frequency domain energy mapping to avoid the burden of calculating the mutual ambiguity function values ​​across the entire plane. In subsequent processes, the algorithm proposed in this invention needs to perform a global scan in the frequency domain to extract the feature point cloud. Although the introduced RANSAC includes an iterative process, each iteration only includes minimum subset sampling and consistency checks, and its computational complexity is determined by the number of iterations and the number of point clouds extracted. Since the mathematical model for ridge fitting only needs to extract two points in the minimum subset extraction process, and the selected number of iterations is greater than the number of iterations determined in step six when the interference ratio has not reached the breakpoint, it does not constitute a computational bottleneck. Meanwhile, compared to the single-slice RAT algorithm, the algorithm proposed in this paper does not use the complex transformation of RAT, but directly uses the local points extracted by the RANSAC algorithm for parameter mapping, thereby reducing one round of search on the single-slice RAT plane and bringing further optimization in computational efficiency.

[0111] Table 1 compares the computational complexity of the algorithm of this invention with that of several classic algorithms for time-frequency parameter estimation;

[0112] Simulation 6: Using the algorithm proposed in this invention and SSRAT, 500 Monte Carlo experiments were conducted with and without interference, with signal-to-noise ratios ranging from -10dB to 25dB, in 5dB steps. The performance of parameter estimation was compared. The interference conditions were an amplitude of 0.35, a time difference of 17, and a scale difference of 0.9998. The simulation results are as follows. Figure 5-7 As shown.

[0113] Depend on Figure 5-7 As can be seen, under interference-free conditions, the time difference and scale difference RMSE curves of the two algorithms almost overlap, both showing a decreasing trend with the increase of signal-to-noise ratio (SNR), and the accuracy of the SSRAT algorithm is slightly better than that of the algorithm proposed in this paper. This is because, in interference-free environments, the SSRAT algorithm uses the least squares criterion for ridge fitting, which can utilize the full sample information in the frequency domain for statistical smoothing; while the RANSAC mechanism in the algorithm proposed in this paper is essentially based on consensus screening of random subsets, and its feature extraction process actively discards some effective samples at the edges, resulting in a slight loss of coherence gain. In complex scenarios with interference, the estimation performance of the two algorithms differs significantly. The RMSE of the SSRAT algorithm decreases slowly with the increase of SNR, and the error curve enters a plateau in the high SNR region, indicating that the systematic bias caused by interference replaces additive noise as the dominant error, resulting in the inability to accurately extract the target parameters; while the algorithm proposed in this paper, although slightly higher in absolute error than in the ideal scenario, maintains a robust convergence trend in its RMSE curve.

[0114] In summary, this invention focuses on how to extract motion parameters of broadband LFM signals through robust ridge estimation, thereby reducing or eliminating the misleading effects of multipath coherent interference and strong noise on the parameter estimation process, and thus improving the robustness and real-time performance of parameter estimation in complex electromagnetic environments. To this end, this invention proposes a cascaded estimation algorithm based on RANSAC-WLS and fine-grained search. By effectively improving the accuracy of ridge projection angle estimation and removing the projection integration step of the traditional RAT transform algorithm, this further enhances the algorithm's survivability and processing efficiency under strong interference. Finally, simulations were conducted to compare the proposed algorithm with the classic single-slice Radon-Ambiguity transform (SSRAT) algorithm under different signal-to-noise ratios, interference ratios, and data sizes to verify that the proposed algorithm effectively improves the anti-interference capability of ridge slope extraction. Ultimately, while maintaining the efficiency advantage of dimensionality reduction search, it achieves highly reliable time-frequency parameter estimation for broadband signals.

[0115] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0116] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for estimating time-frequency difference parameters based on RANSAC-WLS under strong interference conditions, characterized in that, Includes the following steps: S1: Establish a broadband linear frequency modulation signal receiving model. The first receiving station and the second receiving station respectively receive the target signal and superimpose zero-mean Gaussian white noise. The second received signal has a time difference parameter and a scale difference parameter relative to the first received signal. S2: Utilizing the prior structural characteristics of linear frequency modulated signals, the broadband model is converted into a narrowband mutually ambiguous model, and a mapping relationship between the scaling factor and the Doppler frequency shift is established. The Doppler frequency shift is equal to the scaling factor minus 1 multiplied by the signal center frequency. S3: Calculate the narrowband mutual ambiguity function for the two received signals, and form a linear ridge with energy accumulation on the two-dimensional parameter plane composed of time delay and Doppler frequency shift; S4: Perform a two-dimensional Fourier transform on the mutually ambiguous function to obtain the frequency domain energy distribution, and perform local peak detection in the frequency domain modulus plane to obtain a set of candidate energy points; S5: Randomly sample from the candidate energy point set to construct a straight line model, and divide the local point set according to the distance threshold from the point to the model; S6: Select the set with the largest number of local points through multiple random sampling iterations, and determine the optimal set of local points; S7: Establish a weighted linear model based on the optimal set of local points, with the weights determined by the normalization magnitude of each feature point; S8: Solve for the ridge model parameters using the weighted least squares method to obtain the ridge slope and intercept; S9: Calculate the ridge projection angle and radial characteristic parameters based on the ridge parameters; S10: Establish a linear constraint relationship between time delay and scale factor based on the geometric characteristics of the ridge line, and compress the two-dimensional parameter search space into a one-dimensional search path; S11: Calculate the broadband mutual ambiguity function value along the one-dimensional search path; S12: Search for the location of the maximum value in the one-dimensional search space to obtain the time difference estimate, and obtain the scale difference estimate based on the constraint relationship.

2. The method according to claim 1, characterized in that, The narrowband mutual ambiguity function is obtained by compensating for time delay and Doppler frequency shift in a two-dimensional parametric plane. The amplitude of the mutual ambiguity function reaches its maximum when the compensation amount is equal to the actual time difference and frequency difference.

3. The method according to claim 1, characterized in that, The set of candidate energy points is obtained by detecting local peaks in the frequency domain modulus plane, and each candidate point contains two-dimensional coordinates and normalized amplitude information.

4. The method according to claim 1, characterized in that, The number of iterations of the random sample consensus algorithm is determined by the following relationship: The number of iterations is equal to 1 minus the logarithm of the probability value divided by 1 minus the logarithm of the minimum number of samples of the local point proportion raised to the power of 1.

5. A RANSAC-WLS-based time-frequency difference parameter estimation system for strong interference environments implementing the method described in any one of claims 1-4, characterized in that, include: The signal receiving module is used to receive two linear frequency modulated signals and generate complex envelope received data; The mutual fuzziness analysis module is used to calculate the narrowband mutual fuzziness function and generate the time-delayed Doppler two-dimensional energy distribution; The frequency domain mapping module is used to perform a two-dimensional Fourier transform on mutually ambiguous functions and generate a frequency domain energy plane. The feature extraction module is used to perform local peak detection on the frequency domain energy plane and generate a set of candidate energy points; The ridge estimation module is used to estimate ridge model parameters based on the random sample consensus algorithm and the weighted least squares algorithm. The path constraint module is used to establish a linear search path for time delay and scale factor based on ridge parameters; The parameter solving module is used to calculate the broadband mutual ambiguity function and determine the time difference parameter and scale difference parameter on the one-dimensional search path.

6. The system according to claim 5, characterized in that, The ridge estimation module includes a random sampling unit, an in-place point discrimination unit, and a weighted least squares solution unit.

7. The system according to claim 5, characterized in that, The path constraint module is used to calculate the projection angle and radial feature parameters based on the ridge slope and intercept, and to generate a one-dimensional linear search path.

8. A method for estimating the time-frequency difference parameter based on the system described in claim 5, characterized in that, Receives two wideband linear frequency modulated signals; Calculate the narrowband mutual ambiguity function and form a time-delayed Doppler two-dimensional plane; Candidate energy points are obtained in a two-dimensional plane through frequency domain transformation; The random sampling consensus algorithm is used to separate local points from outliers. The parameters of the ridge model are estimated using the weighted least squares algorithm. Construct a linear constraint path for time delay and scale factor based on the ridge geometry; Calculate the broadband mutual ambiguity function value along the constrained path and determine the time difference parameter and scale difference parameter.

9. The method according to claim 8, characterized in that, The one-dimensional search path is determined by the ridge projection angle, radial characteristic parameters, and frequency modulation.

10. The method according to claim 8, characterized in that, The amplitude of the broadband mutually fuzzy function is calculated by discrete sampling along the one-dimensional search path, and the position of the largest amplitude is selected as the final parameter estimation result.

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