RLBI high-resolution angle parameter estimation method and device based on adaptive CS-STFT-IRT

Abstract

The invention discloses an RLBI high-resolution angle parameter estimation method and device based on adaptive CS-STFT-IRT, and the method comprises the steps: receiving a target signal through employing double array elements of a rotating long baseline interferometer, and calculating a cross-correlation signal; multi-resolution analysis is carried out under the condition of multiple preset window lengths, and an adaptive compressed sensing hybrid algorithm is introduced to generate a time-frequency power spectrum matrix. And then, respectively executing inverse Radon transformation on the time-frequency power spectrum matrixes under different window lengths to obtain corresponding inverse Radon domain images, and extracting peak value information through an intelligent peak searching algorithm. And scoring each window length processing result according to a preset quality evaluation criterion, and adaptively selecting an optimal inverse Radon domain image. And accurately calculating the pitch angle and the azimuth angle of the target according to the peak point coordinates in the optimal image. According to the method, the limitation of the traditional method in the aspects of resolution and robustness is effectively overcome, and the angle estimation precision and reliability under the adjacent information source condition are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radio direction finding, and particularly relates to a high-resolution angle parameter estimation method and device for RLBI based on adaptive CS-STFT-IRT. BACKGROUND

[0002] According to whether the system actively radiates electromagnetic signals outward during operation, modern positioning and direction finding systems can be generally divided into two categories: active positioning systems and passive positioning systems. An active positioning system can simultaneously obtain the direction of arrival information and the propagation time delay information of a target by actively transmitting electromagnetic signals of a known form and receiving and processing the target echo, so as to realize joint calculation of the distance and the position of the target. However, such a system is easy to expose its own position due to the need for actively radiating electromagnetic signals, has poor concealment in an electromagnetic countermeasure environment, and is limited by use conditions in some application scenarios.

[0003] In contrast, a passive positioning system only relies on receiving electromagnetic signals radiated by a target itself to work, does not need to actively transmit electromagnetic waves, has good concealment and safety, and is thus widely used in the fields of passive electronic reconnaissance, electromagnetic spectrum monitoring and the like. However, since the passive system lacks a unified transmission time reference, it is generally difficult to directly obtain signal propagation time delay information, and its positioning capability is mainly reflected in the estimation of the angle parameters such as the direction of arrival of the target.

[0004] Among many passive direction finding technologies, interferometer direction finding is an important and mature technical approach. This method can invert the spatial angle information of a target by measuring the phase difference between signals received by different array elements, has the advantages of high direction finding precision, relatively simple system structure, low hardware implementation cost and the like, and can better meet the needs of modern electronic reconnaissance systems for high-precision and wideband direction finding. Therefore, interferometer technology has been widely applied to military and civilian fields such as passive electronic reconnaissance, electromagnetic spectrum monitoring, wireless communication and emergency rescue.

[0005] In a passive interferometer system, the estimation precision of the angle parameters of a radiation source is an important index for measuring the overall performance of the system, and the angle estimation precision is greatly affected by the length of the baseline between array elements. In theory, increasing the distance between array elements and using a longer measurement baseline can significantly improve the angle measurement precision. However, in a traditional fixed single-baseline interferometer structure, the increase in the length of the baseline will cause periodic ambiguity in phase difference measurement, thereby making it difficult to balance between direction finding precision and non-ambiguous field of view.

[0006] To overcome the aforementioned problems, the Rotating Long Baseline Interferometer (RLBI) was developed. This system transforms the originally static and ambiguous phase difference information into a time-varying sinusoidal modulated signal by uniformly rotating the long baseline around the array center. In this signal model, the target's angular information is mapped to key parameters of the modulated signal, where the amplitude of the modulated signal is related to the target's elevation angle, and its initial phase is related to the target's azimuth angle. By analyzing the entire time-varying signal, the phase ambiguity problem can be effectively eliminated while maintaining the high direction-finding accuracy advantage of the long baseline, thus significantly improving the system's direction-finding performance.

[0007] However, while the RLBI system improves direction-finding performance, it also places higher demands on signal processing algorithms. Due to the introduction of rotational motion, the cross-correlation signal between array elements exhibits significant non-stationary characteristics, with its instantaneous frequency changing continuously over time. Traditional time-domain or frequency-domain analysis methods are insufficient to effectively extract the angular parameter information contained within. Therefore, time-frequency analysis techniques must be used to process the cross-correlation signal.

[0008] Currently, the STFT-IRT method, which combines Short-Time Fourier Transform (STFT) and Inverse Radon Transform (IRT), is a widely used technique for estimating angle parameters in rotating long baseline interferometers (RLBIs). For example, Chinese patent CN106959433A discloses an STFT-IRT parameter estimation method based on RLBI, comprising: Step 1, receiving radiation source signals from two antenna channels of an RLBI; Step 2, performing cross-correlation processing on the signals received by the two antenna channels to obtain a cross-correlation signal; Step 3, performing STFT on the cross-correlation signal to obtain a time-frequency image; Step 4, performing IRT on the time-frequency image to obtain IRT domain image highlighting points; Step 5, estimating the amplitude and initial phase of the time-frequency image from the image highlighting points; and Step 6, calculating the elevation and azimuth angles of the radiation source based on the amplitude and initial phase of the time-frequency image.

[0009] This method maps non-stationary signals to the time-frequency domain using STFT to obtain a time-frequency trajectory reflecting the target's motion characteristics. Then, it uses inverse Radon transform to integrate and focus the time-frequency curve, thereby estimating the angle parameters. However, the STFT method itself is limited by the trade-off between time and frequency resolution determined by the fixed window length, making it difficult to simultaneously achieve both time and frequency resolution.

[0010] Specifically, while a shorter window length can achieve higher temporal resolution, it results in insufficient frequency resolution. When multiple targets have similar angles and their corresponding time-frequency trajectories are close in the frequency domain, trajectory aliasing can easily occur, leading to a single energy focusing peak after the inverse Radon transform, thus causing missed detections of nearby targets. Conversely, while a longer window length can improve frequency resolution and separate similar trajectories, the excessively long time span can violate the local linearity assumption upon which the inverse Radon transform relies, leading to a decrease in energy focusing effect and reduced angle estimation accuracy. Therefore, how to balance time-frequency resolution under different window length conditions and achieve high-resolution angle parameter estimation for multiple nearby targets in complex electromagnetic environments remains a pressing technical problem to be solved in the field of rotating long baseline interferometry signal processing. Summary of the Invention

[0011] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a high-resolution angle parameter estimation method and apparatus based on adaptive CS-STFT-IRT for RLBI. By applying compressed sensing time-frequency transformation technology to a rotating interferometer, high-precision analysis in the time-frequency domain and subsequent high-resolution estimation of parameters are achieved. This aims to solve the problem of peak aliasing or redundancy when mapping from the traditional time-frequency domain to the inverse Radon domain, and improve the performance of the interferometer under multi-source conditions and the resolution capability of adjacent sources.

[0012] The objective of this invention can be achieved through the following technical solutions: This invention provides a high-resolution angle parameter estimation method for RLBI based on adaptive CS-STFT-IRT, comprising the following steps: The target signal is received by a dual-element rotating long baseline interferometer (RLBI), and the received target signal is cross-correlated to obtain a cross-correlation signal containing phase difference information. Under a series of preset window lengths, the cross-correlation signals are sequentially subjected to multi-resolution analysis and processing. The adaptive compressed sensing time-frequency transform hybrid algorithm (CS-STFT) is used to perform sparse recovery, noise reduction and interference suppression on the signals under each window length to obtain a high-resolution time-frequency power spectrum matrix. The time-frequency power spectrum matrix generated under each window length is processed by inverse Radon transform (IRT) to convert the time-frequency power spectrum matrix into an inverse Radon domain image; The peak detection algorithm is used to perform peak detection on the obtained inverse Radon domain image, and the peak points in the image are identified and extracted. Based on the location of the peak point, the results under the current window length are scored according to the preset quality evaluation criteria, and the inverse Radon domain image with the highest score is automatically selected as the optimal solution. By using the peak point coordinates in the optimal solution, the elevation and azimuth angles of the target signal can be accurately calculated, thus achieving high-precision angular parameter estimation of the target.

[0013] Furthermore, the received target signal is represented as: in, This indicates the sampling time of the dual array elements of the rotating long baseline interferometer. t The received target signal vector; This represents the array response vector related to the target space angle, which is determined by the elevation angle of the target signal. and azimuth Joint decision; Indicates the target radiation source at the sampling time t The baseband signal; This indicates the noise signal introduced during the receiving process.

[0014] Furthermore, the received target signal is subjected to cross-correlation processing to obtain a cross-correlation signal containing phase difference information, as shown in the formula: in, Indicates at the sampling time t Cross-correlation signal obtained by cross-correlation operation on dual array element signals of a rotating long baseline interferometer; , These represent the sampling times of the first and second elements of the rotating long baseline interferometer, respectively. t Received target signal; superscript Represents the complex conjugate operation; , These represent the signals from the two target radiation sources received by the interferometer array elements, which are the baseband signals of the target at a certain moment; , These represent the power components of the two target signals, respectively. Represents the imaginary unit; Indicates the wavelength of the received signal; , These represent the elevation angles of the two target signals, respectively. , These represent the azimuth angles of the two target signals, respectively. Indicates the angular frequency of the signal; This indicates the element spacing between two elements of a rotating long baseline interferometer, that is, the spatial distance between the first element and the second element.

[0015] Furthermore, under a series of preset window lengths, the cross-correlation signals are sequentially subjected to multi-resolution analysis and processing. An adaptive compressed sensing time-frequency transform hybrid algorithm is used to perform sparse recovery, denoising, and interference suppression on the signals under each window length, obtaining a high-resolution time-frequency power spectrum matrix. Specifically, this includes: Construct an ideal bandpass filter, set the passband cutoff frequency, and filter the cross-correlation signal to remove the DC term and out-of-band noise in the signal, thereby obtaining a pre-processed pure cross-correlation signal. The pure cross-correlation signal is arranged according to the current candidate window length. L Slicing to obtain the signal subsequence within each time window. And apply a window function to each time window. Receive windowing signal : in, This represents the windowed signal subsequence; Indicates the current candidate window length L The extracted cross-correlation signal subsequence; This represents a window function used to suppress edge effects; Constructing a sparse dictionary for orthogonal matching pursuit (OMP) A dictionary column vectors Indicates possible frequency components: in, This represents the total number of possible frequency components in the dictionary; Indicates the corresponding number j A time-domain basis function with a frequency is used to sparsely represent the signal; For each candidate window length L Windowing signal below Perform sparse recovery, initializing the residuals as follows: in, Represents the initial residual vector; Based on the initialization residual and the sparse dictionary A In the k In this iteration, the most relevant dictionary column index is selected through a matching step: in, Indicates the first k The dictionary column index selected in the next iteration; Indicates the first The residual vector of the next iteration; Indicates the complex conjugate transpose; Represents the modulus of a complex number; Index the selected dictionary column Add to current support set The support set coefficients are then solved using the least squares method. in, This represents the sparse coefficient vector corresponding to the support set; This represents the dictionary submatrix corresponding to the support set; Based on the sparse coefficient vector Reconstruct the main signal components within the current time window to obtain the reconstructed signal: in, This represents the reconstructed signal after sparse recovery, denoising, and interference suppression. For reconstructed signals Perform a short-time Fourier transform to obtain a high-resolution time-frequency power spectrum matrix; Repeat the above steps for all candidate window lengths to obtain a high-quality time-frequency power spectrum matrix under multi-resolution.

[0016] Furthermore, the reconstructed signal Performing a short-time Fourier transform yields the high-resolution time-frequency power spectrum matrix, as shown in the formula: in, Represents the time-frequency power spectrum matrix; Represents the complex numerical spectrum of the STFT; f Indicates frequency index; t Indicates a time index.

[0017] Furthermore, the inverse Radon transform is performed on the time-frequency power spectrum matrix generated under each window length to convert the time-frequency power spectrum matrix into an inverse Radon domain image, as shown in the formula: in, Represents the time-frequency power spectrum matrix; Represents coordinates in the inverse Radon domain image The value at that location reflects the signal's spatial position. The degree of energy focusing at that location; The imaginary unit; Represents the frequency components of a signal; This refers to the offset in the Radon transform; , These are the spatial frequency components in the inverse Radon transform; Indicates the first p The position and amplitude of each peak point; Indicates the first p The spatial angle of each peak point; For Dirac delta function; This indicates the total number of peak points.

[0018] Furthermore, the step of using an intelligent peak-finding algorithm to perform peak detection on the obtained inverse Radon domain image, identifying and extracting peak points in the image, specifically includes: Image of inverse Radon domain A local maximum search is performed by comparing the magnitude of each pixel with that of its neighboring pixels to determine possible peak candidate points. For each candidate point... If its amplitude is greater than that of all pixels in the neighborhood, it is marked as a peak point candidate. For all candidate peak points, calculate the amplitude intensity of each candidate point. And threshold filtering is performed to remove candidate points with amplitudes lower than a preset threshold; The peak points selected through threshold screening are subjected to neighborhood clustering, which groups multiple spatially close peak points into a single representative point. Let the total number of peak points obtained in the end be . P The coordinates of each peak point are The corresponding amplitude is .

[0019] Furthermore, the step of scoring the results under the current window length based on the position of the peak point and according to a preset quality assessment standard, and automatically selecting the inverse Radon domain image with the highest score as the optimal solution, specifically includes: For the set of peak points in the inverse Radon domain image obtained under each window length The score is calculated based on the amplitude intensity and spatial distribution. The formula is: in, Indicates the first The amplitude of each peak point reflects the peak energy; This indicates the total number of peak points under the current window length; Score values ​​for all candidate window lengths By comparing the results, the inverse Radon domain image corresponding to the window length with the highest score is selected as the optimal solution.

[0020] Furthermore, the precise calculation of the target signal's elevation and azimuth angles using the peak point coordinates in the optimal solution, thus achieving high-precision angular parameter estimation of the target, specifically includes: Determine the coordinates of each peak point in the optimal inverse Radon domain image. Coordinates of the image center point The difference between the modulus and the modulus is expressed by the following formula: in, , They represent the peak points respectively. With the coordinates of the image center point and The difference between the axes; Indicates peak point The modulus length; Based on the modulus and difference of the peak points, the elevation angle of the target signal is calculated using the geometric relationship of a rotating long baseline interferometer. and azimuth : in, , The first p The elevation and azimuth angles of each target; Indicates the wavelength of the received signal. Indicates the angular frequency of the signal; This represents the element spacing between two elements of a rotating long baseline interferometer, i.e., the spatial distance between the first element and the second element. This is the phase compensation amount corresponding to the group delay introduced by the current window length.

[0021] In another aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the RLBI high-resolution angle parameter estimation method based on adaptive CS-STFT-IRT as described in any one of the above descriptions.

[0022] Compared with the prior art, the present invention has the following advantages: (1) In complex electromagnetic environments, cross-correlation signals are often affected by noise and interference. Traditional STFT methods directly process the original signal, which can easily lead to the diffusion of noise energy in the time spectrum and weaken the distinguishability of the real target trajectory. This invention introduces adaptive compressed sensing and sparse recovery technology before time-frequency analysis. By constructing a sparse dictionary and using the orthogonal matching pursuit algorithm to sparsely reconstruct the signal, noise and interference components are effectively suppressed, and only the main signal components are retained. This significantly improves the signal-to-noise ratio and clarity of the time-frequency power spectrum matrix. By utilizing the sparse recovery characteristics of the OMP algorithm, noise reduction and cross-term suppression can be effectively achieved when reconstructing the signal, resulting in highly concentrated energy, a clear sine curve in the time-frequency domain, and a focused peak in the inverse Radon domain.

[0023] (2) Under the condition of proximity sources, the traditional STFT-IRT is limited by a fixed physical resolution and cannot effectively distinguish two similar time-frequency curves. When the target angles are close, time-frequency trajectory aliasing or insufficient energy focusing is likely to occur. This invention effectively overcomes the problem of insufficient adaptability of the fixed window length method in different scenarios by performing multi-resolution analysis on the cross-correlation signal under a series of preset window lengths and comprehensively evaluating the results under different window lengths. This enables the system to automatically obtain a better time-frequency representation for different target distributions and signal characteristics, and can automatically select a window length that optimizes the final processing result based on the characteristics of the signal itself. This allows the algorithm to use a short window to ensure efficiency and robustness when facing distant targets, and to automatically switch to a long window to pursue high resolution when facing extremely close targets, thereby avoiding distortion in the estimation of the number of target sources and angle parameters.

[0024] (3) In existing methods, when multiple targets are close in angle, the time-frequency trajectories tend to overlap, resulting in an insignificant energy focusing effect after the inverse Radon transform. Multiple targets may be misjudged as a single peak, thus reducing the resolution capability. This invention introduces inverse Radon transform processing on the basis of high-resolution time-frequency power spectrum, mapping the curve structure in the time-frequency domain to the energy focusing point in the inverse Radon domain. This allows the time-frequency trajectories corresponding to different targets to form separate peak points in the spatial domain, thereby significantly enhancing the resolution capability for nearby targets.

[0025] (4) Under the conditions of multi-window length and multi-resolution processing, existing technologies usually lack a unified evaluation criterion to judge the quality of results under different window lengths, which easily relies on manual selection and makes it difficult to achieve adaptive operation of the algorithm. This invention constructs a quality evaluation standard based on peak amplitude intensity and spatial distribution characteristics, quantifies and scores the inverse Radon domain images obtained under different window lengths, and automatically selects the result with the highest score as the optimal solution, thereby automating the selection of window length and the judgment of result excellence, and effectively improving the adaptability of the algorithm in different application scenarios. Attached Figure Description

[0026] Figure 1 This is a flowchart of the RLBI high-resolution angle parameter estimation method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the rotating interferometer used in an embodiment of the present invention; Figure 3 This is a schematic diagram of the theoretical time-frequency curve under two signal sources according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the optimal IRT energy concentration result under two-source conditions according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the theoretical time-frequency curve under the condition of a nearby information source, according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the optimal IRT energy concentration result under the condition of proximity source in an embodiment of the present invention; Figure 7 This is a schematic diagram of the theoretical time-frequency curve under the same pitch angle conditions according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the optimal IRT energy concentration result under the same pitch angle conditions according to an embodiment of the present invention. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0028] Example 1: To address the shortcomings of the STFT-IRT algorithm, this invention proposes a novel processing framework based on Adaptive Compressed Sensing Time-Frequency Transform (Adaptive CS-STFT). The core idea of ​​this invention is to utilize the prior physical property that the signal's spectrum in the Fourier transform domain is sparsity (i.e., composed of a few dominant sine waves) within each time window. The CS-OMP-STFT hybrid algorithm employed in this invention first utilizes the sparse recovery capability of Orthogonal Matching Pursuit (OMP) to find and reconstruct the main signal components within each time window, thus efficiently achieving denoising and suppression of cross-terms in the first step. Then, STFT is applied to this "cleaned" signal to generate a smooth and continuous high-quality time-frequency graph. To resolve the contradiction that a single fixed window length cannot adapt to complex and variable scenarios, this invention proposes a "multi-resolution analysis meta-algorithm" framework. This framework can automatically analyze the signal using a series of different window lengths and autonomously select an optimal window length from the signal analysis results through a quantitative quality evaluation criterion. These improvements enable the algorithm to use a short window to ensure efficiency and robustness when facing distant targets, and to automatically switch to a long window to pursue high resolution when facing extremely close targets. This gives the algorithm stronger resistance to noise interference and resolution, and allows it to achieve higher accuracy in angle parameter estimation.

[0029] This embodiment specifically provides a high-resolution angle parameter estimation method for RLBI based on adaptive CS-STFT-IRT, such as... Figure 1 As shown, it includes the following steps: Step S1: Use the dual-element array of a rotating long baseline interferometer to receive the target signal and perform cross-correlation processing on the received target signal to obtain a cross-correlation signal containing phase difference information; Specifically, a rotating long-baseline interferometer with two array elements is used to synchronously receive the target radiation source signal. The array element spacing is 2 meters, and the system sampling rate is 3 kHz, thereby acquiring the received signals of the two array elements as a function of time during rotation. The signals received by the two array elements can be expressed as: in, This indicates the sampling time of the dual array elements of the rotating long baseline interferometer. t The received target signal vector; This represents the array response vector related to the target space angle, which is determined by the elevation angle of the target signal. and azimuth Joint decision; Indicates the target radiation source at the sampling time t The baseband signal; This indicates the noise signal introduced during the receiving process.

[0030] Based on this, cross-correlation operations are performed on the signals received by the two array element channels to obtain the original cross-correlation signal: in, Indicates at the sampling time t Cross-correlation signal obtained by cross-correlation operation on dual array element signals of a rotating long baseline interferometer; , These represent the sampling times of the first and second elements of the rotating long baseline interferometer, respectively. t Received target signal; superscript Represents the complex conjugate operation; , These represent the signals from the two target radiation sources received by the interferometer array elements, which are the baseband signals of the target at a certain moment; , These represent the power of the two target signals, respectively. Represents the imaginary unit; Indicates the wavelength of the received signal; , These represent the elevation angles of the two target signals, respectively. , These represent the azimuth angles of the two target signals, respectively. Indicates the angular frequency of the signal; This indicates the element spacing between two elements of a rotating long baseline interferometer, that is, the spatial distance between the first element and the second element.

[0031] To improve the accuracy of subsequent time-frequency analysis and IRT processing, the original cross-correlation signal is further subjected to frequency domain ideal bandpass filtering or DC removal processing to filter out DC components and out-of-band noise, obtaining a clean cross-correlation signal. Through the above cross-correlation and filtering processing, the spatial phase difference information in the original dual-channel received signal is explicitly converted into a time-varying complex-valued signal form, so that the target's angle information is effectively modulated into the amplitude and phase changes of the cross-correlation signal, while suppressing noise interference, providing a high signal-to-noise ratio foundation signal for the high-resolution time-frequency power spectrum estimation in the subsequent step S2.

[0032] Through the above cross-correlation processing, the spatial phase difference information in the original dual-channel received signal is explicitly converted into a complex signal form that varies with time. This allows the target's angle information to be effectively modulated into the amplitude and phase changes of the cross-correlation signal. In this way, while suppressing independent noise components, the characteristics related to the target's spatial direction are enhanced. This provides a high signal-to-noise ratio and information-concentrated basic signal for subsequent high-resolution angle parameter estimation based on time-frequency analysis and inverse Radon transform.

[0033] Step S2: Under a series of preset window lengths, perform multi-resolution analysis on the cross-correlation signals sequentially. Employ an adaptive compressed sensing time-frequency transform hybrid algorithm to perform sparse recovery, denoising, and interference suppression on the signals under each window length, obtaining a high-resolution time-frequency power spectrum matrix. Specifically, this includes: Specifically, the cross-correlated signal is processed using multi-resolution cyclic processing under a series of preset candidate window lengths. In each iteration, the time-domain signal is sliced ​​for the current window length, and a CS-OMP-STFT hybrid algorithm is used to perform high-resolution spectral estimation, obtaining the time-spectrum matrix under the corresponding window length. This hybrid algorithm fully utilizes the advantages of orthogonal matching pursuit (OMP) in sparse signal reconstruction, and its iterative process includes matching, updating, projection, and residual calculation steps. Among them, the matching step searches the sparse dictionary A for the residual from the previous round. The dictionary column with the highest relevance has the following mathematical expression: This step is the core of the OMP algorithm. It involves selecting the frequency atom that best explains the energy of the current residual signal from all candidate frequency components, thereby gradually extracting the main signal components.

[0034] By adaptively identifying and reconstructing the dominant frequency components in the cross-correlation signal within each time window, noise, sidelobes, and cross terms are effectively suppressed during the sparse recovery stage, thus improving signal quality from the source. Subsequently, a standard short-time Fourier transform (STFT) is performed on the reconstructed clean signal to further enhance frequency resolution while ensuring the continuity and smoothness of the time-frequency trajectory, ultimately obtaining a high-resolution time-frequency power spectrum matrix.

[0035] Step S2 specifically includes: However, the cross-correlation signal directly generated in step S1 It contains a high-energy DC component (i.e. and These components (including environmental noise) do not contain angular information and their energy is concentrated near zero frequency in the frequency domain, which will seriously interfere with the sparse recovery effect of subsequent compressed sensing algorithms on high-frequency sinusoidal modulated signals.

[0036] Therefore, before performing multi-resolution analysis, this invention... Perform ideal frequency domain filtering. Specifically, calculate the theoretical maximum Doppler frequency based on the interferometer's maximum rotational angular velocity ω, the baseline length d, and the wavelength λ. The passband range is constructed to be [-1.1]. , 1.1 An ideal bandpass filter removes the DC component and noise interference exceeding the theoretical bandwidth, retaining only the AC component containing phase information to obtain a purified cross-correlation signal.

[0037] The purified cross-correlation signal is then processed according to the current candidate window length. L Slicing to obtain the signal subsequence within each time window. And apply a window function to each time window. Receive windowing signal : in, This represents the windowed signal subsequence; Indicates the current candidate window length L The extracted cross-correlation signal subsequence; This represents a window function used to suppress edge effects; Constructing a sparse dictionary for orthogonal matching pursuit A dictionary column vectors Indicates possible frequency components: in, This represents the total number of possible frequency components in the dictionary; Indicates the corresponding number j A time-domain basis function with a frequency is used to sparsely represent the signal; For each candidate window length L Windowing signal below Perform sparse recovery, initializing the residuals as follows: in, Represents the initial residual vector; Based on the initialization residual and the sparse dictionary A In the k In this iteration, the most relevant dictionary column index is selected through a matching step: in, Indicates the first k The dictionary column index selected in the next iteration; Indicates the first The residual vector of the next iteration; Indicates the complex conjugate transpose; Represents the modulus of a complex number; Index the selected dictionary column Add to current support set The support set coefficients are then solved using the least squares method. in, This represents the sparse coefficient vector corresponding to the support set; This represents the dictionary submatrix corresponding to the support set; Based on the sparse coefficient vector Reconstruct the main signal components within the current time window to obtain the reconstructed signal: in, This represents the reconstructed signal after sparse recovery, denoising, and interference suppression. For reconstructed signals Performing a short-time Fourier transform yields the high-resolution time-frequency power spectrum matrix, as shown in the formula: in, Represents the time-frequency power spectrum matrix; Represents the complex numerical spectrum of the STFT; f Indicates frequency index; t Indicates a time index.

[0038] Repeat the above steps for all candidate window lengths to obtain a high-quality time-frequency power spectrum matrix under multi-resolution.

[0039] Step S2 addresses the challenges of non-stationary cross-correlation signals, complex noise and interference components, and significant time-frequency variations in the time-frequency characteristics of rotating long-baseline interferometers. It overcomes the limitations of existing technologies that use a single fixed-window-length short-time Fourier transform, such as limited time-frequency resolution, blurred trajectories, and difficulty in distinguishing nearby targets. By performing multi-resolution cyclic processing on the cross-correlation signal under a series of preset window lengths, and introducing a hybrid algorithm combining adaptive compressed sensing and short-time Fourier transform under each window length, this invention can adaptively identify and reconstruct the main effective signal components from the cross-correlation signal before the signal enters the time-frequency analysis stage, utilizing the sparse recovery characteristics of the orthogonal matched pursuit algorithm. This suppresses noise, cross terms, and irrelevant interference at the source, preventing their spread and amplification in the time-frequency domain. Furthermore, performing a short-time Fourier transform on the sparsely reconstructed clean signal significantly improves frequency resolution while maintaining time-spectrum smoothness and trajectory continuity, making the sinusoidal modulated time-frequency trajectory corresponding to the target clearer, more focused, and separable. By acquiring the time-frequency power spectrum matrix under different window lengths in parallel, a foundational signal is provided for subsequent high-resolution angle parameter estimation based on time-frequency analysis and inverse Radon transform.

[0040] Step S3: Perform inverse Radon transform on the time-frequency power spectrum matrix generated under each window length to convert the time-frequency power spectrum matrix into an inverse Radon domain image; IRT is performed on the power spectrum matrix generated in each cycle, and energy focusing is achieved by integrating the time-frequency domain curve to obtain the inverse Radon domain peak value.

[0041] For the power spectral density, after the inverse Radon transform as shown in the following equation, it is focused in the inverse Radon transform domain as follows: P The image highlights a specific point. The formula is: in, Represents the time-frequency power spectrum matrix; Represents coordinates in the inverse Radon domain image The value at that location reflects the degree of energy focusing of the signal at that spatial location; The imaginary unit; Represents the frequency components of a signal; This refers to the offset in the Radon transform; , These are the spatial frequency components in the inverse Radon transform; Indicates the first p The position and amplitude of each peak point; Indicates the first p The spatial angle of each peak point; For Dirac delta function; This indicates the total number of peak points.

[0042] Step S4: Use an intelligent peak-finding algorithm to perform peak detection on the obtained inverse Radon domain image, identify and extract peak points in the image, specifically including: Image of inverse Radon domain A local maximum search is performed by comparing the magnitude of each pixel with that of its neighboring pixels to determine possible peak candidate points. For each candidate point... If its amplitude is greater than that of all pixels in the neighborhood, it is marked as a peak point candidate. For all candidate peak points, calculate the amplitude intensity of each candidate point. And threshold filtering is performed to remove candidate points with amplitudes lower than a preset threshold; The peak points selected through threshold screening are subjected to neighborhood clustering, which groups multiple spatially close peak points into a single representative point. Let the total number of peak points obtained in the end be . P The coordinates of each peak point are The corresponding amplitude is .

[0043] Step S5: Based on the location of the peak points, score the results under the current window length according to the preset quality evaluation criteria, and automatically select the inverse Radon domain image with the highest score as the optimal solution. Specifically, this includes: For the set of peak points in the inverse Radon domain image obtained under each window length The score is calculated based on the amplitude intensity and spatial distribution. The formula is: in, Indicates the first The amplitude of each peak point reflects the peak energy; This represents the total number of peak points under the current window length; the score. This is used to evaluate the energy focusing effect of inverse Radon domain images under different window lengths. The higher the peak amplitude, the more concentrated the signal is in the inverse Radon domain, meaning that the time-frequency power spectrum matrix can more clearly present the target signal characteristics after window length processing; the larger the sum of peak amplitudes, the higher the overall energy concentration, and the more reasonable the window length selection.

[0044] Score values ​​for all candidate window lengths By comparing the results, the inverse Radon domain image corresponding to the window length with the highest score is selected as the optimal solution.

[0045] Step S6: Accurately calculate the elevation and azimuth angles of the target signal using the peak point coordinates in the optimal solution, completing the high-precision angle parameter estimation of the target. Specifically, this includes: Determine the coordinates of each peak point in the optimal inverse Radon domain image. Coordinates of the image center point The difference between the modulus and the modulus is expressed by the following formula: in, , They represent the peak points respectively. With the coordinates of the image center point and The difference between the axes; Indicates peak point The modulus length; Based on the modulus and difference of the peak points, the elevation angle of the target signal is calculated using the geometric relationship of a rotating long baseline interferometer. and azimuth : in, , The first p The elevation and azimuth angles of each target; Indicates the wavelength of the received signal. Indicates the angular frequency of the signal; This represents the element spacing between two elements of a rotating long baseline interferometer, i.e., the spatial distance between the first element and the second element. This is the phase compensation amount corresponding to the group delay introduced by the current window length.

[0046] Example 2: This embodiment uses simulation to conduct a simulation experiment on the present invention, such as... Figure 2 As shown, the interferometer consists of two array elements with an element spacing of 2m. The carrier frequency is 10GHz, the baseband frequencies are 1.4kHz and 0.1kHz, the signal-to-noise ratio is 10dB, the sampling frequency is 3kHz, the direction-finding time is 1s, and the interferometer rotation speed is 2r / s.

[0047] like Figures 3-8 The following is a simulation result of this embodiment: The signal sources are incident from different elevation and azimuth angles, and the rotating interferometer receives the signals at a sampling frequency of 3kHz. Figure 4 The figure shows the optimal IRT energy focusing result of the method designed in this invention under multi-source conditions. As can be seen from the figure, this method can solve the problem of direction finding limitations of the interferometer method under multi-source conditions, and can calculate the elevation and azimuth angles corresponding to the source. Figure 6 and Figure 8 The figure shows a simulation diagram of the method designed in this invention under the conditions of nearby signal sources and the same elevation angle. As can be seen from the figure, the method can still distinguish nearby signal sources and achieve the purpose of accurate direction finding.

[0048] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0049] 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 person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A high-resolution angle parameter estimation method for RLBI based on adaptive CS-STFT-IRT, characterized in that, Includes the following steps: The target signal is received by a dual-element rotating long baseline interferometer, and the received target signal is cross-correlated to obtain a cross-correlation signal containing phase difference information. Under a series of preset window lengths, the cross-correlation signals are sequentially subjected to multi-resolution analysis and processing. An adaptive compressed sensing time-frequency transformation hybrid algorithm is used to perform sparse recovery, denoising and interference suppression on the signals under each window length to obtain a high-resolution time-frequency power spectrum matrix. The time-frequency power spectrum matrix generated under each window length is processed by inverse Radon transform and converted into an inverse Radon domain image. The peak detection algorithm is used to perform peak detection on the obtained inverse Radon domain image, and the peak points in the image are identified and extracted. Based on the location of the peak point, the results under the current window length are scored according to the preset quality evaluation criteria, and the inverse Radon domain image with the highest score is automatically selected as the optimal solution. By using the peak point coordinates in the optimal solution, the elevation and azimuth angles of the target signal can be accurately calculated, thus achieving high-precision angular parameter estimation of the target.

2. The method for estimating high-resolution angle parameters of RLBI based on adaptive CS-STFT-IRT according to claim 1, characterized in that, The received target signal is represented as: in, This indicates the sampling time of the dual array elements of the rotating long baseline interferometer. t The received target signal vector; This represents the array response vector related to the target space angle, which is determined by the elevation angle of the target signal. and azimuth Joint decision; Indicates the target radiation source at the sampling time t The baseband signal; This indicates the noise signal introduced during the receiving process.

3. The method for estimating high-resolution angle parameters of RLBI based on adaptive CS-STFT-IRT according to claim 1, characterized in that, The received target signal is cross-correlated to obtain a cross-correlated signal containing phase difference information, as shown in the formula: in, Indicates at the sampling time t Cross-correlation signal obtained by cross-correlation operation on dual array element signals of a rotating long baseline interferometer; , These represent the sampling times of the first and second elements of the rotating long baseline interferometer, respectively. t Received target signal; superscript Represents the complex conjugate operation; , These represent the signals from the two target radiation sources incident on the interferometer, which are the baseband signals of the targets at a certain moment; , These represent the power of the two target signals, respectively. Represents the imaginary unit; Indicates the wavelength of the received signal; , These represent the elevation angles of the two target signals, respectively. , These represent the azimuth angles of the two target signals, respectively. Indicates the angular frequency of the signal; This indicates the element spacing between two elements of a rotating long baseline interferometer, that is, the spatial distance between the first element and the second element.

4. The method for estimating high-resolution angle parameters of RLBI based on adaptive CS-STFT-IRT according to claim 1, characterized in that, The process involves sequentially performing multi-resolution analysis on the cross-correlation signals within a preset series of window lengths. An adaptive compressed sensing time-frequency transform hybrid algorithm is employed to perform sparse recovery, denoising, and interference suppression on the signals within each window length, thereby obtaining a high-resolution time-frequency power spectrum matrix. Specifically, this includes: Construct an ideal bandpass filter, set the passband cutoff frequency, and filter the cross-correlation signal to remove the DC term and out-of-band noise in the signal, thereby obtaining a pre-processed pure cross-correlation signal. The pure cross-correlation signal is arranged according to the current candidate window length. L Slicing to obtain the signal subsequence within each time window. And apply a window function to the signal in each time window. Receive windowing signal : in, This represents the windowed signal subsequence; Indicates the current candidate window length L The extracted cross-correlation signal subsequence; This represents a window function used to suppress edge effects; Constructing a sparse dictionary for orthogonal matching pursuit A dictionary column vectors Indicates possible frequency components: in, This represents the total number of possible frequency components in the dictionary; Indicates the corresponding number j A time-domain basis function with a frequency is used to sparsely represent the signal; For each candidate window length L Windowing signal below Perform sparse recovery, initializing the residuals as follows: in, Represents the initial residual vector; Based on the initialization residual and the sparse dictionary A In the k In this iteration, the most relevant dictionary column index is selected through a matching step: in, Indicates the first k The dictionary column index selected in the next iteration; Indicates the first The residual vector of the next iteration; Indicates the complex conjugate transpose; Represents the modulus of a complex number; Index the selected dictionary column Add to current support set The support set coefficients are then solved using the least squares method. in, This represents the sparse coefficient vector corresponding to the support set; This represents the dictionary submatrix corresponding to the support set; x This represents the support set coefficient vector to be solved, belonging to... k A complex space. In a physical sense, it corresponds to the space selected in the current iteration step. k The complex amplitude of each frequency component; Based on the sparse coefficient vector Reconstruct the main signal components within the current time window to obtain the reconstructed signal: in, This represents the reconstructed signal after sparse recovery, denoising, and interference suppression. For reconstructed signals Perform a short-time Fourier transform to obtain a high-resolution time-frequency power spectrum matrix; Repeat the above steps for all candidate window lengths to obtain a high-quality time-frequency power spectrum matrix under multi-resolution.

5. The method for estimating high-resolution angle parameters of RLBI based on adaptive CS-STFT-IRT according to claim 4, characterized in that, The reconstructed signal Performing a short-time Fourier transform yields the high-resolution time-frequency power spectrum matrix, as shown in the formula: in, Represents the time-frequency power spectrum matrix; Represents the complex numerical spectrum of the STFT; f Indicates frequency index; t Indicates a time index.

6. The method for estimating high-resolution angle parameters of RLBI based on adaptive CS-STFT-IRT according to claim 1, characterized in that, The inverse Radon transform is performed on the time-frequency power spectrum matrix generated under each window length to convert the time-frequency power spectrum matrix into an inverse Radon domain image. The formula is as follows: in, Represents the time-frequency power spectrum matrix; Represents coordinates in the inverse Radon domain image The value at that location reflects the signal's spatial position. The degree of energy focusing at that location; The imaginary unit; Represents the frequency components of a signal; This refers to the offset in the Radon transform; , These are the spatial frequency components in the inverse Radon transform; Indicates the first p The position and amplitude of each peak point; Indicates the first p The spatial angle of each peak point; For Dirac delta function; This indicates the total number of peak points.

7. The method for estimating high-resolution angle parameters of RLBI based on adaptive CS-STFT-IRT according to claim 1, characterized in that, The method of using an intelligent peak-finding algorithm to perform peak detection on the obtained inverse Radon domain image, identifying and extracting peak points in the image, specifically includes: Image of inverse Radon domain A local maximum search is performed by comparing the magnitude of each pixel with that of its neighboring pixels to determine possible peak candidate points. For each candidate point... If its amplitude is greater than that of all pixels in the neighborhood, it is marked as a peak point candidate. For all candidate peak points, calculate the amplitude intensity of each candidate point. And threshold filtering is performed to remove candidate points with amplitudes lower than a preset threshold; The peak points selected through threshold screening are subjected to neighborhood clustering, which groups multiple spatially close peak points into a single representative point. Let the total number of peak points obtained in the end be . P The coordinates of each peak point are The corresponding amplitude is .

8. The method for estimating high-resolution angle parameters of RLBI based on adaptive CS-STFT-IRT according to claim 1, characterized in that, The process involves scoring the results under the current window length based on the position of the peak point and according to a preset quality assessment standard, automatically selecting the inverse Radon domain image with the highest score as the optimal solution. Specifically, this includes: For the set of peak points in the inverse Radon domain image obtained under each window length The score is calculated based on the amplitude intensity and spatial distribution. The formula is: in, Indicates the first The amplitude of each peak point reflects the peak energy; This indicates the total number of peak points under the current window length; Score values ​​for all candidate window lengths By comparing the results, the inverse Radon domain image corresponding to the window length with the highest score is selected as the optimal solution.

9. The method for estimating high-resolution angle parameters of RLBI based on adaptive CS-STFT-IRT according to claim 1, characterized in that, The process of accurately calculating the elevation and azimuth angles of the target signal using the peak point coordinates in the optimal solution, thereby achieving high-precision angular parameter estimation of the target, specifically includes: Determine the coordinates of each peak point in the optimal inverse Radon domain image. Coordinates of the image center point The difference between the modulus and the modulus is expressed by the following formula: in, , They represent the peak points respectively. With the coordinates of the image center point and The difference between the axes; Indicates peak point The modulus length; Based on the modulus and difference of the peak points, the elevation angle of the target signal is calculated using the geometric relationship of a rotating long baseline interferometer. and azimuth : in, , The first p The elevation and azimuth angles of each target; Indicates the wavelength of the received signal. Indicates the angular frequency of the signal; This represents the element spacing between two elements of a rotating long baseline interferometer, i.e., the spatial distance between the first element and the second element. This is the phase compensation amount corresponding to the group delay introduced by the current window length.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the RLBI high-resolution angle parameter estimation method based on adaptive CS-STFT-IRT as described in any one of claims 1 to 9.

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