A method for long-time phase-coherent accumulation of a motion spectrum based on matching frequency trajectory estimation

Abstract

The present application belongs to the technical field of underwater target passive sonar signal processing, and discloses a moving line spectrum long-time coherent accumulation method based on matching frequency trajectory estimation. The present application analyzes a received signal and determines a candidate frequency band, and extracts a narrowband complex signal; the narrowband complex signal is short-time segmented and a candidate frequency set is established; the matching response of each segment and each candidate frequency is calculated, and normalization is performed to form a matching response matrix; frequency points are selected and continuously corrected according to the maximum response criterion, a segment-level frequency trajectory is obtained, and the segment-level frequency trajectory is interpolated into a sampling-level frequency trajectory and a cumulative phase compensation term is constructed; the narrowband complex signal is phase-corrected by using the compensation term, and then windowing and long-time Fourier analysis are performed to obtain a long-time coherent accumulation spectrum, so that high-dimensional search of motion parameters is avoided and line spectrum frequency drift compensation is realized. The present application has a more simple structure, and can realize energy focusing of a moving weak line spectrum at a lower calculation complexity under the condition that a target line spectrum trajectory still has searchable time-frequency continuity.

Description

Technical Field

[0001] This invention belongs to the field of underwater target passive sonar signal processing technology, and particularly relates to a long-time coherent accumulation method for motion line spectrum based on matched frequency trajectory estimation. Background Technology

[0002] Passive sonar detects and identifies underwater targets by receiving the radiated noise. The propeller rotation and mechanical vibrations of moving underwater targets often produce narrow-band line spectrum components, which are important acoustic features of targets in passive sonar systems. For frequency-stable line spectra, extending the observation time can improve frequency resolution and time integration gain. However, when there is significant relative motion between the target and the receiver, the received line spectrum is affected by Doppler shift, causing the target frequency to change slowly or even exhibit nonlinear drift with the observation time. In this case, if FFT analysis is performed directly on the full-time signal, the target energy, which should originally be concentrated around a single frequency, will be dispersed across multiple frequency units, resulting in spectral peak broadening and loss of coherent integration gain.

[0003] Existing motion line spectrum enhancement methods mainly include parametric motion compensation methods, time-frequency trajectory tracking methods, and multi-frame accumulation methods. Parametric motion compensation methods typically require searching for the optimal compensation result in a space of velocity, acceleration, distance, nearest pass time, or polynomial frequency parameters, which can be computationally intensive when the parameter dimension is high or the search range is large. While time-frequency trajectory tracking methods can enhance the ability to extract weak trajectories, they often involve state models, transition probabilities, recursive inference, or particle updates, making their engineering implementation and parameter tuning complex.

[0004] In some engineering scenarios, the target line spectrum still retains a certain degree of time-frequency continuity in LOFAR, only broadening due to frequency drift in the long-term spectrum output. For this type of data, if the frequency trajectory can be quickly estimated within the candidate frequency band and phase compensation can be performed accordingly, good line spectrum focusing results can be obtained with low complexity. Therefore, it is necessary to propose a long-term coherent accumulation method for motion line spectra that does not rely on high-dimensional motion parameter search, has a simple structure, and is easy to implement in a single channel, so as to achieve frequency drift compensation and long-term coherent accumulation focusing with low complexity in engineering scenarios where the target line spectrum still has short-term time-frequency continuity.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: (1) When there is significant relative motion between the target and the receiver, the received line spectrum is affected by the Doppler frequency shift, resulting in time-varying frequency drift. Directly performing long-term FFT analysis will cause the target energy to be dispersed to multiple frequency units, resulting in spectral peak broadening and coherent integral gain loss. It is difficult to simultaneously take into account the gain advantage of long-term observation and energy focusing under motion conditions.

[0006] (2) Existing parametric motion compensation methods require searching in a high-dimensional parameter space composed of parameters such as velocity, acceleration, distance, closest passing time, or polynomial frequency to find the optimal compensation result. When the parameter dimension is high or the search range is large, the computational load increases dramatically, making it difficult to meet the real-time processing requirements; moreover, prior information on the target motion parameters is required, which limits its engineering applicability.

[0007] (3) Existing time-frequency trajectory tracking methods usually rely on complex frameworks such as state models, transition probabilities, recursive inference or particle updates. Although they can enhance the ability to extract weak trajectories, the model construction is complex, the parameter tuning is difficult, the engineering implementation threshold is high, and it is not conducive to deployment on resource-constrained underwater acoustic platforms.

[0008] (4) Existing multi-frame accumulation methods improve the signal-to-noise ratio by accumulating multiple frames of incoherent or partially coherent data, but fail to truly solve the phase consistency problem. The accumulation gain is limited, and the effect of improving the spectral peak broadening caused by frequency drift is not ideal. Summary of the Invention

[0009] To overcome the problems existing in related technologies, the present invention discloses an embodiment of a long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation, the technical solution of which is as follows: This invention is implemented as follows: a long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation, comprising the following steps: S1. Perform analytical processing on the received signal, determine the candidate frequency band based on the a priori frequency of the target line spectrum, the short-time spectrum or the spectral peak observation results in the LOFAR plot, and extract the narrowband complex signal within the candidate frequency band. S2. Perform short-time segmentation on the narrowband complex signal, determine the analysis window length based on the condition that the target line spectrum is approximately stable within a single time period, determine the segment shift based on the condition that the frequency trajectory of adjacent time periods is continuously observed, and establish a discrete candidate frequency set within the candidate frequency band. S3. Calculate the complex exponential matching response between each time period and each candidate frequency, and normalize the matching response within each time period to form a piecewise-frequency matching response matrix. S4. In each time period, candidate frequencies are selected according to the normalized matching response maximum criterion to obtain the initial segment-level frequency trajectory. The initial segment-level frequency trajectory is then processed to be continuous according to the frequency change continuity criterion between adjacent time periods to obtain the corrected segment-level frequency trajectory. S5. Interpolate the corrected segment-level frequency trajectory into a sampling-level frequency trajectory, construct a cumulative phase compensation term based on the offset of the sampling-level frequency trajectory relative to the reference frequency, and perform phase continuity processing on the cumulative phase compensation term. S6. The phase correction of the narrowband complex signal is performed using the cumulative phase compensation term, and the corrected signal is windowed and subjected to long-term Fourier analysis to obtain the long-term coherent cumulative spectrum. By combining the segment-by-segment maximum matched frequency trajectory estimation with the sampling-level cumulative phase compensation, the frequency drift of the motion line spectrum is compensated and long-term coherent accumulation is performed without performing a high-dimensional search of motion parameters.

[0010] In step S1, the candidate frequency band is denoted as The reference frequency of the candidate frequency band Determine as follows: ; In the formula, This is the lower limit of the candidate frequency band. This represents the upper limit of the candidate frequency band. The candidate frequency band covers the frequency drift range of the target weak line spectrum caused by relative motion during the observation time; The analytical processing involves Hilbert transform and bandpass filtering to obtain a narrowband complex signal within the candidate frequency band. ,in, , To process the number of sampling points for a segment.

[0011] In step S2, short-time segmentation of the narrowband complex signal includes: using a segment of length... Analysis window and segment shift For narrowband complex signals Divide into segments, the first segment signal Represented as: ; In the formula, It is a discrete-time sampling sequence of a narrowband complex signal. This is a discrete-time index within a segment. To analyze the window length, The number of segments, For segment shift, analysis window length Based on the condition that the target line spectrum is approximately stable within a single time period, the maximum frequency change of the target line spectrum within a single segment is determined so that it does not exceed the preset frequency tolerance error; segment shift The frequency change between the center times of adjacent time periods is determined based on the condition of continuous observation of frequency trajectories between adjacent time periods, so that the frequency change between adjacent time periods does not exceed the preset continuity threshold. Within the candidate frequency band, according to the frequency step size Establish a set of discrete candidate frequencies The expression is: ; In the formula, For the first Candidate frequency points, This is the starting frequency of the candidate frequency band. The index of the candidate frequency point. The number of candidate frequencies. Frequency step size The frequency accuracy of the line spectrum to be estimated, the frequency resolution of the analysis window, and the computing power of the processor are determined.

[0012] In step S3, calculating the complex exponential matching response between each time period and each candidate frequency includes: The time period in the first Matching response at each candidate frequency The amplitude is determined by the inner product of the segmented signal and the complex exponential basis function corresponding to the candidate frequency, expressed as: ; In the formula, For the first Windowed segmented signals for a time period The imaginary unit, For candidate frequencies, The sampling frequency; Used to characterize the Within a certain time period, the target line spectrum is located at the candidate frequency. Degree of local matching in the vicinity; The larger the value, the more significant the number. Segment signal at candidate frequency The higher the probability of the presence of single-frequency line spectrum components in the vicinity; Matching response Used to characterize the target weak line spectrum at candidate frequencies within this time period. The degree of matching in the vicinity, and used as a local observation for the segment-by-segment maximum matching frequency trajectory estimation; The matching responses within each time period are normalized to obtain normalized matching responses. : ; In the formula, For the first Matching responses for all candidate frequencies within a given time period The maximum value is used as the benchmark for matching response normalization within that time period; Normalization is used to eliminate the effects of propagation fading, amplitude fluctuations, and short-term energy changes on segment-by-segment frequency selection, so that the segment-by-segment maximum matching selection is determined by the relative frequency matching peak value within each time period.

[0013] In step S4, the criterion for maximizing the normalized matching response is: In the Within a time period, select the response that matches the normalized response. Candidate frequency index that reaches the maximum value And the candidate frequency corresponding to the candidate frequency index is used as the initial trajectory frequency point for this segment: ; In the formula, For the first Normalized matching responses for all candidate frequencies within a given time period The maximum value, For the first The initial trajectory frequency points estimated over a time period For index Corresponding candidate frequencies; By using the normalized matching response maximization criterion, the frequency trajectory point is directly determined from the local matching response peak within each time period, thus avoiding high-dimensional search in the motion parameter space; the motion parameters include at least one of velocity, acceleration, nearest passing distance, and nearest passing time.

[0014] Furthermore, the initial segment-level frequency trajectory Obtained from the independent maximum matching results of each time period, it is suitable for scenarios where the target line spectrum has a searchable continuous structure in the short-time spectrum or LOFAR plot; for the initial segment-level frequency trajectory A continuous processing method using moving median filtering is employed to obtain the processed segment-level frequency trajectory. For non-boundary time periods, the current time period and adjacent time periods are used. A local window is formed by several trajectory points, and the corrected segment-level frequency trajectory is determined. The expression is: ; In the formula, For the median operation, For the first Initial trajectory frequency points over a time period, For the first Initial trajectory frequency points over a time period For the first Initial trajectory frequency points over a time period For the first Initial trajectory frequency points over a time period This represents the total number of time periods.

[0015] For the first and last time periods, the original estimated value is maintained, the boundary is copied, or a truncated window is formed by adjacent available trajectory points. The moving median filter is used to suppress isolated frequency jumps caused by random noise peaks, local interference line spectra, or missing short-time spectral peaks.

[0016] In step S5, let the first The center time of the segment is Sampling time is , segment-level frequency trajectory Interpolate to the sampling time to obtain the sampling-level frequency trajectory. : ; In the formula, For discrete-time sampling index, Indicates by arrive The interpolation mapping relationship, It is a linear interpolation operator; Based on the sampling-level frequency trajectory relative to the reference frequency The offset constructs the cumulative phase compensation term: Define sampling level frequency offset for: ; Construct a continuous cumulative phase compensation term by recursively accumulating it point by point: ; ; In the formula, The initial value for phase compensation at the initial sampling time. This represents the frequency offset at the initial moment. For the first The cumulative phase compensation value at each sampling time. For the first The cumulative phase compensation value at each sampling time; It is obtained by recursively accumulating the frequency offset point by point; during the phase compensation process, Phase continuity or unwrapping is performed to maintain the continuity of compensated phase changes between adjacent sampling points and avoid... Periodic jumps cause phase correction errors; the continuous cumulative phase compensation term is used to characterize the time-varying additional phase of the target line spectrum relative to the reference frequency. When used for complex exponential phase correction, a continuous phase sequence without modulus is used, and there is no need to perform phase unwinding processing on the compensation phase.

[0017] In step S6, the cumulative phase compensation term is used to adjust the narrowband complex signal. Phase correction is performed to obtain the compensated signal. : ; In the formula, The imaginary unit; The phase correction is used to pull the target weak line spectrum that has drifted along time back to the vicinity of the reference frequency, so that the line spectrum phase at different time periods satisfies the long-term coherent accumulation condition. For the compensated signal Perform a long-time Fourier analysis, the time range of which covers the compensated signal. The complete sequence of observed data, corresponding to the discrete-time index is Finally, the long-term coherent cumulative spectrum was obtained. Includes: the compensated signal Apply a long-term analysis window ; For the windowed signal conduct Point Fourier transform, where, , The long-term coherent cumulative spectrum is obtained by zero-padding: ; In the formula, This represents the number of Fourier transform points (frequency sampling points) after zero-padding. For the first Discrete frequency sampling points, This is the lower bound for the frequency search. This is the upper limit of the frequency search. For long-term analysis window functions; The long-time Fourier analysis is used to concentrate the target line spectrum energy after frequency trajectory compensation to the vicinity of the reference frequency. The zero-padding is used to improve the accuracy of the peak position reading. The long-time analysis window is used to reduce the impact of sidelobe leakage on the observation of weak line spectrum peaks.

[0018] Furthermore, the input to this method includes a received signal. Candidate frequency band Analysis window length Section shift Frequency step size The output includes segment-level frequency trajectories. Sampling-level frequency trajectory Compensated signal and long-term coherent cumulative spectrum .

[0019] Furthermore, this method is applicable to passive sonar data processing in single hydrophones, small-sized underwater sonar platforms equipped with hydrophones, or underwater acoustic observation systems. The method is used when the target line spectrum still has a searchable continuous structure in the time-frequency plot or short-time spectrum, thereby compensating for the spectral peak broadening caused by Doppler frequency drift with low computational complexity.

[0020] Another object of the present invention is to provide a long-time coherent accumulation system for motion line spectra based on matched frequency trajectory estimation. This system is used to execute the aforementioned long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation. The system includes: The narrowband complex signal extraction module is used to perform analytical processing on the received signal, determine the candidate frequency band based on the a priori frequency of the target line spectrum, the short-time spectrum or the spectral peak observation results in the LOFAR plot, and extract the narrowband complex signal within the candidate frequency band. The segmentation and candidate frequency set establishment module is used to perform short-time segmentation on the narrowband complex signal, determine the analysis window length based on the condition that the target line spectrum is approximately stable within a single time period, determine the segment shift based on the condition that the frequency trajectory of adjacent time periods is continuously observed, and establish a discrete candidate frequency set within the candidate frequency band. The matching response matrix construction module is used to calculate the complex exponential matching response between each time period and each candidate frequency, and to normalize the matching response within each time period to form a piecewise-frequency matching response matrix. The segment-level frequency trajectory estimation module is used to select candidate frequencies according to the normalized matching response maximum criterion in each time period to obtain the initial segment-level frequency trajectory, and to perform continuous processing on the initial segment-level frequency trajectory according to the frequency change continuity criterion of adjacent time periods to obtain the corrected segment-level frequency trajectory. The cumulative phase compensation term construction module is used to interpolate the corrected segment-level frequency trajectory into a sample-level frequency trajectory, construct a cumulative phase compensation term based on the offset of the sample-level frequency trajectory relative to the reference frequency, and perform phase continuity processing on the cumulative phase compensation term. The long-time coherent cumulative spectrum output module is used to perform phase correction on the narrowband complex signal using the cumulative phase compensation term, and to perform windowing and long-time Fourier analysis on the corrected signal to obtain the long-time coherent cumulative spectrum. The system combines segment-by-segment maximum matching frequency trajectory estimation with sampling-level cumulative phase compensation to achieve motion line spectrum frequency drift compensation and long-term coherent accumulation without performing high-dimensional search of motion parameters.

[0021] Combining all the above technical solutions, the beneficial effects of this invention are as follows: First, this invention addresses the problems of frequency drift caused by Doppler shift in the line spectrum of moving targets and peak broadening in long-term spectral analysis in single-hydrophone received data. It first analyzes the received signal and selects candidate frequency bands for weak line spectra. Then, it segments the narrow-band complex signal within the candidate frequency bands into short-time segments, constructs candidate frequency sets within each segment, and calculates the continuous wave matching response. After normalization, it extracts the segment-level frequency trajectory according to the segment-by-segment maximum matching criterion. Subsequently, it performs smooth interpolation on the segment-level frequency trajectory to obtain the sampling-level frequency trajectory. Based on its offset relative to the reference frequency, it constructs a phase correction term to compensate the phase of the narrow-band complex signal and outputs the compensated long-term coherent cumulative spectrum. This method does not require high-dimensional searches in the space of motion parameters such as velocity, acceleration, nearest passing distance, or nearest passing time. It can achieve energy focusing of weak line spectra with low computational complexity while maintaining the searchable time-frequency continuity of the target line spectrum trajectory.

[0022] Secondly, the long-term coherent accumulation method for motion line spectra of this invention transforms the long-term focusing problem of weak line spectra of moving targets into a short-term frequency matching problem within candidate frequency bands. It directly extracts frequency trajectory points using a segment-by-segment maximum matching criterion and recovers the long-term coherent accumulation gain through continuous interpolation and cumulative phase compensation. Compared to methods relying on motion parameter space search, this invention does not require prior accurate knowledge of motion parameters such as target velocity, distance, closest passing time, or acceleration. Compared to complex state recursion methods, this invention does not require constructing a transition probability model or performing global path backtracking; the main calculations are concentrated on constructing the short-term frequency matching response matrix and selecting the segment-by-segment maximum value, featuring well-defined parameters, simple implementation, and low computational complexity.

[0023] This invention transforms the problem of compensating for weak line spectra of moving targets into a short-time frequency matching and piecewise maximum selection problem. It can rapidly obtain the frequency trajectory under the condition that the target line spectrum has a certain time-frequency continuity, and construct phase compensation to complete long-time coherent accumulation. Furthermore, it eliminates the need for searching in a high-dimensional motion parameter space, reducing computational complexity and parameter tuning difficulty. Compared to direct long-term Fourier analysis, this invention can reduce the spectral peak broadening caused by Doppler frequency drift of the moving target. Compared to dynamic programming, particle filtering, or high-dimensional parameter search methods, this invention has a simpler structure and lower computational cost.

[0024] Third, this invention obtains segment-level frequency trajectories by analyzing and processing the received signal and performing short-time segmented frequency matching within the candidate frequency band. Phase compensation is then performed based on these trajectories to achieve long-term coherent accumulation of the weak line spectrum of moving targets. This method can improve the energy focusing capability of the moving target line spectrum under single hydrophone conditions, enhance moving target detection performance, and improve spectral feature stability. It has good engineering application value and can be used in underwater target detection and identification systems. Since it does not depend on motion parameters such as target velocity, distance, and closest passing time, this invention can be directly applied to existing passive sonar signal processing workflows, exhibiting strong engineering deployability.

[0025] This invention transforms the long-term coherent accumulation problem of a moving target line spectrum into a short-time frequency matching and segment-level trajectory estimation problem within a candidate frequency band. It obtains the frequency trajectory through segment-by-segment frequency selection and constructs a phase compensation term based on this trajectory to achieve long-term coherent accumulation. Compared to methods that rely on motion parameter estimation, this invention does not require the introduction of external parameters such as velocity, distance, or the closest passing time. Compared to methods based on complex state modeling, this invention constructs the frequency trajectory solely based on the short-time matching results, resulting in a simple computational structure. This invention reduces parameter dependence while achieving coherent focusing of the energy of weak moving line spectra, improving peak concentration and peak gain under long-term observation conditions.

[0026] This invention addresses the problem of spectral peak broadening and energy dispersion in long-term observations of weak line spectra of moving targets under Doppler frequency shift. By constructing a short-time matched response within a candidate frequency band and extracting segment-level frequency trajectories, the frequency drift is represented by discrete trajectories. Long-term coherent accumulation is then achieved through phase compensation, thereby improving the problem of spectral energy diffusion under motion conditions using traditional direct Fourier transform. Even when the target's motion parameters are unknown or difficult to obtain accurately, this invention can still achieve stable frequency trajectory extraction and coherent accumulation processing, improving the detectability of weak line spectra.

[0027] Existing technologies typically employ motion parameter modeling-based methods for frequency compensation, or use segmented local frequency estimation methods to replace trajectory modeling. This invention does not rely on motion parameter modeling, nor does it use independent segmented frequency estimation to replace the overall trajectory. Instead, it constructs segment-level frequency trajectories based on short-time frequency matching and achieves long-term coherent accumulation through trajectory-driven phase compensation, thus breaking through the traditional implementation methods that rely on motion parameters or ignore trajectory consistency. Attached Figure Description

[0028] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the disclosure of this invention and, together with the description, serve to explain the principles of the disclosure of this invention. Figure 1 This is a flowchart of the weak line spectrum long-time coherent accumulation method based on greedy maximum matching frequency trajectory estimation provided in the embodiments of the present invention; Figure 2 This is a schematic diagram of the geometric relationship of uniform linear motion between an underwater moving target and a single hydrophone provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of frequency trajectory estimation under a 10dB signal-to-noise ratio condition provided in an embodiment of the present invention; wherein, (a) is a time-frequency diagram of frequency trajectory estimation, and (b) is a comparison diagram of frequency estimation value and true value; Figure 4 This is a schematic diagram of the spectral processing results under a 10dB signal-to-noise ratio condition provided in the embodiments of the present invention; wherein, (a) is the spectral processing result diagram of the PRPFT method, (b) is the spectral processing result diagram of the LTCILSD method, and (c) is the spectral processing result diagram of the present invention. Figure 5 This is a schematic diagram of frequency trajectory estimation under a 0dB signal-to-noise ratio condition provided in an embodiment of the present invention; wherein, (a) is a time-frequency diagram of frequency trajectory estimation, and (b) is a comparison diagram of frequency estimation value and true value; Figure 6 This is a schematic diagram of the spectral processing results under the 0dB signal-to-noise ratio condition provided in the embodiments of the present invention; wherein, (a) is the spectral processing result diagram of the PRPFT method, (b) is the spectral processing result diagram of the LTCILSD method, and (c) is the spectral processing result diagram of the present invention. Figure 7 This is a schematic diagram of frequency trajectory estimation under a motion speed of 0 m / s provided in an embodiment of the present invention; wherein, (a) is a time-frequency diagram of frequency trajectory estimation, and (b) is a comparison diagram of frequency estimation value and true value; Figure 8 This is a schematic diagram of the line spectrum enhancement results under the motion velocity condition of 0 m / s provided in the embodiment of the present invention; wherein, (a) is the spectrum processing result diagram of the PRPFT method, (b) is the spectrum processing result diagram of the LTCILSD method, and (c) is the spectrum processing result diagram of the present invention. Figure 9 This is a schematic diagram of frequency trajectory estimation under a motion speed of 5 m / s provided in an embodiment of the present invention; wherein, (a) is a time-frequency diagram of frequency trajectory estimation, and (b) is a comparison diagram of frequency estimation value and true value; Figure 10 This is a schematic diagram of the line spectrum enhancement results under the motion speed condition of 5 m / s provided in the embodiment of the present invention; wherein, (a) is the spectrum processing result diagram of the PRPFT method, (b) is the spectrum processing result diagram of the LTCILSD method, and (c) is the spectrum processing result diagram of the present invention. Figure 11 This is a schematic diagram of frequency trajectory estimation under a motion speed of 10 m / s provided in the embodiment of the present invention; wherein, (a) is a time-frequency diagram of frequency trajectory estimation, and (b) is a comparison diagram of frequency estimation value and true value; Figure 12This is a schematic diagram of the line spectrum enhancement results under the motion speed condition of 10 m / s provided in the embodiment of the present invention; wherein, (a) is the spectrum processing result diagram of the PRPFT method, (b) is the spectrum processing result diagram of the LTCILSD method, and (c) is the spectrum processing result diagram of the present invention. Detailed Implementation

[0029] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Any equivalent substitutions or changes made based on the technical concept of the present invention to the candidate frequency band determination method, matching response calculation method, normalization method, segment-by-segment maximum selection strategy, trajectory interpolation method, or compensation spectrum output method should fall within the protection scope of the present invention.

[0030] The performance of this invention relies on the searchability of the target line spectrum trajectory in LOFAR. When the received signal-to-noise ratio (SNR) is extremely low, the target trajectory may be masked by background noise ridges or local random peaks, leading to a decrease in frequency trajectory search accuracy and further affecting phase compensation and coherent accumulation effects. Therefore, this invention is applicable to scenarios with conventional SNR where the target line spectrum still has a certain time-frequency continuity. Its focus is on improving the Doppler broadening and energy dispersion problems of moving target line spectra, rather than solving the blind detection problem under extremely low SNR conditions.

[0031] This invention addresses the problem of long-term spectral peak broadening caused by Doppler frequency drift in the line spectrum of moving targets. It combines candidate frequency band constraints, piecewise frequency matching response matrices, piecewise maximum matching frequency trajectory estimation, moving median continuity, sampling-level cumulative phase compensation, and long-term coherent spectrum output into a low-complexity processing flow. This flow eliminates the need for searching high-dimensional motion parameters such as velocity, acceleration, nearest pass distance, and nearest pass time, and can rapidly complete frequency drift compensation and line spectrum energy focusing even when the target line spectrum trajectory has a searchable continuous structure.

[0032] Example 1, such as Figure 1 As shown, the long-term coherent accumulation method for motion line spectra based on matched frequency trajectory estimation provided in this embodiment of the invention includes the following steps: S1. Perform analytical processing on the received signal, determine the candidate frequency band based on the a priori frequency of the target line spectrum, the short-time spectrum or the spectral peak observation results in the LOFAR plot, and extract the narrowband complex signal within the candidate frequency band. Let the discrete real-valued signal received by the single hydrophone be... The sampling frequency is The signal length is In one implementation, the candidate frequency band is determined as follows: first, the received signal... x [ n Perform a short-time Fourier transform to obtain the LOFAR plot or short-time power spectrum; then search for continuously occurring narrow-band energy ridges or spectral peak elevation regions within the preset monitoring frequency band to obtain the initial value of the target line spectrum center frequency. Further, based on the maximum possible relative radial velocity between the target and the receiver... To estimate the Doppler frequency shift range, the upper and lower limits of the candidate frequency band can be taken as follows: ; ; In the formula, , The speed of sound in water, This serves as a guard bandwidth to cover frequency estimation errors, environmental disturbances, and spectral peak broadening. If a target velocity prior is lacking, it can be determined based on the lowest and highest frequencies of the continuous spectral peak region in the LOFAR plot. and And extend the protection bandwidth to both sides .

[0033] Identify candidate frequency bands for the target weak line spectrum Then, the center of the candidate frequency band is used as the reference frequency for subsequent phase compensation alignment: ; In the formula, This is the lower limit of the candidate frequency band. This represents the upper limit of the candidate frequency band. right Hilbert analysis and bandpass filtering are performed to obtain narrowband complex signals within the candidate frequency band. This step limits the subsequent search to the local frequency region where the target weak line spectrum may appear, reducing the impact of broadband noise and irrelevant line spectra outside the candidate frequency band on the estimation process.

[0034] In a preferred embodiment, narrowband complex signal The construction includes: firstly, using a bandpass filter For the received signal Perform filtering to preserve candidate frequency bands The signal components within are obtained Then on Performing the Hilbert transform yields the analytic signal: ; S2. Perform short-time segmentation on the narrowband complex signal, determine the analysis window length based on the condition that the target line spectrum is approximately stable within a single time period, determine the segment shift based on the condition that the frequency trajectory of adjacent time periods is continuously observed, and establish a discrete candidate frequency set within the candidate frequency band. Short-time segmentation of the narrowband complex signal includes: using a length of Hanning Window and segment shift For narrowband complex signals Perform short-time segmentation, the first The segment signal is represented as: ; In the formula, It is a discrete-time sampling sequence of a narrowband complex signal. This is a discrete-time index within a segment. To analyze the window length, The number of segments, For segment shift, analysis window length Based on the condition that the target line spectrum is approximately stable within a single time period, the maximum frequency change of the target line spectrum within a single segment is determined so that it does not exceed the preset frequency tolerance error; segment shift The frequency change between the center times of adjacent time periods is determined based on the condition of continuous observation of frequency trajectories between adjacent time periods, so that the frequency change between adjacent time periods does not exceed the preset continuity threshold. Analysis window length The selection of the target line spectrum allows it to be approximated as a stable single-frequency component within a single time period; segment shift Can be less than or equal to This allows for overlapping or continuous short-term observations.

[0035] The analysis window length Based on the requirement that the target line spectrum is approximately stable within a single segment, the maximum frequency variation within a single segment is determined to be no more than the preset frequency tolerance. ,Right now: ; In the formula, This serves as the upper bound for estimating the rate of change of the target line spectrum frequency. It can be taken as the frequency search step size. Or analyze window frequency resolution Part of For analysis window duration.

[0036] The segment shift Based on the requirement of continuous observation of frequency trajectories in adjacent time periods, the frequency change between the center times of adjacent segments is determined to ensure that it does not exceed a preset continuity threshold. ,Right now: ; In the formula, Based on candidate frequency step size Or determine the maximum allowable inter-segment drift of the target line spectrum.

[0037] In candidate frequency band Inner frequency step size Establish a candidate frequency set: ; In the formula, For the first Candidate frequency points, This is the starting frequency of the candidate frequency band. The index of the candidate frequency point. The number of candidate frequencies. Frequency step size The frequency accuracy of the line spectrum to be estimated, the frequency resolution of the analysis window, and the computing power of the processor are determined.

[0038] S3. Calculate the complex exponential matching response between each time period and each candidate frequency, and normalize the matching response within each time period to form a piecewise-frequency matching response matrix. For each time period and candidate frequency Calculate segmented signals With this candidate frequency Matching responses between corresponding complex exponential basis functions: ; In the formula, For the first Windowed segmented signals for a time period The imaginary unit, For candidate frequencies, The sampling frequency; Used to characterize the Within a certain time period, the target line spectrum is located at the candidate frequency. Degree of local matching in the vicinity; The larger the value, the more significant the number. Segment signal at candidate frequency The higher the probability of a single-frequency line spectrum component appearing nearby.

[0039] Because target radiation intensity, propagation loss, platform noise, and environmental background may vary over time, the overall energy level may differ significantly across different time periods. To avoid a few high-energy time periods dominating subsequent frequency trajectory estimation, this invention normalizes the matching response within each time period: ; In the formula, For the first Matching responses for all candidate frequencies within a given time period The maximum value is used as the benchmark for matching response normalization within that time period; Based on the total time period and candidate frequency This forms a piecewise frequency-matched response matrix.

[0040] The normalization process ensures that the frequency selection within each time period is primarily determined by the relative matching strength between candidate frequencies, rather than by the overall energy difference across different time periods, thereby improving the stability of subsequent segment-by-segment maximum matching frequency trajectory estimation.

[0041] S4. In each time period, candidate frequencies are selected according to the normalized matching response maximum criterion to obtain the initial segment-level frequency trajectory. The initial segment-level frequency trajectory is then processed to be continuous according to the frequency change continuity criterion between adjacent time periods to obtain the corrected segment-level frequency trajectory. In the piecewise frequency-matched response matrix In this study, a greedy maximum matching criterion is used for frequency trajectory estimation. For the ... For each time period, directly select the candidate frequency index with the largest normalized matching response: ; In the formula, For the first Normalized matching responses for all candidate frequencies within a given time period The maximum value, For the first The initial trajectory frequency points estimated over a time period For index Corresponding candidate frequencies; By using the normalized matching response maximization criterion, the frequency trajectory point is directly determined from the local matching response peak within each time period, thus avoiding high-dimensional search in the motion parameter space; the motion parameters include at least one of velocity, acceleration, nearest passing distance, and nearest passing time.

[0042] Then, the initial segment-level frequency trajectory is constructed from the initial frequency trajectory points of all time periods. This step does not perform motion parameter inversion, does not search in the parameter space of velocity, acceleration, most recent passing time, or most recent passing distance, and does not construct a dynamic programming cumulative objective function and backtracking matrix. Instead, it directly obtains the frequency points within each time period using the local maximum matching results. This significantly reduces the complexity of trajectory estimation and is suitable for execution on single-channel underwater acoustic platforms or low-power processing units.

[0043] S5. Interpolate the corrected segment-level frequency trajectory into a sampling-level frequency trajectory, construct a cumulative phase compensation term based on the offset of the sampling-level frequency trajectory relative to the reference frequency, and perform phase continuity processing on the cumulative phase compensation term. Considering the potential presence of random noise peaks, local interference lines, or missing short-time spectral peaks in the measured data, this invention performs continuity processing on adjacent effective trajectory points based on the frequency trajectory continuity criterion, resulting in a corrected segment-level frequency trajectory. This step reduces the impact of individual noise peaks on the phase compensation results while maintaining low complexity.

[0044] Since the segment-by-segment maximum matching frequency selection is performed independently within each time period, isolated frequency jumps may occur in the initial segment-level frequency trajectory when random noise peaks, local narrowband interference, or short-time spectral peaks are missing within a certain time period. To suppress such isolated outliers while maintaining low complexity, this invention employs moving median filtering to perform continuous processing on the initial segment-level frequency trajectory. Let the initial segment-level frequency trajectory obtained by segment-by-segment maximum matching be... The length of the moving window is The corrected segment-level frequency trajectory is then: ; In the formula, For the median operation, For the first Initial trajectory frequency points over a time period For the first Initial trajectory frequency points over a time period For the first Initial trajectory frequency points over a time period For the first Initial trajectory frequency points over a time period This represents the total number of time periods.

[0045] For the first and last time periods, the original estimated value is maintained, the boundary is copied, or a truncated window is formed by adjacent available trajectory points. The moving median filter is used to suppress isolated frequency jumps caused by random noise peaks, local interference line spectra, or missing short-time spectral peaks.

[0046] Through the above-mentioned continuous moving median processing, when a certain frequency point deviates due to noise peaks, the point can be constrained and corrected by adjacent frequency points; when multiple adjacent time periods show consistent changes, the median filter will not force a pullback, thus preserving the true slow frequency drift trend caused by the target motion.

[0047] S6. The phase correction of the narrowband complex signal is performed using the cumulative phase compensation term, and the corrected signal is windowed and subjected to long-term Fourier analysis to obtain the long-term coherent cumulative spectrum. By combining the segment-by-segment maximum matching frequency trajectory estimation with the sampling-level cumulative phase compensation, the motion line spectrum frequency drift is compensated and long-term coherent accumulation is performed without performing a high-dimensional search of motion parameters. Segment-level frequency trajectory Defined at the center time of each time period To achieve sample-by-sample phase compensation, it is necessary to interpolate it as a sample-level frequency trajectory: ; In the formula, For discrete-time sampling index, Indicates by arrive The interpolation mapping relationship, It is a linear interpolation operator; Relative to reference frequency The sampling level frequency offset is: ; Construct a continuous cumulative phase compensation term by recursively accumulating it point by point: ; ; In the formula, The initial value for phase compensation at the initial sampling time. This represents the frequency offset at the initial moment. For the first The cumulative phase compensation value at each sampling time. For the first The cumulative phase compensation value at each sampling time; It is obtained by recursively accumulating the frequency offset point by point; during the phase compensation process, Phase continuity or unwrapping is performed to maintain the continuity of compensated phase changes between adjacent sampling points and avoid... Periodic jumps cause phase correction errors; the continuously accumulated phase compensation term is used to characterize the target line spectrum relative to the reference frequency. The time-varying additional phase, when used for complex exponential phase correction, adopts a continuous phase sequence without modulo taking, eliminating the need for phase unwinding processing of the compensation phase.

[0048] Using this cumulative phase compensation term for narrowband complex signals Perform phase correction point by point to obtain the compensated signal: ; Through the phase correction described above, the target line spectrum that has drifted along time is pulled back to the vicinity of the reference frequency, so that the phase of the target line spectrum in different time periods meets the long-term coherent accumulation condition, thereby reducing the peak broadening in direct long-time Fourier analysis.

[0049] Long-term coherent cumulative spectrum output.

[0050] For the compensated signal Perform a long-time Fourier analysis, the time range of which covers the compensated signal. The complete sequence of observed data, corresponding to the discrete-time index is Finally, the long-term coherent cumulative spectrum was obtained. Includes: the compensated signal Apply a long-term analysis window ; For the windowed signal conduct Point Fourier transform, where, , The long-term coherent cumulative spectrum is obtained by zero-padding: ; In the formula, This represents the number of Fourier transform points (frequency sampling points) after zero-padding. For the first Discrete frequency sampling points, This is the lower bound for the frequency search. This is the upper limit of the frequency search. For long-term analysis window functions; The long-time Fourier analysis is used to concentrate the target line spectrum energy after frequency trajectory compensation to the vicinity of the reference frequency. The zero-padding is used to improve the accuracy of the peak position reading. The long-time analysis window is used to reduce the impact of sidelobe leakage on the observation of weak line spectrum peaks.

[0051] When the frequency trajectory estimation results can reflect the actual frequency changes of the target weak line spectrum, the compensated target line spectrum will be... This results in narrower and more prominent spectral peaks, thereby improving the observability and detection reliability of weak line spectra of underwater moving targets.

[0052] Example 2, the motion line spectrum long-time coherent accumulation system based on matched frequency trajectory estimation provided in this embodiment of the invention includes: The narrowband complex signal extraction module is used to perform analytical processing on the received signal, determine the candidate frequency band based on the a priori frequency of the target line spectrum, the short-time spectrum or the spectral peak observation results in the LOFAR plot, and extract the narrowband complex signal within the candidate frequency band. The segmentation and candidate frequency set establishment module is used to perform short-time segmentation on the narrowband complex signal, determine the analysis window length based on the condition that the target line spectrum is approximately stable within a single time period, determine the segment shift based on the condition that the frequency trajectory of adjacent time periods is continuously observed, and establish a discrete candidate frequency set within the candidate frequency band. The matching response matrix construction module is used to calculate the complex exponential matching response between each time period and each candidate frequency, and to normalize the matching response within each time period to form a piecewise-frequency matching response matrix. The segment-level frequency trajectory estimation module is used to select candidate frequencies according to the normalized matching response maximum criterion in each time period to obtain the initial segment-level frequency trajectory, and to perform continuous processing on the initial segment-level frequency trajectory according to the frequency change continuity criterion of adjacent time periods to obtain the corrected segment-level frequency trajectory. The cumulative phase compensation term construction module is used to interpolate the corrected segment-level frequency trajectory into a sample-level frequency trajectory, construct a cumulative phase compensation term based on the offset of the sample-level frequency trajectory relative to the reference frequency, and perform phase continuity processing on the cumulative phase compensation term. The long-time coherent cumulative spectrum output module is used to perform phase correction on the narrowband complex signal using the cumulative phase compensation term, and to perform windowing and long-time Fourier analysis on the corrected signal to obtain the long-time coherent cumulative spectrum.

[0053] The motion line spectrum long-time coherent accumulation system based on matched frequency trajectory estimation combines segment-by-segment maximum matched frequency trajectory estimation with sampling-level cumulative phase compensation to achieve motion line spectrum frequency drift compensation and long-time coherent accumulation without performing high-dimensional search of motion parameters.

[0054] To further demonstrate the positive effects of the above embodiments, the present invention conducts the following experiments based on the above technical solutions.

[0055] Experiment 1: Simulation Data Processing; This embodiment uses a simulation scenario of a single hydrophone receiving the radiation spectrum of a moving target. The hydrophone is fixed near the origin of the coordinate system, and the target moves at a constant speed along a straight line through the area near the receiver. The target radiates a narrow-band single-frequency line spectrum. Due to the change in distance and radial velocity between the target and the receiver over time, the frequency of the line spectrum at the receiving end no longer remains constant, but rather exhibits a slow drift during the observation period. Figure 2 The geometric relationship of this motion is shown.

[0056] In specific simulations, the sampling frequency The frequency was set to 1000Hz, the target radiation spectrum frequency was 200Hz, and the observation duration was 300s. The target moved in a uniform linear motion at a speed of 5m / s, with the closest passing distance being 500m. Simulations were performed under two signal-to-noise ratio (SNR) conditions: 10dB and 0dB. 10dB was used to characterize a higher SNR scenario where the target spectrum was relatively clear and the trajectory characteristics were relatively stable; 0dB was used to characterize a typical low SNR scenario where the target spectrum was significantly affected by background noise, but still retained a certain degree of time-frequency continuity and searchability in LOFAR.

[0057] First, candidate frequency bands are determined based on the possible Doppler frequency shift range of the target line spectrum. and calculate the reference frequency. The original received signal is subjected to Hilbert transform, and then narrowband complex signals within the candidate frequency band are extracted by bandpass filtering. .

[0058] Then, considering both the accuracy and computational efficiency of frequency trajectory estimation, the frequency tolerance error is determined. Set to 0.005Hz, preset continuity threshold. Set to 0.001Hz, using the analysis window length. and segment shift right By segmenting the data to meet tolerance requirements, it can be approximated that the frequency within each segment is constant and the frequency is continuous between adjacent segments. Segment signal is Within each analysis window, since the target frequency changes slowly, this segment of the target line spectrum can be approximated as a single-frequency component.

[0059] To estimate the frequency trajectory more accurately, a frequency search step size is selected. Establish a frequency set within the candidate frequency band. Calculate the matched response for the i-th signal segment and the i-th candidate frequency. And normalize according to the maximum value of each segment to obtain .Depend on The resulting piecewise frequency-matched response matrix reflects the frequency distribution of the target line spectrum on a short time scale.

[0060] Unlike global recursive trajectory search, this embodiment directly selects within each time period. The highest frequency is taken as the frequency estimation result for this segment, that is: ; After obtaining all segmented frequency points, linear interpolation is used to obtain the continuous segment-level frequency trajectory. . Figure 3 Figures (a) and (b) in the text and Figure 5Figures (a) and (b) show the relationship between the frequency trajectory estimation results and the true values ​​under signal-to-noise ratio conditions of 10 dB and 0 dB, respectively.

[0061] Will The sampling-level frequency trajectory is interpolated based on the center time of each time period. Calculate its offset relative to the reference frequency. Then, the compensated phase is obtained by accumulating the results. . use Phase compensation is performed on narrowband signals.

[0062] Finally, the compensated signal Long-term Fourier analysis was performed to obtain the long-term coherent cumulative spectrum. . Figure 4 Figures (a)-(c) in the middle and Figure 6 Figures (a) to (c) show the comparison between the original periodogram, PRPFT, LTCILSD and the compensated spectrum output of the present invention under 10dB and 0dB signal-to-noise ratio conditions, respectively.

[0063] As can be seen from the processing results, the target line spectrum energy is broadened along the frequency direction without compensation, and the spectral peaks are not concentrated enough. After processing by the method of this invention, the dispersed energy is refocused to the vicinity of the reference frequency, and the spectral peaks become narrower and more prominent.

[0064] Under a signal-to-noise ratio of 10 dB, the target line spectrum exhibits a relatively clear trajectory structure in the short-time spectrum. This invention can accurately estimate the frequency along the vicinity of the true trajectory, and the spectral peak is significantly enhanced after compensation. Under a signal-to-noise ratio of 0 dB, background noise increases, and local trajectory estimation fluctuations increase. However, while the target trajectory still maintains a certain degree of time-frequency continuity, this invention can still obtain a relatively stable main peak position and a certain spectral focusing effect.

[0065] Experiment 2: Processing under different target velocities; To illustrate the adaptability of this invention to different Doppler variation intensities, this embodiment sets the target velocities to 0 m / s, 5 m / s, and 10 m / s under the same observation duration of 300 s and signal-to-noise ratio of 10 dB. The higher the target velocity, the more pronounced the radial velocity change, the stronger the frequency drift of the receiver's line spectrum, and the more severe the peak broadening in direct long-term Fourier analysis.

[0066] For each target velocity, the steps of this invention are performed as follows: analytical and candidate frequency band extraction, segmented matching response calculation, segmented maximum matching frequency selection, sampling-level trajectory interpolation, phase compensation, and long-time coherent cumulative spectrum output.

[0067] Figure 7 Figures (a) and (b) in the text. Figure 8Figures (a), (b), and (c) in the text. Figure 9 Figures (a) and (b) in the text. Figure 10 Figures (a), (b), and (c) in the text. Figure 11 Figures (a) and (b) in the text. Figure 12 Figures (a), (b), and (c) show the processing results of this invention under different velocity conditions. It can be observed that when the target velocity is low, the target frequency drift is weak, and the traditional periodogram can achieve a certain energy boost, but the spectral peak may still exhibit slight broadening. This invention, by estimating the frequency trajectory and performing phase compensation, can further compress the spectral peak width.

[0068] As the target velocity increases, the target line spectrum in the traditional periodogram method gradually evolves from a relatively concentrated energy rise to a significant peak broadening and energy dispersion, indicating that Doppler time-varying significantly weakens the coherent accumulation effect of long-term Fourier integrals. PRPFT and LTCILSD can achieve certain line spectrum enhancement under certain velocity conditions, but their performance is greatly affected by parameter search and the intensity of Doppler variation. This invention, by estimating the target frequency trajectory segment by segment and performing phase compensation along the estimated trajectory, can effectively refocus the energy of the time-varying line spectrum near the target frequency. Therefore, this invention exhibits good stability and adaptability under different motion velocity conditions, verifying its effectiveness in detecting weak line spectra of moving targets under long-term observation conditions.

[0069] Table 1. Peak gain obtained by the present invention under different velocity conditions.

[0070] Table 1 shows the spectral peak gain obtained by this invention under different speed conditions. The spectral peak gain is calculated as the ratio of the peak value of the line spectrum to the average value of the surrounding noise in decibels. It can be seen that under stationary conditions, there is no Doppler frequency shift, and the performance of each method is relatively excellent. As the speed increases, the Doppler frequency shift destroys the coherent integral gain, and the advantages of this invention gradually become apparent. The spectral peak gain is significantly better than the original spectrum and the other two high-dimensional parameter search algorithms.

[0071] This embodiment illustrates that the present invention is particularly suitable for scenarios where frequency drift caused by target motion has affected long-term spectrum focusing, but the target's short-term line spectrum trajectory can still be searched within the candidate frequency band. In such scenarios, the present invention can achieve good frequency drift compensation results with low complexity.

[0072] As demonstrated by the above embodiments, this invention can rapidly estimate the weak line spectrum frequency trajectory of underwater moving targets based on short-time frequency matching results within candidate frequency bands using a greedy maximum matching criterion, and achieve long-term coherent accumulation through sampling-level phase compensation. Compared with direct long-time spectrum analysis, this invention can mitigate the spectral peak broadening caused by Doppler time-varying characteristics; compared with high-dimensional parameter search or complex state recursion methods, this invention has a simple structure, fewer parameters, and lower computational cost, making it suitable for rapid weak line spectrum enhancement in resource-constrained underwater acoustic platforms.

[0073] The above description is only a preferred 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 long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation, characterized in that, The method includes the following steps: S1. Perform analytical processing on the received signal, determine the candidate frequency band based on the a priori frequency of the target line spectrum, the short-time spectrum or the spectral peak observation results in the LOFAR plot, and extract the narrowband complex signal within the candidate frequency band. S2. Perform short-time segmentation on the narrowband complex signal, determine the analysis window length based on the condition that the target line spectrum is approximately stable within a single time period, determine the segment shift based on the condition that the frequency trajectory of adjacent time periods is continuously observed, and establish a discrete candidate frequency set within the candidate frequency band. S3. Calculate the complex exponential matching response between each time period and each candidate frequency, and normalize the matching response within each time period to form a piecewise-frequency matching response matrix. S4. In each time period, candidate frequencies are selected according to the normalized matching response maximum criterion to obtain the initial segment-level frequency trajectory. The initial segment-level frequency trajectory is then processed to be continuous according to the frequency change continuity criterion between adjacent time periods to obtain the corrected segment-level frequency trajectory. S5. Interpolate the corrected segment-level frequency trajectory into a sampling-level frequency trajectory, construct a cumulative phase compensation term based on the offset of the sampling-level frequency trajectory relative to the reference frequency, and perform phase continuity processing on the cumulative phase compensation term. S6. The phase correction of the narrowband complex signal is performed using the cumulative phase compensation term, and the corrected signal is windowed and subjected to long-term Fourier analysis to obtain the long-term coherent cumulative spectrum. By combining the segment-by-segment maximum matched frequency trajectory estimation with the sampling-level cumulative phase compensation, the frequency drift of the motion line spectrum is compensated and long-term coherent accumulation is performed without performing a high-dimensional search of motion parameters.

2. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to claim 1, characterized in that, In step S1, the candidate frequency band is denoted as The reference frequency of the candidate frequency band Determine as follows: ； In the formula, This is the lower limit of the candidate frequency band. This represents the upper limit of the candidate frequency band. The candidate frequency band covers the frequency drift range of the target weak line spectrum caused by relative motion during the observation time; The analytical processing involves Hilbert transform and bandpass filtering to obtain a narrowband complex signal within the candidate frequency band. ,in, , To process the number of sampling points for a segment.

3. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to claim 1, characterized in that, In step S2, short-time segmentation of the narrowband complex signal includes: using a segment of length... Analysis window and segment shift For narrowband complex signals Divide into segments, the first segment signal Represented as: ； In the formula, For a narrowband complex signal, the discrete-time sampling sequence is denoted by , where is the discrete-time index within the segment. To analyze the window length, The number of segments, For segment shift; Analysis window length Based on the condition that the target line spectrum is approximately stable within a single time period, the maximum frequency change of the target line spectrum within a single segment is determined so that it does not exceed the preset frequency tolerance error; segment shift The frequency change between the center times of adjacent time periods is determined based on the condition of continuous observation of frequency trajectories between adjacent time periods, so that the frequency change between adjacent time periods does not exceed the preset continuity threshold. Within the candidate frequency band, according to the frequency step size Establish a set of discrete candidate frequencies The expression is: ； In the formula, For the first Candidate frequency points, This is the starting frequency of the candidate frequency band. The index of the candidate frequency point. The number of candidate frequencies. This represents the frequency step size.

4. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to claim 3, characterized in that, In step S3, calculating the complex exponential matching response between each time period and each candidate frequency includes: The time period in the first Matching response at each candidate frequency The amplitude is determined by the inner product of the segmented signal and the complex exponential basis function corresponding to the candidate frequency, expressed as: ； In the formula, For the first Windowed segmented signals for a time period The imaginary unit, For candidate frequencies, The sampling frequency is used to characterize the first... Within a certain time period, the target line spectrum is located at the candidate frequency. Degree of local matching in the vicinity; The matching responses within each time period are normalized to obtain normalized matching responses. : ； In the formula, For the first Matching responses for all candidate frequencies within a given time period The maximum value.

5. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to claim 4, characterized in that, In step S4, the criterion for maximizing the normalized matching response is: In the Within a time period, select the response that matches the normalized response. Candidate frequency index that reaches the maximum value And the candidate frequency corresponding to the candidate frequency index is used as the initial trajectory frequency point of this segment, expressed as: ； In the formula, For the first Normalized matching responses for all candidate frequencies within a given time period The maximum value, For the first The initial trajectory frequency points estimated over a time period For index The corresponding candidate frequency.

6. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to claim 5, characterized in that, For the initial segment-level frequency trajectory A continuous processing method using moving median filtering is employed to obtain the processed segment-level frequency trajectory. For non-boundary time periods, the current time period and adjacent time periods are used. A local window is formed by several trajectory points, and the corrected segment-level frequency trajectory is determined. The expression is: ； In the formula, For the median operation, For the first Initial trajectory frequency points over a time period For the first Initial trajectory frequency points over a time period For the first Initial trajectory frequency points over a time period For the first Initial trajectory frequency points over a time period This represents the total number of time periods.

7. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to claim 6, characterized in that, In step S5, let the first The center time of the segment is Sampling time , segment-level frequency trajectory Interpolate to the sampling time to obtain the sampling-level frequency trajectory. : ； In the formula, For discrete-time sampling index, Indicates by arrive The interpolation mapping relationship, It is a linear interpolation operator; Based on the sampling-level frequency trajectory relative to the reference frequency The offset constructs the cumulative phase compensation term: Define sampling level frequency offset for: ； Construct a continuous cumulative phase compensation term by recursively accumulating it point by point: ； ； In the formula, The initial value for phase compensation at the initial sampling time. This represents the frequency offset at the initial moment. For the first The cumulative phase compensation value at each sampling time. For the first The cumulative phase compensation value at each sampling time.

8. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to claim 7, characterized in that, In step S6, the phase of the narrowband complex signal is corrected using the cumulative phase compensation term to obtain the compensated signal. : ； A long-time Fourier analysis is performed on the compensated signal, wherein the time range of the long-time Fourier analysis covers the compensated signal. The complete sequence of observed data, corresponding to the discrete-time index is Finally, the long-term coherent cumulative spectrum was obtained. : For the compensated signal Apply a long-term analysis window For the windowed signal conduct Point Fourier transform, where, , The long-term coherent cumulative spectrum is obtained by zero-padding: ； In the formula, This represents the number of points in the Fourier transform after zero-padding. For the first Discrete frequency sampling points, This is the lower bound for the frequency search. This is the upper limit of the frequency search. This is a long-term analysis window function.

9. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to any one of claims 1 to 8, characterized in that, The input to this method includes the received signal. Candidate frequency band Analysis window length Section shift Frequency step size The output includes segment-level frequency trajectories. Sampling-level frequency trajectory Compensated signal and long-term coherent cumulative spectrum .

10. The long-time coherent accumulation method for motion line spectra based on matched frequency trajectory estimation according to claim 1, characterized in that, This method is applicable to passive sonar data processing in single hydrophones, small-sized underwater sonar platforms equipped with hydrophones, or underwater acoustic observation systems; it is also applicable when the target line spectrum still has a searchable continuous structure in the time-frequency diagram or short-time spectrum.

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