A multi-cycle triangular wave clustering frequency estimation float LFM ranging method

Abstract

The present application relates to the field of radar signal processing, and particularly relates to a multi-cycle triangular wave clustering frequency estimation buoy LFM ranging method. The method comprises: transmitting a multi-cycle triangular wave modulated LFM signal, mixing the echo signal with a local reference signal to obtain a multi-cycle difference frequency signal; performing nonlinear transformation on the difference frequency signal to eliminate the sign flip effect caused by the up and down frequency of the triangular wave; performing time-frequency analysis on the nonlinear transformed signal to obtain time-frequency spectrum characteristics; using a clustering algorithm to perform clustering analysis on the time-frequency spectrum characteristics, extracting stable frequency components from the clustering results; and calculating the target distance according to the frequency components. The present application effectively solves the problems of unstable frequency estimation and enhanced spectral sidelobes under low signal-to-noise ratio conditions by multi-cycle signal accumulation, nonlinear transformation to eliminate sign flip, time-frequency analysis and clustering algorithm to extract stable frequency components, significantly improving the ranging accuracy and stability.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing, specifically to a multi-period triangular wave clustering frequency estimation buoy LFM (Linear Frequency Modulation) ranging method. Background Technology

[0002] With the increasing demand for applications such as ocean observation, maritime target positioning, intelligent shipping, and collaborative operations of marine equipment, buoy systems, as important carriers of maritime information sensing and positioning, have been widely used in marine environmental monitoring, navigation aids, platform positioning, and near-shore operational support. In these applications, the distance information between buoys and shore-based platforms, shipborne equipment, or other maritime nodes is a crucial foundation for target positioning, array coordination, area monitoring, and operational control. Therefore, researching high-precision, high-stability radio ranging technologies suitable for complex marine environments has significant engineering application value.

[0003] In LFM signal radio ranging technology, due to its advantages such as high range resolution, strong anti-interference capability, and ease of engineering implementation, LFM signals have become one of the important technical routes in the field of buoy radio ranging. Specifically, the continuous linear frequency modulation (LFM) system using triangular wave modulation transmits a continuously varying frequency LFM signal and mixes the echo or response signal with a local reference signal to obtain a difference frequency signal. Based on the correspondence between the triangular wave modulation slope and the difference frequency signal, the target distance can be estimated by inversion.

[0004] In existing technologies, the processing of LFM triangular wave radio ranging signals often employs a single-cycle difference frequency signal for Fast Fourier Transform (FFT) frequency estimation, followed by distance calculation based on the difference frequency. This method achieves good ranging results when signal quality is high and the propagation environment is stable. However, in buoy radio ranging scenarios, the received signal is often subjected to low signal-to-noise ratio or even strong disturbance conditions due to factors such as wave fluctuations, platform sway, multipath reflections, sea clutter interference, and long-distance propagation attenuation. In these conditions, the effective energy contained in the single-cycle difference frequency signal is limited, and noise significantly overwhelms the spectral peaks, easily leading to unstable frequency estimation, increased ranging errors, and in severe cases, even failure to complete effective ranging.

[0005] To improve ranging performance under low signal-to-noise ratio (SNR) conditions, using multi-period triangular wave signals for accumulation is a natural approach. Theoretically, multi-period observations can improve the equivalent SNR, thereby enhancing frequency estimation accuracy. However, in practical processing, if the single-period processing method is still used, directly splicing the difference frequency signals from multiple periods for overall FFT analysis, the long spliced ​​sequence no longer represents a single stable frequency sinusoidal signal due to the sign reversal phenomenon between the upper and lower sweep frequency bands in triangular wave modulation. Instead, it exhibits a periodic sequence with alternating frequency signs. This type of sequence is prone to significant spectral sidelobe enhancement and energy diffusion in the frequency domain, blurring the dominant frequency peak and weakening the gain that multi-period accumulation should provide, thus affecting the stability and accuracy of radio ranging results.

[0006] Furthermore, in buoy application scenarios, the dynamic environment of the sea surface will introduce echo envelope fluctuations and periodic characteristic fluctuations, making simple spectral peak detection methods more susceptible to abnormal periods and local noise, and making it difficult to fully utilize the redundant ranging information contained in the multi-period difference frequency signal.

[0007] Therefore, for LFM signal buoy radio ranging scenarios, how to design a signal processing method that can effectively utilize multi-period triangular wave signals, suppress the influence of up and down sweep frequency symbol flipping, reduce spectral sidelobe and envelope fluctuation interference, and achieve stable and high-precision frequency estimation has become an urgent technical problem to be solved in this field. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a multi-period triangular wave clustering frequency estimation buoy LFM ranging method. By performing nonlinear transformation on the multi-period echo signal to eliminate the sign flipping effect caused by the up-and-down frequency sweep of the triangular wave, and combining time-frequency analysis and clustering algorithms to extract stable frequency components, this method effectively suppresses noise and spectral sidelobe interference, improves the estimation accuracy of the difference frequency, and thus achieves high-precision and high-reliability distance measurement in low signal-to-noise ratio environments.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A multi-period triangular wave clustering frequency estimation buoy ranging method includes the following steps:

[0011] S1. Transmit a multi-cycle triangular wave modulated LFM signal, acquire the echo signal of the LFM signal, and mix the echo signal with a local reference signal to obtain a multi-cycle difference frequency signal.

[0012] S2. Perform a nonlinear transformation on the multi-cycle difference frequency signal to obtain the nonlinearly transformed signal;

[0013] S3. Perform time-frequency analysis on the nonlinearly transformed signal to obtain its time-spectrum characteristics;

[0014] S4. Perform cluster analysis on the time-spectrum features using a clustering algorithm, and extract frequency components from the clustering results;

[0015] S5. Calculate the target distance based on the frequency components.

[0016] Furthermore, in S2, the nonlinear transformation process includes:

[0017] S201. Perform full-wave rectification on the multi-cycle difference frequency signal to obtain a rectified signal;

[0018] S202. Perform envelope shaping on the rectified signal to obtain a shaped signal;

[0019] S203. Perform a square operation on the shaped signal.

[0020] Furthermore, the full-wave rectification is achieved by taking the absolute value of the multi-cycle difference frequency signal point by point.

[0021] Furthermore, the envelope shaping includes smoothing filtering, amplitude normalization, and amplitude limiting of the rectified signal.

[0022] Furthermore, the nonlinear transformation process also includes bandpass filtering of the signal after squaring.

[0023] Furthermore, in S3, the time-frequency analysis employs short-time Fourier transform, obtaining time-frequency characteristics by segmenting and windowing the nonlinearly transformed signal.

[0024] Furthermore, in S4, the clustering algorithm is the K-means clustering algorithm, and the process of extracting the frequency components includes: using the frequency points in the time-spectrum features as sample data, iteratively clustering to output cluster centers, and using the frequency corresponding to the cluster centers as the frequency components.

[0025] Furthermore, S5 specifically includes:

[0026] S501. Calculate the propagation delay of the echo signal based on the frequency components;

[0027] S502. Calculate the actual distance between the target and the radar system using the electromagnetic wave propagation speed and the propagation delay.

[0028] Furthermore, the LFM signal is a linear frequency modulation signal with a linear rising slope and a linear falling slope.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0030] (1) This invention effectively improves signal energy by transmitting multi-cycle triangular wave modulated signals and accumulating redundant information from multiple cycles. Simultaneously, by combining nonlinear transformation to eliminate sign-flipping effects, time-frequency analysis to reveal the signal's time-frequency distribution characteristics, and clustering algorithms to extract stable frequency components, it can accurately extract the target difference frequency in noisy environments, significantly reducing the variance of frequency estimation. Simulation results show that, under the same low signal-to-noise ratio conditions, the MSE of the method in this invention is significantly lower than that of the traditional single-cycle FFT method and multi-cycle FFT method, greatly improving ranging accuracy and stability.

[0031] (2) This invention completely eliminates the sign flipping effect by performing full-wave rectification, envelope shaping and squaring operations on the multi-cycle difference frequency signal, and unifies the alternating positive and negative difference frequency to the positive frequency region; combined with time-frequency analysis and clustering, it effectively suppresses the spectrum sidelobe interference, concentrates the energy in the main lobe, and obtains a clear and stable frequency peak, laying the foundation for accurate ranging.

[0032] (3) This invention uses short-time Fourier transform to obtain the distribution characteristics of signal energy in the time-frequency plane, and then uses K-means clustering algorithm to perform cluster analysis on the time-frequency characteristics to extract the most stable and prominent frequency components. This processing method not only makes full use of the time-frequency distribution information of multi-period signals, but also effectively suppresses outliers and noise interference in the time-frequency spectrum. Compared with the simple spectrum peak detection method, it shows higher robustness and adaptability in complex environments such as multipath interference and severe signal attenuation. Attached Figure Description

[0033] Figure 1 A flowchart of the multi-period triangular wave clustering frequency estimation buoy LFM ranging method provided in an embodiment of the present invention;

[0034] Figure 2 This is a schematic diagram of the time-frequency spectrum distribution of the nonlinearly transformed signal obtained when using the ranging method provided in this embodiment of the invention;

[0035] Figure 3 A graph showing the frequency component estimation results of the actual distance to the target using different methods;

[0036] Figure 4 The graph shows the performance analysis of MSE (Mean Square Error) for different methods in estimating the actual distance to the target. Detailed Implementation

[0037] 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 embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] Example

[0039] This embodiment provides a multi-period triangular wave clustering frequency estimation buoy LFM ranging method, which is applied to radar systems that transmit multi-period triangular wave modulated LFM signals to achieve high-precision and high-reliability distance measurement in low signal-to-noise ratio environments.

[0040] The radar system includes a transmitter, a receiver, and a digital signal processing module. The transmitter generates and transmits a multi-period triangular wave modulated LFM signal; the receiver receives the echo signal reflected from the target, mixes it with a local reference signal, and outputs a multi-period difference frequency signal; the digital signal processing module performs nonlinear transformation, time-frequency analysis, cluster analysis, and range calculation on the multi-period difference frequency signal, and finally outputs the actual distance between the target and the radar system.

[0041] refer to Figure 1 The ranging method provided in this embodiment is performed according to the following steps:

[0042] S1, LFM signal transmission and difference frequency signal acquisition

[0043] S101, the triangular wave signal source module at the transmitting end uses a digital waveform transmitter to generate a multi-cycle triangular wave modulated signal with linear rising and falling slopes. The multi-period triangular wave modulated signal is converted into an analog baseband signal by a digital-to-analog converter, and then sent to an RF modulator for up-conversion processing after low-pass filtering to generate an LFM signal. ,LFM signal The transmitted signal is generated after power amplification. And it is radiated out through the transmitting antenna. Multi-period triangular wave modulated signal. As a modulation source for LFM signals, setting multiple cycles can increase signal redundancy and noise immunity.

[0044] Multi-period triangular wave modulated signal It can be represented as:

[0045]

[0046]

[0047] In the formula, A single-cycle triangular wave modulated signal Translation The next A signal per cycle, For unit step function, The period number of the triangular wave. The total number of triangular wave periods. For time variables, The duration of a single-cycle triangular wave.

[0048] Single-cycle triangular wave modulated signal It can be represented as:

[0049]

[0050] In the formula, This represents the slope of the triangular wave frequency modulation.

[0051] LFM signal It can be represented as:

[0052]

[0053] In the formula, The amplitude of the LFM signal. This refers to the radio frequency carrier frequency.

[0054] Transmit signal It can be represented as:

[0055]

[0056] In the formula, To amplify power gain.

[0057] S102, Transmit signal After being reflected by the target, the echo signal is received by the receiving antenna. The received echo signal With local reference signal (i.e., LFM signal) The copy is mixed to obtain a difference frequency signal containing the target time delay information. Difference frequency signal After processing with a bandpass filter, out-of-band interference and noise are removed, retaining only the target difference frequency component to obtain a multi-cycle difference frequency signal. .

[0058] echo signal It can be represented as:

[0059]

[0060] In the formula, The propagation path attenuation coefficient, To transmit signals Time delay The following signal, This is the round-trip propagation time of the signal (i.e., the propagation delay of the echo signal). It is noise.

[0061] In radar signal processing, because subsequent processing involves normalization, the power amplification gain is typically increased. Ignore, therefore the difference frequency signal containing target time delay information It can be represented as:

[0062]

[0063] In the formula, LFM signal Time delay The signal after.

[0064] Multi-cycle difference frequency signal It can be represented as:

[0065]

[0066] In the formula, This represents the convolution operation. This represents the impulse response of a bandpass filter.

[0067] The passband range of the bandpass filter is set according to the difference frequency corresponding to the expected target distance (i.e., the difference frequency corresponding to the maximum ranging capability of the system design). In this embodiment, the filter adopts a Butterworth filter to provide a flat passband response and steep stopband attenuation, effectively suppressing multipath interference and noise.

[0068] S2, Nonlinear Transformation Processing

[0069] S201, for the multi-period difference frequency signal Full-wave rectification is performed to obtain the rectified signal. In this embodiment, full-wave rectification is achieved by taking the absolute value of the multi-cycle difference frequency signal point by point, and the rectified signal... It can be represented as:

[0070]

[0071] In the formula, It represents the absolute value.

[0072] In this step, full-wave rectification eliminates the carrier component of the signal while retaining the low-frequency envelope variation that reflects the target distance information, thereby improving the stability and noise immunity of subsequent frequency estimation.

[0073] S202, the rectified signal Perform smoothing filtering to obtain the filtered signal. ; for the filtered signal Amplitude limiting is performed to remove abnormal amplitudes, resulting in a limited signal. For the signal after amplitude limiting Normalization is performed to obtain the shaped signal. :

[0074]

[0075] This step uses shaping to reduce the impact of amplitude fluctuations and abnormal amplitudes on subsequent squaring operations and time-frequency analysis, and provides stable input for unified frequency performance across up and down sweep bands.

[0076] S203. Due to triangular wave modulation, the difference frequency signal exhibits a sign-reversal characteristic during the rising and falling sweep bands. Regarding the shaped signal... Squaring eliminates the sign-flipping effect and unifies frequency components to the positive frequency region. The squaring operation is implemented using an analog multiplier. The signal after squaring... It can be represented as:

[0077]

[0078] S204, the signal after squaring. It includes a DC component and a difference frequency component proportional to the target distance (frequency twice the original difference frequency). To extract the effective frequency information of the target, the signal after squaring is... Bandpass filtering is performed to remove the DC term and high-frequency noise introduced by the squaring operation, retaining only the target difference frequency component, thus obtaining the nonlinearly transformed signal. .

[0079] S3, Time-Frequency Analysis

[0080] The signal after the nonlinear transformation Time-frequency analysis was performed to obtain the time-spectrum function. From the time-spectrum function The time-spectral features were extracted.

[0081] In this embodiment, time-frequency analysis is implemented using STFT (Short-Time Fourier Transform), and the time-frequency spectrum function... It can be represented as:

[0082]

[0083] In the formula, The signal after nonlinear transformation is in The value at time, The window function is a Bartlett window, used to limit the local time domain range and balance frequency resolution and time resolution. For Centered on, A window function for weighting the time-series signals. The imaginary unit, For frequency variables, This is the time variable for integration.

[0084] This step involves analyzing the time-frequency function. By analyzing the amplitude or power distribution, the energy concentration area of ​​the echo signal difference frequency over time can be clearly observed, thereby enabling the differentiation of echoes of different periods.

[0085] S4, Cluster Analysis

[0086] Clustering algorithms are used to perform cluster analysis on the time-spectral features, and frequency components are extracted from the clustering results.

[0087] In this embodiment, the K-means clustering algorithm is used, taking frequency points in the STFT time-frequency spectrum as sample data and performing iterative clustering based on Euclidean distance. The clustering process includes steps such as initializing cluster centers, assigning sample points, and updating cluster centers until convergence. (Number of clusters) Based on the distribution of time-frequency sample points, the optimal settings are as follows: ≥2, to distinguish between areas of concentrated target energy and outliers / noise points. For ranging applications, in this embodiment... Take 3.

[0088] After clustering is completed, the frequency corresponding to the cluster center of the class with the largest number of samples (i.e., the region with the most concentrated energy) is determined. As the extracted frequency components, they effectively suppress outliers and noise interference.

[0089] S5, Distance Calculation

[0090] S501, Based on the frequency components Calculate the actual difference frequency :

[0091]

[0092] Since the squaring operation in S203 doubles the original difference frequency, it is necessary to extract the frequency components from the clustering. Divide by 2 to restore the actual difference frequency before squaring.

[0093] Based on the actual difference frequency Calculate the round-trip time of the signal :

[0094]

[0095] S502, Utilizing the speed of electromagnetic wave propagation Round-trip time of signal Calculate the actual distance between the target and the radar system. :

[0096]

[0097] To verify the performance of the ranging method proposed in this invention, numerical simulations were conducted, and the following methods were compared in the simulations:

[0098] Single-cycle FFT: Perform FFT directly on a single-cycle difference frequency signal and extract the spectral peak as the frequency component;

[0099] Multi-period non-square FFT: The difference frequency signals of multiple periods are spliced ​​together in the time domain, and the spliced ​​signals are subjected to FFT to extract the peak frequency as the frequency component.

[0100] Multi-period squared FFT: First, the multi-period difference frequency signal is squared, and then the squared signal is subjected to FFT to extract the spectral peak as the frequency component.

[0101] Multi-cycle STFT: Perform STFT directly on multi-cycle difference frequency signals and extract the peak values ​​of the spectrum as frequency components;

[0102] Multi-period STFT+Kmeans: A ranging method provided in this embodiment of the invention.

[0103] The simulation parameters are shown in Table 1.

[0104] Table 1 Simulation Parameters

[0105]

[0106] Figure 2 This is a schematic diagram of the time-frequency spectrum distribution of the nonlinearly transformed signal obtained by STFT when using multi-period STFT+Kmeans, where the horizontal axis represents the time variable. The vertical axis represents frequency. From Figure 2 The energy concentration region of the echo signal difference frequency over time can be clearly observed, demonstrating the effectiveness of the method of this invention in extracting the time-frequency characteristics of the signal.

[0107] Figure 3 This graph shows the difference frequency estimation results of the actual target distance using different methods. The horizontal axis represents the actual distance between the target and the radar system, and the vertical axis represents the frequency components. The theoretical values ​​in the graph represent the theoretical values ​​of the actual distance between the target and the radar system. Figure 3It can be seen that the estimation results of the method of the present invention are closer to the theoretical values ​​and have smaller fluctuations, which verifies the effectiveness and superiority of the present invention.

[0108] Figure 4 This is a graph showing the MSE performance analysis of different methods for estimating the actual target distance, where the horizontal axis represents the actual distance between the target and the radar system, and the vertical axis represents the MSE. Since radar echo signal power attenuates with increasing distance, the greater the actual distance between the target and the radar system, the lower the signal-to-noise ratio. Figure 4 As can be seen, under low signal-to-noise ratio conditions, the MSE of the method of this invention is significantly lower than that of the traditional single-period FFT method and the multi-period direct FFT method, demonstrating higher estimation accuracy and stability.

[0109] The specific embodiments of the present invention are provided to enable those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention.

[0110] It should be understood that the present invention is not limited to the content already described above, and various modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.

Claims

1. A multi-period triangular wave clustering frequency estimation buoy LFM ranging method, characterized in that, Includes the following steps: S1. Transmit a multi-cycle triangular wave modulated LFM signal, acquire the echo signal of the LFM signal, and mix the echo signal with a local reference signal to obtain a multi-cycle difference frequency signal. S2. Perform a nonlinear transformation on the multi-cycle difference frequency signal to obtain the nonlinearly transformed signal; The nonlinear transformation process includes: S201. Perform full-wave rectification on the multi-cycle difference frequency signal to obtain a rectified signal; S202. Perform envelope shaping on the rectified signal to obtain a shaped signal; S203. Perform a squaring operation on the shaped signal, and then perform bandpass filtering on the signal after the squaring operation; S3. Perform time-frequency analysis on the nonlinearly transformed signal. The time-frequency analysis adopts short-time Fourier transform and obtains the time-frequency characteristics by segmenting and windowing the nonlinearly transformed signal. S4. Perform cluster analysis on the time-spectrum features using a clustering algorithm, and extract frequency components from the clustering results; The clustering algorithm is the K-means clustering algorithm. The process of extracting the frequency components includes: using the frequency points in the time-spectrum features as sample data, iteratively clustering to output cluster centers, and using the frequency corresponding to the cluster centers as the frequency components. S5. Calculate the target distance based on the frequency components.

2. The multi-period triangular wave clustering frequency estimation buoy LFM ranging method according to claim 1, characterized in that, The full-wave rectification is achieved by taking the absolute value of the multi-cycle difference frequency signal point by point.

3. The multi-period triangular wave clustering frequency estimation buoy LFM ranging method according to claim 1, characterized in that, The envelope shaping includes smoothing filtering, amplitude normalization, and amplitude limiting of the rectified signal.

4. The multi-period triangular wave clustering frequency estimation buoy LFM ranging method according to claim 1, characterized in that, S5 specifically includes: S501. Calculate the propagation delay of the echo signal based on the frequency components; S502. Calculate the actual distance between the target and the radar system using the electromagnetic wave propagation speed and the propagation delay.

5. The multi-period triangular wave clustering frequency estimation buoy LFM ranging method according to claim 1, characterized in that, The LFM signal is a linear frequency modulation signal with a linear rising slope and a linear falling slope.

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