Instantaneous frequency estimation method based on nonlinear compression transformation

Abstract

The invention discloses an instantaneous frequency estimation method based on nonlinear compression transformation, and aims to solve the problem that the accuracy of measuring the navigational speed of an underwater target is affected by poor anti-noise performance, insufficient ridge continuity, high probability of occurrence of false frequency and the like of the conventional instantaneous frequency estimation method under the complex conditions of low signal-to-noise ratio, multiple components and the like. According to the method, time-frequency analysis is carried out on underwater acoustic signals received by a receiving end by using nonlinear compression transformation to obtain a time-frequency distribution diagram. The time-frequency distribution diagram is analyzed through a ridge line detection method, a ridge line is obtained, and a cost function of the ridge line detection method comprises an energy item, a first-order smooth item and a second-order smooth item. And performing threshold detection on the ridge line by using a dual-energy threshold detection method to obtain an instantaneous frequency estimation result. The invention belongs to the field of underwater acoustic signal processing and time-frequency analysis.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic signal processing and time-frequency analysis, specifically to an instantaneous frequency estimation method based on nonlinear compression transform. Background Technology

[0002] In the process of locating and navigating underwater targets, real-time and accurate estimation of the speed of underwater moving targets (such as autonomous underwater vehicles (AUVs) and underwater robots (ROVs)) provides key information for tasks such as trajectory tracking, behavior recognition, and collision avoidance control.

[0003] In speed estimation methods, passive velocity measurement based on the acoustic Doppler effect is one of the main technical approaches. This method utilizes the acoustic signals actively emitted by the underwater target itself and calculates the target's radial speed by analyzing the frequency shift observed at the receiver. Due to its advantages such as requiring no external sound source, strong real-time performance, and sensitive response to dynamic motion changes, it has been widely applied in scenarios such as ocean observation, AUV autonomous navigation, and multi-platform collaborative control. In practical applications, underwater targets typically periodically emit acoustic positioning signals with known frequencies and fixed waveform characteristics to achieve navigation or positioning. When there is relative motion between the target and a fixedly deployed receiver, the signal undergoes a frequency shift due to the Doppler effect during propagation. The receiver estimates the instantaneous frequency (IF) of the received signal, calculates the deviation between this instantaneous frequency and the known transmitted frequency to determine the Doppler frequency shift, and then, based on this frequency shift and combined with environmental sound speed parameters, calculates the target's instantaneous radial speed.

[0004] The accuracy of velocity measurement based on the Doppler effect is highly dependent on the accuracy of the receiver's estimation of the instantaneous frequency (IF) of the signal. To address this issue, existing technologies primarily employ an IF estimation framework based on time-frequency analysis. This involves first constructing the time-frequency distribution of the signal to characterize its frequency structure, and then using a ridge detection algorithm to extract the main frequency trajectories as frequency estimates. However, the transmitting signal is affected by factors such as marine environmental noise and energy attenuation, leading to a decrease in the signal-to-noise ratio (SNR) of the received signal. This makes ridge detection based on the time-frequency distribution map susceptible to noise disturbances, resulting in instability or deviations in the instantaneous frequency extraction process, which in turn affects the accuracy of the speed calculation. Especially under low SNR and multi-component propagation conditions, traditional time-frequency analysis methods suffer from insufficient noise resistance and severe time-frequency energy diffusion, making it difficult to form a clear and concentrated expression of frequency characteristics. Simultaneously, ridge detection algorithms often exhibit unstable ridge extraction, missed detection of weak components, and false ridges caused by noise spurious peaks under strong noise interference, further reducing the accuracy of instantaneous frequency estimation. Summary of the Invention

[0005] To address the problems of poor noise resistance, insufficient ridge continuity, and the easy occurrence of spurious frequencies in existing instantaneous frequency estimation methods under complex conditions such as low signal-to-noise ratio and multiple components, which affect the accuracy of underwater target speed measurement, this invention proposes an instantaneous frequency estimation method based on nonlinear compression transform.

[0006] The technical solution adopted in this invention is:

[0007] It includes the following steps:

[0008] S1. Use nonlinear compression transform to perform time-frequency analysis on the underwater acoustic signal received at the receiver to obtain the time-frequency distribution diagram;

[0009] S2. Analyze the time-frequency distribution map using the ridge detection method to obtain the ridge lines;

[0010] The cost function of the ridge detection method includes an energy term, a first-order smoothing term, and a second-order smoothing term;

[0011] S3. Threshold detection of the ridge line is performed using the dual energy threshold detection method to obtain the instantaneous frequency estimation result.

[0012] The beneficial effects of this invention are as follows:

[0013] This invention proposes a nonlinear compression transform (NSTFT) method whose time-frequency performance is independent of the amplitude of the input underwater acoustic signal, a ridge detection algorithm that incorporates a second-order smoothing term into the cost function, and a dual energy threshold detection method. The nonlinear compression transform method is used to perform time-frequency analysis on the received underwater acoustic signal. Based on the time-frequency analysis results, the ridge detection algorithm is used to obtain the ridges. Next, the dual energy threshold detection method is used to perform threshold detection on the ridges to obtain an instantaneous frequency estimate.

[0014] This invention significantly improves the accuracy and robustness of instantaneous frequency estimation for multi-component, non-stationary underwater acoustic signals under low signal-to-noise ratio (SNR) conditions (e.g., -10dB) through multi-stage optimization. The effectiveness and noise resistance of the proposed ridge detection algorithm are verified, demonstrating that it achieves better instantaneous frequency estimation accuracy compared to the original ridge detection method under low SNR conditions. The dual-energy threshold detection method combines the differences between weak underwater acoustic signals and noise in the NSTFT time-frequency performance, effectively eliminating false ridge points and improving the accuracy of instantaneous frequency estimation by ridge detection. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention;

[0016] Figure 2 It is the time-frequency function obtained by performing STFT on the underwater acoustic signal;

[0017] Figure 3 This is the time-frequency distribution diagram obtained by performing NSTFT on the underwater acoustic signal;

[0018] Figure 4 This is a graph showing the detection results of the original ridge line detection method when SNR=5dB;

[0019] Figure 5 This is a graph showing the detection results of the ridge detection method proposed in this invention when SNR=5dB;

[0020] Figure 6 This is a graph showing the detection results of the original ridge line detection method when SNR=0dB;

[0021] Figure 7 This is a graph showing the detection results of the ridge detection method proposed in this invention when SNR=0dB;

[0022] Figure 8 This is a graph showing the detection results of the original ridge line detection method when SNR=-5dB;

[0023] Figure 9 This is a graph showing the detection results of the ridge detection method proposed in this invention when SNR=-5dB;

[0024] Figure 10 This is a graph showing the detection results of the original ridge line detection method when SNR=-10dB;

[0025] Figure 11 This is a graph showing the detection results of the ridge detection method proposed in this invention when SNR=-10dB;

[0026] Figure 12 This is a schematic diagram showing the NMSE changes of the ridge detection method proposed in this invention and the original ridge detection method under different SNRs;

[0027] Figure 13 This is a ridgeline diagram before energy threshold detection;

[0028] Figure 14 It is a ridgeline map after global energy threshold detection;

[0029] Figure 15 It is the threshold and detection statistics for global energy threshold detection;

[0030] Figure 16 It is a ridgeline map after local ratio energy threshold detection;

[0031] Figure 17 It is the threshold and detection statistic for local ratio energy threshold detection;

[0032] Figure 18This is a time-domain waveform diagram of the underwater acoustic signal received by the underwater acoustic transducer.

[0033] Figure 19 It is the STFT time-frequency distribution of the underwater acoustic signal received by the underwater acoustic transducer;

[0034] Figure 20 This is the NSTFT time-frequency distribution of the underwater acoustic signal received by the underwater acoustic transducer;

[0035] Figure 21 This is the result obtained by the ridge line detection method of the present invention;

[0036] Figure 22 This is the result obtained from the original ridge line detection method; Detailed Implementation

[0037] Specific implementation method one: Combining Figures 1-17 This embodiment describes an instantaneous frequency estimation method based on nonlinear compression transform, which includes the following steps:

[0038] S1. The received underwater acoustic signal is analyzed in time and frequency using a nonlinear compression transform to obtain a time-frequency distribution map. The specific process is as follows:

[0039] In this embodiment, the receiver receives underwater acoustic signals from an autonomous underwater vehicle (AUV). ,like Figure 2 As shown, the STFT method (Short Time Fourier Transform) is used to perform time-frequency analysis on the underwater acoustic signal to obtain the time-frequency function. :

[0040] (1)

[0041] The time-frequency function contains the amplitude and phase information of the underwater acoustic signal. The time variable is a time-frequency function. The frequency variable is a time-frequency function. For window functions, It is a natural constant, approximately 2.718. For the time variable of integration, It is the imaginary unit.

[0042] calculate Time partial derivative :

[0043] (2)

[0044] in, for The first derivative, To use window functions The time-frequency function obtained by performing STFT transformation on the underwater acoustic signal.

[0045] Since the expression for the time partial derivative is:

[0046] (3)

[0047] in, The instantaneous frequency of the underwater acoustic signal.

[0048] Substituting equation (2) into equation (3), we get:

[0049] (4)

[0050] Right now:

[0051] (5)

[0052] Define time-frequency function If the ratio of the two time-frequency functions mentioned above is equal to the ratio of the two time-frequency functions mentioned above, then:

[0053] (6)

[0054] because There is a nonlinear effect, so the time-frequency function Named nonlinear compression transform, it utilizes nonlinear compression transform on the underwater acoustic signal. Perform time-frequency analysis to obtain the time-frequency distribution map. For example... Figure 3 As shown. The nonlinear compressed transform (NSTFT) is characterized by obtaining a time-frequency representation that depends only on the signal phase and is independent of the input signal amplitude. This makes it suitable for environments with high noise levels, and the obtained time-frequency distribution energy is concentrated, which is beneficial for subsequent instantaneous frequency estimation. Therefore, this invention uses NSTFT for time-frequency analysis (TFA) prior to ridge detection to obtain a highly concentrated time-frequency representation that is independent of the underwater acoustic signal amplitude, thereby enhancing weak underwater acoustic signal components and suppressing noise effects.

[0055] To verify the effectiveness of the NSTFT, simulation verification was performed. The simulated underwater acoustic signal was set as a three-component underwater acoustic signal, represented as follows:

[0056] (7)

[0057] in, , It is a sinusoidal frequency-modulated underwater acoustic signal. It is a linear frequency modulated underwater acoustic signal. It is a single-frequency underwater acoustic signal.

[0058] (8)

[0059] (9)

[0060] (10)

[0061] in, for amplitude, for amplitude, for amplitude, for carrier frequency, To modulate the amplitude of the underwater acoustic signal, To modulate the frequency of the underwater acoustic signal, for The initial frequency, For frequency modulation slope, for carrier frequency, It is a time variable.

[0062] The specific parameters of the three-component underwater acoustic signal are shown in Table 1. This invention is configured... In this case, the results obtained using STFT and NSTFT are as follows: Figure 2 and Figure 3 As shown, the NSTFT method can obtain the time-frequency trajectory of concentrated energy and effectively represent the weak underwater acoustic signal components.

[0063] Table 1

[0064]

[0065] S2. Analyze the time-frequency distribution map using the ridge detection method to estimate the instantaneous frequency information of the underwater acoustic signal on the time-frequency distribution map and obtain the ridge lines. The specific process is as follows:

[0066] This invention sets the cost function of the ridge detection method. This includes the energy term, the first-order smoothing term, and the second-order smoothing term, namely:

[0067] (11)

[0068] in, The weighting factor for the first-order smoothing term. The weighting factor for the second-order smoothing term. This is a first-order smoothing term used to penalize the current frequency deviation. for Candidate frequency values ​​at time 1 The ridge frequency point that has been determined in the previous or next time step. To and Candidate frequency values ​​at time 1 Determined ridge frequency points at intervals of one time frame. This is a second-order smoothing term used for penalty. Candidate frequency values ​​at time 1 Relative to the frequency points of the first two ridges , linear extrapolation value The deviation represents a discrete approximation of the degree of "bending" of the current frequency point relative to the ridge, characterizing the change in the curvature of the function. As the weighting factor for the energy term, For energy terms, for Time frequency value The corresponding time-frequency function.

[0069] The ridge detection method described above is used to analyze the frequency at each moment on the time-frequency distribution map. During the analysis, the ridge detection method adaptively adjusts the weighting factor of the energy term at the corresponding moment based on the local energy characteristics of the underwater acoustic signal on the time-frequency distribution map. Weighting factors of the first-order smoothing term Weighting factors of the second-order smoothing term The specific process is as follows:

[0070] First, based on the local energy characteristics of the underwater acoustic signal at each moment on the time-frequency distribution map, the normalized local maximum energy at each moment is calculated. :

[0071] (12)

[0072] in, For the frequency search range, Indicates the middle value. This represents the maximum value.

[0073] (13)

[0074] in, For at a certain point in time The estimated center frequency at that location, The frequency search half-bandwidth at a given time point limits the maximum allowed frequency deviation at each step of the algorithm. For at a certain point in time The estimated center frequency at that location, The index is a discrete frequency, representing the first available frequency within the frequency search bandwidth. Candidate frequencies, The total number of candidate frequencies, i.e. The upper limit of the value, This is a specific time index, representing the starting point position for the ridge detection method's search. This represents the total time duration.

[0075] Secondly, based on the normalized local maximum energy at each moment Calculate the adaptive scaling factor at each time step. :

[0076] (14)

[0077] in, and These are the low and high thresholds for normalized local energy. The specific values ​​of the thresholds can be determined based on the global normalized energy percentile of the underwater acoustic signal. For example, if the average energy of the underwater acoustic signal is 100, the low threshold can be set to 20% of the average energy, and the high threshold to 60% of the average energy. These two parameters are not sensitive within a reasonable range and can be adjusted according to the actual noise environment. They can be appropriately increased in low signal-to-noise ratio environments. When the main component is very strong, it can be lowered. .

[0078] Finally, based on the adaptive scaling factor at each time step and the corresponding frequency search half bandwidth The weighting factors for the energy term at each time step. Weighting factors of the first-order smoothing term Weighting factors of the second-order smoothing term A dynamic mapping is performed to weaken the smoothing constraint in high-energy regions and strengthen it in low-energy regions. The weighting factor of the energy term at each time step after mapping is obtained. Weighting factors of the first-order smoothing term Weighting factors of the second-order smoothing term :

[0079] (15)

[0080] (16)

[0081] (17)

[0082] Using the weighting factor of the energy term at each time step Weighting factors of the first-order smoothing term Weighting factors of the second-order smoothing term Analyzing the frequencies at corresponding times on the time-frequency distribution map yields the ridge point for each time moment. Connecting all the ridge points at all times creates the ridge line corresponding to the time-frequency distribution map. In this embodiment... Figure 3It contains three time-frequency curves. Each time-frequency curve is analyzed to obtain the corresponding three ridge lines.

[0083] In applications such as weak acoustic signal detection and instantaneous frequency estimation, time-frequency ridge detection methods can effectively extract the main energy trajectory of acoustic signals, achieving accurate tracking of acoustic signal components. Although current ridge extraction algorithms, through gradual optimization of the cost function, have significantly improved the continuity and noise resistance of ridge trajectories, the basic principle still relies on identifying local energy peaks or phase consistency paths in the time-frequency representation. Therefore, under low signal-to-noise ratio conditions, the random fluctuations of noise itself may form transient, seemingly continuous energy accumulation regions on the time-frequency distribution map. These noise-dominated pseudo-structures, because their local features may resemble the ridges of real acoustic signals, may be misjudged by the algorithm as valid acoustic signal ridges, leading to incorrect estimation of acoustic signal parameters.

[0084] This invention incorporates a second-order smoothing term into the cost function of existing ridge detection methods (i.e., Wang S, Chen X, Wang Y, et al. Nonlinearsqueezing time–frequency transform for weak signal detection[J]. Mechanical Systems and Signal Processing, 2022, 167: 108569.). This second-order smoothing term penalizes the deviation of the current candidate frequency point from the linear extrapolation value formed by the two previously determined ridge frequency points, thus characterizing the local curvature change of the ridge. Furthermore, this invention dynamically adjusts the weighting factors of each cost term based on the local energy characteristics of the underwater acoustic signal, ensuring the extraction of a smooth and continuous frequency trajectory even under strong noise interference. The weighting factor of the energy term is used to dynamically balance the contributions of different energy terms. The weighting factor of the first-order smoothing term decreases as the local normalized energy increases, i.e., in regions of high energy, the constraint on first-order smoothing is weakened.

[0085] The ridge detection method proposed in this invention uses the normalized frequency difference between adjacent time points as a penalty term, thereby reflecting the magnitude of the deviation relative to the search window scale. The weight factor of the second-order smoothing term decreases as the local energy increases, allowing for greater curvature changes in strong underwater acoustic signals, while emphasizing the smoothness of the ridge line in weak underwater acoustic signals. The ridge detection method proposed in this invention processes the obtained time-frequency curve, which can effectively remove noise interference and improve the continuity and stability of the ridge line, thus making it more accurately reflect the intrinsic characteristics and frequency variation law of the underwater acoustic signal.

[0086] To illustrate the performance advantages of this invention, the original ridge detection method and the ridge detection method proposed in this invention were tested under different signal-to-noise ratio environments. This was done on a linear frequency modulated underwater acoustic signal with Gaussian white noise. FM underwater acoustic signal The test was conducted with a signal-to-noise ratio ranging from 5dB to -10dB, and the results are as follows: Figure 4-11 As shown in the figure. By comparison, the detection results obtained by this method are more accurate under the same signal-to-noise ratio conditions, especially when the SNR is less than -5dB, the accuracy is significantly higher than the original ridge detection method.

[0087] To quantitatively analyze the actual performance of the ridge detection method proposed in this invention, NMSE was used to quantitatively assess the accuracy of the ridge detection results:

[0088] (18)

[0089] in, For underwater acoustic signals The estimated instantaneous frequency value, underwater acoustic signal The actual instantaneous frequency value, The L2 norm represents the square root of its elements. The input underwater acoustic signal is a linear frequency modulated underwater acoustic signal with Gaussian white noise. By varying the SNR from 15 to -15 and conducting 200 Monte Carlo experiments, the changes in NMSE between the ridge detection method proposed in this invention and the original ridge detection method were obtained. The experimental results are as follows: Figure 12 As shown.

[0090] Compared to the original ridge detection method, the proposed ridge detection method achieves lower NMSE values ​​at all points under low signal-to-noise ratio (SNR) conditions, enabling effective ridge detection and accurate estimation of instantaneous frequency (IF) values. With increasing SNR, the instantaneous frequency (IF) estimation accuracy of both methods improves, and the NMSE values ​​gradually converge to a stable, relatively small value. However, the convergence speed of this method is faster, starting to converge gradually around SNR = -9dB, while the original ridge detection method starts to converge gradually around SNR = -7dB. If the confidence level of NMSE is set to 5%, this invention can effectively estimate the instantaneous frequency of underwater acoustic signals under even lower SNR conditions. Based on the above results, this invention is applicable to the detection of multi-component underwater acoustic signals. Compared to traditional ridge detection algorithms, it has stronger noise tolerance, greater applicability and accuracy under low SNR conditions, and can be used for the detection of weak underwater acoustic signals.

[0091] S3. Threshold detection of the ridge line is performed using a dual energy threshold detection method to obtain the instantaneous frequency estimation result. The dual energy threshold detection method includes global energy threshold detection and local energy ratio threshold detection.

[0092] Global energy threshold detection can filter out ridge points with energy below a threshold. This is due to the time-frequency function obtained from S1. The amplitude of the frequency response is independent of the amplitude of the input underwater acoustic signal. Therefore, even in the problem of detecting weak underwater acoustic signals, it is still possible to solve the problem by calculating the time-frequency function. Low percentile energy estimates noise floor energy :

[0093] (19)

[0094] in, for of quantiles, for , This can be any custom value.

[0095] Define global energy threshold Low energy of noise A number of times, we get:

[0096] (20)

[0097] in, It is a multiple of the threshold. Indicates multiplication.

[0098] Meanwhile, considering the nonlinear compression effect of NSTFT on underwater acoustic signals, which increases the energy concentration of the ridges and enhances the underwater acoustic signal more effectively than it enhances noise, a local energy ratio threshold detection is added to the global energy threshold detection. The threshold selection principle for the local energy ratio threshold detection is as follows:

[0099] First, calculate the energy value of the ridge line in the corresponding time-frequency function at each moment:

[0100] (twenty one)

[0101] in, for The energy value of the ridge line in the corresponding time-frequency function at time step [time]. for The time-frequency function of the ridge at time point.

[0102] Then, at the ridge line corresponding to the energy value ( Frequency search range at time) In the calculation, the total energy excluding the ridge frequency is determined. :

[0103] (twenty two)

[0104] in, For The local frequency search range for the center frequency point. , for Except The frequency of the ridge line at any given moment outside the ridge line. for Except The time-frequency function of the ridge line at any time outside the ridge line.

[0105] Define function The ratio of equation (21) to equation (22) is called the energy concentration ratio of the ridge line, which reflects the degree of energy concentration of the ridge line. Thus, the energy concentration ratio of the ridge line at each moment is obtained:

[0106] (twenty three)

[0107] Along the ridge lines, some false ridge points exist due to noise, relative to the instantaneous frequency changes of the true underwater acoustic signal. These false ridge points are difficult to remove using ridge detection algorithms. Near these false ridge points, there should also exist candidate points representing the true frequency. For any true ridge point, its frequency at that time... The value is the largest, while the false ridge point The value also conforms to this pattern, but within the local frequency search range False ridge points may exist. Points with R values ​​close to those of ridge points, and for ridge points unaffected by noise, within the local frequency search range. Among them, its The value will differ significantly from other points. This phenomenon occurs because, in the absence of noise, ridge points closely match the true frequency trajectory, with energy concentrated solely on the ridge line, without other energy concentration points. However, spurious ridge points generated under noise influence still contain energy concentration points of the true underwater acoustic signal within the candidate point range, resulting in more energy concentration points. Therefore, in selecting the local energy ratio threshold for detection, the energy value corresponding to the ridge line (… Frequency search range at time) The ridge line at each moment Take all The maximum value is used as the frequency search range. Energy threshold base :

[0108] (twenty four)

[0109] Define the frequency search range Local energy ratio threshold yes Several times:

[0110] (25)

[0111] in, The threshold multiple indicates that the ridge point should be greater than the maximum ratio of candidate points. The multiples of. Similarly, according to equation (25), the local energy ratio threshold corresponding to each frequency search range is obtained.

[0112] Detection statistics corresponding to local energy ratio threshold detection for:

[0113] (26)

[0114] Global energy threshold and local energy ratio threshold The preset values ​​are all greater than 1 to ensure that the preserved ridge points have the most significant energy concentration characteristics in their local areas.

[0115] The joint decision expression for the global energy threshold and the local energy ratio threshold is:

[0116] (27)

[0117] Using Equation (27), dual energy threshold detection is performed on the ridgeline at each time point, and the frequency value corresponding to the ridgeline point satisfying Equation (27) is taken as the instantaneous frequency estimation result of the autonomous underwater vehicle (AUV). In applications such as weak underwater acoustic signal detection and instantaneous frequency estimation, the time-frequency ridgeline detection method can effectively extract the main energy trajectory of the underwater acoustic signal and achieve accurate tracking of the underwater acoustic signal components. After obtaining the time-frequency ridgeline, this method uses energy threshold detection to filter out statistically significant effective ridgeline points by setting an energy threshold. Specifically, the point-by-point energy distribution of the ridgeline along its path on the time-frequency distribution map is calculated, that is, the energy distribution of the ridgeline is calculated. and Set dual energy thresholds. , Only ridge points with energy or amplitude exceeding a threshold are retained, thereby eliminating false points caused by noise, weak interference, or time-frequency artifacts, improving the continuity and stability of the ridges, and making them more accurately reflect the intrinsic characteristics and frequency variation patterns of the signal. Secondly, the local energy ratio threshold detection method sets a threshold based on the energy difference between a ridge point and other points within its local search range, further removing false ridge points and improving the accuracy and reliability of instantaneous frequency estimation.

[0118] S4. Detection Results

[0119] underwater acoustic signals The NSTFT time-frequency distribution map is obtained using the ridge detection algorithm proposed in this invention (S2). The time-frequency ridge information is then subjected to dual energy threshold detection. Considering the significant noise interference, 50% of the global energy is selected as the noise floor energy for the global energy threshold. The value is set. =10. Local energy ratio threshold setting. =1.2, meaning the local energy ratio of a ridge point is greater than 1.2 times the maximum local energy ratio of a candidate point, thus the ridge point is considered valid. Ridges before energy threshold detection are shown below. Figure 13 The ridgeline after global energy threshold detection is shown below. Figure 14 The corresponding thresholds and detection statistics are shown in [link to relevant documentation]. Figure 15 The ridge line after local energy ratio threshold detection is shown. Figure 16 The corresponding thresholds and detection statistics are shown in [link to relevant documentation]. Figure 17 Based on the test results, after dual energy threshold testing, some of the sharp points in the ridge were removed, resulting in a smoother overall surface that more closely resembles underwater acoustic signals. The instantaneous frequency change trajectory of the weak frequency modulated component is shown. This demonstrates the effectiveness of the dual energy threshold detection method, which helps eliminate spurious ridge points caused by noise interference during ridge detection. This invention is used for instantaneous frequency estimation of non-stationary underwater acoustic signals in low signal-to-noise ratio environments.

[0120] Example

[0121] Experimental Environment: A hydroacoustic transducer was placed in the water, with its top fixed to the bottom of a boat. A GPS device was installed on the hull. The transducer emitted a linear frequency modulated (LFM) signal with a frequency of 30kHz-35kHz and a pulse width of 10ms. The transducer emitted the signal at 0.078s. After receiving the signal using a hydrophone, the proposed method was applied to process the signal to obtain an instantaneous frequency estimate. The speed of the transducer (boat) was calculated based on this instantaneous frequency estimate. Simultaneously, the theoretical speed of the boat was calculated based on the changes in latitude and longitude before and after signal transmission. The theoretical speed was then compared with the speed obtained by this invention. Figures 18 to 20 As shown.

[0122] The ridge detection method proposed in S2 was used to detect ridges in the time-frequency distribution map obtained by NSTFT. The detection results are as follows: Figure 21 and Figure 22 As shown. Then, based on the dual energy threshold detection method of S3, threshold detection is performed on the ridge detection results to obtain an instantaneous frequency estimate. The speed of the underwater acoustic transducer (ship) is then calculated based on the obtained instantaneous frequency estimate.

[0123] (28)

[0124] in, For the speed of the underwater acoustic transducer (ship), The speed of sound in water, This is the frequency offset. Indicates multiplication.

[0125] The speed obtained by this invention is 3.4843 m / s, while the speed obtained by existing methods is 5.9462 m / s. In this process, the ship's initial position coordinates are A (43.708060, 126.706962), and the final position coordinates are B (43.7080597, 126.7069622). The theoretical speed calculated from this is 3.67 m / s. The speed obtained by this invention (3.4843 m / s) is very close to the theoretical speed of 3.67 m / s calculated from the ship's starting and ending coordinates, with a relative error of approximately 5.1%, verifying the speed measurement accuracy and stability of this invention. In contrast, the speed calculated by existing methods (5.9462 m / s) is approximately 61.9% higher than the theoretical value, indicating a significant systematic error. Therefore, the detection method proposed in this invention has higher accuracy and reliability in real-world environments, and can effectively reduce the speed estimation deviation caused by instantaneous frequency extraction errors in traditional algorithms.

[0126] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for instantaneous frequency estimation based on nonlinear compression transform, characterized in that: It includes the following steps: S1. Use nonlinear compression transform to perform time-frequency analysis on the underwater acoustic signal received at the receiver to obtain the time-frequency distribution diagram; S2. Analyze the time-frequency distribution map using the ridge detection method to obtain the ridge lines; The cost function of the ridge detection method includes an energy term, a first-order smoothing term, and a second-order smoothing term; S3. Threshold detection of the ridge line is performed using the dual energy threshold detection method to obtain the instantaneous frequency estimation result.

2. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 1, characterized in that: In step S1, nonlinear compression transform is used to perform time-frequency analysis on the underwater acoustic signal received at the receiving end to obtain a time-frequency distribution diagram. The specific process is as follows: The receiver receives underwater acoustic signals. The underwater acoustic signal was analyzed in time and frequency using the STFT method to obtain the time-frequency function. : （1） in, It is the time variable of the time-frequency function. The frequency variable is a time-frequency function. For window functions, It is a natural constant. For the time variable of integration, The imaginary unit; calculate Time partial derivative : （2） in, for The first derivative, For use The time-frequency function obtained by performing STFT transformation on the underwater acoustic signal; The expression for the time partial derivative is: （3） in, The instantaneous frequency of the underwater acoustic signal; Substituting equation (2) into equation (3), we get: （4） Define time-frequency function It equals the ratio of the two time-frequency functions mentioned above: （5） time-frequency function Named nonlinear compression transform, the underwater acoustic signal is subjected to time-frequency analysis using nonlinear compression transform to obtain a time-frequency distribution map.

3. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 2, characterized in that: The cost function of the ridge detection method in S2 is: （6） in, Let be the cost function of the ridge detection method. The weighting factor for the first-order smoothing term. The weighting factor for the second-order smoothing term. It is a first-order smoothing term. for Candidate frequency values ​​at time 1 The ridge frequency point that has been determined in the previous or next time step. To and Candidate frequency values ​​at time 1 The determined ridge frequency points separated by one time frame, It is a second-order smoothing term. As the weighting factor for the energy term, For energy terms, for Time frequency value The corresponding time-frequency function.

4. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 3, characterized in that: In step S2, the time-frequency distribution map is analyzed using a ridge detection method to obtain ridges. The specific process is as follows: The time-frequency distribution map is analyzed using a ridge detection method to obtain the ridge points at each time step. The specific process is as follows: Based on the local energy characteristics of the underwater acoustic signal at each moment on the time-frequency distribution map, the normalized local maximum energy at each moment is calculated. : （7） in, For the frequency search range, Indicates the middle value. Indicates the maximum value; Based on the normalized local maximum energy at each moment Calculate the adaptive scaling factor at each time step. : （8） in, and These are the low and high thresholds for normalized local energy; Based on the adaptive scaling factor at each time step and the corresponding frequency search half bandwidth The weighting factors for the energy term at each time step. Weighting factors of the first-order smoothing term Weighting factors of the second-order smoothing term Perform dynamic mapping to obtain the weighting factor of the energy term at each time step after mapping. Weighting factors of the first-order smoothing term Weighting factors of the second-order smoothing term : （9） （10） （11） Using the weighting factor of the energy term at each time step Weighting factors of the first-order smoothing term Weighting factors of the second-order smoothing term Analyze the frequencies at corresponding times on the time-frequency distribution map to obtain the ridge point at each time. Connect the ridge points at all times to obtain the ridge line corresponding to the time-frequency distribution map.

5. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 4, characterized in that: The frequency search range for: （12） in, To modulate the frequency of the underwater acoustic signal, For at a certain point in time The estimated center frequency at that location, For at a certain point in time The estimated center frequency at that location, The index is a discrete frequency, representing the first available frequency within the frequency search bandwidth. Candidate frequencies, The total number of candidate frequencies. This is a time index, indicating the starting point position of the ridge detection method's search. This represents the total time duration.

6. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 5, characterized in that: The dual energy threshold detection method in S3 includes global energy threshold detection and local energy ratio threshold detection.

7. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 6, characterized in that: The threshold for the global energy threshold detection is: Calculate the time-frequency function The lower percentile of the energy is used to obtain the noise floor energy. : （13） in, for of quantiles, for , It can be any user-defined value; Define global energy threshold Low energy of noise of Times: （14） in, Indicates multiplication.

8. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 7, characterized in that: The threshold for the local energy ratio threshold detection is: Calculate the energy value of the ridge line in the corresponding time-frequency function at each moment: （15） in, for The energy value of the ridge line in the corresponding time-frequency function at time step [time]. for The time-frequency function of the ridge at time point; Search range of frequencies corresponding to ridge lines based on energy values In the calculation, the total energy excluding the ridge frequency is determined. : （16） in, For The local frequency search range for the center frequency point. , for Except The frequency of the ridge line at any given moment outside the ridge line. for Except The time-frequency function of the ridge line at any time outside the ridge line; Define function for: （17） Calculate the frequency search range of the ridge line corresponding to the energy value. The ridge line at each moment Take all The maximum value is used as the frequency search range. Energy threshold base : （18） Define the frequency search range Local energy ratio threshold yes Several times: （19） in, It is a multiple of the threshold. Similarly, the local energy ratio threshold corresponding to each frequency search range is obtained according to equation (19).

9. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 8, characterized in that: The global energy threshold Local energy ratio threshold The joint decision expression is: （20）。 10. The instantaneous frequency estimation method based on nonlinear compression transform according to claim 9, characterized in that: In step S3, a dual-energy threshold detection method is used to perform threshold detection on the ridge line to obtain the instantaneous frequency estimation result. The specific process is as follows: Using Equation (20), dual energy threshold detection is performed on the ridges corresponding to each time point on the time-frequency distribution map, and the frequency value corresponding to the ridge point that satisfies Equation (20) is taken as the instantaneous frequency estimation result.

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