Underwater acoustic communication Doppler compensation method based on kinematics constraint and time-varying resampling

Abstract

The invention discloses an underwater acoustic communication Doppler compensation method based on kinematics constraint and time-varying resampling, and belongs to the technical field of underwater acoustic communication. The method comprises the following steps: firstly, performing discrete Doppler rough estimation on a received signal; denoising, kinematics constraint abnormal value correction and smoothing processing are carried out on the sequence through cascade filtering; then, a continuous speed curve is constructed by utilizing partition mixed interpolation, and oscillation is suppressed by adopting nearest neighbor interpolation in an edge region; and finally, performing iterative judgment based on the residual index, and establishing a nonlinear mapping relation through full-time-domain integration to perform time-varying resampling on the signal. According to the method, the problem of synchronization failure caused by correlation peak divergence and interpolation boundary oscillation under non-uniform motion is solved, sampling point level waveform recovery under a high dynamic scene is realized, and the robustness and synchronization stability of the system are improved. The method is suitable for the communication field of an underwater mobile platform represented by an unmanned underwater vehicle and a subsurface buoy in a complex marine environment.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic communication signal processing technology, specifically relating to an underwater acoustic communication Doppler compensation method based on kinematic constraints and time-varying resampling. Background Technology

[0002] With the deepening of marine resource development and underwater exploration activities, underwater mobile platforms, represented by unmanned underwater vehicles and moorings, are being used more and more widely in military and civilian fields. Underwater acoustic communication, as the primary means of information transmission for these platforms, faces severe challenges from the channel environment. Because the speed of sound in water is much lower than that of electromagnetic waves, the relative motion between transmitting and receiving nodes produces a significant Doppler effect. This effect not only causes carrier frequency shifts but also manifests as nonlinear compression or expansion of the signal in the time domain. This is particularly problematic during high-dynamic maneuvers such as platform acceleration and turning, severely impacting frame synchronization and demodulation performance.

[0003] In existing technologies, various schemes have been developed for Doppler compensation in mobile underwater acoustic communication. One type mainly uses average Doppler processing. For example, patent CN119254274A discloses a scheme that uses a Zoom-FFT algorithm combined with fuzzy function search and processes residual Doppler through symbol afterimage cancellation. These schemes typically assume that the velocity is basically constant within a frame of data and can achieve good results in uniform or low-dynamic scenarios. However, when the platform undergoes non-uniform motion, this block constant assumption is difficult to capture time-varying characteristics. Residual nonlinear Doppler can cause the correlation peak of the broadband signal to diverge, leading to phase-locked loop lockout or a significant drop in signal-to-noise ratio, which is difficult to meet the requirements of practical mobile platforms.

[0004] Another approach focuses on more refined time-varying tracking. For example, patent CN118984167B discloses a method for obtaining Doppler estimates by calculating the phase difference between adjacent symbols, and patent CN103354538A discloses an optimization method based on the minimum mean square error criterion to construct an objective function. These techniques improve tracking capabilities to some extent, but most fall under the category of blind estimation, lacking constraints on physical boundaries such as vehicle speed and acceleration. In low signal-to-noise ratio or strong multipath environments, noise can easily induce outlier estimations that violate the principle of inertia, resulting in significantly insufficient robustness. Furthermore, when fitting discrete estimation points to a continuous Doppler curve, spline interpolation, commonly used, is prone to boundary oscillations at the beginning and end of the sequence, known as the Runge phenomenon, causing distortion of the preamble signal at the frame header and highlighting synchronization failure issues.

[0005] Given that existing methods are difficult to achieve high-precision compensation across the entire time domain, stable edge waveforms, and physical authenticity of estimation results in high-dynamic scenarios, there is an urgent need for a sampling-point-level robust Doppler compensation method that can effectively suppress interpolation boundary divergence and integrate carrier kinematic constraints. Summary of the Invention

[0006] To address the challenges in existing technologies, such as the difficulty of handling correlation peak divergence and signal-to-noise ratio (SNR) degradation caused by non-uniform motion due to the block constant Doppler assumption, insufficient robustness of blind estimation algorithms in low SNR environments due to lack of kinematic constraints, and frame header synchronization failure caused by spline interpolation boundary oscillations, this invention proposes a Doppler compensation method for underwater acoustic communication based on kinematic constraints and time-varying resampling. By introducing carrier kinematic boundary conditions, constructing a physically realistic continuous velocity curve, and combining full-time domain integral resampling, high-precision, edge-stable sampling-point-level waveform recovery is achieved. The specific scheme is as follows: A Doppler compensation method for underwater acoustic communication based on kinematic constraints and time-varying resampling includes the following steps: S1. Perform discrete Doppler coarse estimation on the received underwater acoustic communication signal to obtain a discrete Doppler factor sequence containing noise; S2. The discrete Doppler factor sequence is subjected to cascaded filtering processing, including median filtering for noise reduction, outlier correction based on kinematic constraints, and statistical smoothing, to obtain a smooth discrete velocity sequence. S3. Construct a continuous velocity curve based on the smooth discrete velocity sequence; S4. Calculate the residual Doppler error index based on the smoothed discrete velocity sequence, compare it with a preset convergence threshold, and perform iterative convergence determination: If the convergence condition is not met, proceed to step S5; If the convergence condition is met, the currently processed signal is directly output as the final Doppler compensation result, and the iteration is terminated. S5. Based on the continuous velocity curve, establish a nonlinear time mapping relationship in the entire time domain through numerical integration, perform time-varying resampling on the current signal to be processed, generate an updated signal after Doppler compensation, and feed the updated signal back to step S1 as the input signal for the next iteration.

[0007] Further, the discrete Doppler coarse estimation in S1 includes: performing matched filtering on the received signal, extracting the correlation peak position index sequence, calculating the ratio of the time interval between adjacent correlation peaks to the theoretical frame period, and obtaining the discrete Doppler factor sequence.

[0008] Furthermore, the outlier correction based on kinematic constraints described in S2 includes: Set amplitude thresholds and inter-frame mutation thresholds based on the carrier's maximum speed and maximum acceleration; The estimated velocity is judged for compliance with amplitude and continuity of inertia. Perform correction operations on points identified as abnormal to bring the outliers back into the physical feasible region.

[0009] Furthermore, the correction operation performed on points determined to be abnormal includes a zero-order hold strategy or a similar anchoring method, which forcibly replaces the abnormal value with a nearby normal value.

[0010] Furthermore, the outlier correction based on kinematic constraints also includes an iterative variable threshold strategy: a loose threshold is used in the first iteration, and the threshold is gradually tightened in subsequent iterations.

[0011] Furthermore, the construction of the continuous velocity curve described in S3 adopts a partitioned hybrid interpolation strategy, including: using conformal piecewise cubic Hermitian interpolation in the central region and nearest neighbor interpolation in the beginning and end edge regions to lock the edge velocity to the nearest effective velocity value.

[0012] Furthermore, the beginning and end edge regions are automatically switched to nearest neighbor interpolation by detecting intervals with no valid observation data.

[0013] Furthermore, the residual Doppler error index mentioned in S4 is the... Smooth discrete velocity sequence The root mean square error (RMSE).

[0014] Furthermore, the establishment of the full-time domain nonlinear time mapping relationship described in S5 includes: converting the continuous velocity curve into a time scaling factor sequence, constructing a physical time mapping sequence through cumulative integration, and performing debiasing normalization to generate resampled query coordinates.

[0015] Based on the same inventive concept, the present invention also proposes a computer program product, which, when read, implements the method described in the present invention.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The method described in this invention introduces kinematic boundary conditions such as the maximum speed and acceleration of the carrier in the cascaded filtering, and combines three-level processing to automatically identify and eliminate non-physical outliers. Compared with the shortcomings of existing blind estimation algorithms that are susceptible to noise interference and generate outliers, it can still maintain stable tracking in low signal-to-noise ratio and strong multipath environments, thus improving the robustness and adaptability of the system under harsh channel conditions.

[0017] The method described in this invention employs a partitioned hybrid interpolation strategy in the construction of continuous velocity curves. The central region maintains high-precision conformal interpolation, while the beginning and end edge regions switch to nearest-neighbor locking. Compared with the Runge phenomenon and boundary oscillations that are prone to occur in traditional high-order spline interpolation, this method directly suppresses non-physical divergence, ensures the integrity of the preamble synchronization signal waveform, and improves the synchronization stability of communication frames.

[0018] The method described in this invention relies on a closed-loop iterative full-time domain integral mapping mechanism to perform time-varying resampling of the signal at the sampling point level. Compared with the block constant assumption or the residual distortion of traditional methods under non-uniform motion, it can accurately track phase nonlinear changes and optimize waveform recovery accuracy and correlation peak focusing performance.

[0019] The method described in this invention introduces an adaptive convergence decision based on residual error RMSE. Compared with algorithms with a fixed number of iterations, it automatically terminates the calculation when the conditions are met, and usually only 2 to 3 rounds are needed to converge, avoiding redundant calculations and achieving a balance between high-precision compensation and real-time performance.

[0020] This invention features high-fidelity waveform recovery at the sampling point level under non-uniform high-dynamic motion, stable tracking under low signal-to-noise ratio and strong multipath environments, effective suppression of interpolation boundary oscillations to improve frame synchronization reliability, and rapid compensation through an adaptive convergence mechanism. It can significantly improve the frame synchronization stability and demodulation signal-to-noise ratio of underwater acoustic communication systems and is suitable for communication in complex marine environments, such as unmanned underwater vehicles and underwater buoys. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method described in the implementation embodiment; Figure 2 This is a diagram showing the effect of the cascaded filtering system of the method described in the implementation method on the removal of outliers; Figure 3 This is a diagram showing the effect of the boundary value preservation strategy described in the implementation method at the beginning and end of the frame; Figure 4 This is a comparison diagram of the channel impulse response before and after Doppler compensation using the method described in the implementation method. Detailed Implementation

[0022] 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 a part of the embodiments of the present invention, and not all of them. 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.

[0023] Implementation Method 1 like Figure 1 As shown, a Doppler compensation method for underwater acoustic communication based on kinematic constraints and time-varying resampling includes the following steps: S1. Perform discrete Doppler coarse estimation on the received underwater acoustic communication signal to obtain a discrete Doppler factor sequence containing noise; S2. The discrete Doppler factor sequence is subjected to cascaded filtering processing, including median filtering for noise reduction, outlier correction based on kinematic constraints, and statistical smoothing, to obtain a smooth discrete velocity sequence. S3. Construct a continuous velocity curve based on the smooth discrete velocity sequence; S4, according to the above Smooth discrete velocity sequence Calculate the residual Doppler error index and compare it with the preset convergence threshold. Perform iterative convergence judgment: if the convergence condition is not met, proceed to step S5; if the convergence condition is met, output the currently processed signal directly as the final Doppler compensation result and terminate the iteration. S5. Based on the continuous velocity curve, establish a nonlinear time mapping relationship in the entire time domain through numerical integration, perform time-varying resampling on the current signal to be processed, generate an updated signal after Doppler compensation, and feed the updated signal back to step S1 as the input signal for the next iteration.

[0024] The aforementioned closed-loop iterative structure, which combines kinematic constraint filtering, partitioned hybrid interpolation, and full-time integral resampling, can achieve high-fidelity waveform recovery at the sampling point level in highly dynamic and non-uniform scenarios. It typically converges in only a few rounds, significantly improving the correlation peak focusing performance and overall compensation accuracy.

[0025] Further, the discrete Doppler coarse estimation in S1 includes: performing matched filtering on the received signal, extracting the correlation peak position index sequence, calculating the ratio of the time interval between adjacent correlation peaks to the theoretical frame period, and obtaining the discrete Doppler factor sequence. Based on the Doppler time-scaling principle, the discrete Doppler factor... ,in The measured frame period is... Theoretical frame period; response speed ,in The speed of sound in water is given by the negative sign, which indicates that the positive velocity is defined as the direction in which the node approaches. By extracting relevant peaks through matched filtering and calculating the time interval ratio, a reliable initial discrete estimation basis is provided for subsequent filtering, ensuring the initial capture of time-varying Doppler in the coarse estimation stage.

[0026] Furthermore, the outlier correction based on kinematic constraints described in S2 includes: setting amplitude thresholds and inter-frame mutation thresholds based on the maximum speed and maximum acceleration of the carrier; making amplitude compliance and inertial continuity decisions on the estimated speed; and performing correction operations on points determined to be outliers to pull outliers back into the physically feasible region.

[0027] This dual-decision mechanism with kinematic constraints effectively eliminates non-physical outliers caused by noise, maintaining the physical accuracy of the estimation and tracking stability in low signal-to-noise ratio environments.

[0028] Furthermore, the correction operation performed on points determined to be abnormal includes a zero-order hold strategy or a similar anchoring method, which forcibly replaces the abnormal value with a nearby normal value.

[0029] Zero-order hold or anchoring correction is simple and efficient, ensuring the continuity of the velocity sequence and avoiding the impact of outliers on subsequent smoothing.

[0030] Furthermore, the outlier correction based on kinematic constraints also includes an iterative variable threshold strategy: a loose threshold is used in the first iteration, and the threshold is gradually tightened in subsequent iterations.

[0031] The iterative variable threshold strategy balances the inclusion of real large maneuvers in the first round with the fine cleaning of residual jitter in the subsequent rounds, further improving robustness.

[0032] Furthermore, the construction of the continuous velocity curve described in S3 adopts a partitioned hybrid interpolation strategy, including: using conformal piecewise cubic Hermitian interpolation in the central region and nearest neighbor interpolation in the beginning and end edge regions to lock the edge velocity to the nearest effective velocity value.

[0033] The partitioned hybrid strategy maintains high precision at the center while suppressing the Runge phenomenon of traditional high-order interpolation through edge locking, thus ensuring the stability of the waveforms at the beginning and end of the frame.

[0034] Furthermore, the beginning and end edge regions are automatically switched to nearest neighbor interpolation by detecting intervals with no valid observation data.

[0035] The automatic detection and switching mechanism enables intelligent edge processing, avoids manual intervention, and improves the adaptability of the algorithm.

[0036] Furthermore, the residual Doppler error index mentioned in S4 is the... Smooth discrete velocity sequence The root mean square error (RMSE).

[0037] Using RMSE as an indicator objectively quantifies the degree of residual distortion, supports rapid termination of adaptive convergence decision, and compensation can usually be completed in 2 to 3 rounds.

[0038] Furthermore, the establishment of the full-time domain nonlinear time mapping relationship described in S5 includes: converting the continuous velocity curve into a time scaling factor sequence, constructing a physical time mapping sequence through cumulative integration, and performing debiasing normalization to generate resampled query coordinates.

[0039] Accurate time-domain inverse projection is achieved through cumulative integration and normalization operations, and fine-grained correction at the sampling point level is performed on the time axis scaling caused by non-uniform velocity, thereby improving the fidelity of waveform recovery.

[0040] Implementation Method 2 This embodiment is a further explanation of embodiment one.

[0041] A Doppler compensation method for underwater acoustic communication based on kinematic constraints and time-varying resampling includes: Step 1: Discrete Doppler rough estimation.

[0042] First, the received discrete-time signal Perform full-time domain matched filtering. Search for the maximum value of the matched filter output magnitude and extract the time position index sequence of the synchronization signal at the receiver. ,in For the first The sampling point indexes corresponding to each correlation peak are then calculated. Next, the time interval between adjacent correlation peaks is calculated. This refers to the actual frame period of the received signal. Its calculation formula is:

[0043] in, This is the sampling rate at the receiving end. Subsequently, this receiving interval... With respect to the theoretical frame period of the transmitted signal That is, the transmission signal duration plus the protection interval duration are compared, and the coarse Doppler factor at that moment is calculated based on the time scaling principle. :

[0044] Finally, using the formula ,in Let be the speed of sound in water. The negative sign indicates that the positive velocity is defined as the direction in which the node approaches, thus obtaining the original discrete velocity sequence containing measurement noise. .

[0045] Step 2: Construct and execute the "kinematic screening" cascaded filtering system.

[0046] For the original velocity sequence obtained in step one To address the measurement noise and multipath outliers present in the data, a three-stage cascaded processing model consisting of "median filtering for noise reduction, kinematic constraints, and statistical smoothing" was established.

[0047] First, perform median filtering (S2.1) for noise reduction. The window length is used. The moving median filter preprocesses the original sequence to remove single-point impulse noise caused by peak jumps in the matched filter, thus obtaining the intermediate sequence. .

[0048] Next, we move on to the core S2.2 kinematic constraint stage. Kinematic thresholds are set based on the physical and mechanical properties of the underwater acoustic carrier: the maximum speed threshold. and the maximum inter-frame velocity mutation threshold .in, With the maximum acceleration of the carrier and block time interval satisfy .

[0049] Next, hard-decision cleaning is performed on the sequence: if the estimated velocity at a certain moment satisfies... If the velocity change at adjacent moments satisfies the condition, it is determined to be "abnormal amplitude"; If the condition is not met, it is determined to be an "inertial anomaly". For points determined to be anomaly, a kinematic state recovery operation is performed, for example, by using a zero-order hold strategy. Finally, a corrected sequence that conforms to the laws of physics is obtained. .

[0050] Specifically, this step employs an "iterative variable threshold" strategy linked to step four: In the first round of global iteration, an amplitude decision threshold is set. The aim is to perform extensive physical boundary cleaning to avoid mistakenly rejecting real high-maneuver signals; In subsequent global iterations, as the Doppler residual converges, the amplitude decision threshold is automatically tightened to... It aims to precisely eliminate minute non-physical jitters.

[0051] Finally, S2.3 statistical smoothing is performed. The kinematically constrained sequence is then globally smoothed using a robust locally weighted regression algorithm to suppress Gaussian white noise, resulting in a final smooth velocity sequence that conforms to the laws of object motion. .

[0052] Step 3: Constructing a continuous velocity curve based on boundary value preservation.

[0053] The discrete velocity sequence after cascade filtering Mapped onto a continuous time axis at the sampling point level to construct a full-time velocity curve. To eliminate the Runge phenomenon (i.e., non-physical oscillations at the edges) that may occur at the beginning and end of finite-length sequences in higher-order interpolation algorithms, this step adopts a "partitioned hybrid interpolation" strategy: First, define the full-time domain sampling point sequence. ,in This represents the total length of the data frame.

[0054] Central Region: For the central region covered by observations on the time axis, conformal piecewise cubic Hermitian interpolation is used. This algorithm effectively preserves the local monotonicity of the data while ensuring the continuity of the first derivative of the curve, avoiding overshoot and undershoot that may occur with conventional spline interpolation.

[0055] For regions with no observed data on the edge: Before the first observed peak and after the last observed peak on the time axis, the PCHIP algorithm will return NaN (NaN) null values. In this case, the system automatically detects such regions with no valid observed data and adaptively switches to the nearest neighbor interpolation strategy. Specifically, the first valid velocity value in the sequence is extended forward to the signal's starting position, while the last valid velocity value is extended backward to the signal's ending position. This mechanism, through an anchoring-like approach, stably locks the Doppler velocity in the signal's edge region to the nearest valid observed value, thereby effectively suppressing error propagation caused by missing data at both ends of the signal.

[0056] Ultimately, a continuous velocity curve with a sampling rate completely consistent with the original received signal was obtained. .

[0057] Step 4: Iterative convergence decision.

[0058] This step aims to assess the degree of residual Doppler distortion in the current signal.

[0059] Because this invention employs a closed-loop feedback architecture, the input signal for each iteration is the compensated signal from the previous iteration. Therefore, the smoothed velocity sequence output in step two of this iteration... It actually represents the residual Doppler velocity remaining after the previous round of compensation.

[0060] The algorithm calculates the root mean square (RMSE) value of the sequence as a convergence metric. .

[0061]

[0062] Compare this indicator with a preset threshold contrast: convergence( This indicates that the Doppler component in the signal has been largely eliminated. The algorithm directly outputs the current iteration input signal as the final output signal.

[0063] Unconverged ( This indicates that significant Doppler distortion still exists in the signal. The algorithm will then activate step five, using the currently estimated velocity curve to further resample and correct the signal.

[0064] Step 5: Full-time domain integral mapping and resampling.

[0065] Using the continuous velocity curve constructed in step three A nonlinear mapping relationship is established from the "distorted time axis" at the receiving end to the "physical real time axis" at the transmitting end, and time-varying resampling compensation is performed on the signal to be processed accordingly.

[0066] First, the physical-level velocity information is converted into time-scaling information at the signal processing level. According to the Doppler definition, the relative velocity of the carrier... Define the time scaling factor as the positive value that is close to the target value. Therefore, the algorithm performs discrete cumulative integrals on the full-time velocity sequence to construct an unnormalized physical-time mapping sequence. Among them, the first The cumulative value of each sampling point is calculated by the following formula:

[0067] This sequence reflects the absolute physical time elapsed during the transmission of the signal.

[0068] Subsequently, in order to align the reconstructed physical time axis with the discrete index of the digital signal processing system, a debiasing normalization operation is performed on the integral sequence, using the formula... The final nonlinear resampling query coordinates are calculated. .

[0069] Finally, using this nonlinear time sequence To retrieve the index, an interpolation filter is used to extract the corresponding amplitude from the input signal in the current iteration, generating a Doppler-compensated update signal. This allows for the precise reversal of the time stretching distortion caused by the non-uniform motion of the carrier in the time domain, and the updated signal is fed back to step S1 to form a closed-loop iteration.

[0070] Implementation Method 3 This embodiment aims to further verify and explain the technical effects of the present invention.

[0071] This implementation method is based on field test data of high-dynamic underwater acoustic communication at the Danjiangkou Reservoir. The experimental scenario simulates high-speed UUV maneuvering, with the highest relative speed between transmission and reception reaching [missing information]. The transmitted signal is a hyperbolic frequency modulated signal; frequency band ,bandwidth Single frame duration .

[0072] Receiver sampling rate speed of sound .

[0073] To comprehensively evaluate the algorithm's performance under different motion states, the continuously acquired received signals were divided into five typical data segments based on motion characteristics. This implementation specifically selects "Data Segment II" as the typical analysis object, corresponding to the original data indexes 3815000 to 7913000, with a data length of 4098001 points, approximately 22.77 seconds. This data segment corresponds to the typical maneuvering acceleration phase of the carrier, during which the relative speed of transmission and reception increases from approximately... Nonlinear acceleration to The left and right sides contain drastic speed changes and multipath structure jitter, which are typical test samples for testing the dynamic tracking capabilities of algorithms.

[0074] Step 1: Discrete Doppler rough estimation.

[0075] First, the received discrete-time signal Full-time domain matched filtering was performed. The maximum value of the matched filter output modulus was searched, and a total of 112 relevant peaks were extracted. Then, according to the calculation logic in step one above, the motion state was calculated frame by frame.

[0076] Taking the intermediate transition moment of this acceleration process, namely the 60th frame, as an example, the specific numerical calculation process is as follows: First, the algorithm measures the difference in the number of sampling points between the correlation peaks of frames 60 and 61, and then calculates the actual received frame period using the sampling rate. .

[0077] Subsequently, the measured value was compared with the theoretical frame period. By directly substituting into the Doppler calculation formula, the Doppler factor at that moment can be obtained. .

[0078] Finally, according to the formula The instantaneous coarse velocity at that moment is calculated. .

[0079] Repeat the above calculations to obtain the original velocity sequence for the entire segment.

[0080] Step 2: Construct and execute the "kinematic screening" cascaded filtering system.

[0081] For the noisy raw velocity sequence output from step one, the algorithm initiates a cascaded filtering system. First, it utilizes a window... The moving median filter effectively filters out random impulse noise in the sequence.

[0082] Subsequently, the physical kinematic constraints phase began. An initial maximum speed threshold was set for the UUV carrier used in this experiment. Threshold for inter-frame abrupt changes caused by maximum acceleration The algorithm dynamically adjusts the screening strategy based on the current global iteration round: In the first iteration: the algorithm uses a relaxed physical limit threshold. Conduct screening. For example... Figure 2 As shown in the log data, the algorithm detected and removed 7 anomalies that violated physical laws in this round, including 1 amplitude anomaly and 6 inertial mutation anomalies. To verify the comprehensiveness of the algorithm, the following two typical anomaly cases are selected for illustration: Case A: Abnormal amplitude, referring to overspeed wild values.

[0083] At sequence index 60, the algorithm detected a sudden change in the median-filtered velocity estimate to 19.55 m / s. This value directly exceeds the maximum speed threshold designed for the carrier. This is a motion state that is physically impossible. The algorithm determines it as an "amplitude anomaly" and forces a zero-order hold correction to pull it back into the physically feasible region.

[0084] Case B: Inertial mutation, targeting acceleration anomalies.

[0085] At sequence index 36, the estimated velocity is -9.55 m / s. Although its absolute value is within the safe range of 15.0 m / s, the system retrieves the corrected velocity of 4.07 m / s from the previous moment (index 35) for comparison, and calculates the inter-frame velocity change. This change was significantly greater than the mutation threshold of 3.0 m / s, meaning that the vector had experienced an unattainable instantaneous acceleration. Based on this, the algorithm determined it to be an "inertial anomaly" and discarded it.

[0086] In the second iteration: At this point, the algorithm's focus shifts to the "residual error velocity" after the first round of compensation. Theoretically, the residual should approach zero, so the algorithm automatically tightens the amplitude judgment threshold significantly to 3.0 m / s to identify non-physical jitter relative to the zero-velocity reference.

[0087] Under these stringent standards, this round further cleaned up 11 outliers. The typical composite decision logic is as follows: A complex anomaly occurred at index 36. In this round of estimation, the residual velocity estimate at this point was -14.15 m / s. Since its absolute value far exceeded the residual tolerance of 3.0 m / s, and there was a sharp change of 11.67 m / s compared to the previous time step of -2.48 m / s, the algorithm determined it to be a complex error of amplitude anomaly and inertial change, and forcibly corrected it.

[0088] An anomaly in residual amplitude was detected at index 49. The residual velocity at this point was 3.74 m / s. Although this value is small in absolute terms, it represents a sudden jump relative to the previous stationary point in the residual domain. The algorithm identified this as residual noise and implemented a preservation strategy, thereby ensuring the smoothness and high accuracy of the final velocity curve.

[0089] Finally, the rLOWESS algorithm with a window length of 10 was used to smooth the cleaned sequence, generating a smooth and continuous velocity curve, which laid the foundation for subsequent interpolation and reconstruction.

[0090] Step 3: Constructing a continuous velocity curve based on boundary value preservation.

[0091] Using the discrete smooth velocity sequence output from step two, the algorithm constructs a continuous velocity curve across the entire time domain. For the unobserved data intervals at the beginning and end of underwater acoustic signal frames, the system performs strict edge protection. In the first iteration: The algorithm first uses the PCHIP algorithm to achieve a smooth connection of the central region. Then, as... Figure 3 As shown, through null value detection, a total of 56,264 sampling points with no observed data were identified at both ends of the signal, corresponding to a duration of approximately 0.3126 seconds. For this edge interval with no observed data, the algorithm employs a "nearest neighbor locking" strategy: the first valid velocity observation value at the beginning of the signal is maintained forward to the beginning of the sequence, while the last valid velocity value at the end of the signal is maintained backward to the end of the frame. This processing effectively avoids the risk of the velocity curve diverging in non-physical directions in the absence of observed data.

[0092] In the second iteration: As the accuracy of the relevant peak extraction changes, the range of the unobserved data interval at the edge is fine-tuned to 43,786 sampling points, corresponding to a duration of approximately 0.2433 seconds. The algorithm continues to execute a hybrid interpolation strategy, ensuring that the reconstructed velocity curve is both smooth and differentiable throughout the entire time domain, while maintaining convergence and stability in the edge regions.

[0093] In the third iteration: The range of the unobserved data interval at the edge was further fine-tuned to 43,901 sampling points, approximately 0.2439 seconds. The algorithm continues to employ a partitioned interpolation strategy to ensure that the reconstructed velocity curve possesses both the smoothness and differentiability of the central region and the convergence stability of the edge region across the entire time domain.

[0094] Step 4: Iterative Convergence Decision The algorithm calculates the root mean square error based on the residual estimate output in step two.

[0095] First iteration: The velocity sequence output in step two reflects the absolute motion of the carrier. The calculated RMSE is 5.2030 m / s, which is judged as "non-converged", triggering step five to perform the initial compensation.

[0096] Second iteration: The input at this stage is the signal after the initial compensation. The newly estimated velocity sequence in step two represents the "residual error after the initial compensation". The calculated RMSE is 0.0676 m / s, which is judged as "non-converged", triggering step five for secondary compensation.

[0097] Third iteration: The signal after secondary compensation is estimated again. The residual output from step two has a very small velocity. The calculated RMSE is 0.0274 m / s, which meets the threshold condition. The algorithm determines that it has converged and terminates the iteration.

[0098] Step 5: Full-time domain integral mapping and resampling If the convergence decision in step four fails, the algorithm will execute this step. In this implementation, the specific execution logic of this step in each iteration is as follows: In the first iteration: Since the initial residual error RMSE of 5.2030 m / s is far above the convergence threshold, the algorithm must execute this step. The algorithm reads the continuous velocity curve output from step three, which has a total length of 4,098,001 points, and uses the formula... This was transformed into a time scaling factor sequence. Subsequently, a physical time axis exhibiting a non-linear growth trend was constructed through cumulative integration, and query coordinates were generated after normalization and alignment. Finally, a linear interpolator was used to perform full-time domain resampling of the original received signal. The log showed "Time axis non-linear mapping completed, resampling complete," and the generated compensation signal eliminated the main Doppler distortion, then was fed into the second iteration.

[0099] In the second iteration: The residual error RMSE from the previous round was 0.0676 m / s. Based on the updated residual velocity curve from this round, the algorithm reconstructed the fine-tuned time mapping relationship and performed a second resampling on the primary compensation signal. The phase accuracy of the generated secondary compensation signal was further improved.

[0100] In the third iteration: Before proceeding to the third round of processing, step four determines that the current residual error RMSE is 0.0274 m / s, which meets the convergence condition of less than 0.05 m / s. Therefore, the algorithm automatically terminates subsequent resampling operations and directly outputs the signal generated in the second iteration as the final result. The final channel impulse response is as follows: Figure 4 As shown, after the above integral mapping and resampling processing, the multipath delay structure is clearly focused, verifying the physical fidelity of the time domain reconstruction method.

[0101] The above detailed description of the technical solution provided by the present invention is intended to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above detailed embodiments are not intended to limit the scope of protection of the present invention. Any reasonable modifications and improvements to the present invention, recombination of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0102] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims disclosed in the present invention can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in the disclosure of the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle scope of the present invention should be considered to fall within the protection scope of the present invention.

[0103] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A Doppler compensation method for underwater acoustic communication based on kinematic constraints and time-varying resampling, characterized in that, Includes the following steps: S1. Perform discrete Doppler coarse estimation on the received underwater acoustic communication signal to obtain a discrete Doppler factor sequence containing noise; S2. The discrete Doppler factor sequence is subjected to cascaded filtering processing, including median filtering for noise reduction, outlier correction based on kinematic constraints, and statistical smoothing, to obtain a smooth discrete velocity sequence. S3. Construct a continuous velocity curve based on the smooth discrete velocity sequence; S4. Calculate the residual Doppler error index based on the smoothed discrete velocity sequence, compare it with a preset convergence threshold, and perform iterative convergence determination: If the convergence condition is not met, proceed to step S5; If the convergence condition is met, the currently processed signal is directly output as the final Doppler compensation result, and the iteration is terminated. S5. Based on the continuous velocity curve, a nonlinear time mapping relationship in the entire time domain is established through numerical integration. The current signal to be processed is time-varyingly resampled to generate an updated signal after Doppler compensation. The updated signal is then fed back to S1 as the input signal for the next iteration.

2. The method according to claim 1, characterized in that, The discrete Doppler coarse estimation described in S1 includes: performing matched filtering on the received signal, extracting the correlation peak position index sequence, calculating the ratio of the time interval between adjacent correlation peaks to the theoretical frame period, and obtaining the discrete Doppler factor sequence.

3. The method according to claim 1, characterized in that, S2 describes outlier correction based on kinematic constraints, which includes: Set amplitude thresholds and inter-frame mutation thresholds based on the carrier's maximum speed and maximum acceleration; The estimated velocity is judged for compliance with amplitude and continuity of inertia. Perform correction operations on points identified as abnormal to bring the outliers back into the physical feasible region.

4. The method according to claim 3, characterized in that, The correction operation performed on points determined to be abnormal includes a zero-order hold strategy or a similar anchoring method, which forcibly replaces the abnormal value with a nearby normal value.

5. The method according to claim 4, characterized in that, The outlier correction based on kinematic constraints also includes an iterative variable threshold strategy: a loose threshold is used in the first iteration, and the threshold is gradually tightened in subsequent iterations.

6. The method according to claim 1, characterized in that, The continuous velocity curve constructed in S3 adopts a partitioned hybrid interpolation strategy, including: using conformal piecewise cubic Hermitian interpolation in the central region and nearest neighbor interpolation in the beginning and end edge regions to lock the edge velocity to the nearest effective velocity value.

7. The method according to claim 6, characterized in that, The beginning and end edge regions are automatically switched to nearest neighbor interpolation by detecting intervals with no valid observation data.

8. The method according to claim 1, characterized in that, The residual Doppler error index mentioned in S4 is the root mean square error (RMSE) of a smoothed discrete velocity sequence.

9. The method according to claim 1, characterized in that, The establishment of the full-time domain nonlinear time mapping relationship described in S5 includes: converting the continuous velocity curve into a time scaling factor sequence, constructing a physical time mapping sequence through cumulative integration, and performing debiasing normalization to generate resampled query coordinates.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-9.

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