A method for signal time difference, frequency difference estimation for two observation stations

Abstract

The present application relates to a kind of signal time difference, frequency difference estimation method for two observation stations, belong to radiation source signal positioning technical field, solve the problem of the time difference, frequency difference estimation precision of two observation stations in prior art.The estimation method includes: using a plurality of stochastic resonance systems set in advance respectively to the signal to be estimated signal is carried out signal enhancement processing, obtain multiple enhanced signals;Wherein, the signal to be estimated signal includes the sampling signal of two observation stations;The time difference of the sampling signal of two observation stations in multiple enhanced signals is calculated respectively, the average of the multiple time difference obtained is used as the time difference estimation value of signal to be estimated;Using the optimal stochastic resonance system set in advance to the signal to be estimated signal is carried out signal enhancement processing, obtain optimal enhanced signal;Optimal enhanced signal is input to the frequency difference estimation model that is trained in advance, and the frequency difference estimation value of signal to be estimated is predicted to obtain.It improves the estimation precision of time difference, frequency difference.

Description

Technical Field

[0001] This invention relates to the field of radiation source signal localization technology, and in particular to a method for estimating the signal time difference and frequency difference between two observation stations. Background Technology

[0002] TDOA (Time Difference of Arrival) and FDOA (Frequency Difference of Arrival) extraction are core technologies of multi-station passive positioning systems, widely used in radar, sonar, wireless communication, electronic reconnaissance, and other fields. By measuring the time difference and frequency difference of signals arriving at different observation stations, the location and motion state of radiation sources can be accurately calculated, which is of great value in scenarios such as military defense, disaster relief, and drone surveillance.

[0003] Traditional time-frequency difference extraction methods mainly rely on the cross-ambiguity function (CAF) and its improved algorithms. However, the performance of such methods deteriorates significantly in low signal-to-noise ratio (SNR < -10 dB) environments: ① High noise sensitivity: The peak of the cross-ambiguity function is submerged by noise, leading to increased time-frequency difference estimation errors; ② High computational complexity: It requires traversing a two-dimensional search space of time delay and frequency shift, resulting in poor real-time performance and difficulty in meeting the requirements of dynamic target tracking; ③ Insufficient adaptability to broadband signals: Traditional methods are designed for narrowband signals, while modern communication signals (such as BPSK and OFDM) have broadband characteristics, and the spectrum broadening further reduces the estimation accuracy.

[0004] Therefore, there is an urgent need for a new technical solution for estimating the signal time difference and frequency difference between two observation stations. Summary of the Invention

[0005] Based on the above analysis, the present invention aims to provide a method for estimating the signal time difference and frequency difference between two observation stations, in order to solve the problem of poor accuracy in estimating the time difference and frequency difference between two observation stations in the prior art.

[0006] This invention provides a method for estimating the signal time difference and frequency difference between two observation stations. The estimation method includes:

[0007] Multiple pre-set random resonance systems are used to perform signal enhancement processing on the signal to be estimated, resulting in multiple enhanced signals; the signal to be estimated includes the sampled signals from two observation stations. The time difference between the sampled signals of two observation stations in multiple enhanced signals is calculated separately, and the average of the multiple time differences is used as the time difference estimate of the signal to be estimated. The optimal enhanced signal is obtained by using a pre-set optimal stochastic resonance system to enhance the signal to be estimated. The optimal enhanced signal is input into a pre-trained frequency difference estimation model to predict the frequency difference estimate of the signal to be estimated.

[0008] Based on the further improvement of the above estimation method, multiple stochastic resonance systems and the optimal stochastic resonance system are pre-set through the following steps: Multiple signal samples were collected by two observation stations; each signal sample included signals collected by both observation stations from the same radiation source. All possible stochastic resonance systems were determined based on the signal-to-noise ratio of the signals received at the two observation stations. By using multiple signal samples to screen all possible stochastic resonance systems, multiple stochastic resonance systems and the optimal stochastic resonance system are obtained.

[0009] Based on a further improvement to the above estimation method, the process of using multiple signal samples to screen all possible stochastic resonance systems yields multiple stochastic resonance systems and an optimal stochastic resonance system, including: By using multiple signal samples, all possible stochastic resonance systems are evaluated, and evaluation values ​​for all possible stochastic resonance systems are obtained. Multiple stochastic resonance systems and the optimal stochastic resonance system are determined based on the evaluation values ​​of all possible stochastic resonance systems.

[0010] Based on further improvements to the above estimation method, the evaluation value of each possible stochastic resonance system is determined through the following steps: Multiple signal samples are input into each possible stochastic resonance system for signal enhancement processing to obtain multiple signal enhancement samples; Calculate the normalized cross-correlation coefficient for each signal enhancement sample in the multiple signal enhancement samples to obtain multiple normalized cross-correlation coefficients; The average of multiple normalized cross-correlation coefficients is used as the evaluation value for each possible stochastic resonance system.

[0011] Based on the further improvement of the above estimation method, the normalized cross-correlation coefficient of each signal enhancement sample is calculated using the following formula: ; in, This represents the normalized cross-correlation coefficient for each signal enhancement sample. This represents the sequence of signals acquired by one observation station in each signal enhancement sample. This represents the sequence of averaged signals collected from one observation station in each signal enhancement sample. This represents the signal acquired by another observation station in each signal enhancement sample. The sequence of averaged signals from another observation station in each signal enhancement sample.

[0012] Based on a further improvement to the above estimation method, the step of determining multiple stochastic resonance systems and the optimal stochastic resonance system based on the evaluation values ​​of all possible stochastic resonance systems includes: Sort the evaluation values ​​of all possible stochastic resonance systems in descending order to obtain the sorted evaluation values; The stochastic resonance system corresponding to the maximum evaluation value is selected as the optimal stochastic resonance system. From the sorted evaluation values, select a preset number of stochastic resonance systems corresponding to the evaluation values ​​from front to back as multiple stochastic resonance systems.

[0013] Based on a further improvement to the above estimation method, the step of calculating the time difference between the sampled signals of two observation stations in multiple enhanced signals includes: By determining all possible combinations of time difference and frequency difference, multiple combinations of time difference and frequency difference are obtained; Calculate the mutual ambiguity function value corresponding to each enhancement signal for each time difference-frequency difference combination, and obtain multiple mutual ambiguity function values ​​corresponding to each enhancement signal for multiple time difference-frequency difference combinations; The time difference in the combination of time difference and frequency difference corresponding to the maximum mutual ambiguity function value is selected as the time difference between the sampled signals of the two observation stations in each enhanced signal.

[0014] Based on the further improvement of the above estimation method, the mutual ambiguity function value corresponding to each enhanced signal in each time-difference-frequency-difference combination is calculated using the following formula: ; ; in, , This represents the time difference and frequency difference in each combination of time difference and frequency difference. This represents the mutual ambiguity function value corresponding to each enhancement signal for each time-frequency difference combination. Indicates the number of sampling points. This represents the first observation station in each enhanced signal. One sampled signal, Indicates the first observation station in each enhanced signal. One sampled signal, This indicates the sampling rate.

[0015] Based on a further improvement of the above estimation method, the frequency difference estimation model is trained on a preset neural network, which can be any of the following: Convolutional Neural Networks; Recurrent neural networks; Attention mechanisms enhance networks.

[0016] Based on further improvements to the above estimation method, the loss function of the frequency difference estimation model can be any of the following: Mean squared error loss function; Mean absolute error loss function; Huber loss function.

[0017] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: By simultaneously enhancing the sampled signals of two observation stations in the signal to be estimated using multiple stochastic resonance systems, the influence of noise in the signal to be estimated is reduced. The time difference between the sampled signals of the two observation stations in the multiple enhanced signals is calculated, and the average of the multiple time differences is used as the time difference estimate of the signal to be estimated, which greatly improves the time difference estimation accuracy of the two observation stations. Furthermore, by using the optimal resonance system to enhance the signal to be estimated and combining it with the frequency difference estimation model, the frequency difference of the two observation stations predicted is even more accurate.

[0018] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0019] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0020] Figure 1 This is a flowchart illustrating a method for estimating the signal time difference and frequency difference between two observation stations, provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the process for training the frequency difference estimation model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the frequency difference estimation model provided in an embodiment of the present invention. Detailed Implementation

[0021] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0022] In multi-station positioning systems, using the time difference of time (TDOA) of signals received from multiple observation stations to estimate the location of a radiation source is a core technology. This technology calculates the distance difference based on the time difference of the radiation source signal arriving at different observation stations and solves for the coordinates of the radiation source through geometric relationships.

[0023] In low signal-to-noise ratio (SNR) applications, it is often difficult to accurately estimate the time difference and frequency difference between different observation stations. This results in a large error in the accuracy of estimating the location of radiation sources in low SNR applications, which is difficult to meet application requirements.

[0024] A specific embodiment of the present invention discloses a method for estimating the signal time difference and frequency difference between two observation stations, such as... Figure 1 As shown, the estimation method includes: Step S1: Use multiple pre-set random resonance systems to perform signal enhancement processing on the signal to be estimated, and obtain multiple enhanced signals; wherein, the signal to be estimated includes the sampled signals from two observation stations; Step S2: Calculate the time difference between the sampled signals of two observation stations in the multiple enhanced signals respectively, and take the average of the multiple time differences as the time difference estimate of the signal to be estimated; Step S3: Use the pre-set optimal stochastic resonance system to perform signal enhancement processing on the signal to be estimated, and obtain the optimal enhanced signal; Step S4: Input the optimal enhanced signal into the pre-trained frequency difference estimation model to predict the frequency difference estimate of the signal to be estimated.

[0025] Specifically, such as Figure 1 As shown, in step S1, the signal to be estimated includes the sampled signals from two observation stations. When the application environment of the two observation stations is a low signal-to-noise ratio environment, the noise in the acquired signal to be estimated is large, which seriously affects the time difference estimation and frequency difference estimation of the two observation stations.

[0026] Specifically, such as Figure 1 As shown, in step S1, multiple random resonance systems are pre-set. Each of the multiple random resonance systems converts part of the noise energy in the signal to be estimated into signal energy through a specific nonlinear system, thereby enhancing the weak feature signal and improving the signal-to-noise ratio.

[0027] Specifically, such as Figure 1 As shown, in step S3, an optimal random resonance system is pre-set. The optimal random resonance system converts part of the noise energy in the signal to be estimated into signal energy, thereby enhancing the weak characteristic signal, improving the signal-to-noise ratio, and improving the frequency difference estimation between the two observation stations.

[0028] Preferably, multiple stochastic resonance systems and an optimal stochastic resonance system are pre-set through the following steps: Multiple signal samples were collected by two observation stations; each signal sample included signals collected by both observation stations from the same radiation source. All possible stochastic resonance systems were determined based on the signal-to-noise ratio of the signals received at the two observation stations. By using multiple signal samples to screen all possible stochastic resonance systems, multiple stochastic resonance systems and the optimal stochastic resonance system are obtained.

[0029] Specifically, first, the multiple stochastic resonance systems in step S1 are set, and then the optimal stochastic resonance system in step S3 is set based on the multiple stochastic resonance systems.

[0030] Specifically, signals from the same radiation source can be collected by two observation stations, and signals from different time periods can be used as a single signal sample. The sampling is done through discrete sampling, and each signal sample includes a fixed number of consecutive sampling points.

[0031] Specifically, signals from the same radiation source can be collected from multiple observation stations. The signals from any two observation stations within the same time period can be used as multiple signal samples. The sampling is done discretely, and each signal sample includes a fixed number of consecutive sampling points.

[0032] It is worth noting that the same signal sample includes signals collected by two observation stations from the same radiation source at the same time period, which will not be elaborated further here.

[0033] It is understandable that a stochastic resonance system includes a linear stiffness coefficient a and a nonlinear stiffness coefficient b, and each combination of the linear stiffness coefficient a and the nonlinear stiffness coefficient b constitutes a stochastic resonance system.

[0034] Specifically, after obtaining multiple signal samples, the signal-to-noise ratio (SNR) is determined by combining the application scenarios of the two observation stations, i.e., the signal-to-noise ratio of the two observation stations is determined. Based on the signal-to-noise ratio of the two observation stations, the feasible range of the linear stiffness coefficient 'a' and the nonlinear stiffness coefficient 'b' in the stochastic resonance system is determined. Then, all combinations of linear stiffness coefficient 'a' and nonlinear stiffness coefficient 'b' are determined as all possible stochastic resonance systems.

[0035] Specifically, multiple signal samples are used to screen all possible stochastic resonance systems, resulting in multiple stochastic resonance systems and the optimal stochastic resonance system.

[0036] Preferably, the step of screening all possible stochastic resonance systems using multiple signal samples to obtain multiple stochastic resonance systems and the optimal stochastic resonance system includes: By using multiple signal samples, all possible stochastic resonance systems are evaluated, and evaluation values ​​for all possible stochastic resonance systems are obtained. Multiple stochastic resonance systems and the optimal stochastic resonance system are determined based on the evaluation values ​​of all possible stochastic resonance systems.

[0037] Specifically, all possible random resonance systems are numbered, and each numbered random resonance system is evaluated using multiple signal samples to determine the evaluation value corresponding to all numbered random resonance systems, that is, to determine the evaluation value of all possible random resonance systems.

[0038] Preferably, the evaluation value for each possible stochastic resonance system is determined by the following steps: Multiple signal samples are input into each possible stochastic resonance system for signal enhancement processing to obtain multiple signal enhancement samples; Calculate the normalized cross-correlation coefficient for each signal enhancement sample in the multiple signal enhancement samples to obtain multiple normalized cross-correlation coefficients; The average of multiple normalized cross-correlation coefficients is used as the evaluation value for each possible stochastic resonance system.

[0039] Specifically, when determining the evaluation value of a certain numbered stochastic resonance system, multiple signal samples are respectively processed through the stochastic resonance system with that number to obtain multiple signal-enhanced samples.

[0040] Specifically, a normalized cross-correlation coefficient is calculated for each signal enhancement sample, and multiple normalized cross-correlation coefficients are calculated for multiple signal enhancement samples.

[0041] Preferably, the normalized cross-correlation coefficient for each signal enhancement sample is calculated using the following formula: ; in, This represents the normalized cross-correlation coefficient for each signal enhancement sample. This represents the sequence of signals acquired by one observation station in each signal enhancement sample. This represents the sequence of averaged signals collected from one observation station in each signal enhancement sample. This represents the signal acquired by another observation station in each signal enhancement sample. The sequence of averaged signals from another observation station in each signal enhancement sample.

[0042] Specifically, each signal enhancement sample includes multiple sampling points from two observation stations, with the same number of sampling points at both stations. The normalized cross-correlation coefficient for each signal enhancement sample was calculated.

[0043] Specifically, after obtaining multiple normalized cross-correlation coefficients corresponding to multiple signal enhancement samples, the average value of the multiple normalized cross-correlation coefficients is used as the evaluation value of a certain numbered stochastic resonance system.

[0044] Specifically, by iterating through all numbered stochastic resonance systems, the evaluation values ​​of all possible stochastic resonance systems can be obtained.

[0045] It is worth noting that evaluating the same stochastic resonance system using multiple signal enhancement samples improves the robustness and reliability of the evaluation values, laying the foundation for further improving the accuracy of time difference and frequency difference estimates.

[0046] Specifically, after obtaining the evaluation values ​​of all possible stochastic resonance systems, the evaluation values ​​of all possible stochastic resonance systems are analyzed to determine multiple stochastic resonance systems and the optimal stochastic resonance system.

[0047] Preferably, determining multiple stochastic resonance systems and the optimal stochastic resonance system based on the evaluation values ​​of all possible stochastic resonance systems includes: Sort the evaluation values ​​of all possible stochastic resonance systems in descending order to obtain the sorted evaluation values; The stochastic resonance system corresponding to the maximum evaluation value is selected as the optimal stochastic resonance system. From the sorted evaluation values, select a preset number of stochastic resonance systems corresponding to the evaluation values ​​from front to back as multiple stochastic resonance systems.

[0048] Specifically, the evaluation values ​​of all possible stochastic resonance systems are compared and then sorted in descending order to obtain the sorted evaluation values. The stochastic resonance system corresponding to the highest evaluation value is taken as the optimal stochastic resonance system in step S3.

[0049] Specifically, among the sorted evaluation values, starting from the highest evaluation value, a preset number of evaluation values ​​are selected in sequence, and the random resonance systems corresponding to the selected evaluation values ​​are used as multiple random resonance systems, which are used as multiple random resonance systems in step S1.

[0050] Specifically, such as Figure 1 As shown, in step S1, the sampled signals from the two observation stations are input to multiple pre-set stochastic resonance systems in parallel. The multiple stochastic resonance systems process the signal to be estimated independently and simultaneously, and obtain multiple enhanced signals. Each stochastic resonance system corresponds to one enhanced signal.

[0051] Specifically, such as Figure 1 As shown, in step S3, the sampling signals from the two observation stations are input into the pre-set optimal stochastic resonance system. The optimal stochastic resonance system processes the signal to be estimated to obtain the optimal enhanced signal.

[0052] It is worth noting that in the same stochastic resonance system, the sampled signals from two observation stations in the signal to be estimated are respectively enhanced by the stochastic resonance system. The sampled signals from the two observation stations do not interfere with each other during the processing of the stochastic resonance system, which will not be elaborated here.

[0053] Specifically, such as Figure 1 As shown, in step S2, the time difference between the sampled signals of the two observation stations in each enhanced signal is calculated independently. Since multiple enhanced signals were obtained through step S1, the multiple time differences corresponding to these enhanced signals are calculated in step S2.

[0054] Specifically, in step S2, the average value of multiple time differences corresponding to multiple signal enhancement signals is calculated, and the average value is used as the time difference estimate of the signal to be estimated, that is, as the time difference estimate of the sampled signals of the two observation stations in the signal to be estimated, which further improves the time difference estimation accuracy of the sampled signals of the two observation stations.

[0055] Preferably, the step of calculating the time difference between the sampled signals of two observation stations in the multiple enhanced signals includes: By determining all possible combinations of time difference and frequency difference, multiple combinations of time difference and frequency difference are obtained; Calculate the mutual ambiguity function value corresponding to each enhancement signal for each time difference-frequency difference combination, and obtain multiple mutual ambiguity function values ​​corresponding to each enhancement signal for multiple time difference-frequency difference combinations; The time difference in the combination of time difference and frequency difference corresponding to the maximum mutual ambiguity function value is selected as the time difference between the sampled signals of the two observation stations in each enhanced signal.

[0056] Understandably, based on the signal receiving capabilities of the two observation stations, the time difference range and frequency difference range of the signals received by the two observation stations can be determined, and then all possible combinations of time difference and frequency difference can be determined, resulting in multiple time difference and frequency difference combinations of the two observation stations.

[0057] Specifically, each enhanced signal corresponds to a mutual ambiguity function value for each time difference-frequency difference combination, and thus each enhanced signal corresponds to multiple mutual ambiguity function values ​​for multiple time difference-frequency difference combinations.

[0058] Preferably, the mutual ambiguity function value corresponding to each enhanced signal for each time-difference-frequency-difference combination is calculated using the following formula: ; ; in, , This represents the time difference and frequency difference in each combination of time difference and frequency difference. This represents the mutual ambiguity function value corresponding to each enhancement signal for each time-frequency difference combination. Indicates the number of sampling points. This represents the first observation station in each enhanced signal. One sampled signal, Indicates the first observation station in each enhanced signal. One sampled signal, This indicates the sampling rate.

[0059] Specifically, the sampled signal values ​​from multiple sampling points at two observation stations for each enhanced signal are substituted into... The mutual ambiguity function value corresponding to each enhanced signal in each time-frequency difference combination is obtained.

[0060] Specifically, the time difference in the time difference-frequency difference combination corresponding to each enhanced signal is compared with the time difference-frequency difference combination corresponding to the maximum time difference-frequency difference combination, and the time difference is selected as the time difference between the sampling signals of the two observation stations in each enhanced signal.

[0061] It is worth noting that at this time, the frequency difference between the sampled signals of the two observation stations in each enhanced signal can be calculated synchronously using the mutual fuzzy function method. This frequency difference is discarded and not used as the frequency difference estimate in this invention.

[0062] Specifically, such as Figure 1 As shown, in step S2, the time difference between the sampled signals of the two observation stations in each of the multiple enhanced signals is calculated. Since there are multiple enhanced signals, the multiple time differences between the sampled signals of the two observation stations are obtained synchronously. The average value of the multiple time differences is used as the time difference estimate of the sampled signals of the two observation stations, that is, as the time difference estimate of the signal to be estimated.

[0063] Specifically, such as Figure 1 As shown, in step S4, the optimal enhanced signal is input into the pre-trained frequency difference estimation model, and the frequency difference estimation model is used to predict the frequency difference of the sampled signals of the two observation stations, that is, to predict the frequency difference estimate of the signal to be estimated.

[0064] Preferably, the frequency difference estimation model is trained based on a preset neural network, and the preset neural network is any one of the following: Convolutional Neural Networks; Recurrent neural networks; Attention mechanisms enhance networks.

[0065] Specifically, a convolutional neural network is a type of feedforward neural network. Its core structure includes convolutional layers, pooling layers, and fully connected layers. Convolutional layers extract local features through sliding kernels, pooling layers reduce dimensionality while retaining key information, and fully connected layers complete regression or classification tasks. Using a convolutional neural network as the structure of a frequency difference estimation model can utilize the convolutional kernels in the convolutional neural network to extract features from signal bit transitions and spectral peaks, resulting in higher accuracy of the predicted frequency difference estimate.

[0066] Specifically, recurrent neural networks (RNNs), as a type of neural network that processes sequential data, have internal state memory capabilities, enabling them to capture temporal dependencies. It's understandable that frequency difference is essentially the rate of change of signal phase over time; RNNs can directly model this dynamic evolution. Furthermore, RNNs do not require a fixed input length, making them suitable for processing continuous stream signals and offering high flexibility.

[0067] Specifically, attention-enhanced networks are techniques that allow a network to focus on key parts of the input. A typical example is the Transformer model, which calculates weights through query-key-value pairs and dynamically allocates attention resources. Attention-enhanced networks can automatically weight important time points or frequency components of the signal, ignoring noisy regions and improving estimation accuracy. Furthermore, when processing broadband signals, attention-enhanced networks can extract frequency difference information that may be scattered throughout long sequences.

[0068] Specifically, when selecting a preset neural network, one can make a reasonable choice, which will not be elaborated here.

[0069] Preferably, the loss function of the frequency difference estimation model adopts any of the following: Mean squared error loss function; Mean absolute error loss function; Huber loss function.

[0070] Specifically, the mean squared error loss function has the advantages of being smooth, differentiable, and convergent, but it also has the disadvantage of being sensitive to outliers. It is suitable for environments with clean labels and has a relatively fast training speed.

[0071] Specifically, the mean absolute error loss function is robust to outliers, but it is not differentiable at zero, has a slow convergence speed, is suitable for scenarios with low signal-to-noise ratios, and has a slow training speed.

[0072] Specifically, the Huber loss function balances sensitivity and robustness by fusing the mean squared error loss function and the mean absolute error loss function.

[0073] It is worth noting that when selecting the loss function for the frequency difference estimation model, three different loss functions can be selected for training at the same time, and the final loss function of the frequency difference estimation model can be determined based on the actual usage requirements.

[0074] Preferably, such as Figure 2 As shown, the frequency difference estimation model is trained through the following steps: Step S41: Conduct multiple experiments by changing the location of the radiation source signal. In each experiment, use two observation stations to receive the signal. Take the signals from the same radiation source received by the two observation stations as a group of signals and mark the frequency difference of each group of signals. Step S42: Use the pre-set optimal stochastic resonance system to perform signal enhancement processing on each group of signals, and use each group of signals after signal enhancement processing and the frequency difference of each group of signals as a training sample to obtain the training set of the frequency difference estimation model. Step S43: Train the frequency difference estimation model based on the training set to obtain the trained frequency difference estimation model; wherein the frequency difference estimation model adopts a convolutional neural network.

[0075] Specifically, such as Figure 2 As shown, in step S41, multiple tests are conducted using two observation stations. Multiple tests can be conducted at the same location. In each test, the signal can be randomly generated and received using two observation stations.

[0076] Specifically, a set of signals can be obtained through each experiment. The peak difference of the two station signals is measured using a high-resolution spectrum analyzer and used as a benchmark for frequency difference labeling.

[0077] Specifically, such as Figure 2 As shown, in step S42, each group of signals is input to a pre-set optimal random resonance system. The optimal random resonance system performs signal enhancement processing on each group of signals to obtain each group of signals after signal enhancement processing. Finally, each group of signals after signal enhancement processing and the frequency difference of each group of signals are used as a training sample, thereby obtaining multiple training samples as a training set.

[0078] Specifically, such as Figure 2 As shown, in step S43, the frequency difference estimation model composed of the convolutional neural network is trained using the training set obtained in step S42 to obtain the trained frequency difference estimation model.

[0079] Preferably, such as Figure 3 As shown, the frequency difference estimation model includes an input layer, a feature extraction layer, and a fully connected regression layer; The input layer receives each set of signals and transmits each set of signals to the feature extraction layer. The feature extraction layer is used to extract features from each group of signals and then transmit the extracted features to the fully connected regression layer. The fully connected regression layer is used to predict the frequency difference of each signal based on the extracted features of each signal.

[0080] Specifically, such as Figure 3As shown, the preferred frequency difference estimation model in this embodiment of the invention is a convolutional neural network, which includes an input layer, a feature extraction layer, and a fully connected regression layer connected in sequence. The input layer receives each set of signals and transmits each set of signals to the feature extraction layer. The feature extraction layer extracts features from each set of signals to obtain the extracted features of each set of signals. In the fully connected regression layer, the frequency difference prediction value of each set of signals is predicted based on the extracted features of each set of signals.

[0081] Preferably, the feature extraction layer includes multiple feature extraction sub-layers connected in sequence, and each feature extraction sub-layer includes a convolutional layer, a batch normalization layer and an activation function layer connected in sequence. Convolutional layers are used to perform convolution operations on the input signals and then transmit the convolutional signals to the batch normalization layer. The batch normalization layer is used to perform batch normalization on the input signal and then transmit the batch normalized signal to the activation function layer. The activation function layer is used to activate the input signal and then transmit the activated signal to the next layer of the network.

[0082] Specifically, such as Figure 3 As shown, the feature extraction sub-layers in the frequency difference estimation model provided in this embodiment of the invention have the same structure, and each feature extraction sub-layer includes a convolutional layer, a batch normalization layer and an activation function layer connected in sequence. The convolutional layer performs convolution operation on the input signal, the batch normalization layer performs batch normalization operation on the input signal, and the activation function layer performs activation operation on the input signal.

[0083] Preferably, the feature extraction layer includes 3-5 feature extraction sub-layers.

[0084] Specifically, after determining the network structure of the frequency difference estimation model, the frequency difference estimation model is trained using multiple training samples from the training set obtained in step S2.

[0085] Preferably, the loss function of the frequency difference estimation model is: ; in, Indicates the number of training samples. Indicates the first Signal frequency difference label values ​​in each training sample Indicates the first Predicted signal frequency difference values ​​from each training sample. This represents the minimum constant.

[0086] It is worth noting that since the "relative error" of frequency difference is more important than the "absolute error," for example, the error is 1Hz when the frequency difference is 10Hz, and the error is 1Hz when the frequency difference is 100Hz. The former has a larger relative error. Therefore, the frequency difference estimation model provided in this embodiment of the invention adopts the relative mean square error loss function during the training process.

[0087] Specifically, in step S43, when training the frequency difference estimation model, a training cutoff condition is set in advance, such as when the number of training rounds reaches a threshold or the loss function used meets the threshold, and the training is completed to obtain the trained frequency difference estimation model.

[0088] Specifically, such as Figure 1 As shown, in step S4, the optimal enhanced signal is input to the pre-trained frequency difference estimation model. The frequency difference estimation model makes predictions based on the optimal enhanced signal, thereby obtaining the frequency difference between the signals of the two observation stations in the optimal enhanced signal, which is used as the frequency difference estimate of the signal to be estimated.

[0089] Compared with the prior art, the signal time difference and frequency difference estimation method for two observation stations provided in this embodiment of the invention enhances the sampled signals of the two observation stations in the signal to be estimated by using multiple random resonance systems simultaneously, thereby reducing the influence of noise in the signal to be estimated. The time difference of the sampled signals of the two observation stations in the multiple enhanced signals is calculated, and the average value of the multiple time differences is used as the time difference estimate of the signal to be estimated, which greatly improves the time difference estimation accuracy of the two observation stations. Furthermore, the optimal resonance system is used to enhance the signal to be estimated, and combined with the frequency difference estimation model, the predicted frequency difference accuracy of the two observation stations is even higher.

[0090] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0091] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for estimating the signal time difference and frequency difference between two observation stations, characterized in that, The estimation method includes: Multiple pre-set random resonance systems are used to perform signal enhancement processing on the signal to be estimated, resulting in multiple enhanced signals; the signal to be estimated includes the sampled signals from two observation stations. The time difference between the sampled signals of two observation stations in multiple enhanced signals is calculated separately, and the average of the multiple time differences is used as the time difference estimate of the signal to be estimated. The optimal enhanced signal is obtained by using a pre-set optimal stochastic resonance system to enhance the signal to be estimated. The optimal enhanced signal is input into a pre-trained frequency difference estimation model to predict the frequency difference estimate of the signal to be estimated.

2. The estimation method according to claim 1, characterized in that, Multiple stochastic resonance systems and the optimal stochastic resonance system are pre-configured through the following steps: Multiple signal samples were collected by two observation stations; each signal sample included signals collected by both observation stations from the same radiation source. All possible stochastic resonance systems were determined based on the signal-to-noise ratio of the signals received at the two observation stations. By using multiple signal samples to screen all possible stochastic resonance systems, multiple stochastic resonance systems and the optimal stochastic resonance system are obtained.

3. The estimation method according to claim 2, characterized in that, The process of using multiple signal samples to screen all possible stochastic resonance systems yields multiple stochastic resonance systems and an optimal stochastic resonance system, including: By using multiple signal samples, all possible stochastic resonance systems are evaluated, and evaluation values ​​for all possible stochastic resonance systems are obtained. Multiple stochastic resonance systems and the optimal stochastic resonance system are determined based on the evaluation values ​​of all possible stochastic resonance systems.

4. The estimation method according to claim 3, characterized in that, The evaluation value for each possible stochastic resonance system is determined through the following steps: Multiple signal samples are input into each possible stochastic resonance system for signal enhancement processing to obtain multiple signal enhancement samples; Calculate the normalized cross-correlation coefficient for each signal enhancement sample in the multiple signal enhancement samples to obtain multiple normalized cross-correlation coefficients; The average of multiple normalized cross-correlation coefficients is used as the evaluation value for each possible stochastic resonance system.

5. The estimation method according to claim 4, characterized in that, The normalized cross-correlation coefficient for each signal enhancement sample is calculated using the following formula: ； in, This represents the normalized cross-correlation coefficient for each signal enhancement sample. This represents the sequence of signals acquired by one observation station in each signal enhancement sample. This represents the sequence of averaged signals collected from one observation station in each signal enhancement sample. This represents the signal acquired by another observation station in each signal enhancement sample. The sequence of averaged signals from another observation station in each signal enhancement sample.

6. The estimation method according to claim 3, characterized in that, The process of determining multiple stochastic resonance systems and the optimal stochastic resonance system based on the evaluation values ​​of all possible stochastic resonance systems includes: Sort the evaluation values ​​of all possible stochastic resonance systems in descending order to obtain the sorted evaluation values; The stochastic resonance system corresponding to the maximum evaluation value is selected as the optimal stochastic resonance system. From the sorted evaluation values, select a preset number of stochastic resonance systems corresponding to the evaluation values ​​from front to back as multiple stochastic resonance systems.

7. The estimation method according to claim 1, characterized in that, The calculation of the time difference between the sampled signals of two observation stations in multiple enhanced signals includes: By determining all possible combinations of time difference and frequency difference, multiple combinations of time difference and frequency difference are obtained; Calculate the mutual ambiguity function value corresponding to each enhancement signal for each time difference-frequency difference combination, and obtain multiple mutual ambiguity function values ​​corresponding to each enhancement signal for multiple time difference-frequency difference combinations; The time difference in the combination of time difference and frequency difference corresponding to the maximum mutual ambiguity function value is selected as the time difference between the sampled signals of the two observation stations in each enhanced signal.

8. The estimation method according to claim 7, characterized in that, The mutual ambiguity function value for each enhanced signal in each time-frequency difference combination is calculated using the following formula: ； ； in, , This represents the time difference and frequency difference in each combination of time difference and frequency difference. This represents the mutual ambiguity function value corresponding to each enhancement signal for each time-frequency difference combination. Indicates the number of sampling points. This represents the first observation station in each enhanced signal. One sampled signal, Indicates the first observation station in each enhanced signal. One sampled signal, This indicates the sampling rate.

9. The estimation method according to any one of claims 1-8, characterized in that, The frequency difference estimation model is trained based on a preset neural network, which can be any of the following: Convolutional Neural Networks; Recurrent neural networks; Attention mechanisms enhance networks.

10. The estimation method according to claim 9, characterized in that, The loss function of the frequency offset estimation model can be any of the following: Mean squared error loss function; Mean absolute error loss function; Huber loss function.

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